NIELS BOHR C O L L E C T E D WORKS GENERAL EDITOR
ERIK RUDINGE R T H E NIELS BOHR ARCHIVE, COPENHAGEN
VOLUME 9
N U C L E A R PHYSICS (1929-1 952) E D I T E D BY
SIR R U D O L F P E I E R L S PROFESSOR EMERITUS, UNIVERSITY O F OXFORD
1986
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FOREWORD TO VOLUME 9
In this volume we collect Bohr’s work on nuclear physics. This started in the pre-1932 days with his thinking deeply, but inconclusively, about the seeming contradictions then presented by the evidence about the nucleus. In 1936 he surprised us all by the speed with which he recognised and described the insights provided by neutron scattering experiments; the excitement of this new understanding, and its extension and consolidation occupied much of the subsequent years. In 1939 he was again first in understanding the essential features of the newly discovered phenomenon of fission, applying successfully the point of view of nuclear reactions which he had developed during the previous three years. Later, in 1949-50, he became impressed by the success of the nuclear shell model, which on the face of it seemed hard to reconcile with the picture of the closely interacting nucleons which he had pioneered in 1936, and he put much effort into clarifying this paradox. We follow the pattern of earlier volumes in supporting the published papers by appropriate selections from unpublished notes and drafts, and by relevant correspondence. On most problems the available material makes it possible to follow the development of Bohr’s thoughts. But the genesis of the idea of the compound nucleus is left in some uncertainty. There are indeed some apparent contradictions concerning the timing of his first statement of the idea. In section 2 of the Introduction we attempt to give a resolution of the contradictions, which seems plausible, but hard to prove. Yet the sequence of steps by which he reached the idea remains unknown. As in earlier volumes, English translations are provided of papers published in other languages, and of letters in languages other than English or German. An exception is made again in the case of the correspondence with Heisenberg and Pauli, where also the German replies to Bohr’s Danish letters are translated, for reasons explained in the General Editor’s preface to volume 5 . Translating Bohr is not an easy task, as other editors have found. He used to
V
FOREWORD TO VOLUME
9
say that clarity and truth were complementary, and between these two extremes he tended to lean far towards the full truth. The translator has to keep a balance between a text that is easily intelligible and one that preserves Bohr’s very personal way of expressing nuances of meaning. We have aimed at writing in the way Bohr would have written in English. Manuscripts and notes in English are of course reproduced verbatim, except that trivial slips and typing errors have been corrected. There is one exception t o this: Document IX is of uncertain date and purpose; it was felt that the exceptionally poor quality of the typing may contain a clue to its origin, and it is therefore reproduced with all the errors. As explained in the General Editor’s preface to volume 5 , the editorial footnotes have been numbered in the Introduction and in Part 11, while footnotes made by the authors of letters and passages quoted are indicated by asterisks. For the manuscripts the inverse notation is used (and editorial footnotes are put in square brackets). The material reproduced in this volume is taken mainly from the Niels Bohr Archive in Copenhagen; however I have included quotations from a letter by Rutherford to Max Born (see p. [21]), which was brought to my attention by Dr. Joan Bromberg (who worked for a time on the nuclear physics papers, and whose notes I was able t o use). The relevance of letters from Frisch to Lise Meitner (p. [53]) was pointed out to me by Dr. Roger Stuewer. Further material of interest may well exist in other libraries or archives, but a comprehensive search would have delayed the completion of the volume unduly. If this volume comes anywhere near achieving its aim, much of the credit belongs t o Erik Riidinger, whose contributions to the work of editing went far beyond the call of duty of the series editor. The patient efficiency of the secretaries, Lise Madsen and Helle Bonaparte, was also of great help. To Mrs. Bonaparte and Erik Rudinger I am grateful for many helpful suggestions for improving my translations. I wish to thank Carsten Jensen for his assistance with the index and the proof-reading, and Dr. Hilde Levi and Mrs. Joan Warnow for their help with selecting and providing the photographs. I also wish to acknowledge the efficient and careful work of the publishers’ editor, Mrs. Jane Kuurman. My work involved several periods in the Niels Bohr Institute and NORDITA and I am grateful for the hospitality of these institutions. The visits were made more enjoyable by the friendly reception by Professor Aage Bohr and his colleagues. Rudolf Peierls
VI
ABBREVIATED TITLES OF PERIODICALS
Ann. d. Phys.
Annalen der Physik (Leipzig)
Aiii Arc. d. ’Italia
Atti della R . Accademia d’ltalia
Ber. Sachs. Akad., mathphys. Kl.
Berichte uber die Verhandlungen der Sachsischen Akademie der Wissenschaften zu Leipzig. Mathematisch-physikalische Klasse
Comm. Dublin Inst. Adv. Siudy, Series A .
Communications of the Dublin Institute for Advanced Studies. Series A
Compt. Rend. Compres Rendus
Comptes rendus hebdomadaires des seances de I’Academie des sciences (Paris)
Danske Vidensk. Selsk. math . -fys. Medd. D. Kgi. Danske Vidensk. Selsk. math.-fys. Medd. Det Kgl. Danske Vidensk. Selsk. Math.-fys. Medd.
Matematisk-fysiske Meddelelser udgivet af Det Kongelige Danske Videnskabernes Selskab ( K ~ b e n h a v n )
Fys. Tidsskr.
Fysisk Tidsskrift (Krabenhavn)
J . Chem. SOC. London Journ. Chetn. SOC.
Journal of the Chemical Society (London)
Journ. de Physique J . Phys.
Le Journal de physique et le radium (Paris)
Xlll
ABBREVIATED TITLES OF PERIODICALS
XI\'
Kgl. Dan. Vid. Selsk. ibIath.-fys. Medd. Kgl. Danske Vid. Selsk., Math. Phys. Medd. Mat.-Fys. Medd. Dan. Vidensk . Selsk . Math.-fys. Medd. Math.-phys. Comm. Copenhagen Academy
Matematisk-fysiske Meddelelser udgivet af Det Kongelige Danske Videnskabernes Selskab (Krabenhavn)
Nu furwiss.
Die Naturwissenschaften (Berlin)
Overs. Dan. Vidensk. Selsk. Virks.
Oversigt over Det Kongelige Danske Videnskabernes Selskabs Virksomhed (Kobenhavn)
Phil. Mag.
Philosophical Magazine (London)
Phys. Rev. Phys. Review
The Physical Review (New York)
Phys. Z S
Physikalische Zeitschrift (Leipzig)
Phys. Z . d. So wjefunion
Physikalische Zeitschrift der Sowjetunion (Charkow)
Proc. Camb. Phil. Soc.
Proceedings of the Cambridge Philosophical Society
Proc. London M a f h . Soc
Proceedings of the London Mathematical Society
Proc. Nut. Acad. of Sci.
Proceedings of the National Academy of Sciences of the United States of America (Washington D.C.)
Proc. Phys. Soc. London
Proceedings of the Physical Society of London
Proc. Phys.-Marh. Soc. Japan
Proceedings of the Physico-Mathematical Society of Japan (Tokyo)
Proc. Roy. Soc. London Proc. Roy. Soc.
Proceedings of the Royal Society of London
Rev. of Mod. Phys Rev. Mod. Phys.
Recieus of Modern Phytics (New York)
Ric. Scienf.
Ricerca scientifica (Roma)
Sov. Phys. Sow. Phys.
Physikalische Zeitschrift der Sowjetunion (Charkow)
ABBREVIATED TITLES OF PERIODICALS
Truns. Furuduy SOC.
Transactions of the Faraday Society (London)
Verh. d. deursch. Phys. Ges. V w h . der Deursch. Phys. Ges.
Verhandlungen der Deutschen Physikalischen Gesellschaft (Braunschweig)
2.Phys.
Zeitschrift f u r Physik (Braunschweig)
Z.f. Phys. 2s. j : Phys. Zeits. .f: Physik
Zeirs. f.physik. Chemie
Zeitschrift fur physikalische Chemie (Leipzig)
xv
ABBREVIATIONS
Bohr MSS BSC Mf MS
XVI
Bohr Manuscripts Bohr Scientific Correspondence Microfilm Manuscript
ACKNOWLEDGEMENTS
N. Bohr, “Chemistry and the Quantum Theory of Atomic Constitution”, J . Chem. SOC.London, 1932, pp. 379-383 is reprinted by permission of the Royal Society of Chemistry. N. Bohr, “Atomic Stability and Conservation Laws”, Atti del Convegno di Fisica Nucleare della “Fondazione Alessandro Volta”, Ottobre 1931 . Reale Accademia d’Italia, Rome 1932, pp. 119-130 is reprinted by permission of the publisher, Accademia Nationale dei Lincei. N. Bohr, “Transmutations of Atomic Nuclei”, Science 86 (1937) 161-165, 0 1937 by the AAAS, is reprinted by permission of The American Association for the Advancement of Science. N . Bohr, “Om Spaltning af Atomkerner”, 5 . nordiske Elektroteknikerm~de, J.H. Schultz, Copenhagen 1937, pp. 21-23, is reprinted by permission of the publisher. N. Bohr, “On the Transmutation of Atomic Nuclei by Impact of Material Particles. I. General Theoretical Remarks” (with F. Kalckar), Mat.-Fys. Medd. Dan. Vidensk. Selsk. 14, no. 10 (1937) is reprinted by permission of the Royal Danish Academy of Sciences and Letters. N. Bohr, “Mecanique nucltaire” , Reunion internationale de physique-chimiebiologie, Congrks du Palais de la dkcouverte, Paris, Octobre 1937, Hermann et Cie, Paris 1938, Vol. 11, pp. 81-82 is reprinted by permission of the publisher.
XVll
ACKNOWLEDGEMENTS
The following abstracts from Overs. Dan. Vidensk. Selsk. Virks. are reprinted by permission of the Royal Danish Academy of Sciences and Letters: N. Bohr, “Om Neutronernes Egenskaber”, Juni 1931-Maj 1932, p. 52; “Om Atomkernernes Egenskaber og Opbygning”, Juni 1935-Maj 1936, p. 39; “Om Atomkernereaktioner”, Juni 1937-Maj 1938, p. 32; “Om Atomkernernes Reaktioner”, Juni 1938-Maj 1939, p. 25; “Den teoretiske Forklaring af Atomkernernes Fission”, Juni 1939-Maj 1940, p. 28; “Tunge Atomkerners S~nderdeling”,Juni 1940-Maj 1941, p. 38; “Om Atomkernernes Omdannelser”, Juni 1945-Maj 1946, p. 31. The following articles are reprinted by permission from Nature, 0 Macmillan Journals Limited: N. Bohr, “Neutron Capture and Nuclear Constitution”, 137 (1936) 344-348; (report) 351; “Properties and Constitution of Atomic Nuclei” (abstract), 138 (1936) 695; “Nuclear Photo-Effects”, 141 (1938) 326-327; “Resonance in Nuclear Photo-Effects”, 141 (1938) 1096-1097; Report on “Symposium on Nuclear Physics”, 142 (1938) 520-521 ; “Reactions of Atomic Nuclei” (abstract), 143 (1939) 215; “Disintegration of Heavy Nuclei”, 143 (1939) 330; “Nuclear Reactions in the Continuous Energy Region” (with R. Peierls and G. Placzek), 144 (1939) 200-201. N . Bohr, “Nyere Unders~gelser over Atomkernernes Omdannelser”, Fys. Tidsskr. 39 (1941) 3-32, is reprinted by permission of the publisher. N. Bohr, “Wirkungsquantum und Atomkern”, Ann. der Phys. 32 (1938) 5-19 is reprinted by permission of the publisher, Ambrosius Barth Verlag.
The following articles from the Physical Review are reprinted by permission of The American Physical Society: N. Bohr, “Resonance in Uranium and Thorium Disintegrations and the Phenomenon of Nuclear Fission”, 55 (1939) 418-419; “Mechanism of Nuclear Fission” (with J.A. Wheeler), (abstract), 55 (1939) 1124; “The Mechanism of Nuclear Fission” (with J.A. Wheeler), 56 (1939) 426-450; “The Fission of Protactinium” (with J.A. Wheeler), 56 (1 939) 1065-1066; “Successive Transformations in Nuclear Fission”, 58 (1940) 864-866; “Mechanism of Deuteron-Induced Fission”, 59 (1941) 1042.
XVlll
Jacobsen and Bohr at the cyclotron
INTRODUCTION bY RUDOLF PEIERLS
Niels Bohr followed the early development of nuclear physics with deep interest. He realised that this was a subject which was bound to touch the limitations of the existing quantum mechanics, or to extend them. He had many personal contacts, not least his friendship with Rutherford, which kept him informed about progress in this field. In the earliest phases physicists were groping for a rational description of nuclear phenomena, and much of the thinking of that period, including some of Bohr’s work, has been superseded. Nevertheless it is of great interest in showing the development of his thoughts. During the nineteen-thirties a rapid sequence of discoveries opened up possibilities of a better understanding, and Bohr kept a close interest in these developments. Nuclear problems played an increasing part in the conferences held from time to time in his Institute. At the same time the weight of the experimental work in the Institute, in which he took a close personal interest, shifted progressively towards nuclear physics. The facilities for this were enriched in 1935 by the gift to Bohr on the occasion of his 50th birthday of half a gramme of radium for the Institute, and later by the provision of a high-tension set and a cyclotron. One of the uses made of this equipment was the production of radioactive isotopes for the work of Hevesy and his group with radioactive tracers in chemical and biological research. Bohr supported this application of nuclear physics enthusiastically. The late nineteen-thirties also were the time of Bohr’s most intense output of work on nuclear problems. This included his introduction and use of the concept of the compound nucleus, and his detailed explanation of the mechanism of fission, both of which had a great impact on nuclear physics.
P A R T 1: P A P E R S A N D M A N U S C R I P T S R E L A T I N G TO N U C L E A R P H Y S I C S
George de Hevesy
This introduction is divided according to topics, which are arranged in approximate chronological order, though there is much overlap both in time and in subject matter. 1. NUCLEAR COMPOSITION AND ENERGY CONSERVATION
Before the discovery of the neutron in 1932, it was taken for granted that nuclei consisted of protons and electrons (some perhaps combined into CYparticles). The confinement of an electron to such a small volume was hard to reconcile with quantum mechanics. By the uncertainty principle electrons inside the nucleus would have to have highly relativistic energies, and there were difficulties in finding a description of such a situation in terms of relativistic quantum mechanics. Even the assumption of an extremely strong force of unknown origin would not be sufficient, since on confinement to a small region the electron would, by Klein’s paradox, escape to a state of negative energy, or on the
P A R T 1: P A P E R S A N D M A N U S C R I P T S R E L A T I N G T O N U C L E A R P H Y S I C S
later interpretation of the theory there would be pairs created until the attractive potential was compensated. Experiments on the spin and statistics of nuclei did not seem to agree with the results expected from the presence of electrons, and were consistent with the view that only protons contribute to the spin and the statistics of the nucleus. Above all, there was the puzzle of the continuous energy spectrum of the electrons in 0-decay. Bohr was seriously worried by this situation. The earliest statement of his ideas which is available is an incomplete typescript', undated, but with the date 21.6.29 on an amended page. This must be in substance the same as the note he sent to Pauli on 1 July 1929 with a request for critical comment: "The other is a little piece about the 0-ray spectra, which I have had in mind for a long time, and which has been typed in the last few days, but I have not yet made up my mind to send it off, since it yields so few positive results and has been written so sketchily. I shall be happy to hear your opinion about all of this, no matter how severe or how mild the expressions which you feel it appropriate t o use."
Bohr t o PdUiI, 1 J u l y 29 Danlch In
,";1,P;on[4,:'l "01
6, P ~ 4 3 1
In this note Bohr discusses the possibility of energy conservation being violated in 0-decay. He emphasises that this cannot be claimed to be a consequence of the uncertainty principle, as implied in papers by G.P. Thomson'. He also envisages the possibility that this lack of energy conservation might be related to the energy production in the sun. Pauli's comment was very negative. After commenting favourably on another note3, he continues: "It is quite different with the note about the 0-rays. I must say that this gave me very little satisfaction. It already starts so depressingly with a reference to the nonsensical remarks by G.P. Thomson, and from this the people in England will only draw the erroneous conclusion that you regard these remarks as important, Then comes the unpleasant introduction of the electron diameter, d. I do not mean to say that this is actually illegitimate, but it is always a risky matter. One should then also take into account that for electrons moving almost with the velocity of light, d becomes, because of the Lorentz contraction, much smaller thar, 2, e 2
moc
namely 7e(2m
mc
=
mo J Sat)least , in ~
Manuscript, P-Ray Spectra and Energy Conservation, 1929. Reproduced on p. [85]. G.P. Thomson, The Disintegration of Radium E f r o m the Point of View of Wave Mechanics, Nature 121 (1928) 615-616; On the Waves associated with @-Rays, and the Relation between Free Electrons and their Waves, Phil. Mag. 7 (1929) 405-417. This relates to the question of a Stern-Gerlach experiment on a free electron; see Vol. 6, p. [307]. I
Paul! 10 Bohr, 17 J u I \ 29 German In
,"~1nP,a~on[4,~] "01
6, P 14461
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
the longitudinal direction. In Zurich Miss Meitner gave us a beautiful lecture about the experimental aspect of the question, and she almost convinced me that the continuous 6-ray spectrum cannot be explained by secondary processes (y-ray emission etc.). So we really don’t know what is the matter here. You don’t know either, and can only state reasons why we understand nothing. After all, you write yourself that the purpose of the note is to emphasise ‘how little basis we possess at present for a theoretical treatment of the problem of 6-ray disintegrations’. But here I must raise the question whether such a negative purpose can at all serve as a justification for publishing a note! In any case let this note rest for a good long time and let the stars shine in peace!’ ’ Bohr never published his note; it is not known how far this decision was influenced by Pauli’s criticism. However, he did not abandon the possibility of a violation of energy conservation. He had already wondered earlier whether even in proton emission by a bombardment there might be a lack of energy balance. He wrote to R.H. Fowler in Cambridge on 14 February 1929: Hohr 10 R H Fouler, 14 Frb 29 I ull text on p 15551
“In connection with Rutherford’s new experiments on the expulsion of protons by bombardment of atomic nuclei with a-rays, I have been wondering whether he thinks it excluded that the observed velocity distribution of the protons may arise from different discrete stages of excitation of the resulting nucleus, and if an emission of y-rays accompanying this excitation would escape observation. If even in proton transformations we witness a want of definition of energy, new aspects indeed seem to open. Lately I have been thinking a good deal of the possible limitation of the conservation theorems in relativistic quantum theory, and we have just been discussing, if in the reversal of 6-ray transformations we might find the mysterious source of energy claimed by Eddington’s theory of constitution of stars.” Bohr’s query was prompted by the realisation that his idea of attributing the lack of energy conservation to the difficulties of relativistic quantum theory would not easily explain such a violation in a reaction not involving any relativistic particles. When Bohr heard from George Gamow that Dirac had found a way out of the difficulties arising from negative-energy states in his relativistic wave equation, he wrote to Dirac4 on 24 November 1929, asking for details, and outlining again
Letter from Bohr to Dirac, 24 November 1929. Reproduced on p . [547].
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
the suspected connection between the difficulties of relativistic quantum mechanics and the @-rayparadox. In his reply’ Dirac agreed that the 0-ray spectrum was a serious problem, but explained his answer to the negative-energy difficulty. Bohr was sceptical. He wrote to Kramers on 30 November 1929: “By the way, I have just heard from Dirac about some very interesting and bold considerations, through which he hopes to avoid the difficulties in relativistic quantum mechanics. He believes that he can save energy conservation, but I am not yet quite sure that this is possible.”
Bohr 10 Kramers, 30 Nov 2 9 Danish text in Vol: 6, p . 14251 Translation in Vol. 6, p . 14271
He had no patience with glib attempts to get around the problem. When Johann Kudar asked him to comment on his paper on P-decaysa, he wrote in his typical courteous but firm manner: “ ... I have read the considerations in your paper with great interest, but I must confess that I do not properly understand on what basis you are arguing.’’
There follows a devastating list of objections. The first published account of Bohr’s views on this subject is contained in his Faraday Lecture to the Chemical Society in London. The lecture was delivered on 8 May 1930, but in the transcript of the lecture6 there is only a single sentence near the end, referring to possible limitations in the applicability of such ideas as energy and momentum in nuclear physics. The published text of the lecture was written much later’. The last part of this paper contains a detailed discussion of the difficulties involved in accounting for the presence of electrons in the nucleus, of the difficulties with spin and statistics, and of the continuous 0-spectrum. The arguments for believing in the identity of all nuclei in their initial states and also that of all nuclei after 0-decay, are summarised, so that, if varying amounts of energy are emitted, the violation of energy conservation must follow. Bohr goes as far as to doubt whether one may really regard the electrons in the nucleus as particles in the normal sense, and suggests that 0-decay may be the creation of the electron as a mechanical entity.
Letter from Dirac to Bohr, 26 November 1929. Reproduced on p. [548]. J . Kudar, Der wellenmechanische Charakter des ,8-Zerfalls, 11, Z . Phys. 60 (1930) 168-175. Manuscript, Chemistry and the Quantum Theory, in folder: Faraday Lecture, 1930. Shorthand report. Bohr MSS, microfilm no. 12. N . Bohr, Chemistry and the Quantum Theory of Atomic Constitution, J . Chem. SOC.London, 1932, pp. 349-384. Pages 379-383 are reproduced on p. [el]; the entire paper is reproduced in Vol. 6, p . [371].
’
Bohr to K u d a r , 28 J a n 30 German text on p . [6051
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Similar arguments are given in the published account of Bohr’s contributions to the discussions at the Volta Congress in Rome in October 1931 It stresses the fact that the size of the nucleus and the distances between its constituents are no longer large compared to the classical electron radius, so that, contrary to the situation for the atomic electrons, it is no longer permissible to treat an electron in the nucleus as a point charge. All this time Bohr was aware of the revolutionary nature of the idea that energy might not be conserved. This is brought out in an interchange of letters with Gamow. Gamow writes on 31 December 19329 that, in a discussion with Ehrenfest, Landau and others, the conclusion was reached that a violation of energy conservation would be inconsistent with the equations of general relativity, which have solutions only if the sources of the gravitational field conserve energy. Bohr replies:
’.
Bohr
10
Gamou,
21 J a n 33
Dani\h l t x l on p, 15701
Tran4ation on p. [5711
“ ... I fully agree that a renunciation of energy conservation will bring with it equally sweeping consequences for Einstein’s theory of gravitation, as a possible renunciation of conservation of charge would have for Maxwell’s theory, where the charge conservation is after all an immediate consequence of the field equations.”
This objection is again referred to in Bohr’s remarks at the 1933 Solvay Conference, In a passage occupying pp. 226-228 of the Proceedings of the conference” Bohr repeats his belief in the violation of energy conservation in 0decay, but admits the serious consequences this would have for the theory of gravitation. There might be a question whether the violation of the field equations, which would then result, could be observable. By this time Pauli had put forward the hypothesis of the neutrino, and Bohr refers to this: “Therefore, until we have further experience within this area, it seems to me difficult to judge Pauli’s interesting suggestion to resolve the paradoxes of the @-ray emission by assuming that the nuclei emit, together with the electrons, neutral particles, much lighter than the neutrons. In any case, the possiN. Bohr, Atomic Stability and Conservation Laws, Atti del Convegno di Fisica Nucleare della “Fondazione Alessandro Volta”, Ottobre 1931, Rome 1932, pp. 119-130. Reproduced on p. [99]. Letter from Gamow to Bohr, 31 December 1932. Reproduced on p. [568]; translation on p. [569]. l o Structure et propridtes des noyaux atomiques, Rapport et discussions du septieme Conseil de physique, tenu a Bruxelles du 22 au 29 Octobre 1933, Gauthier-Villars, Paris 1934. Bohr’s contribution, with the title Sur la methode de correspondance dans la theorie de I’electron, loc. cit., pp. 216-228, is reproduced with a translation in Vol. 7. The passage relating to energy conservation is reproduced in translation on p. [129] of this volume.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Pauli, Bohr, Schrodinger and Lise Meitner at the 1933 Solvay Conference
ble existence of this 'neutrino' would represent an entirely new element in atomic theory, and the correspondence method would not offer sufficient help in describing its rBle in nuclear reactions."
In the further discussion at the Solvay conference, he stresses again" (pp. 327-328) the point made in his unpublished note' that the uncertainty principle will not lead to a continuous energy distribution in P-decay. He draws attention" (pp. 287-288) to the theory of Guido Beck and Kurt Sitte'', which, on the basis of a specific energy non-conserving model, tries to make quantitative predictions about the P-spectrum.
" Discussion remarks at the conference referred to in ref. 10, pp. 72, 175, 180, 214-215 (see Vol. 7 ) , (266), 287-288, 327-328, 329, 329-330, 331, 334. Reproduced with translations on p. [133]. G . Beck and K . Sitte, Zur Theorie desfl-Zerfulls, Z. Phys. 86 (1933) 105-119.
''
The Copenhagen conference 1932
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
In other interventions in the discussion, Bohr showed his intense interest in problems of P-decay. In connection with positron emission he asked” (p. 180) for information whether there was also a violation of energy conservation in artificial positron emitters: “ ... since we d o not yet know how the positron emission isproduced. If, as Joliot assumes, the positrons really come from inside the nucleus, the circumstances are very similar to those of the P-rays.”
He showed similar caution in the discussion of pair creation” (p. 175). One must collect as many experimental facts as possible, without relying on Dirac’s theory:
‘‘I believe that the conclusion as regards the charge is right, but that concerning the spin seems to me less certain. Indeed, as the electric field of the nucleus is essential to allow the incident light quantum to produce the two particles, it is by no means excluded that the nucleus participates in the angular momentum balance.” At the time of the conference the existence of the neutron was well established, but the idea that there were electrons inside the nucleus remained. In the course of the talk already referred to” Bohr stresses that the ordinary methods of current theory cannot describe 6-decay, “whether one regards the proton as a combination of a neutron and a positron, which ... might well be the most natural hypothesis, or whether one regards it as the product of a dissociation of a neutron, with the associated emission of an electron...”. He had referred to the neutron earlier, in an unpublished note13, which represents an extract from a talk given to a conference in Copenhagen in April 1932. This also discusses the description of a neutron as made of a proton and an electron, and the impossibility of describing such a system by current methods. He also shows that one can understand, even with this model, the absence of any detectable interaction between neutron and electron, since the wavelength of the electron would be very much larger than the radius of the neutron, and this would make the wave-mechanical scattering quite negligible.
’’
Manuscript, On the Properties of the Neufron. Extract from address to conference in Copenhagen, 7 to 13 April 1932. There are several versions of this. One version is reproduced on p . [ I 151.
P A R T I : P A P E R S A N D M A N U S C R I P T S R E L A T I N G TO N U C L E A R PHYSICS
Of a lecture to the Royal Danish Academy on 29 April 1932 on “The Properties of the Neutron” only a summary is a ~ a i l a b l e ’ ~This . suggests that the talk was similar to that given at the conference. The possibility that there might still be some neutron-electron interaction was presumably in his mind when he wrote on 30 April 1932 to the Joliot- Curie~ ’~ asking whether there was any evidence that neutrons could eject electrons from atoms. Other consequences of the neutron containing an electron come up in correspondence with Heisenberg, who writes on 18 July 1932 1 6 , pointing out that electrons in the nucleus, even if contained inside neutrons, should contribute to the scattering of y-rays coherently, thus making the scattering amplitude proportional to the number of neutrons. In his reply, dated 1 August 1932, Bohr says: “The energy with which neutrons and protons are bound together in aparticles is after all not insignificant in relation to the binding energy measured by the mass defect of the electron in a free neutron. I could therefore believe that it might be as correct to set the scattering proportional to the square of the number of a-particles, as to the square of the number of neutrons; but the measurements are not yet reliable enough to decide this.”
H o t i r 10 Heircnberp I ziig 3 2 l)dni\ii ICXI o n p 15751 TIan\lalmn on p 15761
c
0 1 r L i l l O n 5crll
2 \ue 32 I)ani,h 1 ~ x 1on p 15771 Tian$ldtioii o n 13 15771
Bohr gave much further thought to the question of the nuclear constituents. These are reflected in an undated typescript, headed “The Electron and the P r ~ t o n ” ‘ This ~ . firmly accepts that the positron is an unavoidable consequence of Dirac’s relativistic wave equation. Presumably it was written later than the discussion remarks at the Solvay conference, in which Bohr still felt doubtful about the relation of the positron to Dirac’s theory. The note points out that for the validity of Dirac’s theory it is essential that the radius of the electron is smaller than its Compton wavelength h/mc. If the radius of the neutron or proton is assumed to be about 10- l 3 cm, a value suggested by their mutual collision cross section, the corresponding statement is no longer true for protons. Dirac’s discovery has totally removed the dissymmetry in the sign of the electric charge. From this he concludes that there might exist a negative proton, which, however, need not be the antiparticle of the proton, but could result from the reflection of the proton around the neutron, if the latter was charge-symmetric. He quotes
N. Bohr, Om Neutronernes Egenskaber, Overs. Dan. Vidensk. Selsk. Virks. Juni 1931 - Maj 1932, p. 52; The Properties o f t h e Neufron, Nature 130 (1932) 287 (changed and condensed into a single sentence; see p. [120]). The Danish text is reproduced with a translation o n p. [119]. I s Letter from Bohr to M. and Mme Joliot-Curie, 30 April 1932. Reproduced o n p. [591]. 16 Letter from Heisenberg to Bohr, 18 July [1932]. Reproduced on p. [573]; translation on p. [574]. 17 Manuscript, The Elecrron and the Proton, catalogued as of [1932]. Reproduced on p. [123]. l4
PART I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Gamow for the suggestion that the presence of stable negative protons in the nucleus might help in overcoming difficulties in nuclear theory, and in explaining isomers. The same idea is referred to later in a letter to Heisenberg: “AS regards the complete symmetry with respect to the sign of the charge, which characterises the present point of view of electron theory, we have also speculated somewhat whether this symmetry also appears in nuclear problems, and I enclose two papers by Gamow” and Williams” which have just been sent to the Physical Review, and in which they discuss the possibility of negative protons existing both inside nuclei and in the cosmic radiation. Particularly in respect of the former the question does seem very hypothetical, and sometimes I am inclined to think that in the nucleus we may, strictly speaking, talk only of the total charge of the whole system, just as in the surrounding electron system we can talk unambiguously only about the total angular momentum.”
In the notes referred to17, Bohr invokes the lack of applicability of the Dirac theory to the proton as an explanation of the fact that its magnetic moment is not a nuclear magneton. (The connection between this fact and the existence of a nucleon structure extending over a distance comparable to its Compton wavelength is of course entirely in line with later formulations.) Bohr’s last word on the question of energy conservation was a note in Nature written on 6 June 193620. The occasion was the claim by Shankland to have discovered energy violation in the Compton effect, and its disproof in experiments by Bothe and Maier-Leibnitz, and by Jacobsen2’. The last sentence of Bohr’s paper reads: “Finally, it may be remarked that the grounds for serious doubts [here the Faraday Lecture is cited] as regards the strict validity of the conservation laws in the problem of the emission of P-rays from atomic nuclei are now largely removed by the suggestive agreement between the rapidly increasing experimental evidence regarding P-ray phenomena and the consequences of the neutrino hypothesis of Pauli so remarkably developed in Fermi’s theory.”
‘’G. Gamow, Negative Protons in Nuclear Structure, Phys. Rev. 45 (1934) 726-729. ‘’
E . J . Williams, Nature of the High Energy Particles of Penetrating Radiation and Status oflonization and Radiation Formulae, Phys. Rev. 45 (1934) 729-730. N . Bohr, Conservation Laws in Quantum Theory, Nature 138 (1936) 25-26. Reproduced in Vol. 5 , p. [213]. *’ This controversy is discussed in Vol. 5, p. [94]. See also the letter from Bohr to Kramers, 14 March 1936, reproduced o n p. [598]. Translation on p. [600].
*”
Bohr to Heisenberg, 20 April 34 text
Translation
on p , [57Rl On
P [5791
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
This acceptance of the neutrino hypothesis was not easily arrived at. O n 17 February 1934 Bohr wrote to Felix Bloch: “We have of course also all been very interested in Fermi’s new paper21a, which no doubt will be very stimulating for the work on electric nuclear problems, although I must confess that I don’t yet feel fully convinced of the physical existence of the neutrino.”
Hohi !o Hloch, 17 Feb 34 Dani\h texi on p [5401 Translation on p . (5411
2.
NEUTRON CAPTURE AND NUCLEAR CONSTITUTION
In the early nineteen-thirties Fermi and his collaborators pioneered the use of neutrons in nuclear studies. It was then generally assumed that one could treat the passage of a neutron through a nucleus in a good approximation as if it was moving in a potential field, which would be the average field of the particles inside the target nucleus. This picture, taken over from atomic theory, would of course have to be corrected for exchange of energy between the neutron and particular target nucleons, but this was taken to be a small correction. On this basis one would have expected the main result of a neutron-nucleus collision to be elastic scattering of the neutron, with an occasional inelastic event, leading to excitation of the nucleus, and only very rarely the capture of the neutron with the emission of radiation. However the experiments showed that neutron capture was a very frequent event. Bohr saw at once the very surprising nature of this result, and at first raised the question whether the experiments had been correctly interpreted. In a letter to Rutherford he wrote: “ ... we are very doubtful as regards Fermi’s idea, that neutrons are in certain cases directly attached to nuclei under emission of radiation, and it appears to me more probable that in such cases, where isotopic radioactive elements are formed, the collision resulted in the expulsion of two neutrons from the nucleus instead of the attachment of one. This would give rise to the subsequent emission of a positron instead of an electron and might perhaps explain some observations of Joliot regarding unexpected appearance of positrons. Another fact, however, which might perhaps be explained by the emission of several neutrons as result of a nuclear collision is the remarkable difference in the life time of the active nitrogen formed on one hand by bombarding Boron with ol-particles and on the other hand by bombarding Carbon with protons or diplons22. It seems to me probable that in the first place two neutrons are
Bohr 10 Rurherford, 30 J u n e 34 Full !ex\ on p. (6511
’la
E. Fermi, Versuch einer Theorie der P-Strahlen. I , Z . Phys. 88 (1934) 161-177. was the name used at the time instead of “deuteron”.
’’ “Diplon”
P A R T I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
emitted with the resulting formation of a nitrogen of atomic weight 12, while in the second case a nitrogen of atomic weight 13 is formed according to the usual scheme.” But the experimental evidence was convincing. Even more surprising results were found with slow neutrons. Not only was the collision cross section in some cases very much larger than the geometrical cross section of the nucleus (this much could have been explained by the wave-mechanical resonance of a particle scattered by a suitable static potential) but, contrary to all expectation, the cross section for radiative capture greatly exceeded that for scattering. Moreover, in the nuclei with large cross sections for slow neutrons, the cross section showed an extremely strong variation with energy. These findings completely mystified theoretical physicists until the solution was presented by Bohr early in 1936. He gave a lecture to the Danish Academy on 24 January 193623,the contents of which were published in Nature24. The ideas he introduced there are so well known that it is hardly necessary to summarise them. Briefly, the point was that the constituents of the nucleus are interacting very strongly with each other, and with the incident particle, so that its kinetic energy is shared between many particles, with the result that none of them can escape until enough energy happens to be concentrated on one of them. This means that the neutron must remain in the nucleus for a much longer time than the picture of a single particle in a potential would have predicted, and during that time the chance of the emission of a photon is appreciable. In the case of a slow neutron, for which practically the whole excess energy is required to escape, the escape becomes a very infrequent event, and the emission of radiation dominates. The long lifetime of the unstable state of the nucleus implies, by the uncertainty principle, a very narrow width in energy, thus accounting for the great selectivity of the cross section. The resonances with which one is concerned are not those of a single particle, but of a many-body system, excited above its ground state by the binding energy of the incident neutron, and the level density of such a system is enormously greater than that for a single particle, so that the existence of very numerous resonances is accounted for.
N . Bohr, Om Atornkernernes Egenskaber og Opbygning. Abstract in Overs. Dan. Vidensk. Selsk. Virks. Juni 1935 - Maj 1936, p . 39; Properties and Constitution ofAtomic Nuclei, Nature 138 (1936) 695. The Danish and English texts are reproduced on p . [149]. 24 N. Bohr, Neutron Capture and Nuclear Constitution, Nature 137 (1936) 344-348. Reproduced on p. [151]. (A footnote describes this as an address to the Copenhagen Academy o n 27 January. This must be an error for 24 January. It is unlikely that Bohr gave two talks three days apart, and 24 January 1936 was a Friday, then the usual day for the meetings of the Academy.) 23
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
In this note Bohr speaks about the compound system, and more frequently about an intermediate system. The now familiar term “compound nucleus” is introduced only later. Also, although the dynamical picture of the nucleus, which he describes, resembles a liquid drop in the sense of a very close interaction between its constituents, he does not use the term “liquid drop” at this stage. There has been much speculation about when and how Bohr arrived at these ideas, but there is very little evidence to help settle the argument. Frisch has given a very dramatic account of a seminar at which Bohr put forward these ideas25: “According to what was then believed about nuclei, a neutron should pass clean through the nucleus, with only a small chance of being captured. Hans Bethe in the U.S.A. had tried to calculate that chance and I remember the colloquium in 1935 when some speaker reported on that paper26.On that occasion Bohr kept interrupting, and I was beginning to wonder, with some irritation, why he didn’t let the speaker finish. Then, in the middle of a sentence, Bohr suddenly stopped and sat down, his face completely dead. We looked at him for several seconds, getting anxious. Had he been taken unwell? But then he suddenly got up and said with an apologetic smile, ‘Now I understand it”’’ He gives a slightly different version of the story2’ on another occasion: “It must have been late in 1935 that Bohr conceived his idea of a compound nucleus as a long-lived intermediate state in a nuclear reaction. I vividly remember the occasion: Bohr repeatedly (more than usually) interrupted a colloquium speaker who tried to report on a paper (by Hans Bethe, I believe) on the interaction of neutrons with nuclei; then, having got up once more, Bohr sat down again, his face suddenly quite dead. We watched him for several seconds, getting anxious; but then he stood up again and said, with an apologetic smile, ‘Now I understand it all’; and he outlined the compound nucleus idea.” This time he suggests that the date was in late 1935, but he does not feel quite sure that the subject of the talk was Bethe’s paper. Wheeler also remembers a seminar2’: O.R. Frisch, What Little I Remember, Camb. Univ. Press, 1979, p. 102. See also ref. 97, p. 141. H . A . Bethe, Theory of Disintegration of Nuclei by Neutrons, Phys. Rev. 47 (1935) 147-759. 27 O.R. Frisch, Experimental Work With Nuclei: Hamburg, London, Copenhagen, in: Nuclear Physics in Retrospect. Proceedings of a Symposium on the 1930s (ed. R . H . Stuewer), Univ. of Minnesota Press, 1979, pp. 63-79. See p. 69. 28 J.A. Wheeler, Some Men and Moments in the History of Nuclear Physics. Ibid., pp. 217-306. See p. 253. 25
26
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“The news hit me at a Copenhagen seminar, set up on short notice to hear what Christian Merller had found out during his Eastertime 1935 visit to Rome and Fermi’s group. The enormous cross sections Merller reported for the interception of slow neutrons stood at complete variance to the concept of the nucleus then generally accepted. On that view the nucleons have the same kind of free run in the nucleus that electrons have in an atom, or planets in the solar system. Merller had only got about a half hour into his seminar account and had only barely outlined the Rome findings when Bohr rushed forward to take the floor from him. Letting the words come as his thoughts developed, Bohr described how the large cross sections lead one to think of exactly the opposite idealization: a mean-free path for the individual nucleons short in comparison with nuclear dimensions. He compared such a collection of particles with a liquid drop. He stressed the idea that the system formed by the impact of the neutron, the ‘compound nucleus’, would have no memory of how it was formed. It was already clear before Bohr finished and the seminar was over that a revolutionary change in outlook was in the making. Others heard his thoughts by the grapevine before he gave his first formal lecture on the subject, before the Copenhagen Academy on January 27, 193624,with a subsequent written account in Nature.” One is tempted to think that these accounts refer to the same occasion. However, this guess would raise a number of difficulties. Wheeler is definite that the meeting was in April 1935, and it could not have been much later, as Wheeler returned to the United States in May. He also reports that Christian Merller was the speaker. Merller did remember that about that time he gave a talk about Fermi’s work in Rome, from where he had just returned, but he never gave a talk on Bethe’s paper, and he did not remember any major intervention by Bohr during his talk29. While Frisch’s recollection about the date might be mistaken, it is not easy to believe that Bohr had the picture so completely clear in April, and did not until the following January mention the idea to anybody in writing. In many letters to friends, particularly to Pauli and Heisenberg, during that period, he talks about the problems currently engaging his attention, but not about the compound nucleus concept. The Nature article was, in fact, first sent in as a Letter to the Editor on 23 December 1935 30, but the editor regarded it as too long for a letter, and had it
*’Personal communication from Christian
Maller.
’’ Letter from Bohr to the editor of Nature, 23 December 1935. Bohr General Correspondence, file:
Nature.
P A R T I: P A P E R S A N D M A N U S C R I P T S R E L A T I N G TO N U C L E A R P H Y S I C S
set up as an article31. Bohr kept the proofs until some date after 14 January, in order to adapt the wording to a style appropriate for an article32. The earliest mention of this article in any correspondence with colleagues is in a letter from Oskar Klein to Bohr. This is dated “2.2.1935”, but it is clear that the date is in error. The correct date must be between 18 November 1935 and 9 January 1936, probably the date was meant to read 2.12.193533. “We had recently a pleasant visit from K a l ~ k a rwho ~ ~ ,told us about the nice progress you have made with the nuclear problem and that you have written a note to Nature about this. At the same time he told us that the experimental work in the Institute has also advanced. This is of concern to me, as I keep thinking about the generalised Dirac equation, to see how this relates to your results. One could imagine that such an equation might be used for an approximate description of what, according to Kalckar, you call the compound system. ’’ Bohr writes to Klein, in a letter which is evidently the reply to the above:
“I have not yet sent you the promised note, because I have tried lately, with Kalckar’s help, to improve both the content and the form. It really seems as if the considerations have very general validity, and as soon as the note is complete, Kalckar and I have in mind to get down to a thorough review of the whole material about nuclear reactions, and we hope to be able to learn a great ,deal from this. I hope, as I said, to send you the new edition of my note in a few days . . .”. It is not clear when and how Bohr promised Klein a copy of the note, but since Klein’s letter gives the impression that he had not previously heard of this work,
3 ’ Letter from the editor of Nafure to Bohr, 1 January 1936. Bohr General Correspondence, file: Nature. 3 2 Letter from Bohr to the editor of Nature, 14 January 1936. Bohr General Correspondence, file: Nature. The mention as early as 2 February 1935 of a letter to Nature about nuclei, in which Kalckar was involved, would indeed be most surprising. However, the main substance of Klein’s letter is to report calculations with a generalized Dirac equation, to which he refers as something already familiar to Bohr. He wrote a letter to Bohr about the same subject on 18 November 1935 (BSC, microfilm no. 22) to which the letter in question appears to be a continuation. On the other hand, it mentions the minimum spacing of energy levels as 1 volt, which is referred to in Bohr’s letter of 9 January; this must therefore be Bohr’s reply. This suggests that the correct date of Klein’s letter must be between 18 November and 9 January, and 2 December is a plausible guess, since it would involve only omitting one digit. Note also that Klein’s letter ends with good wishes for the New Year. 34 For a biographical note on Fritz Kalckar, see Vol. 1 , p. XLIII.
’’
PART I: PAPERS AND MANUSCRIPTS RELATING TO XUCLEAR PHYSICS
until Kalckar’s visit, it could well be that Bohr meant that the note had been asked for by Klein rather than promised. We know that on 9 January the note had already been sent to Nature; the “new edition” is therefore the change in proof. He mentions the new note to Rosenfeld: “By the way, I have lately been very busy with quite a different question, namely the capture of neutrons by nuclei. I have taken up an old idea again, which already occurred to me in the discussions with Bethe during the last conference in Copenhagen, namely that the motion of a neutron which penetrates into the nucleus can in no way be described as a one-body problem in a static potential, but on the contrary the neutron will so-to-speak instantaneously share its energy with the other nuclear particles, and create an intermediate system with a sufficiently long lifetime so that there remains a large probability of a radiative transition, before a neutron or another particle leaves the system as a result of an escape process which has no direct connection with the capture process. This point of view seems not only to explain the neutron capture, but also to solve a large number of other difficulties, with which Gamow has struggled on the basis of his schematic model of the nucleus.”
Bohr to Rosenfcld. 8 Jan 36 Danish text on p . 16411 Tran4ation o n p. (6421
He refers to his forthcoming visit to London, but gives the subject of his lecture at University College as “Space and Time in Atomic Theory”. The title of the lecture is altered only on 4 February, when in a letter to Professor Goodeve in London35 he proposes the change. To Heisenberg Bohr writes on 8 February 1936: “For this reason I worked hard to the last minute finishing the small article on nuclear reactions which I promised you long ago, but the matter was continuously developing for me, and it gradually became a more comprehensive point of view, which I believe to be of use for the understanding of many different nuclear properties. The details concerning nuclear reactions and the help which the new understanding provides compared with the earlier one, will be discussed in a more complete paper on which I have been working at the same time with Kalckar. The small note of which I enclose a manuscript, and which I think will appear in Nature, is only an approximate reproduction of a lecture in which I have talked about the opening which the neutron capture has provided for an attack on this problem. I shall be very glad if you can write a few words on what you think of all this to me in Cambridge, where I shall stay with
’’
Letter from Bohr to Goodeve, 4 February 1936. Bohr General Correspondence, file: Chemical and Physical Society (London).
Bohr 10 H c i m b e r e , 8 F r b 36 Danish t e x t on p [57Y] Trandalion on p [ S R I ]
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Rutherford, Newnham Cottage, Queens Road. You should not worry too much about my remarks on the constituents of the nucleus, which in this context are of minor importance. This does not imply any lack of understanding of your and Fermi’s great contributions, but only a certain scepticism concerning the details, not least in the application of the Pauli principle, which the new points of view have introduced. About this I shall write further, just as soon as I get time on my trip to refine in detail the minor remarks in the article which relate to this.’’ A little later he wrote to Gamow: “As you will see from the enclosed article, which will soon appear in ‘Nature’, this is a development of a thought which I already brought up at the last Copenhagen conference in the autumn of 1934, immediately after Fermi’s first experiment on the capture of fast neutrons, and which I have taken up again after the latest wonderful discoveries about the capture of slow neutrons. Kalckar and I are at this moment engaged in working out a detailed formulation of the consequences of the theory, and we shall send you a copy of the manuscript as soon as it is ready.”
ilOl1, I < > o‘llno\* 26 t ti’ 76 l)‘IIll,tl
I
zriii\l
l L \ l 011
p 15-21
ition on p 15731
These letters show that the idea was not just a flash of inspiration, in which Bohr saw the whole theory, as Frisch’s account might suggest, but a gradual development. The conjecture therefore suggests itself that there were two meetings: One in April 1935, in which Bohr mentioned in the discussion some of the new ideas, which struck Wheeler by their novelty, but made no impression on the others in Copenhagen, who probably had heard similar statements from Bohr before. The colloquium which Frisch remembers might well have been in late 1935, and it presumably was an occasion on which Bohr saw another important piece of the puzzle fall into place. The letters suggest that there must have been several drafts of the note, but amongst the papers surviving in the Niels Bohr Archive the only possible candidate for such a draft is an undated typescript36on the same subject. In this the standard of typing is extremely poor, and there are many errors which suggest either dictation to someone not familiar with physics and not proficient in English or typing, or possibly the transcript of shorthand notes of a lecture. If we accept the conjecture that there were two meetings, it is an intriguing question in what sequence the ideas were developed. What did Bohr report to the 1934 conference? How much more did he explain at the seminar in April 1935?
36
Manuscript, The Nuclear Constitution and Neutron Captures, [1935?]. Reproduced on p. [143].
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
What was the important insight which came to him at the colloquium described by Frisch? There is very little evidence which would help us guess an answer to these questions. Some light is thrown on them by a passage in a letter from Rutherford to Max Born3’ written after Bohr’s visit to Cambridge in February 1936: “The main idea is an old one of his [Bohr’s], viz. that it is impossible to consider the movements of the individual particles of the nucleus as in a conservative field, but that it must be regarded as a ‘mush’ of particles of unknown kind, the vibrations of which can in general be deduced on quantum ideas. He considers, as I have always thought likely, that a particle on entering the nucleus remains long enough to share its energy with the other particles.” The “old” idea referred to by Rutherford is one that plays a prominent part in Bohr’s thinking about the constituents of the nucleus in connection with the possible limitations of the quantum-mechanical description, as we have seen above. Of course the statement that no mechanical description in terms of welldefined particles is possible, is much more drastic than the statement that the interaction between these particles is too strong for them to be treated approximately as moving in a field of force. But it is plausible that thoughts about the one limitation may prepare one for considering the other. Indeed there is a paragraph in the Nature note which introduces the doubts about the individual existence of particles within the nucleus, but it is followed by the remark: “Quite apart from the problem of the nature of the nuclear constituents themselves, which is not of direct importance for the present discussion, , . .”. It is plausible to assume that the problem is referred to, although it is of no direct importance, because it played a part in the development of Bohr’s thoughts on the matter. The comments in the letter to Heisenberg quoted above are of a similar nature. The later steps might then have been the recognition of the very narrow width of the resonances and its consequences, or of the great density of levels; both of these are explained with particular emphasis in the Nature note and in the lectures based on this. But all this is conjecture. 37 Letter from Rutherford to Born, 22 February 1936. Rutherford Correspondence, Cambridge University Library. During his visit to England in February 1936, Bohr had travelled from London, where he gave his lecture at University College on 11 February, to Cambridge, where he stayed with the Rutherfords for about a week from 12 February and gave some lectures. We are indebted to Joan Bromberg for drawing our attention to this letter.
Rutherlord t o Born,
22 Feb 36 Eng,,sh
P A R T 1: P A P E R S A N D M A N U S C R I P T S R E L A T I N G T O N U C L E A R P H Y S I C S
The issue of Nature of 29 February 1936, which contained Bohr’s note, also gave a summary of a lecture he gave at University College, London, on 11 February3’. This included two diagrams, based on slides shown at the lecture, illustrating respectively the sharing of energy in a system containing many particles, and the rapid increase of the level density of a nucleus as a function of energy. There exists a Danish version of the Nature article39 which appears to have been intended for a Danish edition of the article, which was never published. There are two versions, the first being an almost verbatim translation of the English text, with only very minor textual alterations. In this a number of alterations have been made by hand, which are also of no great significance. The second version is a re-typing of the first, with these alterations, and a few further minor alterations by hand. The only change of any interest is the fact that the typical binding energy of a neutron in a heavy nucleus, which was given in the Nature article as 10 MeV, was altered by hand in the first Danish version to 9 MeV, and after re-typing it was changed again by hand in the second version to 8 MeV4’. Because of these alterations from a text so very similar to the English one it is clear that this note was not a draft for it, but written subsequently. A German translation was published in Naturwis~enschaften~’, and correspondence with Max Delbruck, who arranged for the translation, is of interest in illustrating Bohr’s attitude to the choice of phrases. Following an invitation from the editor of Naturwissenschaften, and an offer from Delbruck to arrange for such a translation, Bohr wrote to Delbruck accepting his offer42. In due course he received proofs of the translation, which had been carried out jointly by Delbruck and Mr. H. Reddemann, who evidently had to struggle, like most translators, with Bohr’s notoriously difficult use of language. Bohr returned the proofs which, he said, had been looked at carefully by Kalckar, Rosenfeld and himself. “We found the translation excellent, but have taken the liberty of suggesting a number of minor alterations, which are mainly concerned with clarifying the
Liohi l c I k l b r u L k , I X Cldriti 76 Clelnl‘lll i C \ I Oil p [511]
N. Bohr, Neutron Capture and Nuclear Constitution, Nature 137 (1936) 351. Reproduced on p . [157]. 79 Manuscript, Neutroners Indfangning og Atornkernernes Opbygning [Neutron Capture and the Constitution of Nuclei], catalogued as of [I9361 (see however footnote 40). Bohr MSS, microfilm no. 14. 40 Since the value used in the 1937 Bohr-Kalckar paper (see section 3), first completed in January 1937 and amended in October 1937, is 10 MeV this would place the Danish typescript in 1937 or later. 41 N. Bohr, Neutroneneinfang und Bau der Atornkerne, Naturwiss. 24 (1936) 241-245. 42 Letter from Bohr to Delbruck, 27 February 1936. BSC, microfilm no. 18. 3x
PART I: PAPERS A N D MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
~
~~
Bohr, Born and Delbruck
text where the English version was not understandable enough. I hope your artistic conscience will not be burdened too heavily by our suggestion of recombining in a few places two sentences which, in your generally very successful and welcome efforts, you have separated.” This diplomatic presentation of the alterations did not, however, placate Delbruck. The reply was a postcard: Dear Professor Bohr, 1 am very bitter about your changes, and 1 regard them as a crime against the readership. However, since I regard it as hopeless to convince you of the inadequacy of your use of the German language, I have passed on the proofs without change, and have confined myself to expressing my disapproval ‘symbolically’ by deleting my name as translator. Yours sincerely, M. Delbruck
DelbrucktoBohr, 20 March 36 (postmark) t e x t on p , [5451
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
The reply to this outburst came from Rosenfeld: “Bohr has shown me your card, and we are both very sad that our suggestions for changes in your proofs have annoyed you so much that you could even think of declining all responsibility for the translation. This would cause real worry to Bohr, who was very grateful for your interest in his paper.”
Rosenfeld to Delbruck, 2 2 [?I March 36 ( r e m a n text o n p (5451
There must have been a misunderstanding; it was not the intention to criticise or even improve the language, but to make a few sentences clearer, where Delbruck’s proposals went a little too far from the intention as regards certain nuances. The changes were only suggestions, and Bohr would have been very happy indeed if Delbruck could have put them into proper German of the same quality as the rest. As regards the recombining of sentences which the translators divided, “ ... I know very well from personal experience (with the French translation of Bohr’s book) that one initially starts boldly breaking up Bohr’s sentences, only to find on reflection that that cannot be done very easily without weakening the sense. I believe nothing can be done about this; the readership will have to reconcile themselves to the fact that there is no ‘via regia’ to Bohr’s thoughts.”
Delbruck did not change his mind. In his reply to Rosenfeld he said: “Only this: I want to avoid absolutely collaborating over the nuances. I fail to recognise a difference in the sense, I do not care about their artistic value, and from the point of view of clarity and persuasive power I regard them as undesirable. Bohr is fully entitled to write in his own way, but he cannot insist that I argue with him over nuances ...”.
Delbruik to Rosenfeld. 2 5 March 36 German texl on p (5461
He offers to continue the discussion of the principle, but not the details, during his forthcoming visit to Copenhagen. But the translation was published without his name, mentioning only Reddemann as translator. The basic idea of Bohr’s Nature article, concerning the nature of the compound nucleus, seems to have found immediate acceptance by the physics community. No paper was published disagreeing with him, and it is characteristic that Bethe, who in May 1935 had published a paper43discussing neutron-nucleus collisions as a one-body problem, submitted in June 1936 a paper based on Bohr’s viewpoint44, and concerned with the evaluation of the level density, an See ref. 26. H.A. Bethe, A n Attempt to Calculate the Number of Energy Levels of a Heavy Nucleus, Phys. Rev. 50 (1936) 332-341.
43 44
P A R T 1: P A P E R S A N D M A N U S C R I P T S R E L A T I N G T O N U C L E A R P H Y S I C S
important ingredient in the practical application of Bohr’s result. A slight note of doubt is in a letter from Kramers, asking: “The situation of the many equally heavy particles in the nucleus is reminiscent in many respects of the situation of the free electrons in a metal. Now the latter can be described very successfully by Bloch’s even though this meets with notorious difficulties if one tries to determine the validity of the approximation. Will there not nevertheless exist a similar treatment for the nucleus; i.e., one would assume a Fermi law for the protons and one for the neutrons (or one for both together); even if this gives an error if one uses it to describe the total energy, it could still be right for determining the approximate distribution of the higher energy levels of the nucleus.”
Kramerr to Bohr. Danish 11 M a r c h 36on j5s61 Trans’ar1onOn P [5971
Bohr does not seem to find the question very constructive: “About your questions on the nuclear problems I don’t quite know what to say. In particular the analogy between the motion of the particles in the nucleus and that of the electrons in a metal is not sufficiently clear to me. If I might venture a paradox in this connection I would sooner say that the inadequacy of Gamow’s and Heisenberg’s point of view in explaining nuclear reactions reminds us rather of the failure of Bloch’s method for the problem of superconductivity. Nor do I think that there is any simple analogy between the behaviour of metals at higher temperatures and the highly excited states of nuclei. It appears to me at least that the possible progress in the new considerations about nuclei should lie primarily in the recognition that even at the very high energy levels of the compound system with which we have to do in the usual nuclear reactions we cannot talk in any way of the independently quantised motion of single nuclear particles. I hope however that before long we shall have an opportunity to talk together further about all these questions, and in particular I shall send you a copy of the manuscript of the more detailed paper on which Kalckar and I are working, as soon as it is ready.”
Bohr to Krarner5, 14 hlarch 36 D a n l i h ,ext on [5981 O n P [6001
Kramers explained his question more fully: “As regards my remarks about the possibility of describing the state of a nucleus by Bloch’s method, you may have thought that I completely misunderstood the most essential points of your view. However, the fact is that I have lately become involved with the old question why Bloch’s theory for electrons in metals, taken as a whole, is so tolerably correct, and I believe F. Bloch, Uber die Quantenmechanik der Elektronen in Kristallgittern, Z . Phys. 52 (1928)
Ida
5 5 5-600.
Kramers t o Bohr, 20 M a r c h 36 D a n l c h t e x t on ,hOZl Tranc’at’on
p
lho31
P A R T 1: P A P E R S A N D M A N U S C R I P T S R E L A T I N G T O N U C L E A R P H Y S I C S
Weisskopf and von Weizsacker
nobody really knows this. After all Bloch gets the possibility of currentcarrying states in a metal crystal, with the assumption that two* electrons can, practically speaking independently of each other, be located near the same nucleus, yet the various ‘energy bands’ (in any case the lowest, or the two or three lowest ones) should resemble more or less the lowest level(s) of the free metal atom. My idea was therefore that Bloch’s method might nevertheless not be wholly unsuitable for describing your nuclear states. Bear in mind that when energy is transmitted to the metal electrons (compare for example Weizsacker’s theory of the stopping of a-particles in metals45 (admittedly a little
* “If
there is one electron per atom”.
C.F. von Weizsacker, Durchgang schneller Korpuskularstrahlen durch ein Ferrornagnetikum, Ann. d. Phys. 17 (1933) 869-896. 45
P A R T I : P A P E R S A N D M A N U S C R I P T S R E L A T I N G TO N U C L E A R P H Y S I C S
crude)) there is by no means always a definite electron state which changes. (In the usual theory of the photo-effect it looks indeed as if a definite electron from the Fermi sea escaped, but I can well imagine that this theory is absurd, or at least absurd in the same way as Gamow’s theory of the Geiger-Nuttall curve.) One more question (which you need answer as little as everything else): By what method do you reconcile the large distances between the levels in the level scheme of RaC nuclei with the high level density which you need? I can think of several answers, but I do not find any of them satisfactory.” The question was presumably discussed further when Kramers came to Copenhagen in June for a conference. The question he raised about the comparison with the electron theory of metals was in fact much deeper than appeared at the time. The same idea was used much later by Weisskopf 4 5 a to explain how the Pauli principle can weaken an otherwise strong interaction, and this helped us understand the validity of the independent-particle model at low energy. For later discussions of the relation between different nuclear models, see section 6. 3.
THE COMPOUND NUCLEUS. CONSOLIDATION AND APPLICATIONS
The ideas put forward in the seminal article in Nature in early 1936 dominated Bohr’s work for several years. He was now working with Kalckar on a more detailed formulation of the theory. The forthcoming paper with Kalckar was mentioned as early as February 1936 in the letters already quoted, and is again referred to on many other occasions. It was completed in October 193746. Compared to the Nature article, there are a number of new points in this paper. Q 2 discusses the level distribution using, by way of example, the volume and shape oscillations of a liquid drop, and mentioning also rotational states using the results for a rigid sphere. Q 3 deals with radiative transitions and introduces the notion (though not the name) of collective quadrupole transitions. 0 4 examines the probability of neutron emission and its relation to the classical thermodynamics of evaporation. It refers in this context to a paper by Frenke14’ and criticises this on two grounds: Firstly Frenkel underestimates the temperature of the excited nucleus which is sensitive to the level spectrum or, in
V.F. Weisskopf, Nuclear Models, Science 113 (1951) 101. N. Bohr and F. Kalckar, On the Transmutation of Atomic Nuclei by Impact of Material Particles. I . General Theoretical Remarks, Mat.-Fys. Medd. Dan. Vidensk. Selsk. 14, no. 10 (1937). Reproduced on p. [223]. 4 7 J . Frenkel, On the Solid Body Model of Heavy Nuclei, Phys. Z. d. Sowjetunion 9 (1936) 533-536.
15Li
46
The Copenhagen conference 1936
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
the model used in both papers, to the distribution of vibration frequencies. Secondly Frenkel overlooks the fact that, in contrast to the situation of the evaporation from a macroscopic drop of matter, the binding energy of the escaping particle may be comparable to the excitation energy, so that the “temperature” of the nucleus after the emission is appreciably lower than before. It is also pointed out that in collisions at high energy, in which the excitation energy of the compound nucleus is much higher than the binding energy of one particle, the final energy may be sufficient for the emission of one or more further particles. D 5 discusses the resonances which are particularly important for slow neutrons. Here the paper makes use of the results of Breit and Wigner, whose paper4*, written before Bohr’s Nature article, but published later, went some way towards Bohr’s description of neutron collisions, by assuming that the incident neutron’s energy is shared with one other particle in the target nucleus. It is more important, however, that Breit and Wigner derive a general formula for the scattering and reaction cross sections in the presence of a resonance level, which is quite general and model independent. This leads to a simple quantitative discussion of reactions in terms of very few parameters. There is also mention of the paper by Bethe and P l a ~ z e kwhich ~ ~ generalised the result of Breit and Wigner to take account of spin, and used it for a discussion of experimental results from Bohr’s viewpoint. 5 6 is concerned with the emission of charged particles, and asks in particular whether in the case of wemission by radioactive nuclei one also had to allow for a small probability of there being an a-particle of suitable energy available. This had been concluded by Bethe in a paper already mentioned5’, and if correct it would have called for a revision of the estimate of nuclear radii from the Gamow theory of a-decay. Bohr and Kalckar conclude that such a correction is not necessary. In 5 7 reactions initiated by charged-particle impact are considered. Here the Coulomb repulsion plays an important part, of course, but making due allowance for this, the collision can again be described in terms of the formation of a compound nucleus. The preface states that this paper was in print in January 1937, but that publication was postponed. Meanwhile an “admirable complete report” had been published by Bethe” which also commented on some of the authors’ con-
‘’ G . Breit and E. Wigner, Capture of
Slow Neutrons, Phys. Rev. 49 (1936) 519-531. H . A . Bethe and G. Placzek, Resonance Effects in Nuclear Processes, Phys. Rev. 51 (1937) 450-484. See ref. 44. ” H . A . Bethe, Nuclear Physics, B. Nuclear Dynamics, Theoretical, Rev. Mod. Phys. 9 (1937) 69-244.
4y
’”
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
siderations, which were discussed at a conference in Washington in February 1937. For this reason the planned further parts were abandoned, but a number of addenda were attached with brief comments on recent progress. Addendum I gives an example of the large level density obtained by assuming the energy of each level to be a sum of quantities capable of equidistant values. Addendum I1 refers to estimates by Bethe of the level distribution on the basis of a Fermi gas, and alternatively for a dense liquid or solid. It also mentions the results of Landau5’ and W e i ~ s k o p flinking ~~ the level density to a macroscopic equation of state. Addendum I11 makes a reservation concerning the idea of a rotating liquid drop presented in Q 2. Addendum IV quotes the paper by Kalckar, Oppenheimer and Serber54 as relevant to the problem of the coupling of spins and orbital moments. Addendum V similarly draws attention to another paper by the same authors concerning the nuclear p h ~ t o - e f f e c t which ~ ~ , leads to a surprisingly high estimate of the radiative transition probabilities. Addendum VI returns to the evaporation problem and refers to the general thermodynamic treatment in the paper by Weisskopf already cited53. Addendum VII deals with the special case of the neutrons from Be bombarded with a-rays, and VIII announces that Kalckar plans to publish a paper dealing with the situation when the compound resonances form a continuous spectrum, a problem which already came up in the paper mentioned in Addendum VS5.Finally Addendum IX refers to the controversy with Bethe over the a-emission probability and the nuclear radii. In his review article5’ Bethe tried to counter the arguments in Q 6 of the Bohr-Kalckar paper, which were mentioned at the Washington conference in February 1937. The authors still do not agree, and cite the careful analysis of the problem by Landau52. A number of manuscripts appear to be drafts for the Bohr-Kalckar paper. A set of papers labelled “Transmutation of Atomic Nuclei”56 contains’a number of typed pages which appear to be different drafts of the introductory section. They differ from each other and from the published paper in presentation, but not in substance. Some handwritten pages are dated March, April and May, without year, others, in Danish, show dates in November 1936. There is also a draft (or re-draft?) of the end of Q 6, already showing a reference to Addendum
L. Landau, Zur statistischen Theorie der Kerne, Phys. 2. d. Sowjetunion 11 (1937) 556-565. V . Weisskopf, Statistics and Nuclear Reactions, Phys. Rev. 52 (1937) 295-303. 54 F. Kalckar, J.R. Oppenheimer and R. Serber, Note on Resonances in Transmutations of Light Nuclei, Phys. Rev. 52 (1937) 279-282. 5 5 F. Kalckar, J . R . Oppenheimer and R. Serber, Note on Nuclear Photoeffect at High Energies, Phys. Rev. 52 (1937) 273-278. 5 6 Folder, Transmutation of Atomic Nuclei, [1936-19371. Bohr MSS, microfilm no. 14. 52
53
P A R T I : P A P E R S A N D M A N U S C R I P T S R E L A T I N G TO N U C L E A R P H Y S I C S
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P A R T I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
IX. There are several handwritten versions of the same material, and a brief outline of Addendum IX. A manuscript headed “Selective Capture of Slow N e u t r ~ n s ” ~ ’with , handwritten additions by Kalckar, relates to an attempt to estimate the partial width of a resonance level for neutron emission and for radiation from experimental data. This takes the form of the dispersion relation from Bethe’s paper, and therefore was probably written before Bohr was aware of the Breit-Wigner paper. It may have been intended for a separate paper which was never published. Another set of manuscriptsSs contains an incomplete draft of a paper headed “Excitation and Radiation of Atomic Nuclei”. It refers to the absence of electric dipole emission in the case of collective motion, and gives estimates (all formulae are missing) of the radiation in the case of a vibrating liquid drop. These ideas are used in 8 3 of the Bohr-Kalckar paper. The present draft was no doubt intended for a different paper, as indicated by phrases like ‘‘I should like . . . ”, inconsistent with a joint paper, and the reference to “interesting discussions in this journal (Bethe and Bloch)” suggesting a paper intended for the Physical Review. (However, no relevant paper by Bethe and Bloch could be found, but there is one by Bloch and GamowS9,which does relate to the question of dipole transitions.) Another draft which appears to have been intended as a separate paper, but contains ideas eventually incorporated in the Bohr-Kalckar paper, deals with the impact of charged particles6’. About the same time Bohr drafted, jointly with Kalckar, a note discussing the particular case of the impact of a-particles on aluminium6’. The approximate date of this, and the fact that it was written jointly with Kalckar, can be inferred from a letter to Peierls: Iiorii i o h L r I 5 , 1 - o c i 36 Oillll,1I1 l i \ l
011
p [hlli]
“Incidentally, Kalckar and I have just written a small paper about the aluminium disintegration, in which we discuss in more detail various features which are characteristic of nuclear reactions. I shall send a copy of this to Cambridge together with the article I mentioned.” There is no indication why this paper was never published. One problem to which Bohr devoted much thought was that dealt with in
8 2,
’’ Manuscript, Selective Capture of Slow Neutrons, [1936]. Reproduced o n p. [179]. ’*Manuscript, Excitation and Radiation of Atomic Nuclei, [1936]. One version of this is reproduced on p . [191]. 5 9 F. Bloch and G. Gamow, On the Probability of y-Ray Emission, Phys. Rev. 50 (1936) 260. 6o Manuscript, Disintegration of Aromic Nuclei /I/, [1936-19371. Bohr MSS, microfilm no. 14. 61 Manuscript, On the Disintegration of Aluminium by @-Rays, [1936]. Reproduced on p . [183].
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Kalckar and Bohr
Lev Landau
PART I: PAPERS A N D MAKUSCRIPTS RELATING TO NUCLEAR PHYSICS
and Addendum I1 of the Bohr-Kalckar paper, i.e., how to describe the internal state of the nucleus, and how to reconcile his idea of strongly-coupled particles with the approach by others, for example Heisenberg, to the binding energies and low excitations of nuclei, which are essentially weak-coupling schemes, but which he believed to be successful. In the paper these questions are not argued out in detail. It is therefore very interesting to see an expression of Bohr’s reasoning in a letter to Heisenberg: “After much vacillation I now believe that I understand better how the results obtained in your paper on nuclear structure can be reconciled with the point of view about nuclear reactions which I developed in my Nature article. On the one hand I understand completely how essential your use of the Pauli principle for neutrons and protons is for the equilibrium between kinetic and potential energy in the nuclei, which in the first place determines the mass defect, and how this leads naturally to an assumption about the strong exchange forces between neutrons and protons. On the other hand I d o not believe that one can get to an explanation for such nuclear properties as the possible stationary states and transition probabilities which dominate the nuclear reactions, from a procedure which treats the neutrons and protons in first approximation as free. Here, I believe, the only procedure is to start from a liquid-like nuclear substance, without a direct use of the Pauli principle for the nuclear constituents, comparing the excited states with the vibrations of a drop under the influence of elasticity or surface tension. To take an extreme case, let us consider a drop of liquid helium containing 100 atoms. From the size of the drop one can then calculate the kinetic energy corresponding to a Fermi distribution of 200 electrons, and find an average energy of about 20 volts per electron. From the energy of separation of electrons from the drop one can then determine the potential energy per electron, and will find values corresponding to the Coulomb force in the helium atom, and similarly the kinetic energy mentioned will roughly correspond to the zeropoint motion of an electron in the ground state of the helium atom. Nevertheless the mechanical properties of the drop will be determined by the van der Waals force between the atoms, and the possible vibrational states will have to do neither with the excitation energies of a single atom, nor with the energy values calculated from the consideration of the Fermi distribution of electrons in the volume of the drop. This analogy is of course much too crude, since in the nuclei we are very far from having as close a localised substructure as in the atoms in the helium drop. Yet I have a suspicion that we have in the nucleus a virtual substructure which goes far beyond that due to the exchange forces between neutrons and protons. This is because it seems to me hardly possible
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Bohr and the Heisenbergs at Frederiksborg Castle in 1937
Heisenberg and Bohr
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Bohr, Heisenberg and Pauli
to explain the peculiar alternation between the spin and stability properties of ‘even’ and ‘odd’ nuclei without assuming ‘exchange forces’ between particles of the same charge but different spin, whose effect will be not nearly as strong as the charge exchange forces, but which nevertheless have a much greater influence than the spin-dependent forces between atomic electrons.” This is perhaps the fullest available statement of Bohr’s view at that time of the justification of the “liquid-drop model”. It may be of some interest to note that the discussions in 1936 do not constitute the first use of the term “liquid-drop model” applied to the nucleus. In his visit to Copenhagen in 1928-29, Gamow had obviously discussed such a model for the a-particles in the nucleus, following the general trend of the time to consider the nucleus made of a-particles and electrons (with a few odd protons). In a letter from Leiden he says: ( l c 1,)~ noill ~ ~ l ~ ~
6 Id,, 29 l ~ ‘ ~ l l l ~I C 1 Y11 011
1I
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p
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on p [567]
“Ehrenfest is very interested in the ‘liquid-drop model’; he thinks one should perhaps also consider ‘capillary vibrations’ in the explanation of y-ray levels.”
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO N U C L E A R PHYSICS
Pauli a n d G a m o w
This reference shows that Bohr had heard of the idea, but there is no indication of his reaction t o it at the time. Gamow’s idea is set out in greater detail in his first book62. The only mention of the idea by Bohr is in a discussion remark at the 1933 Solvay C ~ n f e r e n c e in ~ ~which , he describes Gamow’s liquid-drop model as too idealised. One might wonder whether Bohr’s thoughts of a liquid-drop model were influenced by these early ideas. While there is not enough evidence to be certain, this is made unlikely by the fact that the early liquid-drop model was introduced for quite different purposes, and that the only mention of it by Bohr is critical. The question of the correct description of the state of the nucleus came up
62 G . G a m o w , Constitution of Atomic Nuclei and Radioactivity, Oxford Univ. Press, 1931. See especially p. 18. See the reference in footnote 11, p. 334. Reproduced o n p. [141].
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
repeatedly in correspondence, for example in reply to a letter from P e i e r l ~who ~~, claimed to be able to show that the assumption of a level density given by noninteracting particles was not inconsistent with Bohr’s picture, though a strong enough interaction could change the level density to that appropriate to a liquid or solid. In his reply, Bohr says: liol,, <J
\L
1 0 I’L1‘1/\
p
h
( r r l l i I l l I L \ I 011
,)
[6OY]
“ I was therefore interested to see that you share my conviction that a more penetrating analysis of the level scheme should be possible only through a closer study of the type of motion of nuclear matter which is called collective in my article. One must however be very careful with a simple comparison with the vibrations of a solid because, as I stressed at the conference, the amplitudes of the motion in the nucleus are, even in the lowest states, of the order of magnitude of the nuclear dimensions.” Later in the same letter Bohr refers to the question whether there should be electric dipole transitions between low-lying levels: “We entirely agree with your criticism of the remarks by Bloch and Gamow; as we have also discussed here in the Institute, they seem to depend on a quite unjustified interpretation of the formalism of exchange forces.” The “discussions” referred to are evidently those underlying the manuscript5* mentioned on p. [32], and this supports the conjecture that “Bethe and Bloch” was there meant to read “Bloch and Gamow”. The discussions about the state of matter in the nucleus also attempted to include other phenomena. One set of typescript^^^ consists of various drafts of the beginning of a note trying to explain the absence of spin in even-even nuclei, by assuming that the strong coupling suppresses all orbital moments and that there is no collective rotation in the ground state. Some of the work during the same period was concerned with very specific examples of nuclear reactions. There is the draft of a note on the collision of protons with lithium66. This suggests that the y-rays come from the compound nucleus 8Be, which cannot decay into two @-particlesif it has angular momentum 1. It would therefore have a very long life, and this could explain the sharp
Letter from Peierls to Bohr, 17 August 1936. I n the collection of Peierls Papers in the Bodleian Library, Oxford. 6 5 Manuscript, Spin Exchange in Atomic Nuclei, [1936]. Reproduced on p. [195]. 66 Manuscript, On the Transmutations of Lithium by Proton Impacts, [1936]. Reproduced on p. [199].
P A R T 1: P A P E R S A N D M A N U S C R I P T S R E L A T I Y G T O N U C L E A R P H Y S I C S
resonances in the excitation curve. This draft appears to be complete, although there are pages suggesting a partial re-wording. It is not clear why this was never published. This, as well as the note about aluminium61, may have been intended for the planned publication in the Proceedings of the Royal Society, mentioned in a letter to Bethe: “Further we have discussed a number of features of nuclear reactions, for which the extreme facility of energy exchange allows to understand various experimental results which hitherto were quite unexplained. While the former part of our work will be published in the Proceedings of the Copenhagen Academy, we have found it more practical first to publish a more qualitative discussion of the latter problems in a paper to appear in the Proceedings of the Royal Society, the manuscript of which we are just finishing, and of which we hope to be able to send you a copy in a few weeks.” Apart from the fragments mentioned, no such draft seems to have survived. By the summer of 1936, Bohr’s approach to nuclear reactions had become the generally accepted treatment. He was asked on many occasions to lecture on this subject, and some accounts of such lectures are available. Of a lecture given to the Nordic Scientists’ Meeting in Helsinki in August 1936, a fairly detailed summary is published in the conference proceedings, and also in Fysisk Tidsskriff7. This contains an outline of the development of nuclear physics, leading up to Bohr’s analysis of the compound-nucleus problem. A major lecture tour started with a visit to Paris, where he lectured on 18 and 19 January 1937. From there he went to the United States and Canada, where he gave talks at several universities, including the University of California (Berkeley and Los Angeles), Duke, Harvard, Johns Hopkins, Michigan, Princeton, Rochester, and Toronto. An account of these lectures is published in Science6’. The contents are very similar to the first note in Nature”, but there is also some of the material from the later paper by Bohr and K a l ~ k a r In ~ ~par. ticular there is a discussion of the escape of a neutron as an evaporation process. There exist some brief notes of two lectures, taken by Wheeler68a, which suggest a selection of material similar to the summary in Science; the lectures gave rough
h7 N. Bohr, Atomkernernes Egenskaber, in: Nordiska (19. skandinaviska) naturforskarmotet i Helsingfors den 11-15 august; 1936, Helsinki-Helsingfors 1936, pp. 73-81; Fys. Tidsskr. 34 (1936)
186-194. Danish text reproduced on p. [159], translation on p. [172]. N.Bohr, Transmutations of Atomic Nuclei, Science 86 (1937) 161-165. Reproduced o n p. [205]. “’ John A . Wheeler’s papers, on deposit at the library of the American Philosophical Society, Philadelphia. A copy of these notes is deposited in the Niels Bohr Archive. 6x
Bohr t o Bethe,
Fullhob 23 re*t36on
[5391
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Bohr lectures on the liquid-drop model in Princeton in 1937
PART I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
quantitative estimates of the parameters entering the theory, such as the level densities and the radiative decay probabilities. From the United States Bohr travelled to Japan. There is no detailed record of the lectures he gave there, but those dealing with the nucleus were presumably similar to the ones in the United States. In June 1937 Bohr lectured on nuclear physics in Moscow on his return from Japan, and the Niels Bohr Archive contains a very garbled shorthand transcript of that talk69, which suggests that it resembled the previous ones. There is a more complete summary of a talk given on 27 August to a meeting of Nordic Electrical Engineers7’. This gives a historical survey of the development of nuclear physics, including only a brief mention of the compoundnucleus picture. In the course of the talk, Bohr stresses, for this particular audience, how much of this development is owed to the work of the electrical engineer. In October 1937 he spoke at the Congres du Palais de la dkcouverte in Paris. A brief summary published in the congress proceeding^^^ resembles the approach of the Nature or Science articles. There exist a number of successive partial drafts under the same title, “Nuclear mechanic^"^^, which are dated after the conference, and could be intended as a full text for publication in the conference proceedings, or as a separate paper. The exposition seems rather different from that in the published summary. Of a paper read to the Copenhagen Academy on 19 November 1937, only an abstract is published under the title “On Nuclear reaction^"^^. This is published in English in Nature, with the title “Mechanism of Nuclear Reactions”. The abstract refers to the use of thermodynamic analogies, and is presumably a report on the material of 5 2 and Addendum I1 of the 1937 paper46. Meanwhile, Bohr retained an active interest in the rapidly developing experimental material, and in the problems involved in its interpretation. An exam-
‘’ Manuscript, Moscow Lecture, 1937. Bohr MSS, microfilm no.
14. N . Bohr, Om Spaltning af Atomkerner, in: 5 . nordiske Elektroteknikerm~de,J . H . Schultz Bogtrykkeri, Copenhagen 1937, pp. 21-23. Reproduced o n p. [213], translation on p. [218]. -1 N.Bohr, Mecanique nucleaire, in: Reunion internationale de physique-chimie-biologie, CongrG du falais de la decouverte, Paris, Octobre 1937, Hermann et Cie, Paris 1938, Vol. 11, pp. 81-82 ( A c /ualitds scientifiques et industrielles). Reproduced on p. [265], translation on p . [269]. A brief report of Bohr’s talk is given in Nature 140 (1937) 711. 72 Manuscript, Nuclear Mechanics, 1937. An extract is reproduced on p. [271]. 7 3 N . Bohr, Om Atomkernereaktioner, Overs. Dan. Vidensk. Selsk. Virks. Juni 1937 - Maj 1938, p. 32; Mechanism ofNuclear Reactions, Nature 141 (1938) 91 (condensed into a single sentence; see p . [288]). The Danish text is reproduced with a translation o n p . [287]. 70
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
ple of this is in a note concerned with isomeric states74.Of this, dated 7 December 1937, there remain only four pages of typescript with a carbon copy. In the top copy, page 4 is cut off after 8 lines, suggesting that the rest was going to be redrafted or abandoned. The point discussed is that such isomeric states are produced only by neutrons of certain energies, even in regions in which the level spectrum is very dense. This might imply, it is suggested, that a single degree of freedom, perhaps vibrational, is involved in the first place. The collision might produce first a short-lived state with special properties. But this raises the difficulty why the special nature of this state affects the final result if its lifetime is short enough to result in broad energy bands. The problems touched upon here are similar to those arising in the nuclear photo-effect, and are mentioned in papers on that subject, which will be reviewed in the next section. This may be the reason why this note was not completed for publication. Isomeric states are also mentioned in the paper Bohr contributed to the issue of the Annalen der Physik honouring Planck’s 80th birthday75. This is also a detailed historical account of the development of nuclear physics, including Bohr’s ideas. At the end the problem of isomeric states is mentioned, with the conjecture by von Weizsacker that these are states of high angular momentum. In later correspondence with T r ~ m p y Bohr ~ ~ , takes it for granted that isomers are due to large spin differences. It is interesting that the many different periods found by Hahn and Meitner in reactions of neutrons with uranium are quoted as examples of isomeric states, a phenomenon which found a very different explanation about a year later. So long as these reactions were interpreted as capture of the neutron, the compound nucleus had to have the same charge as uranium, and a mass number exceeding that of the uranium isotope involved by one unit. If there were many different radioactive species resulting, they had to be isomers. In an unfinished draft77the question is raised whether in such experiments the impact of a fast neutron might result in the ejection of several nucleons, which would increase the number of nuclear species that could be formed. Amongst the other applications of the compound-nucleus theory, the nuclear
Manuscript, Nuclear Excitations and Isomeries, 1937. Reproduced on p. [291]. N. Bohr, Wirkungsquantum und Atomkern, Ann. d. Phys. 32 (1938) 5-19. Reproduced o n p. [301], translation o n p. [318]. 7 6 Letter from Trumpy to Bohr, 12 February 1943; Norwegian text on p. [653], translation on p. [654], and letter from Bohr to Trumpy, 16 February 1943; Danish text and translation on p. [656]. ” Unpublished manuscript about (n, 2n) reactions, [1937-1938?]. Reproduced on p. [283].
74 75
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
photo-effect and the related problem of dealing with the region of overlapping resonance levels, were major preoccupations of Bohr’s, particularly in 1938. This will be discussed in the following section.
4.
NUCLEAR PHOTO-EFFECT AND THE CONTINUOUS ENERGY REGION
In late 1937 and in 1938, Bohr devoted much thought to the problem of the nuclear photo-effect, because he reaiised that this phenomenon contained very valuable information about nuclear dynamics, and could give rise to interesting points of principle. His interest in this phenomenon was aroused in particular by two surprising features: one was the irregular variation from element to element of the cross section for Li + p y-rays, as found by Bothe and Gentner78,the other was the fact that the magnitude of the cross section for some elements seemed to require radiative transition probabilities much larger than those estimated from neutron capture. In his note in Nature79 Bohr points out that both these puzzles could be resolved if the absorption of the y-ray first resulted in the formation of a shortlived state, rather like the excitation of an infrared active lattice vibration in a solid, from which the excitation energy would then spread to other degrees of freedom by virtue of the coupling between them. (This concept is similar to what in contemporary terminology would be called a “doorway state”.) Applying the ideas used in the discussion of the formation and decay of a compound-nucleus state, he derives for the photo-nuclear cross section the result
where X is the wavelength of the y-ray, v its frequency, vi are the resonance frequencies of the short-lived states; r R is the width of such a state for the radiative transition to the ground state, and r c its width due to the coupling to other degrees of freedom. If r R Q Fc, the cross section at resonance becomes (y2/n) x rR/rC. From the observed cross section one finds r R / F C to be about Bohr adds the conjecture that the width of the resonance is comparable with the frequency spread of the y-rays, and this gives I‘C 1019 sec- and therefore r R - l O I 5 sec-’. These figures are not unreasonable, and the radiation probability
-
-’W . Bothe and W . Gentner, Atomurnwandlungen durch y-Strahlen, Z. Phys. 106 (1937) 236-248. 79
N . Bohr, Nuclear Photo-Effects, Nature 141 (1938) 326-327. Reproduced on p. [297].
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from the short-lived state to the ground state is much greater than that from the compound states ultimately formed. Bohr was aware of the intuitive nature of the conjectures in this model, and sent a copy of the note to Bloch immediately after sending it t o Nature, requesting Bloch’s and Pauli’s opinion: “In connection with the discussions with Bothe in Bologna it may interest you and Pauli to see the little note on nuclear photo-effects which I have just sent t o ‘Nature’ and of which I enclose a copy. It seems to me that the argumentation is not only very natural from a theoretical standpoint, but also a very plausible description of the experimental facts, and I shall be very happy to hear the criticism of the more learned gentlemen, ... ”. Pauli’s reply is somewhat critical: “The essence seems t o me to lie in the sentence at the bottom of p. 1, starting ‘This apparent contradiction ... ’ and ending ‘singular radiation properties’ (top of p. 2). It seems t o me here that this sentence is long, but still too short! For in order to understand the treatment in terms of a model it seems to me absolutely essential that the concept ‘special vibratory motions’ in the first place be made more precise, and secondly be derived in more detail from a model.
...
In the nucleus everything is of course much more complicated than in the solid, where the exchange of atoms between sites can be neglected. Hence my desire for a more accurate model explanation. In addition I must leave the judgment on the quality of the experiments, and the certainty of the conclusions that can be drawn from them, to the competent experts.” Bloch’s reply distinguishes the point of principle made by Bohr from the question of the model: Bloch 10 Bohr, I5 I-cb 3R Gcrrnan 1 ~ x 1oil p I5431
“My attitude is perhaps more positive inasmuch as I accept completely that the experiments of Bothe and Gentner require empirically that in the continuum of highly excited levels there are well-defined states, or groups of states, which interact especially strongly with radiation; I therefore agree also that you have found in your note a natural description of the facts. But for a ‘theory’ I feel the lack of an understanding of the underlying mechanism, and I find myself in a similar situation as when we talked about the dipole and quadrupole radiation of nuclei. If one treats the nucleus as a droplet with a completely smeared-out charge, its vibrations will of course be coupled to the radiation only by its quadrupole moment, and if the ‘special vibratory mo-
PART I: PAPERS AND MANUSCRIPTS RELATING TO KUCLEAR PHYSICS
tions’ are to have a dipole moment they should not be treated by a liquid-drop model. This model does not seem to me altogether reliable enough to regard its consequences concerning the vanishing dipole moment as certain, and if one is to make exceptions for special vibrations then I would indeed want to know, like Pauli, what is the nature of their special position. But perhaps you have something quite different in mind; in any case I look forward eagerly to your more detailed paper.” Bohr had also sent a copy to Peierls, whose reply was in favour of Bohr’s view, but raised some queries: “As far as I can see now, it seems to me likely that the form of the absorption line will not be that of the natural line shape. That form follows only if the probability of the transfer of excitation energy from the special wave packet in long-lived states which communicates with the ground state is independent of the extent to which this transfer has already taken place (because only then will the special state decay exponentially with time). As far as I have been able to see there is no reason why this should apply in this case, and if one thinks of the analogy with a solid, the absorption bands there also have a more complicated form. Your results are of course independent of the line shape, except for numerical factors. I also did not find it easy to see how you conclude that the line width is about equal to the width of the y-ray, but evidently you have used here some experimental material with which I am not familiar. I would be interested to know whether you agree with my remark about the line shape. It is of course not significant for practical purposes, but can be of interest for the choice of a method suitable for the mathematical treatment.”
Peierls t o Bohr, 8 Feb 38 German on
,6111
Heisenberg agrees with Bohr’s treatment in general, but also queries the assumption about r c : “Many thanks to you also for your manuscript. One cannot doubt that your explanation of the strong photo-effect is the right one; if I understand correctly you liken these selective photo-effects perhaps to something like the infrared ‘Reststrahlen’ of a crystal, which also lead to a vibration which has nothing to do with ordinary thermal radiation. I am still not very clear why the quantity rc l O I 9 sec- is a hundred times smaller than ordinary nuclear frequencies. This means a considerable stability of that mode of vibration, whereas in the Reststrahlen r c is almost of the order of v. How reliable is the estimate r c / v - 1/100?”
-
There is no record of Bohr’s immediate reaction to these doubts and questions,
Heisenberg 10 Bohr, 9 Feb 38 German text on [5851 Translarlon O n p lSs61
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Hilde Levi, Pauli and Peierls
but in discussing the photo-effect in his paper in the Planck i s s ~ e ’ ~which , was submitted at the end of February, he uses rather more tentative language. Further reservations are made in a second letter to Nature”. He stresses there that the interpretation in his earlier note must be regarded as preliminary, and that further experiments about the variation of the cross section with frequency would make it possible to estimate the strength of the coupling. He also points out (perhaps as a result of someone’s criticism, though he does not mention that) that, strictly speaking, it is inconsistent to talk of the time development of a reaction if its energy is given. He explains that this was of course meant in the sense of a wave packet of limited duration, which would not have a sharply defined energy, so that the argument precludes conclusions about energy.
N. Bohr, Resonance in Nuclear Photo-Effects, Nature 141 (1938) 1096-1097. Reproduced on p . [331].
8o
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
He also corrects a statement in the first paper, where the impression was given that the selectivity would occur only if the transition by the emission of a single quantum to the ground state was more likely to happen during the short-lived initial state than during the rest of the long life of the compound nucleus. The selectivity does not, however, depend on this relation. For the detailed justification of these statements he refers to a future paper with Peierls and Placzek in the Proceedings of the Copenhagen Academy, which in fact never appeared. About this unpublished paper more will have to be said below. In August of 1938, Bohr addressed a meeting of the British Association for the Advancement of Science, and a brief account is published8’. Here he refers to the liquid-drop model more definitely than before: “Thus the system behaves in many respects like a drop of fluid, and the states of excitation can be compared with the oscillations in volume and shape of a sphere under the influence of its elasticity and surface tension.” Further discussions of the problems of the photo-effect, including those with Peierls and Placzek to which Bohr had referred in the second Nature note, showed up a fundamental difficulty. This occurs whenever, as in the case of the photo-effect at 17 MeV, one is concerned with the region of continuous energy. (A more nearly correct description would be the region of overlapping resonance levels, since the energy spectrum is always continuous above the threshold for particle escape, though there may be narrow resonances; but we shall use the terminology used in the papers at the time.) The general theory of resonance processes, first derived by Breit and Wigner48 for the case of a single resonance level, was at first applied also to the case in which the width of the resonance levels is greater than their spacing, so that at any energy a number of levels contribute. On the other hand one can derive the cross section for the formation of a compound nucleus by the capture of a particle from the general theorem of detailed balancing in terms of the decay constant, i.e., the probability of escape of the same particle from the compound nucleus. As long as the levels do not overlap, the two methods give the same answer, but in the case of overlapping levels, they differ by a factor aI’/2d,
Symposium on Nuclear Physics, Introduction. Abstract in: Brit. Ass. Adv. Sci., Report of Annual Meeting 1938, Cambridge, August 17-24, London 1938, p. 381. Reproduced on p. [333]. Report on meeting: Nature (Suppl.) 142 (1938) 520-522. Reproduced on p. [336]. There exists one page of a typescript with an identical text (Various Notes [III], September 1938, Bohr MSS, microfilm no. 1 9 , ahich makes it likely that the summary published in Nature was written by Bohr. xi
P A R T I : P A P E R S A N D MANUSCRIPTS RELATING TO N U C L E A R PHYSICS
A group including Placzek (left) a n d Peierls (right)
where r is the total width of a level (i.e., the inverse lifetime of the compound nucleus) and d the level spacing. This discrepancy had already been noticed by Kalckar, Oppenheimer and Serber”, who concluded that the result obtained from the extension of the Breit-Wigner formula was the correct one. If this is applied to the case of the photo-effect, the data would require for the probability of radiative transition from a compound state to the ground state a much larger value than very general considerations would permit. The conclusion of Bohr, Peierls and Placzek, summarised in a letter to Nature82,was that, in fact, the answer from the detailed balancing argument was the right one. The failure of the other result was due to the fact that, in the case of overlapping levels, the state of the compound nucleus is not uniquely defined by its energy, since it can be a superposition of several states whose energies agree
N . Bohr, R. Peierls and G . Placzek, Nuclear Reactions in the Continuous Energy Region, Nature 144 (1939) 200-201. Reproduced on p . [391].
82
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
with the given one within their definition, and the phases of this superposition depend on the way in which the compound nucleus has been formed. For the details the reader was again referred to the promised paper in the Proceedings of the Copenhagen Academy. Bohr read a paper to the Academy on 21 October 1938, of which only an abstract is availableg3,which describes this talk as “in connexion with the communication of a paper, written in collaboration with G. Placzek and R. Peierls”. No such joint paper was available at the time, but perhaps Bohr reported in his talk the stage which the discussions and partial drafting of a paper had reached. The published abstract is not sufficiently detailed to indicate this. The drafting of a paper, which was meant to be a sequel to the Bohr-Kalckar paper46, had in fact been underway since the spring of 1938. The difficulties in trying to arrive at an agreed draft were mostly concerned with presentation, rather than substance. Peierls and Placzek were anxious to base the arguments on a complete theoretical foundation, for which the method of Kapur and Peierlsg4seemed to offer a convenient basis. Bohr found these calculations rather complicated and formal. He tried to use more intuitive arguments which the others in turn did not find convincing. The drafting of a joint paper was discussed during visits of Peierls to Copenhagen where Placzek spent most of the period June 1936 to May 1938, during visits by Placzek and by Bohr to Birmingham, and by correspondenceg5. A file in the Niels Bohr Archiveg6contains numerous partial and complete drafts. All of these appear to have been written by Peierls, some together with Placzek, and some attempted to take into account Bohr’s wishes as regards presentation. But none of them seem to have met with approval by Bohr, and they are therefore not reproduced here. Because of the slow progress it was suggested that a short note for Nature be prepared: “On my next visit I should be very happy if we could work in [for] a few days together on a brief note to ‘Nature’ about the main results of our common work on the nuclear dispersion theory ... . Due to the unquiet times and my N . Bohr, Om Atomkernernes Reaktioner, Overs. Dan. Vidensk. Selsk. Virks. Juni 1938 - Maj 1939, p. 25; Reactions ofAtomic Nuclei, Nature 143 (1939) 215. The Danish and English texts are reproduced on p. [339]. 84 P . L . Kapur and R . Peierls, The Dispersion Formula for Nuclear Reactions, Proc. Roy. SOC.London A166 (1938) 277-295. ” See the correspondence between Bohr and Peierls, 7 May 1938 - 13 September 1939 (as in ref. 64). ‘6 Manuscripts, Nuclear Reactions in the Continuous Energy Region, 1938-1940. Bohr MSS, microfilm no. 15. 83
Bohr t o Peierls. 6 J u n e 39
on
j6,Zi
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unavoidable occupation with the fission problem I regret that I have not yet found opportunity to finish our article with Placzek but, as Placzek suggested, it would be nice if a short account of the results could appear in ‘Nature’ in a near future, and I shall bring with me a draft Placzek and I have written.” This was the note already mentioneds2. In the course of it, it is pointed out that the selectivity indicated by the early experiments of Bothe and Gentner was not confirmed by later work. This would imply that there was no need to introduce the intermediate short-lived state postulated by Bohr in his earlier notes. We do know today that such a selectivity does exist, for example in the so-called “giant dipole”, to which the ideas of Bohr, if perhaps not all quantitative details, are directly applicable. In the autumn of 1939 the collaboration was interrupted by the outbreak of war. Bohr continued his work on the paper, with the assistance of Rosenfeld. This resulted in an incomplete draft”, with many pages being re-written many times, as was not uncommon with Bohr’s writings. The calculations generally followed the suggestions of Peierls and Placzek, with one major exception: There is a contribution to the scattering, particularly to elastic scattering, called ‘‘potential scattering”, in which the incident particle is deflected without a compound nucleus being formed. Peierls and Placzek had tended to omit this from the quantitative discussion, for simplicity, and deal only with results for which the potential scattering is negligible. Bohr attempted to include the potential scattering, but this led to considerable difficulty, and this appears to be the reason why his draft remained incomplete. No further work was done on the paper during the war. All three authors met again in Los Alamos during 1944-45, but they were preoccupied with other matters. However, copies of some draft circulated during that period, and as a result the paper was cited repeatedly in the literature, making it one of the most cited unpublished papers. After the war the question was resumed, and at a Copenhagen conference in September 1947 it was agreed that Peierls would try to complete the draft made by Bohr in 1939-40 ”: This material was therefore re-typed and sent to Birmingham”. Peierls sent an amended drafts9 to Copenhagen with a covering
Separate folder, dated 1939-1940, in the file of ref. 86. Bohr MSS, microfilm no. 15. Manuscript, On the Mechanism of Transmutations of Atomic Nuclei. II. Processes in the Continuous Energy Region ofthe Compound State, 1947. Reproduced on p. [487]. We reproduce the only existing draft written by Bohr, though incomplete, and (ref. 89) the only complete draft resembling Bohr’s presentation. ‘ 9 Second manuscript with the same title as ref. 88. Reproduced on p. [503].
”
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letter explaining the reasons for certain changes”. There is no record of Bohr’s reaction. Presumably he still was not satisfied with the new draft, otherwise he would have had it prepared for publication. Placzek approved of the new version of the paper, except for a number of minor amendments”. In the typescript referred to in footnote 89 there are a few amendments by Placzek and 6 sheets of handwritten notes for amendments are attached. Probably this copy and the amendments were given to Bohr by Placzek when they met in Princeton in May 1948 92. It is interesting that the supplementary sheets have a few alterations in pencil in Bohr’s handwriting, and also that a few of Placzek’s alterations, and a few other, minor ones, have been made by Bohr in another copy, now in the possession of Jens Lindhard93. All these corrections are of a minor, textual nature; they show that Bohr read the paper, but evidently he meant to consider the draft further. For some time after this, the only references to this work were remarks from time to time in Bohr’s letters94 about the desirability of completing the paper. By this time the main results of the paper including the “Optical Theorem” had been mentioned in the book by Mott and Massey”. The discussion about the publication of the paper took a new turn when Bohr revised his views of nuclear dynamics (see section 6). In sending to Peierls a note on his new viewpoint, he adds: “
...I will try t o incorporate such views in our old manuscript.”
Peierls opposes the idea of extending the treatment: “It seems to me that the contents of the paper as at present drafted are largely, if not entirely, independent of the model one makes of the nucleus, though the values one would tend to guess for the various constants occurring in the equations do, of course, depend very much on the model. In the past there has been a tendency to confuse the two matters, i.e. to identify the model that you first proposed of a nucleus, with the mathematical formalism developed to investigate this model, which, however, is far more general. For this reason I entirely agree that it would be desirable in the introduction t.o explain this ... .
...
’” Letter from Peierls to Bohr, 2 November 1947. Reproduced on p. [613].
Letter from Peierls to Bohr, 6 February 1948. Reproduced on p. [615]. from Bohr to Peierls, 9 September 1948. BSC, microfilm no. 31. A photocopy of this manuscript is in the Niels Bohr Archive. It has not yet been microfilmed. y4 Letters from Bohr to Peierls, 18 March 1948 (as in ref. 64), 9 September 1948 and 9 March 1949 (BSC, microfilm no. 31). y 5 N.F. Mott and H.S.W. Massey, The Theory ofAtomic Collisions, Second Edition, Oxford Univ. Press, 1949. See p. 133.
91
’)’ Letter
’’
Bohr to Peierls, 22 Aug 49 Full text on p. [6161
Peierls t o Bohr, 7 Dec 49 Full text on p. [6,91
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
... for the present paper it would be wiser to admit the existence of unsolved problems rather than to attempt a complete answer in this context.” Bohr’s reply suggested further discussion about the question: “ I was most interested in your remarks about the nuclear problem and I look forward very much to discuss the whole situation thoroughly with you.”
i3Olli 1 0 I’LILII5 1 7 iiiCJY f (111 I i Y l ill1 p [hZO]
No further work was done on the joint paper. 5.
FISSION
The story of the discovery of fission has been told many times. For the present purpose it may therefore be sufficient to give a brief sketch, by way of a reminder. It started with the discovery by Hahn and S t r a ~ s m a n nof~ a~ radioactive isotope of barium amongst the products of the bombardment of uranium with neutrons, which previously had been believed to contain only transuranic elements. At first Hahn and Strassmann had difficulty in believing this result, which suggested that the uranium nucleus had split in two. When this surprising result was reported in a letter to Lise Meitner, she and her nephew Otto Robert Frisch discussed the situation and concluded that the cause for the splitting of the nucleus must be the electric repulsion between its parts. It was clear from the mass defects that a considerable amount of energy could be released by splitting a heavy nucleus in half, but normally surface tension prevented this from happening. The surface tension was reduced by the electric repulsion, and the additional disturbance due to the incoming neutron could set up vibrations which would make the nucleus unstable. Meitner and Frisch estimated the energy released in the process, which appears as the kinetic energy of the fragments, accelerated by their mutual repulsion. This discussion took place in Sweden. On his return to Copenhagen Frisch gave an outline of these conclusions to Bohr. In the words of Frisch9’: “When I reached Bohr he had only a few minutes left; but I had hardly begun to tell him, when he struck his forehead with his hand and exclaimed: ‘Oh what idiots we all have been! Oh but this is wonderful! This is just as it must be! Have you and Lise Meitner written a paper about it?’ I said, we hadn’t yet but 0. Hahn and F. Strassmann, Uber den Nachweis und das Verhalten der bei der Bestrahlung des Urans mittels Neutronen entstehenden Erdalkalimetalle, Naturwiss. 21 (1939) 11-15, O . R . Frisch, The Interest is Focussing on the Atomic Nucleus, in: Niels Bohr, His Life and Work as Seen by his Friends and Colleagues (ed. S . Rozental), North-Holland Publ. Co., Amsterdam 1967,
96
’’
pp. 137-148. See p. 145.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
would at once, and Bohr promised not to talk about it before the paper was out. Then he was off to catch his boat. The paper was composed by several long-distance telephone calls, Lise Meitner having returned to Stockholm in the meantime. I asked an American biologist who was working with Hevesy what they call the process by which bacteria divide; ‘fission’, he said, and so I used the term ‘nuclear fission’ in that paper. Placzek was sceptical; couldn’t I do some experiments to show the existence of those fast-moving fragments of the uranium nucleus? Oddly enough, that thought hadn’t occurred to me, but now I quickly set to work, and the experiment (which was really very easy) was done in two days, and a short note about it was sent off to ‘Nature’ together with the other note I had composed over the telephone with Lise Meitner”.” Some of this is contradicted by passages in letters to Lise Meitnergsa: “ I could talk to Bohr only today about the exploding uranium. The conversation lasted only five minutes, since Bohr agreed with us at once and in all respects. He was only surprised that he had not thought earlier of this possibility, which follows so directly from current ideas of nuclear structure. He also agreed with us that the breakup of a heavy nucleus into two large pieces is a classical process, which does not take place at all below a certain energy, but very easily immediately above it ... Bohr will think this through quantitatively and talk to me again about it tomorrow.”
“I wrote a first draft on Friday [6 Jan.] and at Bohr’s request went to Carlsberg in the evening, where Bohr once more discussed the matter with me in detail. He let me show my estimate about surface tension and was in complete agreement; he had himself thought of the electric term in passing, but did not think it contributed so much. About the resonance he did not want to say anything directly, but did not seem to see any difficulty there. I later thought a little differently about this point, as you will see from the final part of the note; on this Bohr did not comment. Bohr made that night only some proposals to formulate several points more clearly, but otherwise was in complete agreement. I then started next morning writing down the new draft, and could
L. Meitner and O.R. Frisch, Disintegration of Uranium by Neutrons; a New Type of Nuclear Reaction, Nature 143 (1939) 239-240; O.R. Frisch, Physical Evidence for the Division of Heavy Nuclei under Neutron Bombardment, Nature 143 (1939) 276. (Both these papers were dated 16 January 1939.) ’*.I Letters from Frisch t o Meitner, 3 January 1939 and 8 January 1939. Meitner papers in the archives o f Churchill College, Cambridge.
”
Frisch 10 Meitner, 3 J a n 39
German
Frisch t o Meitner, 8 Jan 39 German
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Otto Robert Frisch
bring Bohr only two pages to the station (10.29) where he pocketed them, he had no time to read.” Meanwhile Bohr and Rosenfeld, who had sailed on 7 January, discussed the implications of the new phenomenon. They agreed with the argument of Meitner and Frisch, but found the large fission yield surprising. Soon, however, Bohr realised that the explanation was to be found in his analysis of the compound nucleus. The compound nucleus lives long enough for statistical equilibrium to be established, with equipartition of the energy between all degrees of freedom. The fission process therefore competes on equal terms with radiation or with neutron escape. This point was made in a letter to Nature99 dated 20 January, y9 N . Bohr, Disintegration of Heavy Nuclei, Nature 143 (1939) 330. Reproduced o n p . [341]. The mention of Frisch’s letter and experiment must have been one of the later changes, see ref. 101, as Bohr had not heard of these on 20 January.
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Emilio Segre and Lise Meitner
four days after Bohr's arrival in New York, and also in a letter to Frisch'oo. In another letter to Frisch, written a few days later"', Bohr makes some corrections to his Nature note (the original draft does not appear to have survived) and mentions plans for experiments to look for the simultaneous occurrence of different p-emitters (which from the old point of view would have been seen as successive decays and therefore would have shown a different variation with time). The thought of looking for fission fragments does not at this stage seem to have occurred to Bohr. In the same letter Bohr also begins to show impatience at the lack of news from Copenhagen. This no doubt was aggravated by a somewhat embarrassing situation which had arisen. In the words of Rosenfeld"*: Letter from Bohr to Frisch, 20 January 1939. Danish text on p. [ 5 5 6 ] , translation on p. [557]. Letter from Bohr to Frisch, 24 January 1939. Danish text on p. [560],translation on p. [561]. L . Rosenfeld, Nuclear Reminiscences. Selecred Papers of LPon Rosenfeld (ed. R.S. Cohen and J . J . Stachel), D. Reidel Publ. Co., Dordrecht 1979, pp. 335-345. See pp. 342-343. '0(1 '("
'"'
PART I: PAPERS AKD MANUSCRIPTS RELATIXG TO NUCLEAR PHYSICS
“On arrival in New York we were met by Wheeler; Bohr was detained by some business, so Wheeler and I proceeded to Princeton without him. On that night they happened to have a meeting of their ‘journal club’ at the physics department. I attended, in spite of the fatigue of the voyage, and was politely asked whether I had anything to tell them. Well, I had: I told them all about the problem we had struggled with during the journey. I did not know that Bohr had no intention of giving out the news so quickly, because he was anxious that Frisch’s note should first come out in print. I was under the impression that the note was already sent off and would appear in the next number of Nature; in fact it only appeared a few weeks later. The effect of my talk on the American physicists was more spectacular than the fission phenomenon itself. They rushed about spreading the news in all directions, and very soon the fission fragments had been seen in the oscilloscope in several laboratories in the United States, a very striking demonstration that was quite easy to produce.” The impact of these communications is also shown in the following extract from a letter in Phys. Rev. by Roberts, Meyer and Hafstad’03: “The Fifth Washington Conference on Theoretical Physics, sponsored jointly by George Washington University and the Carnegie Institution of Washington, began January 26, 1939, with a discussion by Professor Bohr and Professor Fermi of the remarkable chemical identification by Hahn and Strassmann in Berlin of radioactive barium in uranium which had been bombarded by neutrons. Professors Bohr and Rosenfeld had brought from Copenhagen the interpretation by Frisch and Meitner that the nuclear ‘surface tension’ fails t o hold together the ‘droplet’ of mass 239, with a resulting division of the nucleus into two roughly equal parts. Frisch and Meitner had also suggested the experimental test of this hypothesis by a search for the expected recoil-particles of energies well above 100,000,000 electron-volts which should result from such a process. The whole matter was quite unexpected news to all present lo4. We immediately undertook to look for these extremely energetic particles, and at the conclusion of the Conference on January 28 were privileged to demonstrate them to Professors Bohr and Fermi. It was subsequently learned that the particles had been observed independently by Fowler and Dodson at I o 3 R.B. Roberts, R.C. Meyer and L.R. Hafstad, Droplet Fission of Uranium and Thorium Nuclei, Phys. Rev. 55 (1939) 416-417. Io4 There exists in the Niels Bohr Archive a report on this conference by C.F. Squire, F.G. Brickwedde, E. Teller a n d M.A. Tuve. It has not yet been microfilmed.
PART I: PAPERS AKD MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Johns Hopkins the same day, by Dunning and co-workers at Columbia on January 2 5 , and by Frisch in Copenhagen two weeks earlier. For observations of the high energy particles, an ionization-chamber, about five mm deep, was placed about three cm below the neutron-source and was so arranged that interchangeable copper disks about three cm in diameter could be placed on the collector, which was connected to a linear pulseamplifier. The upper faces of these disks were then coated with the materials to be tested.” Bohr’s impatience grew, and on 30 January he decided to cable for information. There exist copies of two cables of that date, but these are on Postal Telegraph forms, therefore they are not the actual copies handed in or transmitted. It follows, however, from the replies that these, or similar, messages were sent. The draft copies read: [Princeton,] JANUARY 30 [ 19391 SCHULTZ INSTITUT FOR TEORETISK FYSIK BLEGDAMSVEJ
Draft Telegram, Bohr to Betty Schultz ( I n s i . ) , 30 Jan 39 English
COPENHAGEN TELEGRAPHIC INFORMATION FRISCH EXPERIMENTS NUCLEAR SPLITTING URGENTLY
EXPECTED
BECAUSE
EXPERIMENTS
VARIOUS
AMERICAN
LABORATORIES PLEASE SEND COPY FRISCH MEITNER NOTE AND TELEGRAPH DATE PUBLICATION NATURE STOP DELAY RETURNING PROOF MY NATURE NOTE UNTIL FURTHER NOTICE BOHR VANSTITUTE PRINCETON
and: [Princeton,] JANUARY 30 [ 19391 INSTITUT TEORETISK FYSIK
Draft Telegram, Bohr to the Institute, 30 Jan 39 English
BLEGDAMSVEJ COPENHAGEN DESIRE ESPECIALLY INFORMATION WHETHER NUCLEAR SPLITTING FOLLOWS IMMEDIATELY NEUTRON IMPACT OR PRECEDED BY BETA DISINTEGRATION AND WHETHER EFFECT OBTAINABLE ALSO WITH THORIUM BOHR
By this time Bohr had heard of Frisch’s experiment. According to a remark
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
in a letter to R a s m u ~ s e n ' ~he~ had , heard about it on 30 January, the day he sent the cables, from a casual remark in a letter from Hans Bohr in Copenhagen to Erik, who had come with his father to Princeton (see p. [624]). Frisch sent a cable at 23.03 on 31 January, evidently in reply: C O P E N H A G E N , 3 1 [January 19391 BOHR VANSTITUTE PRINCETON NJ LINEAR AiMPLIFlER DEMONSTRATES DENSELY IONISING SPLIT NUCLEI BOTH URANIUM T H O R l U M DETAILED INFORMATION POSTED TWENTYSECOND NEW EXPERIMENTS DEMONSTRATE SPLITTING WITHIN FIFTIETH SECOND GREETINGS
CARLSBERG"~ FRlSCH
On the next day he added more detail: I clcgl tllll, I n \ c h 10 Hohr, I f.ch 39 ill@lltll
COPENHAGEN, 1 [February 19391 BOHR VANSTITUTE PRINCETON NJ EXPERIMENTS CONSISTED IN RECORDING PARTICLES MAKING UNTIL T W O MILLION IONPAIRS IN URANIUMLINED HYDROGENFILLED IONCHAMBER T H R E E CENTIMETERS DIAMETER O N E CENTIMETER THICKNESS CROSSECTION AGREES WITH MEITNERS TRANSURANIUM EXPERIMENTS THORIUM CROSSECTION H A L F O F URANIUM BOTH FRLMEITNERS A N D MY NATURE LETTER PROBABLY APPEARS FRIDAY lo'
Bohr was so impatient that he could not wait for these replies, and, at 20.43 on 31 January, he cabled to Betty Schultz, his secretary: PRINCETON, 31 [January 19391 SCHULTZ INSTITUTE TEORETISK FYSIK BLEGDAMSVEJ KH ENDEAVORING
CORRECTING
DEPLORABLE
MISTAKEMENT
[misstatements?]
105 Letter from Bohr to Rasmussen, 14 February 1939. Danish text on p. [621], translation on p . [623]. By "Carlsberg" was meant Bohr's residence, and therefore the greetings were from his family. lo' This was a very optimistic estimate; the joint letter appeared only on 11 February and Frisch's a week later.
P A R T I : P A P E R S A N D M A N U S C R I P T S R E L A T I N G T O N U C L E A R PHYSICS
AMERICAN NEWSPAPERS ABOUT NUCLEAR SPLITTING STOP AWAITING FULLEST TELEGRAPHIC INFORMATION SOONEST STOP GREETINGS BOHR
Frisch’s letter mentioned in his first telegram arrived on 2 February’” shows the date of his experiment:
,
This
“The second paper contains the report of an experiment, which I decided to undertake on Thursday Jan. 12th; I was so lucky as to get a positive result the next day, which I confirmed, and got details of, during the next three days, and on Monday night I sent off the letters. Yesterday I got the proofs and sent them back last night; so I hope both papers will come out very soon. (Of course, there is no ‘Tavshedspligt’ [secrecy] any longer!; Hahn’s paper came out the day you left.)”
Frisch to Bohr, 22 J a n 39 Full rert o n p. [5591
The last quoted sentence suggests that he and Bohr discussed the need for discretion while Hahn’s discovery was unpublished. Bohr cables in reply on 3 February: PRINCETON, 3 [February 19391 SCHULTZ INSTITUT TEORETISK FYSIK BLEGDAMSVEJ KH
Telegram, Bohr to Betty Schultr (Inst.), 3 Feb 39 English
RECEIVED MEITNER FRISCH NATURE NOTES HEARTIEST CONGRATULATIONS FRISCH STOP TROUBLE DUE LACK IMMEDIATE INFORMATION NOW LARGELY SETTLED STOP KEEP SENDING TELEGRAMS ABOUT PROGRESS AND PLANS RESEARCH STOP BESIDES EXPERIMENTS SUGGESTED FRISCH LETTER ALSO TESTING LEAD MINERALS DIFFERENT ISOTOPIC CONSTITUTION IMPORTANT FOR THEORETICAL DISCUSSION = BOHR
On the same day he wrote to Frisch, this time in English, no doubt so that the letter could be typed by a secretary: “The experiments of Hahn, together with your aunt’s and your explanation have indeed raised quite a sensation not only among physicists, but in the daily press in America. Indeed, as you may have gathered from my telegrams and perhaps even, as I feared, from the Scandinavian press, there has been a rush in a number of American laboratories to compete in exploring the new field. On the last day of the conference in Washington (January 26-28), where
‘(I8
According to a pencil note on the letter.
Bohr to Frisch, 3 Feb 39 F u , l text on [5631
P A R T I : P A P E R S A N D M A N U S C R I P T S R E L A T I N G TO N U C L E A R P H Y S I C S
Rosenfeld and I were present, the first results of detection of high energy splitters [splinters?] were already reported from various sides. Unaware as I was, to my great regret, of your own discovery, and not in possession even of the final text of your and your aunt’s note to Nature, I could only stress (which I did most energetically) to all concerned that no public account of any such results could legitimately appear without mentioning your and your aunt’s original interpretation of Hahn’s results. When Hahn’s paper appeared, information about this could of course, for your own sake, not be withheld and was, in fact, the direct source of inspiration for all the different investigators in this country. When I came back to Princeton I learned from an incidental remark in a letter from Hans the first news of the success of your experiments. I at once telephoned this information to Washington and New York, and succeeded in obtaining a fair statement in a Science Service circular108aof January 30, of which I have sent a copy to my wife, but I could not prevent various misstatements in newspapers. This is of course regrettable but without any importance for the judgment of the scientific world, which here even more than in Denmark is accustomed to such happenings.” The phrase “for your own sake” is presumably meant as an explanation of the fact that Bohr had talked about the ideas of Lise Meitner and Frisch, although he had intended not to do so. In the same letter Frisch is also asked to see that Bohr’s letter to Nature be published as soon as possible. Frisch’s reply with an apology was written only on 15 March’”. Meanwhile Bohr had been very concerned about press reports which failed to give the proper credit to Meitner and Frisch. He writes in a letter to Fermi: B o h r 10 T r i m I t e h 19 Full text on p (5501
“ I felt therefore most strongly how justified I had been in urging so insistently that Tuve and you should not publish anything before the actual text of Meitner and Frisch’s note was at hand, since the whole idea was brought to the notice of scientists in this country only by the authors’ kind and confidential communication to me.” On the following day, when he has seen the article in Science Service, which gives due credit, he writes to Fermi that this puts things right. He adds:
I h h r 10 F a m i , 2 Feh 79 Full I L X I on p [ 5 5 2 ]
“I know that you realize that it has not been my intention unduly to stress personal matters, but that I was only afraid that an unhappy concourse of cirW. Davis and R.D. Potter, Release o f A f o m i c Energyfrom Uranium, Science (Suppl.) 89 (1939) 5-6. ‘09 Letter
from Frisch to Bohr, 15/18 March 1939. Reproduced on p. [ 5 6 5 ] .
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Fermi and Bohr on the Via Appia in 1931 (Courtesy AIP)
cumstances, each most pleasant in itself, should lead to discomfort for my friends and collaborators who had confided in me." The Niels Bohr Archive contains correspondence in a similar vein with others, including Tuve and Pegram. However, this did not finally dispose of the problem of credit and priorities. When Dunning at Columbia sent Bohr a copy of the Phys. Rev. Letter on the experiments he had done with Fermi and others"', and asked for suggestions, Bohr talked to Dunning in New York"' and requested some change in the way the history was presented. Fermi reports later that it was too late to make the changes Bohr requested, but he defends their version: ' I 0 Letter from Dunning to Bohr, 20 February 1939 (Niels Bohr Archive, not yet microfilmed); H.L. Anderson, E.T. Booth, J . R . Dunning, E. Fermi, G . N . Glasoe and F.G. Slack, The Fission of Uranium, Phys. Rev. 55 (1939) 511-512. ' I ' I n his letter to Fermi of 2 March, referred to below, Bohr mentions a conversation with Dunning "last Saturday", i.e., on 26 February. This was the last day of the New York meeting of the American Physical Society, at which Bohr spoke on the Friday afternoon (Phys. Rev. 55 (1939) 67).
PART I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Bohr and Placzek; in the background Jacobsen and his wife
I erini 10 Bohr, I March 39 I ill1 t c x i un p 15531
“According to what Dunning told me of the conversation he had with you, it seems that you dont consider as quite fair to give to Hahn the credit for the discovery of the splitting process and to Frisch and Meitner the credit for clearing up the energetic relations that make such a splitting process understandable. Now I reread Hahn’s paper and I found there a very clear suggestion that the process should consist in a division of the uranium nucleus into two approximately equal parts. How far this statement of Hahn has been influenced or determined by the correspondence that he had on the subject with Lise Meitner and with Frisch, I am of course unable to say, since he does not mention it. But, judging from the evidence of the papers that have been written, it seems to me that what we said was quite accurate.”
PART I: PAPERS A X D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
In his reply Bohr makes his point of view clear: “The point which I discussed at length with him [Dunning] and as regards which I am afraid from your letter that he did not quite understand me was the question of what may be said to be the merit of Meitner and Frisch in this matter. In your letter to Phys. Rev. they are credited with the remark about the release of energy, and I felt that it was in some way almost too much, since this point by itself would be clear to everyone who first believed in the fission phenomenon. To my mind their merit was rather to have grasped the fission idea so thoroughly and given so reasonable an explanation of the mechanism of energy-release that it would appeal immediately to the interest of all physicists. That was in any case my personal experience and also the impression of the circle here in Princeton. As Placzek will probably have told you himself the whole phenomenon appeared indeed so strange and impossible to explain even to a man with his great experience in nuclear theory that he refused to believe in Hahn’s discovery when he first heard about it. As regards the credit due to Hahn and Strassmann, I agree of course entirely with you and Dunning, and I do not understand what may have induced you to believe that I should take a different point of view. Even if, as I without any first-hand knowledge suggested as a possibility in the talk with you in Washington, Meitner and Frisch’s enthusiastic interest might have fortified Hahn’s confidence in his surprising findings, this would be entirely a matter of exchange of views between intimate friends and would have no influence whatsoever on the merit of Hahn and Strassmann for their great discovery.”
Bohr t o F ~
,
,
~
~
~ ,5541 ~ x ~
There exists a memorandum summarising the various points of view expressed on questions of credit and priority112. There are also comments on this situation in a letter from Placzek to Frisch113: “In addition you may be interested in a brief report about the events concerning uranium in Paris and in America.
...
b) America. About the shenanigans around here you have heard already in part through Bohr. I need not therefore cover you with reproaches; it would
‘ I 2 Memorandum, Discussion i Arnerika vedr0rende Meitners og Frischs Indsats i de ny Opdagelser [Discussion in America concerning Meitner’s and Frisch’s Contribution to the New Discoveries], dated 12 February 1939. Not yet microfilmed. ’ I 3 Letter from Placzek to Frisch, 2 March 1939. Frisch papers in the library of Trinity College, Cambridge.
~
Placzek Frlrch, 2 March 39 German
~
~
,
PART I: PAPERS AND MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
of course have been much better for ensuring your priority if you had communicated your discovery at once to Bohr in America and to me in Paris, and this would also have made Bohr’s psychological situation much easier. As it was, he had to listen at the Washington meeting to Tuve’s fanfare about his first, rather dilettantic experiments as great discoveries, without being able to say anything exact about you, because he then knew only from a letter from Hans that you had found something beautiful, but not what it was. I went to Princeton on 3 February and for a few days helped Bohr with his note for the Phys. Rev. I have hardly ever seen him so excited, particularly about the historically incorrect reports in the daily press ... and various journals. Now he is in a better frame of mind, particularly since the Phys. Rev. of 15 February has appeared, and at the New York meeting last week he gave a review lecture about the ‘fissure’. If I might ask you a favour, it would be to report to Bohr on every possible or impossible occasion by telegram about the further progress of your research, even if it is only a matter of trifles, since by any communication you can now give him great pleasure. ...” During all this time Bohr had continued to think intensely about the physics o f the fission process. This resulted in a further major step in the theoretical understanding. How this came about is described rather dramatically by Rosenfeld’ 14: “Some time in January, Placzek who had just come over from Europe, came to see us as we were sitting at breakfast at the Faculty Club. The conversation soon turned upon fission. Bohr casually remarked: ‘It is a relief that we are now rid of those transuranians.’ This elicited Placzek’s protest: ‘The situation is more confused than ever’, he said, and he explained to us that there was a capture resonance at about 10 volts both in uranium and thorium, showing, apparently, that transuranians were produced concurrently with fission. Bohr listened carefully; then he suddenly stood up and, without a word, headed towards Fine Hall, where we had our office. Taking a hasty leave of Placzek, I joined Bohr, who was walking silently, lost in a deep meditation, which I was careful not to disturb. As soon as we entered the office he rushed to the blackboard, telling me: ‘Now listen: I have it all.’ And he started - again without uttering a word - drawing graphs on the blackboard. The first graph looked like this:
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Clearly, the idea was to show, for thorium, the capture cross section, with its resonance at about 10 volts, and the fission cross section starting at a much higher threshold. Then he drew exactly the same graph, with the mention U238 instead of Th, and he wrote the mass number 238 with very large figures - he broke several pieces of chalk in the process. Finally, he drew quite a different picture which he labelled U235.This intended to show the fission cross section, with nonvanishing values over the whole energy-range:
Having drawn the graphs, he started developing his argument: obviously the resonance capture must belong to the abundant uranium isotope, otherwise, its peak value would exceed the limit set by wave theory. For the same reason the fast neutron fission must also be ascribed to the abundant isotope, whose behavior is thus entirely similar to that of thorium. Consequently, the observed slow-neutron fission must be attributed to the rare isotope U235:this is a logical necessity. The next step was to explain the similarity between the two even-mass nuclei Th and U238and the essential difference respecting fissility between the evenmass and the odd-mass uranium isotope. I need not repeat this explanation, which is now common knowledge.” This newly gained insight was, of course, the subject matter of another famous
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
paper115.It was dated 7 February. In retrospect, we may have the impression that this was a fairly obvious conclusion from the facts. However, at the time it was far from obvious, and very few physicists accepted Bohr’s explanation. Fermi, in particular, disagreed strongly. Bohr had evidently disagreed with him about how to look at the fission dynamics already at the Theoretical Physics Conference in Washington, according to a remark in his letter to Fermi on 1 February, which has already been referred to: B n h r to Ferrni, I Fcb 79 l u l l ~ C Y Ion p 15501
“Since we met in Washington, I have myself got considerably further as regards the estimation of the barrier effects for the heavy elements. Especially has the consideration of the stability, not only of U238,but also of all the other isotopes of this and the other heavy elements lent strong support to the views I presented in Washington.” After a talk with Fermi in mid-February, he writes:
Bohr i n Fermi, I’ Fcb 39 Full text on p 15521
“Of course, I quite realize the soundness of your arguments for doubting my conception of the fission mechanism, until further experiments as regards a comparison of the statistical distributions of the nuclear fragments produced by thermal and by fast neutrons have been carried out.” Fermi’s interpretation can be seen from a statement in the memorandum mentioned as ref. 112: “At the first meeting in Washington on 26 January, Bohr gave a talk on Frisch and Meitner’s interpretation of Hahn’s experiment and their explanation of it, and also on the related comments he had given in his own Nature note. According to this view the fission phenomenon should be regarded as a quasi-classical problem, for whose occurrence the excitation of the nucleus was a necessary condition. Fermi, on the other hand, maintained that one should think of fission as a typical quantum-mechanical phenomenon, in which the new compound nucleus after returning to its ground state with the emission of radiation, underwent a division, contrary to normal nuclei. On the basis of this interpretation Fermi insisted that the phenomenon should be far more sensitive to a change in the mass number and particularly in the charge than Bohr would expect according to his interpretation, and that one should therefore not expect any corresponding effect in other materials, including thorium. ” The controversy is also referred to in the letter of Placzek to Frisch, already m e n t i ~ n e d ”: ~
“’
N . Bohr, Resonance in Uranium and Thorium Disintegrations and the Phenomenon of Nuclear Fission, Phys. Rev. 55 (1939) 418-419. Reproduced on p . [343].
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
“Now about the physics part of the story. There were very heated discussions here, particularly between Bohr and Fermi, but also to some degree between Bohr and me. Fermi estimates the height of the potential barrier for fission rather crudely in the following manner: Take the masses of any pair of reaction products (extrapolated in a rough and ready manner from mass defects), add the Coulomb energy at the stage when the two nuclei touch each other, and subtract the energy of the original compound nucleus. This procedure leads to the result that the height of the potential barrier rises rapidly with decreasing atomic number, and therefore only the very heaviest nuclei can be split. (A weak point of the procedure is of course the crude definition of the touching point.) Bohr and Wheeler arrive at a diametrically opposite result by estimating the height of the barrier using model arguments, which seem t o me very special, from the study of the energy changes accompanying the elastic deformation of a droplet. According to this the barrier height should not vary much between the heaviest nuclei, and therefore more nuclei can undergo fission than according to Fermi. As for me, although Fermi’s method appears to me very crude, I have even less confidence in the Bohr-Wheeler result. Then there is still the question whether the fission of slow neutrons is due to U 235 or 238. Bohr insists on 235, because the idea of adjacent compound levels having a different behaviour (as you also discuss in your note) appears to him unattractive for theoretical reasons. It seems to me on the other hand that such a difference in behaviour has been established experimentally in other cases (e.g., the difference in the ratio between isomers in Rh according to its being excited by very slow or medium fast neutrons); and it could be an argument against 235 that one would then have to assume that the different ‘transuranics’ result from 235 and 238 in exactly the same ratio (this seems to be established by the old experiments of Hahn, Meitner and Strassmann and also by Curie & Co., where no variation with velocity of the ratio of the two ‘isomeric’ decay series was found).” Bohr’s conclusion that the slow-neutron effect was due to the rare isotope, 23sU,with which Fermi and others disagreed, was, of course, of enormous practical importance, because it implied, on the one hand, that there was no danger of an explosive chain reaction from natural uranium, but that, on the other hand, separated 235Uwould easily sustain such a reaction. The argument between Bohr and Fermi could be definitely settled by experimental evidence. For a final decision between the effects of the two uranium isotopes one had to wait for samples enriched in one or other isotope and that was possible only later. Meanwhile any new experimental details about the fission process might give some further clue, and Bohr followed the progress of experiments with great interest.
Placzek to Frisch, 2 March 39 German
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
He also kept in close touch with his Institute, both to keep the people there informed about the latest American results, and also to suggest problems for work in the Institute and to get their results. One particularly interesting item in this correspondence is a note which summarises the knowledge at the time and discusses experiments which might help to clarify matters further1I6. This is presumably the note mentioned in a letter to Rasmussen: I3otii 10 R d i i i i u i i e n 10 ‘\.larch 39 L)nni\h ILXI on p [hi31 I , iIlilaI,oIl 011 p [ h i s ]
“In an enclosure to a letter sent to my wife a few days ago, I have tried to give a review of the problems as they appear to me at this moment; also as regards the requests made there for further experiments, one should of course do only what fits reasonably into the working programme of the Institute.” Although this note was sent shortly before 10 March, it must have been written slightly earlier, since it refers to a paper “to be published” in the Physical Review of 1 March. Rasmussen mentions the receipt of this review on 24 March’17 and says that he has had it copied and distributed in the Institute to those interested. The note mentioned above116also refers to the discovery of delayed neutrons, and to its explanation, about which there exists the incomplete draft of a short manuscript”*. The details of the correspondence with the Institute are not of great significance for Bohr’s work, but they illustrate the interest he took in the details of what was going on in the Institute. At normal times such communications were verbal, and therefore there is no record of them, but here we have a period of intense activity during Bohr’s absence, and therefore written communications. For this reason a selection of these is reproduced”’. Quite early in his visit to Princeton, Bohr had started to work with John A. Wheeler on a full theory of the fission process. An abstract of this work, published in the report of the Washington Meeting of the American Physical Society in April 1939 120, is a summary of a talk given by Wheeler at the meeting; the ’ I 6 Memorandum, [Summary on fission], 1939. Danish text reproduced o n p. [347], translation o n p . [351]. The identification of this document is made plausible by there being a carbon copy of the
original, typed in America, with a few corrections in Rosenfeld’s writing, and two carbon copies of a re-typed version, in which these corrections have been made. ‘ I 7 Letter from Rasmussen to Bohr, 24 March 1939. Danish text on p. [638], translation on p. [639]. ‘ I s Manuscript, Residual Excitation of Heavy Nuclei after p-ray Emission, in folder, Notes from Bohr’s Stay in Princeton, 1939. Reproduced on p. [355]. See Bohr’s correspondence of February and March 1939 with Frisch, the Institute, Jacobsen and Rasmussen. A selection of these letters and telegrams is reproduced in Part 11. N. Bohr and J . A . Wheeler, Mechanism of Nuclear Fission, Phys. Rev. 55 (1939) 1124. Reproduced on p. [359].
PART I: PAPERS AND MAKUSCRIPTS RELATIYG TO NUCLEAR PHYSICS
John A. Wheeler (Courtesy AIP)
audience insisted on doubling the usual 10-minute time limit for contributed papers. The genesis of the full paper’2’ is described by Wheeler in a talk’22, from which the following extracts are taken: “Bohr once arrived in Princeton, we set to work to go from Frisch and Meitner’s broad-brush picture to a detailed analysis of the mechanism along the lines of the compound nucleus model and liquid drop model that Bohr - and I - had already been expounding and applying. This work took not only the three months of Bohr’s stay in Princeton but two additional months of finishing up until I could send it in for publication (June 28, 1939).
...
The whole enterprise was very much to Bohr’s taste, liking as he did to see
“ I N . Bohr and J.A. Wheeler, The Mechanism of Nuclear Fission, Phys. Rev. 56 (1939) 426-450. Reproduced on p . [363]. ”* See ref. 28, pp. 273-278.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
any part of physics with which he was concerned’brought together in a comprehensive and harmonious whole. In addition, he had always loved the subject of capillarity. For one of his first pieces of student research he had experimented on the instability of a jet of water against breakup into smaller drops’23.
...
A new feature of capillarity entered in the case of fission, the concept of fission barrier. The very idea was new and strange. More than one distinguished colleague objected that no such quantity could even make sense, let alone be defined. According to the liquid drop picture, is not an ideal fluid infinitely subdivisible? And therefore cannot the activation energy required to go from the original configuration to a pair of fragments be made as small as one pleases? We obtained guidance on this question from the theory of the calculus of variations in the large, maxima and minima, and critical points. This subject I had absorbed over the years by osmosis from the Princeton environment, so thoroughly charged by the ideas and results of Marston Morse. It became clear that we could find a configuration space to describe the deformation of the nucleus. In this deformation space we could find a variety of paths leading from the normal, nearly spherical configuration over a barrier to a separated configuration. On each path the energy of deformation reaches a highest value. This peak value differs from one path to another. Among all these maxima the minimum measures the height of the saddle point or fission threshold or the activation energy for fission. The fission barrier was a well-defined quantity! Bohr knew from earlier days that a work of Lord Rayleigh would have something to say about the capillary oscillations of a liquid drop. We rushed up to the library on the next floor of Fine Hall and looked it up in the Scientific Papers of Rayleigh. This work furnished a starting point for our analysis. However, we had t o go to terms of higher order than Rayleigh’s favorite second-order calculations t o pass beyond the purely parabolic part of the nuclear potential, that is, the part of the potential that increases quadratically with deformation. We determined - as soon also did Feenberg, von Weizsacker, Frenkel, and others - the third-order terms to see the turning down of the potential. They enabled us to evaluate the height of the barrier, or at least the height of the barrier for a nucleus whose charge was sufficiently close to the critical limit for immediate breakup.”
I2’See
V O ~ . 1,
Part I .
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
A full calculation of the height of the barrier would have been too difficult, and much ingenious work on this has been done by several authors since then. Wheeler continues: “For our immediate needs, however, our simple ‘poor man’s’ interpolation was adequate. With it, knowing - or estimating from observation - the fission barrier for one nucleus, we could estimate the fission barrier for all the other heavy nuclei, among them plutonium 239. Thanks to the questioning of Louis A. Turner ... we came to recognize that this substance, which up to then one had never seen except through its radioactivity ... , would be fissile. ... The barrier height of a compound nucleus against fission was not the only factor relevant for fission. Equally important in governing the probability of this process was the excitation, or ‘heat of condensation’, delivered up by the uptake of a neutron to form the compound nucleus in the first place. ... ... Fortunately Bohr and I had just been through the systematics of nuclear energies in the course of calculating the release of energy in various actual and potential fission processes. Therefore, we could estimate the difference between the excitation developed by neutron capture in the two uranium isotopes as almost a million volts, in favor of fission of U235.From our interpolation for fission barriers we estimated on the other hand a barrier almost 1 MeV lower for U235than for U238.... Placzek, wonderful person that he was, a man of the highest integrity, often a thoroughgoing skeptic about new ideas, said to me over and over in those early spring days of 1939 that he could not believe that the small amount of U235could be the cause of the slow neutron effects in natural uranium. I therefore bet him a proton to an electron, $ 18.36 to a penny, that Bohr’s diagnosis was correct. A year later Alfred Nier at Minnesota had separated enough U238to make possible a test and sent it to John Dunning at Columbia to measure its fission cross section. On April 16, 1940, I received a Western Union money order telegram for one cent with the one-word message ‘Congratulations! ’ signed Placzek.” Bohr’s judgment had been proved right. In July 1939, Wheeler sent Bohr the proofs of the paper. Bohr’s reply is along not unfamiliar lines:
“I read through it with great pleasure and admiration for all the work you have done with it and it was of course very tempting to wire that it could be published in the present state. Still I felt that a few smaller alterations were advisable and I hope that the delay of publication caused by this letter will only be small.”
Bohr to Wheeler, 20 Jul) 39 text on [6571
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
The paper was published on 1 September 1939. It remains today the basis of our description of the fission process. Bohr immediately realised the relevance of the theoretical results for the question of the possibility of a chain reaction. In an unpublished note dated 5 August 1939 124 he discusses the conditions for this and concludes that no chain reaction is possible in ordinary uranium without the presence of a moderator, i.e., a substance containing light nuclei which would slow down the neutrons to thermal velocities, but that the situation would be very different for isotopically pure or substantially enriched uranium. As a sequel to the main fission paper, Bohr and Wheeler were able to show that the fission of protactinium, which had been observed, agreed with the predictions from their theory. There is a draft by Wheeler’25 of a note on this subject, sent to Bohr for his approval. Bohr replies by telegram on 4 October 1939: [Copenhagen, 4 October 19391
IDrali Telegram, Bohr 10 Wiieeier, 4 OCl 39 EngliiIi
WHEELER PALMER LABORATORY PRINCETON NJ THANKS LETTER WITH PROPOSED PROTACTINIUM NOTE STOP CONTENTS EXCELLENT BUT ADVISE CHANGES IN TEXT STOP LETTER AIRMAILED TODAY BOHR
That letter126explained Bohr’s view more fully, but the re-draft sent with it does not seem to have survived. The text of the published paper12’ is quite different from the first draft, and presumably substantially the same as Bohr’s version. In the paper the authors correct the value of the binding energy of an additional neutron in 231Pa,for which the figure shown in the previous paper was in error. As more complete data about the mass distribution of the fission fragments showed a tendency for fission into two unequal masses, Bohr thought about this problem and found a tentative explanation. This is mentioned in a letter to Wheeler: “YOUwill remember that we discussed this problem last spring in connection with the Columbia experiments, but that we did not then arrive at any final conclusion as regards the explanation. In the last weeks, however, I have been
H o h r t o \?heeler, I h Dec 39 Full i c x l o n p . [hh2]
I24
Manuscript, Chain Reactions of Nuclear Fission, 1939. Reproduced on p. [395]. Manuscript, The Fission of Protactinium, 1939. Reproduced on p. [399]. ‘ 2 6 Letter from Bohr to Wheeler, 4 October 1939. Reproduced on p. [661]. N . Bohr and J . A . Wheeler, The Fission of Protactinium, Phys. Rev. 56 (1939) 1065-1066. Reproduced on p. [403].
PART I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
reconsidering the matter and find, if I am not wrong, that it is not only possible by means of the calculations in our paper to obtain a simple interpretation of the observed asymmetry in the nuclear fissions, but that even our estimate of the fission probability and its variation with neutron energy strictly speaking involves the assumption that the mode of division of the nucleus in two parts is practically confined to a very small number of possibilities. I have, therefore, written a short note which I am enclosing and which I should propose, if you agree, that we send jointly to the Physical Review as an addendum to our paper.” A typescript headed “On the Statistical Distribution of Fission Fragments”’** may not be exactly the version mentioned in this letter, but is no doubt very similar. The available text is actually a carbon copy, labelled “old”. There are also pages 2-4 of a slightly different draft. Bohr’s argument was essentially that the reduced mass for the relative motion of the two fragments is smaller for asymmetric than for symmetric fission, and that this increases the barrier penetrability. Wheeler at first agrees with Bohr’s draft except for minor changes: PRINCETON, 19 [January 19401 PROFESSOR NIELS BOHR CARLSBERG KH
Telegram, Whceler 10 Bohr, 19 Jan 40 English
MOST INTERESTING MANUSCRIPT RECEIVED WEDNESDAY WILL MAKE FEW SLIGHT ADDITIONS THEN SEND IT TO TATE’29 COPY TO YOU AND HOLD PROOF FORYOURAPPROVALREGARDS WHEELER
But he is led into further calculations which alter the situation: PRINCETON, 12 [February 19401 PROFESSOR NIELS BOHR CARLSBERG KH NEW CALCULATIONS GIVE SINGLE SYMMETRICAL TRANSITION STATE BUT DYNAMICAL PREFERENCE UNEQUAL MASSES DUE ELECTROSTATIC ARGUMENTS WILL FINISH I N WEEK ALTERATIONS CONSIDERABLE ADDITIONS BEFORE SUBMISSION UNLESS OBJECTIONS EXPERIMENTAL RATIO 3/2 REGARDS WHEELER 12’ Manuscript, On the Statistical Distribution of Fission Fragments, catalogued as of [ 1939-19401. Reproduced on p . [467]. 12’ J o h n T. Tate, then editor of the Physical Review.
Telegram, Wheeler 10 Bohr. I2 Feb 40 Engli\h
P A R T I : PAPERS A N D MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
Wheeler concluded that the reduced mass was too simple a concept for such a complex situation, but was led to invoke the zero-point energy of the degree of freedom determining the degree of asymmetry as facilitating asymmetric fission. The calculations took longer than estimated, and after further messages indicating that the work is nearing conclusion, he reports on 27 June‘30 that the calculations are almost finished, but that there may now be difficulty in getting them published, presumably because of concerns about the possible military significance of fission. The question was resumed after many years. In 1949 Wheeler sent a draft of a paper on this s ~ b j e c t ’ ~to ’ , which David L. Hill had also now contributed, to Bohr, who replied: “The manuscript you sent me came as a great surprise but, realizing that it more represents an account of the discussions we through the years have had about the theme rather than some original contribution of which I feel innocent, I do not only agree with the plan, but welcome it as a token of the continuation of our cooperation.”
Bolir 10 \I heeler, 4 J u l \ JY F u l l lcxi on p 16651
He will read the paper carefully. In a later letter’32 he expressed a number of criticisms, and these were discussed during visits by Wheeler to C ~ p e n h a g e n ” ~ in September 1949 and in January 1950. A further draft by Wheeler’31 was sent shortly after this, and Bohr, Hill and Wheeler met in April 1950 in Princeton, but had too little time to discuss this paper. Meanwhile it had become clear that the problems discussed in the paper involved the understanding of the liquiddrop model and its connection with the shell model which was then finding acceptance. It is therefore discussed further in section 6 . Returning to 1940, there is a further contribution by Bohr to fission physics. It had been shown by experiments in Rome’34 that the fission cross section of uranium, which becomes energy independent for neutron energies above about 1 MeV, rises again when the energy exceeds 10 MeV. In a paper published in Phys. Rev. in 1940 1 3 5 , he shows that this can be understood, since a nucleus formed by neutron capture at such high energies may, even after emitting a neutron, remain sufficiently highly excited to undergo fission subsequently. Telegram from Wheeler to Bohr, 27 June 1940. BSC, microfilm no. 26. Folder, Work on Fission by Bohr, Hill and Wheeler, The folder contains two typescripts dated 1949 and 1950, respectively. Bohr MSS, microfilm no. 19. 1 3 2 Letter from Bohr to Wheeler, 13 July 1949. Reproduced on p. [665]. 1 3 3 For the dates of Wheeler’s visits and the meeting at Princeton, see the correspondence between Bohr and Wheeler between 24 August 1949 and 16 November 1950. BSC, microfilm no. 33. ‘ 3 4 M. Ageno et al., Fission Yield by Fast Neutrons, Phys. Rev. 60 (1941) 67-75. ‘35 N . Bohr, Successive Transformations in Nuclear Fission, Phys. Rev. 58 (1940) 864-866. Reproduced on p. [4751. I3O
13’
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Another paper published during that period'36 is concerned with interpreting the experimental evidence on deuteron-induced fission. The observed ratio between the fission cross sections of uranium and thorium did not seem to agree with theoretical predictions based on the assumption that the reaction proceeds with the absorption by the nucleus of the whole deuteron. Bohr points out that at 9 MeV deuteron energy it is also possible that fission may be caused in collisions in which only the neutron enters the nucleus while the proton escapes. In this process the excitation energy of the nucleus is lower because of the energy carried away by the proton, but it may nevertheless be sufficient to cause fission, particularly in uranium. The behaviour of fission products in passing through matter, and their ionising power, pose interesting questions, which immediately attracted Bohr's attention, since the passage of charged particles through matter was a field to which he had made contributions of decisive importance. His work on these problems belongs properly to Volume 8, and is reviewed there. Bohr had many occasions to lecture on the subject of fission. On 3 November 1939 he gave a talk to the Royal Danish Academy, of which only an abstract is p ~b l i s h ed ' ~'His . notes for this talk13* suggest that this was in the main an account of the Bohr-Wheeler paper. A later talk to the Academy, on 10 January 1941 was, according to the ab ~t r a ct ' ~' a, review of recent progress on the fission problem. A review article on the whole of nuclear physics, but stressing the fission phen~rnenon'~',is based on a lecture given to the Society for the Dissemination of Natural Science on 6 December 1939. It includes an explanation why no explosive chain reaction is possible with natural uranium. After the war, Bohr's talk to the Academy would of course relate fission to atomic energy. Such a talk was given on 19 October 1945; only an abstract is p u b l i ~ h e d ' ~Atomic '. energy and its effect on national and world affairs was a
13' N. Bohr, Mechanism of Deuteron-Induced Fission, Phys. Rev. 59 (1941) 1042. Reproduced o n p. [483]. Reprinted without change in Nature 148 (1941) 229. 13' N. Bohr, Den teoretiske Forklaring af Atomkernernes Fission, Overs. Dan. Vidensk. Selsk. Virks. Juni 1939 - Maj 1940, p. 28. Reproduced with a translation o n p. [409]. 13' Manuscript, [Den teoretiske Forklaring af Atomkernernes Fission], 1939. Reproduced o n p. [405], translation on p . [408]. N. Bohr, Tunge Atomkerners Snnderdeling, Overs. Dan. Vidensk. Selsk. Virks. Juni 1940 - M a j 1941, p. 38. Reproduced with a translation on p. [481]. I4O N. Bohr, Nyere Undersngelser over Atomkernernes Omdannelser, Fys. Tidsskr. 39 (1941) 3-32. Reproduced on p. [411], translation o n p . [443]. N. Bohr, Om Atomkernernes Omdannelser, Overs. Dan. Vidensk. Selsk. Virks. Juni 1945 - M a j 1946, p. 31. Reproduced with a translation on p. [485].
'"
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
subject he had thought about deeply since the time he first realised the possibility, and later the imminence, of the release of atomic energy. His thoughts and writings on that topic are part of the subject matter of Volume 10. 6.
NEW THOUGHTS ABOUT NUCLEAR MODELS
When Bohr introduced the concept of the compound nucleus in 1936, and showed how it helped to describe nuclear reactions, it seemed obvious to most physicists that this proved that the nucleons were interacting very strongly in all cases, and that therefore one should think about the ground state of the nucleus as an object rather like a liquid drop. In any event, it seemed to follow that there was no hope of getting anywhere with a shell model, in which the particles were regarded in first approximation as moving independently, just as one would not expect a description of a water drop in terms of independently moving particles to get anywhere. It is true that Bohr was puzzled by the fact that Heisenberg and others had seemed to obtain reasonable estimates of overall nuclear properties by using an independent-particle picture, but this seemed intelligible, as, for example he explained in his letter to Heisenberg of 8 February 1936 (see p. [579]). But he believed firmly that any shell-model treatment of nuclear states in detail was doomed to failure. This is illustrated by his encounter with a young theoretical physicist in Japan in 1937, which is described in a letter from Professor Takahiko Yamanouchi to Peierls (translated by Toshiuki Toyoda): Y ~ i m u o u L l i1i0 Pcicrl5 II
coi
7')
I'lp'in
"One day in 1937 I was introduced by Dr. Yoshio Nishina to Professor Niels Bohr on the occasion of his visit to Japan. In my recollection the interview took place in a room of the Physico-Chemical Research Institute (RikagakuKenkyujo) in Tokyo and lasted for about half an hour. At the time I had almost completed my work concerned with the application of group theoretical methods to nucleon systems'42 and intended to develop it. Thus I spoke briefly of the work, showing my results on the binding energy of atomic nuclei. Professor Bohr listened to my talk kindly and gave me the following comments on my work, and also advice on my intended research programme: in his opinion the single-particle approximation, which I proposed to use there, could not be a good approximation to describe nuclear properties. Professor Bohr also suggested to me in a gentle way that the formula which I had ob142 T. Yamanouchi, On the Binding Energy of Atomic Nuclei. I, Proc. Phys.-Math. SOC.Japan 19 (1937) 557-565; I I , ibid., pp. 790-797.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
tained group-theoretically might be nothing but a kind of interpolation formula. I was certainly discouraged by such a fundamental criticism of my approach, and abandoned my research plan, in which I had intended to carry out a more concrete calculation of the nuclear binding energy by making use of state functions for centrally-symmetric fields. I t was a great pity that I did not continue my work in that direction. I have, however, no regrets now, because it seems to me very unlikely that one could construct a unified theory of nuclei on the assumption that nuclei consist simply of nucleons. Instead I have been expecting a theory which includes at least mesons.
...
At present I dream of the possibility of constructing a unified theory based upon more fundamental models, such as an assembly of quarks.” In 1948, when the experimental knowledge of nuclei had become more extensive, thoughts about the dynamics of nuclei began to be strongly influenced by the evidence for a shell structure. In particular, Maria Mayer published a paper in Phys. Rev.’43in which she collected all relevant evidence, and showed that this led to the inescapable conclusion that the “Magic Numbers” had some physical reality. Such facts had been noticed by many other authors, but Maria Mayer’s paper was more complete and convincing. There is no evidence in Bohr’s writings that he was influenced by this paper, or even knew of it, but in a passage in his Nobel lecture, Hans J e n ~ e n describes ’~~ his first visit to Copenhagen after the war: “A few years after the war, I had the good fortune to return to Copenhagen for the first time. There I found in a recent issue of the Phys. Rev. the paper by Maria Goeppert-Mayer ‘On Closed Shells in Nuclei’, in which she also collected the ‘empirical evidence’ for the importance of such [magic] numbers. This encouraged me to talk in the seminar about our work and at the same time about our results. This seminar meeting became for me unforgettable. Niels Bohr listened very attentively, and intervened with questions, which became more and more lively - on one occasion: ‘but that is not in Mrs. Mayer’s paper!’. Bohr, it transpired, had already read the paper very thoroughly and thought it through. The seminar became a long and lively discussion. I was deeply impressed by the intensity with which Niels Bohr took in, weighed, and Maria G . Mayer, On Closed Shells in Nuclei, Phys. Rev. 74 (1948) 235-239. J . H . D . Jensen, Zur Geschichte der Theorie des Aromkerns, in Les Prix Nobel en 1963, Stockholm 1964, pp. 153-164. See p . 161 and p. 162.
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Fierz, Pauli and Jensen
compared these empirical facts, which did not really fit into his picture of nuclear structure. It is only then that I started to ponder seriously about the possibility of de-magifying the magic numbers.” Jensen’s visit to Copenhagen was from 4 November to 4 December 1948, according to the Institute’s visitors book. At this time many others tried to “demagify” the magic numbers, many no doubt encouraged by Maria Mayer’s paper, but for a time it seemed impossible to find a model which would yield the correct numbers. As is well known, the answer was found independently by Maria M a ~ e r and ’ ~ ~by Haxel, Jensen and S u e s ~ at ’ ~about ~ the same time, in terms of a strong spin-orbit coupling. Bohr evidently continued reflecting about the problem, probably less in terms of the actual numbers obtainable from any particular model, but on the general principles. He wrote down his views in a note14’, whose title, “Tentative Com-
Maria G. Mayer, On Closed Shells in Nuclei. II, Phys. Rev. 75 (1949) 1969-1970. J.H.D. Jensen and H.E. Suess, On the “Magic Numbers” in Nuclear Structure, Phys. Rev. 75 (1949) 1766. 14’ Manuscript, Tentative Comments on Atomic and Nuclear Constitution, 1949. Reproduced on p , 145
146 0. Haxel,
[521].
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ments on Atomic and Nuclear Constitution” indicates that he had not reached any final conclusions. There are several versions of this note available, which are almost identical, except for an addition dated 15.8.49, to which we shall return. His purpose in writing this note is shown clearly in a letter to Pauli: “In the last few weeks, however, I have become greatly interested in a completely different matter, namely in the very interesting papers on nuclear struc- Bohr 10 Pauli, IS Aug 49 ture which have appeared, particularly in the Physical Review, and which I Danish text ,,, vol discussed with much pleasure and benefit with Lindhard, who was on a visit Trans’at’on ’” “O’ here in Tisvilde. In these papers, particularly by Feenberg14* and N ~ r d h e i m ’ ~ ~ , it appears that a number of phenomena, which so far were quite incomprehensible, are simply explained by the assumption that the individual particles in the nucleus in first approximation are bound independently of each other like the electrons in an atom. It is of course difficult to judge the basis for such an assumption, but it appears to me that we are here concerned with a straightforward consequence of quantum mechanics, which has sometimes been overlooked so far because of a too literal comparison with a classical drop model. I am by no means clear about the situation and find it particularly difficult to assess.the frequency of the exchange effect, but I have written down some general remarks which I also enclose in the hope of severe criticism. ’ ’ However, Pauli was not willing to enter into a discussion of nuclear problem^'^'. It is interesting that Bohr refers to Feenberg and Nordheim, but not to the 1948 paper by Maria Mayer, which, according to Jensen’s account, he had read, or to her 1949 letter145which contained the idea of spin-orbit coupling, and which was published in the same issue of Physical Review (15 June 1949) as the Nordheim and Feenberg papers. Possibly this issue had not yet been received, and the mention of the papers is based on advance copies. The main content of the note relates to the shell model. However, there is a passage going further, which reads: “On the one hand, we may have higher energy states in which one or more nucleons have quantum numbers different from those corresponding to the lowest energy states. On the other hand, we may have excited states of the
I J 8 Presumably E. Feenberg and K.C. Hammach, Nuclear Shell Structure, Phys. Rev. 75 (1949) 1877-1893. 149 L. Nordheim, On Spins, Shells and Moments in Nuclei, Phys. Rev. 75 (1949) 1894-1901. I 5 O Letter from Pauli t o Bohr, 21 August 1949. BSC, microfilm no. 30.
’,
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
nucleus corresponding to oscillation of its boundary, the periods of which will in general be long compared with the orbital periods of the nucleons, with the result that their motions will in the first approximation only be adiabatically influenced. In particular, it is under these circumstances evident that there cannot be question of stationary states corresponding to the rotation of the whole nucleus as a solid body and that the angular momentum and spin of the nucleus will be determined directly by the specification of the binding states of the individual nucleons.” The last sentence was added in the amendment dated 15.8.49. This passage shows that Bohr understood that one had to include in the description both particle and collective degrees of freedom, although, of course, the question of rotational degrees of freedom was clarified only much later. A passage in Jensen’s account’44 shows again Bohr’s confidence in the new ideas and in his views on rotation: “Nevertheless I was not comfortable with the whole picture, and I was not really surprised when a serious journal refused to print our first ‘letter’ with the explanation: ‘it is not physics but only playing with numbers.’ Only when I recalled the lively interest Niels Bohr had shown in the magic numbers I sent the ‘letter’ to Weisskopf, who passed it on to Phys. Rev. But I gained confidence only after I could lecture in the Copenhagen seminar about our thoughts and discuss them with Niels BohrI5l. One of the first comments by Bohr seems to me remarkable: ‘now I understand why nuclei do not show rotational bands in their spectra’.’’ Bohr also invited Rosenfeld’s opinion: Hohi 16
10
\us
“ ... I see new possibilities for rounding off the treatment of the old problems which I discussed with Peierls and Placzek, and with which you helped me so much before you had to leave Copenhagen during the War.’’
Rownield 49
I 1 , i n i ~ h1 ~ x 1on
lrnnilaiioii
011
p [641] p 16451
Rosenfeld was sceptical: “Above all I am a little worried that you have got an altogether too optimistic impression of the generality of the model. I am not prepared to attach to such general and schematic considerations as Feenberg’s and Nordheim’s more than a qualitative and tentative value.”
K o w i l d d i o Bohr I9 2irg 4‘1 llciiii\h 1 ~ x 1on p 16461 lr.in\intion on p 16471
’”
The Institute’s visitors book shows that Jensen was there from 10 to 19 October 1950, and the seminar in question must have been during that period, unless an earlier visit failed to be recorded.
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Bohr defended his point of view: “You are of course right that Feenberg’s and Nordheim’s considerations are very qualitative and tentative; but the reason that their results made a great impression on me was that this concerns a possible explanation of regularities of a kind which could not be approached even qualitatively on the basis of any other views of the nuclear constitution. ... the main question is how far the nuclear matter is impermeable for nucleons, or better: to what extent the individual nuclear particles perturb the wave functions which correspond to motion in a common field of force. For unless these perturbations alter the problem completely I really think that one should start from the hypothetical idealised nuclear model as a first approximation instead of from a purely classical drop model. ... If one concludes from the formal application of the Pauli principle that the mean free path of nucleons in the nucleus is infinite, one is led to the point of view that the binding of each nucleon in the nucleus can in first approximation be treated independently.”
Bohr lo Ro5enfeld 29 Aug 49 Dan,\h leXl on On
164Rl p
wO1
These remarks have a much more modern ring than those in the original noteI4’. It is worth noting, in particular, that the importance of the Pauli principle in suppressing the effect of the mutual interaction of nucleons is mentioned at this early stage. A copy was also sent to Aage Bohr, then at Columbia University. In his replylS2 Aage accepts his father’s arguments and finds them inspiring. Another copy went to P e i e r l ~ ’who ~ ~ , does not accept his reasoning154,and to Wheeler155, stating ‘‘I feel that one has sometimes taken the drop model too literally”. Wheeler’s reply also expresses some doubt: “Thank you for your recent letter and for your considerations on the relation between the liquid drop model and the independent particle model of the nucleus. I am especially anxious to learn from you your feeling about the quantitative side of this question - how far for example, a nucleon of typical energy can travel through the nucleus without large exchange of energy with the other nucleons.” Meanwhile the questions of the nuclear model also influenced the development
’” Is4 155
Letter Letter Letter Letter
from from from from
Aage Bohr to Niels Bohr, 3 October 1949. Niels Bohr Private Correspondence Bohr to Peierls, 22 August 1949. Reproduced on p. [616]. Peierls to Bohr, 26 August 1949. Reproduced on p. [617]. Bohr t o Wheeler, 24 August 1949. BSC, microfilm no. 33.
\ h e e l e r to Bohr, 3 Sepi 49 Full lexl on [667]
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of the paper with Wheeler, which was still aimed at an explanation of asymmetric fission (see section 5). Wheeler writes to Bohr: M I i L L l i r 10 Hohi I2 L)ei 49 I iill i i \ i on p [6681
“The principal points which have taken the most time are the question of quadrupole moments and the question of justifying the liquid drop model from the point of view of the individual particle picture by standard quantum mechanical methods, in addition to the clear - and of course to us convincing - reasoning of the paper as it stood when we separated. It has turned out to be possible to show very clearly that the quadrupole moment created by deformation of the nucleus by a single particle in an otherwise empty shell exceeds by a factor of approximately five the quadrupole moment directly due to the charged distribution of that particle itself. This result explains the paradox pointed out in the last Physical Review by Foldy, which has up to now presented great difficulties for the explanation of nuclear quadrupole moments. It also turns out that the deformation of the nucleus caused by one unbalanced particle greatly affects the energy level spacing for the next particle. Consequently there is a coupling effectively brought into play between one particle and another which must greatly influence the order of filling of incomplete shells.” He goes on to describe what is now known as the Hill-Wheeler method of generator coordinates. Bohr’s reply expresses agreement with the explanation of the quadrupole moments, but is more critical of the other part:
B o h r 10 \\heeler 21 DeL 49 1 iill I C \ I on p (6701
“AS regards the problem of the treatment of the oscillations of an excited nucleus, starting from an individual particle picture, we are, however, not certain that we fully understand your considerations. The attack is surely of a very direct kind, but it seems not beforehand quite clear to me how one can analyse the effect of the nuclear deformations and their time derivatives so generally. It would seem that the actual physical problem is rather to examine the semiadiabatic changes of the individual particle binding accompanying the oscillatory deformations of the whole nucleus, and that the justification for the customary treatment of the problem should be the appearance of additional terms in the whole nuclear energy of a type corresponding to those of capillary oscillations of a liquid drop.” Bohr and Wheeler discussed these questions further during several visits by Wheeler to Copenhagen, and there are further letters by Wheeler on his point of view, but no substantive replies from Bohr. The project of ajoint paper by Bohr, Hill and Wheeler was never completed. The last discussion on this subject took place during a visit by Wheeler to Copenhagen early in 1950. After this Wheeler
PART I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
was occupied with other urgent business for three years. Then he received an invitation from Leonard Schiff to contribute an article at short notice. He was anxious to submit a joint paper with Bohr and Hill, but Bohr did not think it possible to agree on a text at such short notice, and suggested that the other two publish the paper in their own The paper was published in 1953 l S 7 , with an acknowledgment of Bohr’s permission to use part of the joint work. There is no written record of Bohr’s views, but Wheeler, in conversation with the author, emphasised the extent to which this paper owed its inspiration to Bohr. Bohr followed the further progress of the understanding of nuclear dynamics with great interest, and took an active part in discussions’”, but he did not write anything further, and there is no correspondence about these questions, because the further developments took place so largely in the Copenhagen Institute.
Private communication from John Wheeler. D.L. Hill and J. A . Wheeler, Nuclear Constitution and the Interpretation of Fission Phenomena, Phys. Rev. 89 (1953) 1102-1145. International Physics Conference, Copenhagen, 3-17 June 1952, pp. 16 and 19. Reproduced on p. [527]. IT‘
lii
I. P-RAY SPECTRA AND ENERGY CONSERVATION UNPUBLISHED MANUSCRIPT 1929
See Introduction, sect. 1 , ref. 1.
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
This manuscript consists of 5 pages of which the first 3 constitute a carbon copy of a typed manuscript with a few corrections in ink. There is an additional page 3 (with corrections in pencil in Oskar Klein’s handwriting), dated 21 June 1929, whose relation to the rest is not clear, and a page in Klein’s handwriting, numbered 3a. The manuscript is in English. We have reproduced the corrected text, except for retaining one section which was crossed out. According to a note in the margin this was to be replaced by page 3a. The manuscript is on microfilm Bohr MSS no. 12.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
&ray spectra and energy conservation. Due to its contrast to the definiteness of the laws, which otherwise govern radioactive phenomena, the discovery, that the primary /3-ray emission from disintegrating nuclei exhibit a continuous energy spectrum, has given rise to much discussion. Lately the idea of connecting the variability of the energy of the P-particles with a possible limitation of the principle of conservation of energy has been brought into discussion by Professor G.P. Thomson (see Nature, April 21. 1928, and also Phil. Mag. 7, 405, 1929) who bases his considerations on the wave picture of the electron and the general properties of wave groups which find their typical expression in the reciprocal uncertainty relations of Heisenberg. This argument, however, can hardly be reconciled with the general ideas of quantum mechanics* in their present form. The well known difficulties of obtaining a pictural description of atomic processes due to the existence of the quantum of action d o not in themselves involve a violation of the conservation principles. The situation can rather be described by saying (compare the writer’s article “The quantum postulate and the recent development of atomic theory”, Nature, April 14. 1928) that the principles of conservation of energy and momentum in quantum theory are not contradictory to the space time description of the behaviour of the elementary particles, but complementary in that sense that the applicability of these principles is limited only by the disturbance of the phenomena involved in any observation of the space time coordinates of the individual particles. This peculiar character of quantum theory is strikingly brought out just by the successful explanation recently obtained of the remarkable relation between the decay constant of a-ray disintegrations and the energy of the emitted a-particles (see Gurney and Condon, Nature, September 22. 1928, and especially Gamow, Nature, November 24. 1928), which forms a particularly instructive example of the complementary nature of the particle and wave conceptions of the emitted rays. In view of this explanation it would seem, that the existence of a well defined rate of decay of 0-ray disintegrations would exclude any simple explanation of the continuous 0-ray spectra based on the ordinary ideas of wave mechanics, which rest upon a proper quantum theoretical correspondence with the laws of classical mechanics. Only a reference to the problem of the constitution of the elementary electric particles which as well known has so far escaped a proper treatment on the basis of classical electrodynamics might possibly defend a violation of the principles *
[Corrected from “wave mechanics”.]
MS, p . 2
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V S , p. 3
MS, new p . 3 2116 1929.
of conservation in radioactive processes. In this connection I should like to call attention to the new possibilities which would seem to be opened by the original ideas as regards the introduction of the conception of an electromagnetic field in relativistic quantum theory put forward by Klein in the above letter to the editor.* Since on this theory the conception of force is inherently bound up with the idea of mass the suggestion presents itself, that the laws of interaction between particles of different mass may conflict with a simple identification of action and reaction, as that underlying the classical conservation principles. While the quantum laws of propagation in free space offer no basis for a violation of the conservation principles, a departure from these laws might still result from the close interaction of the constituent particles of the nucleus. If this view as to the origin of continuous 6-ray spectra should prove correct we may be prepared for a disturbance of the energy balance also in certain large scale phenomena. Indeed, if as ordinarily assumed, the reversal of radioactive processes takes place in the interior of celestial bodies, it would depend on the temperature whether energy in the mean would be gained or lost through the capture of an electron by a nucleus and its subsequent expulsion as a 6-ray. Perhaps in considerations of this kind we can find an explanation of the energy source which according to present astrophysical theory is wanting in the sun, and the origin of which is generally sought in the transformation of elementary electric particles into radiation. The purpose of these remarks is to emphasize, how little basis we possess at present for a theoretical treatment of the problem of 6-ray disintegrations. Indeed, the behaviour of electrons bound within an atomic nucleus would seem to fall entirely outside the field of consistent application of the ordinary mechanical concepts, even in their quantum theoretical modification. From this point of view the disintegration of the nucleus should rather be regarded as the creation of the dynamical individuality of the electron expelled. ((**If therefore experimental evidence should really corroborate the suggestion, that the principles of conservation of energy and momentum fail in accounting for 6-ray emission, we can hardly reject this suggestion on purely theoretical grounds. Indeed it must be remembered that these principles in their roots are of purely classical origin. At the same time the prospect of their failure would be very disquieting when
* [We could find no published paper by Klein on this subject from that time.]
* * [The section in double parentheses is crossed out. According t o a note in the margin this section was to be replaced by p. 3a.l
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
remembering how unerring a guide the conservation principles have hitherto been in the development of atomic theory.) ) We shall not here enter on the much debated question whether the experimental evidence available permits definite conclusions as regards the applicability of the principles of conservation of energy and momentum to @-raydisintegrations. We shall only call attention to the peculiar aspect of this problem with which we meet when considering the reversed process, the capture of an electron by an atomic nucleus. Indeed, a failure of the conservation principles means that the energy of the 6-ray subsequently expelled would in general differ from the energy of the electron before its capture, and that on the average there would be a gain or loss of energy depending on the initial conditions. A test of these consequences might perhaps be obtained from a closer analysis of astrophysical evidence regarding the evolution of stars, in the interior of which, as ordinarily assumed, the reversal of radioactive processes takes place on a large scale. Remembering that the principles of conservation of energy and momentum are of a purely classical origin the suggestion of their failure in accounting for @-ray emission can on the present state of quantum theory hardly be rejected beforehand. At the same time the loss of the unerring guidance, which the conservation principles have hitherto offered in the development of atomic theory, would of course be a very disquieting prospect.
MS.
,.
3a
11. CHEMISTRY AND THE QUANTUM THEORY OF ATOMIC CONSTITUTION EXTRACT
J . Chem. SOC.London, 1932, pp. 349-384 Faraday Lecture, delivered to the Fellows of the Chemical Society at Salters’ Hall on 8 May 1930 PAGES 379-383 FULL TEXT REPRODUCED IN VOL. 6
See Introduction, sect. 1, ref. 7.
QVAXTUM THEORY O F ATOMIC CONSTITUTION.
379
This situation must above all be kept in mind when we turn t o the problem of the constitution of atomic nuclei. The empirical cvidence regarding the charges and the masses of these nuclei, as well as the evidence concerning the spontaneous and the excited nuclear disintegrations, leads, as we have seen, t o the assumption that all nuclei are built u p of protons and electrons. Still, as soon as we inquire more closely into the constitution of even the simplest nuclei, the present formulation of quantum mechanics fails essentially. For instance, it is quite unable t o explain why four protons and two electrons hold together t o form a stable helium nucleus. Evidently we are here entirely beyond the scope of any formalism bascd on the assumption of point electrons, as it also appears from t h e fact that the size of the helium nucleus, as deduced from the scattering of a-rays in helium, is of the same order of magnitude as the classical electron diameter. J u s t this circumstance suggests that the stability of the helium nucleus is inseparably connected with the limitation imposed on classical electrodynamics by t h e existence and the stability of the electron itself. This means, however, that no direct attack on this problem, based on the usual correspondence argument, is possible as far as the behaviour of the intra-nuclear electrons is concerned. As regards the behaviour of the protons, the situation is essentially different, since their comparatively large mass permits of an unambiguous use of the idea of space co-ordination even within nuclear dimensions. Of course, in absence of a general consistent theory accounting for the stability of the electron, we cannot make any direct estimate of the forces which hold the protons in the helium nucleus, but it is interesting to note that the energy liberated by the formation of the nucleus, as calculated from the so-called mass-defect by means of Einstein’s relation, is in approximate agreement with the binding energy of the protons t o be expected on quantum mechanics from the known nuclear dimensions. Indeed, this agreement indicates that the value of the ratio of the masses of the electron and the proton plays a fundamental part in the question of the stability of atomic nuclei. I n this respect, the problem of nuclear constitution exhibits a characteristic difference from that of the constitution of the extranuclear electron configuration, since the stability of this configuration is essentially independent of the mass-ratio. When we pass from
380
BOHR:
CHEMISTRY A N D THE
the helium nucleus t o heavier nuclei, the problem of nuclear constitution is, of course, still more complicated, although a certain simplification is afforded by the circumstance that the u-particles can be considered to a large extent to enter as separate entities into the constitution of these nuclei. This is not only suggested by the general facts of radioactivity, but appears also from the smallness of the additional mass defect, expressed by dston’s wholenumber rule for the atomic weights of isotopes. The main source of knowiedge regarding the constitution of atomic nuclei is the study of their disintegrations, but important information is also derived from ordinary spectral analysis. As was mentioned, the hyperfine structures of spectral lines allow us to draw conclusions concerning the magnetic moments and angular momenta of the atomic nuclei, and from the intensity variations in band spectra we deduce the statistics obeyed by the nuclei. A s might be expected, the interpretation of these results falls largely outside the scope of present quantum mechanics, and, in particular, the idea of spin is found not to be applicable t o intra-nuclear electrons, as was first emphasised by Kronig. This situation appears especially clearly from the evidence concerning nuclear statistics. It is true that the fact, already mentioned, that the helium nuclei obey the Bose statistics is just what was to be expected from quantum mechanics for a system composed of a n even number of particles which, like the electrons and protons, satisfy Pauli’s exclusion principle. But the next nucleus for which data concerning statistics are available, namely the nitrogen nucleus, obeys also the Bose statistics, although it is composed of an uneven number of particles, namely 14 protons and 7 electrom, and thus should obey the Fermi statistics. Indeed. the general experimental evidence concerning this point seems to follow the rule that nuclei containing an even number of protons obey the Bose statistics, while nuclei containing an uneven number of protons obey the Fermi statistics. On the one hand, this remarkable “passivity ” of the intra-nuclear electrons in the determination of the statistics is a very direct indication, indeed, of the essential limitation of the idea of separate dynamical entities when applied to electron>. Strictly speaking, we are not even justified in saying that a nucleus contains a definite number of electrons, but only that its negative electrification is equal to a whole number of elementary units, and, in this sense, the expulsion of a @-rayfrom a nucleus may be regarded as the creation of an electron as a mechanical entity. On the other hand, the rule just mentioned regarding nuclear statistics may be considered, from this point of view, as a support for the essential validity of a quantum mechanical treatment of the behaviour of the a-particles and protons in the nuclei. Actually, such a treatment
QUANTUM THEORY OF ATOMIC CONSTITUTION.
381
has also been very fruitful in accounting for their part in spontaneous and controlled nuclear disintegrations. I n the ten years that have elapsed since Rutherford’s fundamental discoveries, a large amount of most valuable material on this subject has been accumulated, owing, above all, to the great exploration work in the new field carried on in the Cavendish Laboratory under his guidance. Kow, from the theoretical standpoint, it is one of the most interesting results of the recent development of atomic theory that the use of probability considerations in the formulation of the fundamental disintegration law, which for its time was a quite isolated and very bold hyypothesis,has been found to fall entirely in line with the general ideas of quantum mechanics. Already a t the more primitive stage of the quantum theory, this point was touched upon by Einstein in connexion with his formulation of the probability laws of elementary radiation processes. and was further stressed by Rosseland in his fruitful work on inverse collisions. It is the wavemechanical symbolism, however, which first offered the basis for a detailed interpretation of radio-active disintegrations, in complete conformity with Rutherford’s deduction of nuclear dimensions from the scattering of u-rays. As was pointed out by Condon and Gurney, and independently by Gamow, the wave-formalism leads, in connexion with a simple model of the nucleus, to a n instructive explanationof the law of a-raydisintegration as well as of the peculiar relationship, known as the rule of Geiger and Kuttall, between the mean life-time of the parent element and the energy of the a-ray expelled. Gamow, especially, succeeded in extending the quantum mechanical treatment of nuclear problems to a general qualitative account of the relationship between a- and y-ray-spectra, in which the ideas of stationary states and elementary transition processes play the same part as in the case of ordinary atomic reactions and the emission of optical spectra. I n these considerations, the uparticles in the nuclei are treated similarly to the extra-nuclear electrons in the atoms, with the characteristic difference, however, that the u-particles obey the Bose statistics and are kept within the nucleus by their own interaction, while the electrons, obeying the Fermi statistics, are held in the atom by the attraction of the nucleus. This is, among other causes, responsible for the smallness of the rate of energy emission, as y-radiation, from excited nuclei which is even comparable with the rate of mechanical energy exchange between such nuclei and the surrounding electron clusters, the so-called internal conversion. I n fact, in contrast to an atom built up of separate positive and negative particles, a nucleus-like system composed only of a-particles will never possess an electric moment, and, in this respect the additional protons and negative electrific-
382
BOHR:
CHEMISTRY ANI) THE
ation of actual nuclei can hardly be expected t o make much difference. Apart from such simple applications of the correspondence argument, our ignorance of the forces acting on the cc-particles and protons in the nuclei, which must be assumed t o depend essentially on the negative electrification, prevents at present theoretical predictions of a more quantitative character. A promising means of exploring these forces is afforded, however, by the study of controlled disintegrations and allied phenomena. As far as the behaviour of u-particles and protons is concerned, it may therefore be possible i o build up gradually, by means of quantum mechanics, a detailed theory of nuclear constitution, from which in turn we may get further information about the new aspects of atomic theory uresented by the problem of negative nuclear electrification. As regards this last question, much theoretical interest has recently been aroused by the peculiar features exhibited by the p-ray expulsions. On the one hand, the parent elements have a definite rate of decay, expressed by a simple probability law, just as in the case of the a-ray disintegrations. On the other hand, the energy liberated in a single P-ray disintegration is found t o vary within a wide continuous range, whereas the energy emitted in an u-ray disintegration, when due account is taken of the accompanying electromagnetic radiation and the mechanical energy conversion, appears to be the same for all atoms of the same element. Unless the expulsion of p-rays from atomic nuclei, contrary to expectation, is not a spontaneous process but caused by some external agency, the application of the principle of energy conservation t o p-ray disintegrations would accordingly imply that the atoms of any given radioelement would have different energy contents. Although the corresponding variations in mass would be far too small to be detected by the present experimental methods, such definite energy differences between the individual atoms would be very difficult t o reconcile with other atomic properties. I n the first'place, we find no analogy t o such variations in the domain of non-radioactive elements. I n fact, as far as the investigations of nuclear statistics go, the nuclei of any type, which have the same charge and, within the limits of experimental accuracy, the same mass, are found t o obey definitt: statistics in the quantum mechanical sense, meaning that such nuclei are not t o be regarded as approximately equal, but as essentially identical. This conclusion is the more important for our argument, because, in absence of any theory of the intra-nuclear electrons, the identity under consideration is in no way a consequence of quantum mechanics, like the identity of the extra-nuclear electronic configurations of all atoms of an element in a given stationary state, but represents a new fundamental feature of atomic stability. Secondly,
QUANTUM THEORY O F ATOMIC CONSTITUTION.
383
no evidence of an energy variation of the kind in question can be found in the study of the stationary states of the radioactive nuclei involved in the emission of E - and y-rays from mcmbcrs of R radioactive family preceding or following a $-ray product. Finally, the definite rate of decay, which is a common feature of c(- and p-ray disintegrations, points, even for a ?-ray product, t o a n esscntial sirnilarity of all the parent atoms, in spite of the variation of the energy liberated by t h e expulsion of the p-ray. In absence of a general consistent theory embracing the relationship between the intrinsic stability of electrons and protons and t h e existence of the elcmciitary quanta of electricit). and action, it is verv tlifficult to arrive a t a definite conclusion in this matter. At the present stxge of atomic theory, however, we may say that we have no argumcnt, either empirical or theoretical, for upholding the energy principle in the case of p-ray disintegrations, and are cven led t o complications and difficulties in trj-ing to do so. Of course, a radical drparture from this principle would imply strange consequences, in ease such a process could be rewrsed. Indeed, if, in ii collision process. an electron could attach itself t o a nucleus with loss of its mechanical individuality, and subsequently be recreated as a ?-ray, we should find that the energj- of this ?-ray would generally differ from that of the original electron. Still, just as the account of those aspect>s of atomic constitution essential €or the explanation of the ordinary physical and chemical properties of matter implies n renunciation of the classical ideal of causality, the features of atomic stability, :jtill deeper-lying, responsible for the existence and the properties of atomic nuclei, may force us t o renounce the very idea of energy balance. I shall not enter further into such speculations and ?heir possible bearing on the much debated question of the source of stcllttr energy. I ha\-e toiiched upon them here mainly t o emphasise that in atomic theory, notwithstanding nll the rcccnt progress, we must still be prepared for new surpriscs.
111. ATOMIC STABILITY AND CONSERVATION LAWS Atti del Convegno di Fisica Nucleare della ‘‘Fondazione Alessandro Volta” , Ottobre 1931. Reale Accademia d’Italia, Rome 1932, pp. 119-130 Elaboration of Discussion Remarks at the Volta Conference in Rome, 11 to 18 October 1931
See Introduction, sect. I , ref. 8.
m
U
ed
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REALE
ACCADEMIA
D’ITALIA
N. B O H R
ATOMIC STABILITY AND CONSERVATION LAWS
ESTRATTO DAGLI DELLA
((
ATTI D E L CONVEGNO DI FISICA NUCIJSARE m FONUAZIONE ALKSSANDRO VOI,TA* O T T O B I ~ 1931-IX E
ROMA REALE ACCADICMIA D’ITALIA 1932-x
ATOMIC STABILITY AND CONSERVATION LAWS (1) N. B O H R
Although the explanation of the essential features of atomic stability is beyond the reach of classical physical theories, it has been possible, as is well known, in the account of atomic phenomena to make a wide use of ordinary mechanical and electromagnetical concepts and, above all, to retain the law of the conservation of energy which plays so prominent a r81e in classical physics. Still, serious doubt has recently arisen, whether the concept of energy can find an unambiguous application t o radioactive disintegrations in which electrons are expelled from atomic nuclei, which processes also in other ways defy the application of present atomic theory. The following remarks may serve as an introduction to a discussion of this problem.
8
1. FOUNDATIONS OF ATONIC
MECHANICS.
The foundations of the present treatment of atomic: phenomena are the discoveries of the ultimate electrical particles and the elementary quantum of action, which rely upon quite separate lines of experimental evidence and a t the present stage of atomic theory we introduced in essentially different and independent ways. The definition of the specific properties of the particles rests on a direct application of classical mechanics and electrodynamics. Of coiirse, it is impossible in these theories to account for the existence and intrinsic stability of the electron or the proton, but taking this stability for granted it has been possible to build up a scheme of a high degree of consistency in which the existence of the particles is combined with the classical theory of electromagnetic fields. This scheme, the so-called classical (1) This article forms an elaboration of the remarks made by the author in the course of the discussions a t the congress. The views here exposed have also been discussed in a lecture on chemistry and quantum theory, published in (( Journ. Chem. S o c . ~ ,p. 349, 1932.
- 120 electron-theory, is so constructed t h a t it satisfies the laws of conservation of energy and momentum and may be said to form a n appropriate extension of classical mechanics in which radiation effects are included. St8ill, the classical electron-theory is subject t o an eswntial limitation which may be symbolised by the so-called electron diameter
where e and m are the electronic charge and mass respectively and c the velocity of light. As is well known, this diameter definies a lower limit for the region within which the charge of the electron can be concentrated without essentially affecting its mass and thud represents the limit of the idealisation of the electron as a charged material point on which rests the unambiguous use of mechanical concepts. I n contrast to the particle idea, which is compar;ibie with classical mechanics and even may be said to form its basis, the very idea of th e quantum of action is an irrationality from the standpoint of ordinary inechanics. Of course, the dcterniination of Planck’s c o n s t a t rests, like the measurements of the charge and the mass of the electron, on evidences described hv classical concepts. I n the latter case, however, w e have to do with a n unambiguous use of classical theories, while any eralustion of the quantum 01 action essentidly implies a statistical clewription of atomic. phenomena. ’Chis situation finds its proper pression in the fornialisin of quantum-mechanics, which retains the fundamental equations oQ mechanics in their classical canonical forin, and in which the quantum of action enters only in the so-cwlled ruler of coinniutation of canonically con,iug:ited 1 ariables. I n accordanc e with the correspondence argument quantum-mechanics thus contains classical mechanics as th e limiting case Then the quantum of action can be nezlected. but in the general case the description is of a n essentially statistical character, qualitatively formulated in Reisenberg’s uncertainty principle, according to which the product of the uncertainties of two conjugated mechanical varizbles i\ never smaller th a n Planck’s conytant. The statistical character of quantum-mechanics, however, does not imply th at the laws of conservation of momentum a n d energy lose their validity, b u t only th a t their application stands in a n exclusive, so-called ( i complementary ”, relationship to the analysis of the motions of the particles. This is an immediate consequence of th e existence of the quantum of action, since any control of the space-time coordinates of the particles involves a finite and essentially incontrollable transfer of momentum and energy t o fixed scales and clocks, which, serving as ~
7
~
-
- 121measuring instruments, do not belong to the system under investigation, Conversely, any well-defined use of the conservation laws implies an essential renunciation of spacetime analysis. I t is just this circumstance which allows us to apply the law of energy conservation in the description of such features of atomic stability, as the properties of stationary states of atoms, which defy an explanation in terms of motions of the constituent particles. It may also here be emphasized that the difficulties regarding energy conservation in radioactive disintegrations, referred t o in the beginning, cannot be explained, as it has been sometimes suggested, by means of the complementary uncertainty of the quantum-mechanical description. Indeed, in these processes, just as in the spontaneous radiative transitions of atoms between stationary states, we do not have t o consider any interaction with external measuring instruments. The possibility of treating the elementary particles and the quantum of action as independent foundations of the theory of the electronic constitution of atoms rests essentially upon the fact that the atomic dimensions, as deduced from quantum-mechanics and symbolised by the radius ” of the hydrogen atom
?I 1 are very large compared with the electron diameter given by [l]. Obviously, this is a necessary condition for considering the electron as a charged material point in the fundamental mechanical equations. I n this connexion it is, however, important to remember that the effects which are accounted for by the so-called electron spin are specific features of the quantum-mechanical symbolism which defy any interpretation by means of classical ideas. Thus, in contrast to the charge and the mass of the electron, no unambiguous determination of its intrinsic angular momentum or magnetic moment is possible. This is directly indicated by the fact that the angular momentum of a particle about a fixed axis is canonically conjugated to the azimuthal angle. Any knowledge of the position of the particle which claims an uncertainty of this angle smaller than 2 x will therefore imply in the definition of the angular momentum about the axis an uncertainty larger than 72/2x. A change in angular momentum of this magnitude, resulting from an inversion of the spin axis of the electron, will therefore not be measurable by any method resting on the idea of motion. Similarly, it follows that it is impossible to determine the magnetic moment of a free electron. I n fact, the magnetic force exerted by a moving electron a t a certain point will be, on classical electrodynamics, the same
- 122 as that exerted by a magnetic dipole with an axis parallel t o the angular momentum of the electron about that point and with a moment equal t o this momentum multiplied by
e ~
2mc
. Due to the uncertainty of angular
momentum, it is, therefore, never possible to distinguish between the magnetic force produced by the motion of the electron and the force which would arise from an intrinsic magnetic moment [31 the so-called magneton. The possibility of measuring the magnetic moment of an atomic system composed of electrons and nuclei in terms of this magneton rests entirely on the fact that in such measurements, the idea of path is only applied to the motion of the system as a whole, and that due to the large inass of the nuclei the ratio between charge and mass of such a system is much smaller than that of a free electron. It is true that the ideas of angular momentum and spin variables have offered an adequate basis for the classification of stationary, states and especially for the formulation of Pauli’s exclusion principle, but i t must not be forgotten that we have here t o do with features of this classification which allow of no unambiguous description in terms of classical concepts. Abowe all, it is essential that in any application of the exclusion principle we have to do with properties of composed systems which cannot be interpreted by mechanical pictures taking account of the behaviour of the individual particles. It is important for our discussion, however, that the formulation of the quantum-mechanical statistics rests ultimately, on the fact that in the fundamental equations of motion. common to classical mechanics and prosent quantum theory, the individuality of the particles is strictly upheld.
5
2 . DIFFICULTIESO F RELATIVISTIC
QUANTUM MECHANICS.
Notwithstanding its fertility, the attack on atomic problems in which the particle idea and the quantum of action are considered as independent foundations is of an essentially approximative character, since it does not allow of a rigorous fulfilment of the claim of relativistic invariance The possibility of treating ra’diation phenomena and other effects of the finite propagation of forces to a considerable extent rests entirely on the smallness of the two dimensionless constants of atomic theory, the fine structure constant r41
a=- 2xe2
hc
- 123 -
and the ratio between the masses of the electron and the proton
Thub, as will be seen from [l] and [2], it is the small value of a which is responsible for the smallness of the ratio between d and a, which is just equal to a2. Further, the classically estimated ratio between the radiative reactions on the electron and the nuclear attraction is, for a hydrogen atom even in the states of firmest binding, of the same order of magnitude as 2 . It is just this circumstance which affords a justification for the neglect of the radiative reaction in a description of the stationary states including the fine structure. Moreover, it is only the small value of p which allows us, in the treatment of effects depending on the finite propagation of forces, to distinguish to so large an extent between the intrinsic properties of the atom and its motions as an entity. At the present stage of the theory, the two constants c( and p are to be taken as empirical quantities of which no theoretical deduction would seem possible. The essential limitation of the quantum-mechanical description has been accentuated by the peculiar difficulties which present themselves in the attempt to develop a proper relativistic treatment of atomic problems. Thus Dirac’s quantum theory of the electron, which accounts in such an appropriate way for the spin-effects, includes, as is well known, the occurrence of transition processes inconsistent with the stability of the electron. These processes involve changes of energy exceeding the ciitical value me2 and lead to states in which the energy and the mass of the electron would be negative. Moreover, the attempts to treat the radiation effects on rigorous lines by considering the atoms and the electromagnetic field as a closed quantum-mechanical system led to para. doxcr arising from the appearance of an infinite energy of coupling bc tween atoms and field. The solution of these difficulties will certainly claim a formalism in which the elementary particles and the quantum of action appear as inseparable features. I n judging the situation. especially with reference to a possible limitation of the conservation laws of energy and momentum in the atomic theory, it is important, however, to examine more closely to what extent the present theory offers a reliable guidance for the analysis of the phenomena. In the first place, it may be emphasized that the radiation phenomena, which are typical relativistic effects, can be accounted for to a large extent by means of the so-called correspondence method. This method rests on the argument that the classical description of electromagnetic fields must be valid in the limiting case where the effects of
- 124 th e individual radiative processes can be neglected. I n accordance with th e general superposition principle. common t o classical field theory and quantum mechanics, the classical picture of electromagnetic field is therefore used as a symboiic means of estimating th e probabilities of spontaneous and induced radiative transitions in atoms. I n this procedure, in which the radiation field is not considered as a part of th e system under investigation, the conservation of energy and momentum in radiation processes finds its expression in the idea of photon. This idea may be said t o exhibit a complementary relationship to the field concept in the same sense as the idea of stationary states of atomic systems t o the classically defined properties of elementary pnrticles. Especially, it may be remarked th at it is not possible, from Einstein’s original analysis of the energy fluctuations of temperature radiation within a n enclosure, to draw definite conclusions as t o a limitation of classical field theory, since any attempt to detect spatial discontinuitieb in the energy distribution within the enclosure would necessitate the use of measuring instruments which would make the argument illusory. Quite generslly, we may say th at the photon idea loses all significance in cases where it is possible to obtain an unambiguous knowledge of the quantities essential for the classical, description of a n electromagnetic field. I n the account of the simplest features of the radiation phenomena, we inay neglect entirely the radiative reaction in th e calculation of tho transition probabilities. By a proper application of the quantum mechanical formalism it has been possible, hotrever, to extend the correspondence method, in accordance with the conserpation lamb, to the treatment of such problems a5 the width of spectinl 1in.s and the retardation effeclc in the interaction of electrons hound in atoms. Still, the condition for such applications is th at the effects in questicn can he treated as small pertnrbations of the phenomena to be expected if the finite propagation of forces would be neglected. Due to the smallnesb of the constant a. mentioned above, this condition is widely fiilfillcti in problems of atomic constitution, since even f o y the electlms most firmly Found in atoms of high nuclear rharge, ‘( orbital ” dimensions and spectral wave-lengths are very large compared with the classical electron diameter. I n this connevion it may be noted th a t Then regard is taken of the quantitm of action, the limit symhdised b y the elect,ron diameter mnst not be taken too litei~dlp. Consider for instance the scattering of radintion by free electrons. I n the classical treatment, where the f i eqiiency of the radiation is not changed by the scattering, it is a n obvions conclitiofi for the estimation of the force exerted t y Ihe incident radiation on the electrm, as well as of the radiative reaction, th a t the wave-length of the liqht be large compared with the electyon diameter. I n quantum theor:;, however, an ebsential modification arises f i om the filct t h a t the velocity
- 125 acquired by the electron in the individual scattering process comes very near t o the velocity of light as soon as the wave--length is comparable with the so-called Compton wave-length
Thich is of the same order of magnitude as d / a . For a simple application of the correspondence argument it. is therefore essential that the scattering process be considered not from a Jystem of reference where the ve1oc.ity of the elect’ron is initially zero, but from one where t.he resultant momentum of the photon and the electron wanishes, and in which thc frequency of the radiation is not changed by the scattering. Since! for hiqh frequencies, the wavelength in this system is approximately equal t o the geometrical mean between the original wavelength and twice the Coinpton wavelength, we find that it will be large compared with t h e critical length defined by [I] if only the w-ave-length in the original system is large compared with a d . From this argument we see that the apparently dubious a,pplication of the Rlein-Xishina formula for the Colripton effect t o the absorption of cosmic rays of wavelength of t?ze ne order of i-imgnitude as d is really qnitlejustifiable. This is also indicatme3bg the smallness of the scattering intensity for short wavelengths ah compared with that given by the classics! formula of Thomson, which lor ion2 wave-lengths holds Ltualtered also on quantum theory. The scattering of free electrom i:: an especially simple case where li critical ” transitions to stmates of neqative energy are excluded on account of the conservation of energy and momentum, at any rete if the intensity 0: the light, is not so large that several photons are simultaneously involved in the process. In the case of elect’rons bound in atoms the situetion is more complicated, since the present formalism includes the occurrence of . ntaneous rndistive transit,ions to states of negative energy with a ;:;.olvibility not negligible in comparison with that of the actual radiation piocesses. It ma,y be emphasized, however, tha)t we have here to do with consequences of the formalism which do not allow of a,n unambiguous interpretation on the basis of the correspondence argument. Indeed, it is an implicit assumptJion of the symbolic use of the field idea that the a8ct8ion on atomic systems of radiat>ionfields which contwin a number of il photons ” large enough t.o permit of an unambiguous measurement of t’heelectric and magnetic forces, can still be treated as small perturbations. While this assumption is widely fulfilled for ordinary spectral phenomena, it is not satisfied to the same extent in the case of oritkal transitions. Still it, is difficult to draw definite conclusions about this point, on account of the paradoxes mentioned above concerning the coupling of atoms and
- 126 -
radiation, which appea.r when we attempt to t'reat the radiat'ion field as an observable part of the system, and which hinder the development) of a ra8tional quant,um electfrodynamics on the lines so snccessfnllv followed in quantum mechanics. I n this respect, t'he difficulties of relativistic quantum mechanics appear in another light t.hrough the occurrence of critical transitions in cases where radiation and retardatmioneffect9 are of secondary import
- 127 -
might determine the field of applicability of the' conservation laws. It must not be forgotten, however, th at the complement'ary relations between the uncertaint,ies of space-time coordinates and conjugate moments are relativistically covariant. This follows directly from the relat'ivist'ic invariance of action, stressed from the beginning b y Planck himself as an argument for the general validity of t,he formulat'ion of his discovery. From relat'ivistic kinematics it is therefore not possible t o deduce 1im.itations of the application of space-time concept,s other th a n t'hose expressed by the usual uncert8aintp principle and those symbolised b y the classical electron diameter. The situation is essentially changed, of course, if we take intJo account th at the difficulties of relativistic quantum mechanics hold just as much for the descritpion of the measuring instruments as for the systems under investigat,ion, b u t this very circumstance introduces complications which make it difficult a t present to reaxh definite conclusions as to the necessary modifications of the formalism. I n the absence of a, consist'ent, relativistic theory, it is important to stress the f a a t that, as far as the extranuclear electrons in at,oms are concerned, there is no experimental indication of a, failure of the con; ervation laws of energy and momentum. I n particula.r, all evidence regarding atomic spectra is in agreemeni; with the combination-principle, which stands in so intimate a comexion with tJheanplication of energy conservation t o radiation processes. MoreoTer, all conclusions bmed on the exclusion princiyle are found t o be verified without except,ion, even for the electrons most firmly bound in atoms where we are fa'r beyond the reach of non-relativistic theory. Thmefore, it seems that, in all atomic problems where, the nuclei can be regarded as independent ent'ities, the individualit,y of the electron is maintained t o t,he degree assumed in the formulation of the classical conservation laws.
.
9
3. PROBLEMS OF INTRA-NUCLEAR
ELECTRONS.
The experimental evidence regarding tjhe charges and the masses of atomic nuclei and their disintegrations finds, as is well known, a n immediate explanation on the view t h a t all nuclei are built up of protons and electrons. The extent to which these constituents of nuclear structures can be treated as independent mechanicad entities is, however, far more limited than the possibility of considering the nuclei and elect'rons as separate particles in ordinary problems of atomic constitution. This point is most strikingly exhibited b y the failure of the fundamental quantum mechanical rules of statistics when applied to nuclei. In fact, according t o experimental evidence, th e statistics of a n ensemble of identical nuclei is determined solely b y the number of protons .contained in each
- 128 nucleus, while the intra-nuclear electrons show in this respect a remarkable passivity, contrasting with the exclusion principle. From the preceding remarks it will also be clear that a treatment of the intra-nuclear electronic constitution is far beyond the reach of present atomic mechanics. Since nuclear dimensions are of the same order as the classical electron diameter, me have, in fact, left the ground for an unambiguous application of classical mechanical ideas and of any formalism which, like present quantum mechanics, is essentially based on such ideas. The paradoxes of relativistic quantum-mechanics, which here take a most acute form, must also be taken as a serious warning against the reliability of such a formalism as a guidance in the investigation of the electron binding in nuclei. Especially, it may be emphasized that any use of the idea of an intrinsic magnetic moment in the estimation of the forces between intrenuclear electrons and protons lacks all theoretical basis. Indeed, in the problem of the electronic constitution of nuclei, we are faced with entirely new aspects of atomic stability, and our only reliable gnidance is so far afforded by the conservation and the atomicity of electric charge. I n this situation, we are led to consider the capture or the expulsion of an electron by a nucleus plainly as an extinction or a creation, respectitely, of the electron as a mechanical entity. We cannot therefore be surprised if those processes should be found not to obey such principles as the conservation laws of energy and momentum, the formulation of mhich is essentially based on the idea of material particles. While the properties of nuclear electrons are radically different from those of the electrons belonging t o extra-nuclear configurations, the situation of the protons within nuclei resembles to a large extent that assumed for the constituent atomic particles in the usual applications of quantum-mechanics. Thus there is no reason to expect essential restrictions in the application to the protons of the idea of material particle with well-defined mass, and even the limitations of relativistic quantum mechanics would seem to be of secondary importance. In fact, the energy of binding of protons in nuclei, as deduced from the mass defects, is very smail compared with the critical value Me2, where M is the proton mass. Of course, in contrast to ordinary problems of atomic constitution, our knowledge of the binding forces is not sufficient for a direct quantum niechanical calculation of nuclear energies, or even for an explanation of the stability of the simplest composed nuclei. It is, however, very satisfactory that the empirically determined dimensions and mass defects of nuclei exhibit an approximate relationship consistent with quantum mechanics. I n fact, if for the protons in a helium nucleus orbital dimensions are comparable with the electron diameter d given by [l], and if tho binding energy of each proton is taken equal to the kinetic energy
- 129 corresponding to an orbital motion with angular momentum h/2x, simple calculation shows that the ratio between the mass defect of the a-particle and its total nuclear mass should be approximately equal to the square of the ratio between the non-dimensional constants p and a given by [5] and [4], which is actually nearly equal to the experimental value. Although such a calculation is, of course, only of a qualitative significance, it indicates very strongly that the smallness of the mass ratio p is still more fundamental for the stability of nuclei than for that of extra-nuclear configurations. Indeed, if the ratio between the masses of the electron and the proton were much greater, the existence of nuclei containing several protons would hardly be conceivable. The treatment of heavier nuclei is greatly simplified by the fact that for many purposes they can be considered to contain a-particles as independent constituents. On this occasion few words will suffice to remind of the beautiful application of quantum mechanics to the interpretation of nuclear disintegrations in which a-particles are emitted. As is well known, this theory explains not only the fundamental law of radioactive decay, but also the remarkable connexion between the decay constants and the energies of the expelled a-particles. Still, it must not be forgotten that our ignorance of the interaction between the nuclear constituents prevents a t present an understanding of the peculiar variation of these constants within each family of radioactive elements. While in this respect the account of the radioactive properties under discussion lacks the quantitative completeness of the explanation of the periodic variations of physical and chemical properties of the elements, the qualitative validity of this account has found a most suggestive support in the relationships disclosed between the energy levels of a-particle binding in nuclei and the y-ray spectra. Indeed, the ideas of stationary states and individual radiative transitions find here a field of application quite analogous to the interpretation of optical spectra and offer similar possibilities for deriving from simple correspondence considerations more detailed information about the constitution of the emitting system. Quite different features are revealed, as is well known, by the investigation of @-ray disintegrations. Just like the a-ray products, all p-ray products have a well-defined rate of decay, but nevertheless for each product the energy of the emitted @-particle varies continuously within wide limits. If energy were conserved in these processes, it would imply that the individual atoms of a given radioactive product were essentially different, and it would be difficult to understand their common rate of decay. If, on the other hand, there is no energy balance, it is possible t o explain the law of decay by assuming that all nuclei of the same product are essentially identical. This conclusion would also be in accordance with the general evidence on the nuclear statistics of non-radioac-
- 130-
tive elements, which has revealed the essential identy of any two nuclei containing equal numbers of protons and electrons. I n this connexion, i t may be emphasized th at t h e identity of two such nuclei is just a n experimental fact for which, a t the present stage of atomic theory, no explanation can be given, and which exhibits most strikingly the universal character of intrinsic atomic stability. I n concluding these remarks, I need hardly stress the fact th a t a departure from the law of energy conservation in nuclear disintegrations would involve very strange consequences under such conditions, as probably occur in the interior of stars, where these processes are reversed. Still, we must remember, after all, th a t the essential stability of atoms in an implicit assumption in the whole classical description of natural phenomena, and we cannot therefore be surprised if classical concepts fail in accounting for their own foundation. J u s t as we have been forced to renounce the ideal of causality in the atomistic interpretation of the ordinary physical and chemical properties of matter, we may be led to further renunciations in order to account for the stability of the atomic constituents themselves.
IV. ON THE PROPERTIES OF THE NEUTRON [l] Extract from an Address Delivered at a Conference in Copenhagen 7-13 April 1932 UNPUBLISHED MANUSCRIPT DATED 25 APRIL 1932
See Introduction, sect. 1, ref. 13.
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
The folder “Properties of the Neutron”, 1932, contains 3 manuscripts comprising altogether 10 pages, written in English. The first is a typed manuscript of 4 pages with a few corrections and equations in pencil in Bohr’s handwriting. It has the title: “Extract from an address delivered at a conference on actual atomic problems held in Copenhagen in April 7.-13. 1932.” The pages are dated 18 and 19 April 1932. The second manuscript is a carbon copy of this with some corrections in pencil in Rosenfeld’s handwriting. The third manuscript, which is reproduced here, is a carbon copy of a manuscript of 2 pages, entitled: “On the properties of the neutron”. It is dated (in pencil) 25 April 1932. The manuscripts are on microfilm Bohr MSS no. 13.
PART I: PAPERS A N D MANUSCRIPTS RELATIUG TO NUCLEAR PHYSICS
15/4
32 On the properties of the neutron.'
The discovery, announced by Chadwick', that the remarkable penetrating radiation emitted by certain light elements when exposed to a bombardment of a-rays consists essentially of electrically neutral material particles with inertial mass approximately equal to that of an hydrogen atom, presents us with several new and very interesting features of atomic theory. As the linear dimensions of these neutrons must be very small compared with the diameters of ordinary neutral atoms and probably are of the same order as the dimensions of the positively charged nuclei of such atoms, a neutron may be regarded from a formal descriptive point of view as a nucleus of an element of atomic number zero. Just as little as it is possible at the present stage of atomic mechanics to account in detail for the stability of ordinary nuclei, it is impossible at present to offer a detailed explanation of the constitution of the neutron. Of course its mass and charge suggest that a neutron is formed by a combination of a proton and an electron, but we cannot explain why these particles combine in such a way as little as we can explain why 4 protons and 2 electrons should combine to form a helium nucleus or a-particle. As is well known, atomic nuclei do not even obey the simple fundamental rules of statistics holding for atomic systems formed by the combination of elementary particles. Thus a nitrogen nucleus which should consist of 14 protons and 7 electrons obeys the Einstein-Bose statistics, although a system containing an odd number of particles satisfying the Pauli exclusion principle should obey the Dirac-Fermi statistics. It appears that the statistics of all nuclei are determined solely by the number of protons contained, and, as I have expressed it on a recent occasion3 we may say that the electrons in nuclei have lost their individuality as separate mechanical units to an extent which allows us to speak in a definite way only of the total negative electrification of the nucleus, but not of the numbers of separate electrons. This view is also suggested by the fact that the linear dimensions of nuclei are of the same order as the so-called electron diameter, which represents the minimum extension to be ascribed to an electron according to the fundamental ideas of electrodynamics. Moreover, it may offer a clue to the understanding of the remarkable features exhibited by P-ray disintegrations, by which we may say that electrons which have lost their
'
Extract from an address delivered at a conference on actual [current] atomic problems, held in Copenhagen in the first weeks of April 1932. Nature, February 27. 1932; see also Lord Rutherford, Nature, March 26. 1932. Journal of the Chemical Society, February, 1932.
'
w,
2
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
dynamical individuality in the nucleus are recreated as mechanical entities. The account of processes of this kind, of which the formation of a neutron or its splitting up in a proton and an electron would form the simplest possible example, is entirely outside the reach of present atomic mechanics; and in this domain we must be prepared to meet with quite new features of the essential stability of atomic structures, as well as with new limitations of the applicability of the fundamental ideas of mechanics, including the conservation laws of energy and momentum.
V. ON THE PROPERTIES OF THE NEUTRON [2] OM NEUTRONERNES EGENSKABER Overs. Dan. Vidensk. Selsk. Virks. Juni 1931 - Maj 1932, p. 52
Communication to the Royal Danish Academy on 29 April 1932 ABSTRACT TEXT AND TRANSLATION
See Introduction, sect. 1 , ref. 14.
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
In the report in Nature 130 (1932) 287, this abstract was changed and condensed into a single sentence: “The remarkably small interaction between neutrons and electrons is a simple consequence of quantum mechanics”.
NIELS BOHR gav en Meddelelse: O m Neutronernes Egenskaber. Underssgelser, udfmrt i den seneste Tid paa forskellige Lahoratorier, af den ejendomnielige Straalevirkning, der udgaar fra visse Grundstoffer, naar disse udszttes for Uestraaling fra radioaktive Stoffer, h a r fsrt ti1 Erkendelsen af, at disse Yirkninger skyltfes en Udsendelse fra de bestraalede htomers Kerner a f mnterielle Partikler uden elektrisk Ladning, de saakaldte S e u troner. I Foredraget vil blive vist, hvorledes visse fra den scttdv a n 1i ge 31ek a n i k s Stand p ti n kt over ra s ke n d e I: ge n sk a be r a f S e u tronerne kan forklares paa sinipel Maade ud fra Kvanteteorien.
TRANSLATION Niels Bohr presented a communication: On the Properties of the Neutron. Investigations, carried out recently at various laboratories, of the peculiar radiative action emanating from certain elements when they are exposed to radiation from radioactive substances, has led to the recognition that these actions are due to an emission from the nuclei of the irradiated atoms of material particles without electric charge, the so-called neutrons. In the lecture it will be shown how certain properties of the neutron, surprising from the standpoint of ordinary mechanics, can be explained in a simple way on the basis of the quantum theory.
VI. THE ELECTRON AND THE PROTON UNPUBLISHED MANUSCRIPT [ 1933- 19341
See Introduction, sect. 1, ref. 17
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
The folder “Electron and Proton”, catalogued as of [1932], contains two different manuscripts, both entitled: “The Electron and the Proton”. They are both in English. The first manuscript consists of 2 pages written in pencil in Mrs. Schultz’ handwriting. The second manuscript, reproduced here from the carbon copy where the formulae are filled in, consists of 4 typewritten pages. The manuscripts are on microfilm Bohr MSS no. 13.
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
The electron and the proton. As regards the properties of the constituent atomic particles it is essential to distinguish between such properties which are unambiguously defined by classical concepts and such for the interpretation of which the quantum theory is indispensable. To the first type of properties belong the inertial mass and the electric charge of the particles, the values of which are deduced from measurements completely interpretable in terms of the classical theories of mechanics and electrodynamics. To the second type belong such quantities as the spin and magnetic moment of the electron, the definition of which is inseparable from the symbolism of quantum theory and which accordingly are not capable of direct measurement in the ordinary sense.’ As is well-known, this situation finds its adequate expression in Dirac’s theory of the electron, where all spin effects appear as characteristic consequences of the quantum theoretical reinterpretation of the classical electron theory on the lines of the general correspondence argument. It is true that the appearance of positive electrons under certain circumstances is an inherent feature of any consistent theory of this kind, and that the existence of these particles, the mass and charge of which are susceptible of direct measurement, is an equally important part of the classically defined foundations of electron theory. Indeed this discovery of Dirac’s has totally removed the dissymmetry in the sign of the charge, which was so unsatisfactory a feature of classical electron theory, and the dissymmetry in this respect, which still remains in atomic theory, is so far entirely connected with the positive charge of the atomic nuclei, which again finds its expression in the common view that these nuclei are entirely built up of neutrons and protons. At the present stage of atomic theory the neutron may be considered as an elementary particle in the sense that no more a priori reasons for its existence can be given than for the existence of the electron. Our attitude towards the problem of the proton, on the other hand, has undergone an essential change through the recent development of the electron theory, since the positive unit charge of this particle is no longer an isolated feature of atomic theory. At present, it is therefore reasonable, as was first suggested by Curie and Joliot, to consider the proton as a combination of a neutron and a positive electron; or, what amounts to the same for our purpose, to consider it as a disintegration product of a neutron from which an ordinary electron is expelled, conforming with the view of P-ray disintegration of nuclei advocated by Heisenberg. The point, however, to which I should like to draw attention in this connection, is that we must expect
’
[This footnote was probably meant to refer to Bohr’s unpublished note, The Magnetic Electron, reproduced in Volume 6, p . [331].]
MS, p. 2
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
that also particles with the same mass as the proton but with opposite charge will exist, and that such “negative protons” will show a relation to ordinary protons which in essential respects will differ from the relationship between negative and positive electrons in Dirac’s theory. These differences have their root in the finite size of the neutron, whose linear dimensions deduced by Chadwick from the study of collisions between neutrons and protons is approximately cm. If we compare this length with the critical quantity
which appears in the relativistic quantum theory of an elementary particle of mass m, we find namely that it is only small compared with the value of X corresponding to the electronic mass, but large in comparison with the value corresponding to the proton mass. Now all the characteristic consequences of Dirac’s theory depend on the circumstance that X for an electron is very large compared with the so-called electron diameter
\IS, p 3
where e is the elementary charge.2 If we associate the dimensions of the proton with those of the neutron, we cannot therefore expect that the characteristic consequences of Dirac’s electron theory will hold unmodified for the positive and negative protons. This applies not only to the problem of the mutual annihilation of a pair of such particles, but also for the finer features of the description of the behaviour of each kind of particles separately. Indeed this view would appear to offer a simple explanation of the, at first sight, surprising result of Stern, who from his refined experiments of deflection of hydrogen atoms in a magnetic field concluded that the magnetic moment of the proton is several times larger than that given by the expression for the magneton he
p=GK if m is identified with the proton mass. A direct indication of the stable existence of negative protons would seem to be offered by the experiments of Millikan and Anderson on the magnetic deflection of cosmic rays, from which the existence of positive and negative particles of equal masses was originally concluded. The suggestion, first put forward by
’ [Left blank.]
P A R T I: P A P E R S A N D M A N U S C R I P T S R E L A T I N G TO N U C L E A R P H Y S I C S
Geiger, that the primary cosmic rays have rest-masses of the same order as the proton, seems namely, as has been shown by Williams, strongly supported by a closer consideration of the ionizing and penetrating power of these rays. If this view be taken, the photographs of Millikan and Anderson should therefore offer direct evidence of the existence of negative as well as positive protons in the cosmic rays. Moreover Gamow has shown that the assumption that negative protons exist as stable constituents in atomic nuclei together with neutrons and ordinary protons might be of essential help in overcoming certain difficulties in Heisenberg’s promising nuclear theory and would especially explain the appearance of isomeric nuclei with the same charge and approximately the same mass. In concluding I might briefly refer to the fact, which surely is commonly understood, that the distinction between positive and negative atomic constituents is wholly arbitrary. We realize even that if we consider matter as built up of neutrons and equal numbers of positive and negative electrons, it is entirely accidental what kind of charge the atomic nuclei and the electronic cluster take. It is also interesting to remember that we have no knowledge, however, whether the situation in this respect at the removed part of the universe differs from that of the earth. About this point the optical spectra of course do not tell us anything, and our only sources of possible information are the material messengers of the cosmic rays.
MS, p. 4
VII. ON THE CORRESPONDENCE METHOD IN THE THEORY OF THE ELECTRON EXTRACT SUR LA METHODE DE CORRESPONDANCE DANS LA THEORIE DE L ' EL E cTR oN
Structure et proprie'te's des noyaux atomiques, Rapports et discussions du septieme Conseil de physique, Bruxelles, 22.10.-29.10.1933, Gauthier-Villars, Paris 1934, pp. 216-228 Elaboration of Discussion Remarks at the 7th Solvay Conference in Brussels, 22 to 29 October 1933 TRANSLATION OF PAGES 226-228 FULL TEXT IN FRENCH AND ENGLISH REPRODUCED IN VOL. 7
See Introduction, sect. 1, ref. 10.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
In the French original the fine-structure constant is denoted by E . However, in the English translation we have preferred to use the conventional symbol cx which is also used by Bohr himself in the original Danish manuscript from which the French text was prepared by Rosenfeld (see Vol. 7 ) .
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
TRANSLATION
I would like to add a few words about the relation between the correspondence theory of the electron and the problem of nuclear constitution. We here meet with an entirely new characteristic of atomic theory in the existence of the neutron, the stability of which, from the current point of view of atomic theory, is as elementary a fact as the existence of the electron. In particular, the ratio p = rn/M between the electron mass rn and the neutron mass M is a constant of nature, the smallness of which compared to unity is certainly as important for the constitution of nuclei as the smallness of the constant Q is for the constitution of the configuration of electrons surrounding the nuclei. Indeed it is, above all, the relatively large masses of the nuclear particles which make it possible to explain the laws of radioactive a-disintegrations and the relations between the energy levels observed in these disintegrations, and the y-ray spectra by means of the fundamental concepts of the quantum theory of atomic constitution, such as stationary states and individual transition processes. The only characteristic difference between the problem of nuclear constitution and the theory of atomic constitution is that in the former case, as opposed to the latter, we cannot draw a priori any conclusions about the forces between the nuclear particles from the laws of classical electromagnetism, but all deductions about these forces rest on an entirely new empirical basis. I n particular I would like to stress the fact that there is no possibility at all of applying the concepts of electron theory directly within the proper domain of nuclear phenomena. Whether one regards the proton as a combination of a neutron and a positron, which, according to the latest evidence, might well be the most natural hypothesis, or whether one regards it as the product of a dissociation of a neutron with the associated emission of an electron, we are here concerned with processes which cannot be described on the present basis, and the possibility of which has to be sought in the fact that the empirically known dimensions of the neutron are of the same order of magnitude as the electron diameter 6, which represents the limit beyond which the concepts of classical electron theory, and their application according to the correspondence principle, fail completely. In this connection one may also note that the interesting discovery by Stern, according to which the magnetic moment of the proton differs appreciably from the value of the magneton times p, must no doubt also find its explanation in the fact that the diameter of the neutron, and therefore also that of the proton, is appreciably larger than* pX; indeed, as already mentioned, the
* [X is t h e Cornpton wavelength.]
P A R T I : P A P E R S A N D M A N U S C R I P T S R E L A T I N G TO N U C L E A R P H Y S I C S
application of Dirac’s electron theory to proper relativistic effects depends just on X being large compared to the electron diameter 6 . In conclusion, I would like to remark that if I have advocated that one seriously consider the idea of a possible failure of the theorems of conservation of energy and momentum in connection with the continuous 6-ray spectra, my intention was above all to emphasise the total inadequacy of the classical conceptual edifice for treating this problem, which could still hold great surprises for us. I fully appreciate the weight of the argument that such a possibility would be difficult to reconcile with the theory of relativity, and would in particular stand in a rather unlikely contrast to the absolute validity of the theorem, analogous according to general field theory, of conservation of electric charge, which extends also to the region of nuclear phenomena. In this connection one may however remark that this comparison itself indicates how difficult it would be to prove a direct deviation from the theory of relativity, even if the total mass and energy associated with the particles and the radiation fields were not conserved in nuclear processes. Just as the conservation of charge inside a region whose boundary is not crossed by charges is, at least macroscopically, a necessary consequence of the validity of the electromagnetic field equations outside of this boundary, so, as Landau has pointed out, it is a necessary consequence of the theory of gravitation that any variation of the energy inside a certain region must be accompanied by variations in the gravitational forces outside this region, which would correspond exactly to a mass transport across its boundary. However, the question is whether we must necessarily require that all such gravitational effects are associated with atomic particles in the same way as the electric charges are associated with electrons. Therefore, until we have further experience within this area, it seems to me difficult to judge Pauli’s interesting suggestion to resolve the paradoxes of the P-ray emission by assuming that the nuclei emit, together with the electrons, neutral particles, much lighter than the neutrons. In any case, the possible existence of this “neutrino” would represent an entirely new element in atomic theory, and the correspondence method would not offer sufficient help in describing its r6le in nuclear reactions.
VIII. DISCUSSION REMARKS AT THE 7th SOLVAY CONFERENCE 1933 Structure et proprides des noyaux atomiques, Rapports et discussions du septieme Conseil de physique, Bruxelles, 22.10.-29.10.1933, Gauthier-Villars. Paris 1934 TEXTS AND TRANSLATIONS
See Introduction, sect. 1 , ref. 1 1 , a n d sect. 3, ref. 63.
1NSTlTUT INTERNATIONAL DE PHYSIQUE SOLVAY SEPTIEME CONSElL DE PHYSIQUE
H. A. KRAMERS
N. F. MOTT
E. STAHEL E. HEWRIOT
F. JOLIOT W. HEISENBERG
E. SCHROOlfJCER
N. BOHR
A. JOFFE
M. COSYNS
P. BLACKETT
l u g . PICCARO
C. 0. ELLIS
1. ERRERA B. CABRERA W. BOTHE
CURIE
0. W. RICHARDSON
W. PAUL1
Lard RUTHERFORO
P. LANGEVIN Abseats : A. EINSTEIN el Ch:Eug.
E. 0. LAWRENCE
L. ROSENFELO
Ed. BAUER 1. E. VERSCHAFFELT 1. D. COCKROFT
M. S. ROSENBLUM
E. FERMl WLB1. IOLIOT
6. GAMOW
BRUXELLES.22-29 OCTOBRE 1933
P. A. M. DlRAC
E.T.S. WALTON P. DEBVE
F. PERRIN
--
E. HERZEN M. de BROGLIE
Th. DE OONnER GUYE
R. PEIERLS
L. de BROGLIE
M’la
L. MEITNER
1. CHADWICK
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Remarks by Niels Bohr during Discussions at the Solvay Conference, 1933
J.D . Cockcroft, La dksint&gration des elements par des protons accderes, pp. 1-56. Discussion, pp. 57-79. Page 72 (Discussion of Lawrence’s deuteron stripping experiments):
51. BOIIR.- L’hypothkse que la dksintegration, dont il est question, est produite dans le champ coulombien du noyau, se heurte e n effet B de graves difficultks. Si, d’autre part, on veut admettre qu’elle se produit dans le noyau, dans lequel les deutons pknktrent, la thkorie actuelle n’offre pas de base simple qui nous permet de comprendre pourquoi les protons liberes quittent le noyau avec une vitesse qui ne depend pas du nombre atomique. BOHR: The hypothesis that the disintegration in question takes place in the Coulomb field of the nucleus, actually encounters serious difficulties. If, on the other hand, one wants to assume that it takes place inside the nucleus, with the deuterons entering it, current theory provides no simple argument which would enable us to understand why the emitted protons leave the nucleus with a speed which does not depend on the atomic number.
M. et Mme Joliot, Rayonnement penne‘trant des atomes sous l’action des rayons a , pp. 121-156. Discussion, pp. 157-202. Page 175 (Discussion on the positive electron):
M. B O A R. I1 est de la plus haute importance d’essayer, comme le fait 31. Blackett, de tirer des conclusions aussi nombreuses
que possible d’expkriences sur les Blectrons positifs, sans devoir recourir ila thkorie de Dirac. J e pense que la conclusion relative B la charge est juste, mais celle concernant le spin me semble moins certaine. E n rkalitk, comme c’est la presence du champ nuclkaire qui permet a u qua nt um de lumikre incident de produire les deux particules, il n’est pas du t out exclu que le noyau prenne part au mecanisme de la conservation d u moment angulaire.
M. PAULI.- Contrairement a ce que pense M. Bohr, je suis d’avis que la conclusion de M. Blackett concernant la charge de
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
1’6lectron positif ne saurait en aucune facon &re considkr6e comme plus certaine que celle concernant son spin.
JI. BOHII.- hlors que la conservation de la charge est like directement des lois comprises dans la th6orie classique, il y a une difficult6 pour ce qui regarde le moment angulaire des particules, puisque nous ne disposons d’aucun moyen de mesurer cette quantit6, qui soit bas6 directement sur des conceptions classiques. BOHR: It is of the greatest importance to try, as Blackett does, to draw as many conclusions as possible from the positive-electron experiments without relying on the Dirac theory. I believe that the conclusion as regards the charge is right, but that concerning the spin seems to me less certain. Indeed, as it is the electric field of the nucleus which allows the incident light quantum to produce the two particles, it is by no means excluded that the nucleus participates in the angular momentum balance. PAULI: Contrary to the view of Bohr, I believe that Blackett’s conclusion concerning the charge of the positive electrons could not in any way be considered as more certain than that concerning its spin. BOHR: Whereas the conservation of charge is related directly to laws contained in classical theory, there is a difficulty as regards the angular momentum of particles, because we do not possess any means of measuring this quantity which is based directly on classical concepts. Page 180 (Discussion on artificial positron emitters):
M. BOHR.- C’est un problkme de la plus haute importance que de savoir si dans les processus o h l’aluminium est bombard6 par des particules a, 1’6nergie est conserv6e ou non. Sans doute, I’observation que les positrons n’ont pas tous la m6me vitesse, n’est pas, par elle-mdme un argument contre la conservation de l’knergie, puisque nous ne savons pas encore comment l’e‘mission des positrons se produit. Si vraiment, comme le suppose M. Joliot, les positrons viennent de l’intkrieur du noyau, les circonstances seront fort semblables A celles des rayons p. BOHR: It is a problem of the greatest importance to know whether energy is conserved in the bombardment of aluminium by a-particles. Doubtlessly the observation that the positrons do not all have the same velocity, is not by itself
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
an argument against energy conservation, since we d o not yet know how the positron emission is produced. If, as Joliot assumes, the positrons really come from inside the nucleus, the circumstances are very similar to those of the P-rays. [As regards Bohr’s discussion remark (pp. 214-215) in connection with Dirac’s report, Theorie du positron, see Vol. 7.1
G. Gamow, L’origine des rayons y et les niveaux d’knergie nucleaires, pp. 231-260. Discussion, pp. 261-288. Pages 287-288 (Discussion on P-rays):
M. B O H R. RBcemment, M. Guido Beck a esquissi: une thBorie des spectres continus des rayons p qui, m&mesi elle ne rBsout pas les difficult& fondamentales, merite cependant toute notre attention. Comme point de dkpart, il admet, tout comme MM. Ellis e t Mott, que la limite suphieure du spectre continu indique la vraie diffkrence Bnergbtique entre le noyau initial et le noyau restant. Dans cet ordre d’idkes, il a Bgalement analysi: le bilan Bnerghtique dans les cas o h il y a un embranchement dans les series radioactives. Or, & a n t donnkes les dificultks qui se rattachent l’application de la thkorie quantique I? un systbme o h un electron serait enfermi: dans une ritgion de l’espace de l’ordre de 1 0 - l ~cm, M. Beck admet que la particule p est cr6i:e hors du noyau, dans une r6gion de l’espace assez &endue, par suite d’un processus de matkrialisation qui donne lieu en mkme temps a l’apparition d’un positron. Ce positron, M. Beck admet qu’il est absorbi: par le noyau, dont la charge est ainsi augmentke d’une unite. La theorie actuelle ne nous offre pas de base pour discuter les details de ce processus d’absorption. Tandis que l’exc8s de 1’i:nergie que possbde le noyau initial sur l’energie du noyau final est consider6 comme la source d’Bnergie du processus de mathialisation, on admet que le processus global est accompagne d’une veritable perte d’hergie, correspondant a 1’i:nergie cinetique d u positron absorbi:. Ru moyen d’hypothkses appropriees, M. Beck peut calculer la distribution des vitesses des Blectrons ainsi cr6ks. I1 trouve que toutes les vitesses entre zero et le maximum doivent &re representhes, mais qu’il y a diverscs possibilitks theoriques pour la
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forme exacte de la loi de distribution, correspondant aux valeurs diff Brentes que peuvent prendre les nombres quantiques d’impulsion angulaire des deux particules. J e voudrais demander jusqu’i quel point I’expBrience permet de vhrifier ces consBquences de la thborie de M. Beck. BOHR: Recently, Guido Beck has developed a theory of the continuous ,&ray spectra which, even if it does not resolve the fundamental difficulties, nevertheless merits serious attention. As his starting-point he assumes, like Ellis and Mott, that the upper limit of the continuous spectrum indicates correctly the energy difference between the initial and the residual nucleus. In this context, he has also analysed the energy balance in the cases in which the radioactive series are branched. Then, in view of the difficulties associated with the application of quantum theory t o a system in which an electron is enclosed in a region of space of the order of cm, Beck assumes that the &particle is created outside the nucleus, in a fairly extended region of space, as a result of a materialisation process which at the same time causes the appearance of a positron. Beck assumes this positron to be absorbed by the nucleus, whose charge is thereby increased by one unit. Current theory does not offer us any basis for discussing the details of this absorption process. Since the excess of energy of the initial nucleus over that of the final nucleus is regarded as the source of energy for the materialisation process, one assumes that the total reaction is accompanied by an actual loss of energy, corresponding to the kinetic energy of the absorbed positron. By means of suitable assumptions, Beck can calculate the velocity distribution of the electrons created in this way. He finds that all velocities between zero and the maximum will occur, but that there are several different theoretical possibilities for the exact distribution law, according to the different possible values of the quantum numbers which the angular momentum of the two particles can take. I would like to ask how far these consequences of Beck’s theory can be verified experimentally.
W. Heisenberg, Considerations thkoriques generales sur la structure du noyau, pp. 289-323. Discussion, pp. 324-344. Pages 327-328 (Further discussion on P-decay):
M. BOIIR.- En discutant le pr oblhie des rayons p, MM. Heisenberg et Pauli s’efforcent d’appliquer jusqu’au bout les lois
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connues de la thkorie des quanta, e t j e suis parfaitement d’accord avec cette tendance. Dans le m&me ordre d’idkes, il n’est pas inutile, peut-&tre, de remarquer que t o u t effort pour Btablir une relation entre le spectre continu des rayons p et le principe d’incertitude de Heisenberg est bask sur u n malentendu. E n effet, ce principe exige un dBfaut de prkcision e n ce qui concerne la valeur de 1’Bnergie d’une particule, si l’expkrience nous permet de constater la prksence de cette particule un instant bien dktermink; ce manque de prkcision est la conskquence d’une interaction incontrBlable de la particule e t de l’appareil qui nous permet de d6terminer cet instant. Dans ces conditions, la loi de conservation de 1’6nergie n’est pas violke; mais elle kchappe a u contrble de l’expkrience. Or, dans le cas de l’expulsion d’une particule p, la situation est toute diffkrente; on mesure son Bnergie d’une faCon bien dkfiriie, et la question d u bilan de 1’6nergie s’impose nkcessairement. g t a n t donnkes les difficultks thkoriques que soulkve la solution de ce problkme, c’est peut-&re une question de gofit que de savoir quel point de vue l’on prkfbre. Aussi longtemps que nous n’aurons pas de nouvelles donnkes expbrimentales, il est sage de ne pas abandonner les lois de conservation, mais, d’autre part, personne ne sait quelles surprises nous attendent encore.
BOHR: In discussing the problem of the @-rays,Heisenberg and Pauli have insisted on applying consistently all the known laws of quantum theory, and I am in perfect agreement with this tendency. In the same context it is perhaps not useless to remark that any attempt to establish a relation between the continuous 6-ray spectrum and Heisenberg’s uncertainty principle must be based on a misunderstanding. This principle requires, in effect, a lack of accuracy in the value of the energy of a particle if the experiment allows us to observe the presence of this particle at a well-defined instant; this inaccuracy is the result of an uncontrollable interaction between the particle and the apparatus which allows us to determine this instant. Under these conditions the law of energy conservation is not violated; but it loses its experimental verifiability. But in the case of the emission of a &particle the situation is completely different; one measures its energy in a well-defined manner, and the question of the energy balance arises necessarily. Given the theoretical difficulties raised by the solution of this problem, it is perhaps a matter of taste to decide which point of view one prefers. As long as
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we do not have new experimental results, it is wise not to abandon the conservation laws, but on the other hand nobody knows what surprises are still awaiting us. Pages 329-330 (Discussion of the radioactivity of K and Rb):
M. B O I I R. La question de la radioactivitb du K e t du R b est loin d’&tre Bclaircie. A cause de la longue durBe de vie de ces BlBments, ies idBes de hl. Beck ne sont guBre applicabies ici. M. Jacobsen, k Copenhague, est en train de chercher ii I’aide de la mBthode des coincidences, si d a m ces corps deux particules ne sont pas parfois Bmises en m&metemps. Reste aussi la question de savoir si le I< e t le R b n’kmettent pas de particules positives. BOHR: The question of the radioactivity of K and Rb is far from cleared up. Because of the long lifetime of these elements the ideas of Beck are hardly applicable here. Jacobsen in Copenhagen is trying to find out by coincidence methods whether these substances do not sometimes emit two particles at the same time. There also remains the question whether K and Rb do not emit positive particles.
...
M. BotrR.
- M. Hevesy, qui a effectuB une separation partielle
des isotopes du potassium et a pu conclure que la radioactivit6 est due k l’isotope iourd, m’a dit que les exp6riences sont tellement dificiles, qu’on ne pourrait afirmer avec certitude que c’est I’isotope 41K, et non pas un isotope 42K ou 431< qui est radioactif. BOHR: Hevesy, who has carried out a partial separation of the potassium isotopes, and has been able to conclude that the radioactivity is due to a heavy isotope, has told me that the experiments are so difficult that one cannot state with certainty that it is the isotope 41K and not an isotope 42K or 43K which is radioactive. Page 331 (Discussion of Heisenberg’s statement that the neutron seems to be an elementary particle):
M. B O H R. A mon avis, le sens qu’on doit attacher h la distinction entre particules Bl6mentaires e t particules complexes ne peut pas 6tre indiqui: sans ambigui’tk.
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BOHR: In my opinion the meaning to be attached to the distinction between elementary and composite particles cannot be stated unambiguously. Page 334 (General discussion on nuclear structure):
M. 13orrn. - La cornparaison d’un noyau avec une gouttelette liquide, faite par Gamow, est trbs schkmatique h cause du nombre relatiyement petit de particules a entrant dans la constitution des noyaux. Jlitme dans les no;\’aux les plus lourds, ce nonibre ne dkpasse pas la cinquantaine, et si I’on imagine rkalisk l’entassenient le plus dense possible. on trouve qu’il ne peut y avoir qu’une dizaine de particules h l’intkrieur du noyau, les autres formant la surface. Pour cette mPme raison un modkle tel que celui qu’a proposC RI. Delbruck, oh le noyau esl considkrk comme u n cristal, n’a pas un caractkre hien dkfini. .\lais toutes les reprksentations de ce genre ne jouent d’ailleurs qu’un r6le secondaire pour l’interprktation donnBe par la mkcanique quantique de la relation de Geiger-Xuttall; car cette interpretation est determinke essentiellement par le comportement Bnergetique de tout le s y s t h e e t sa charge klectrique totale. BOHR: The comparrson of a nucleus with a liquid droplet made by Gamow is very schematic because of the relatively small number of a-particles contained in the structure of nuclei. Even in the heaviest nuclei this number does not exceed fifty, and even imagining the densest possible packing one finds that one could have only about ten particles in the interior of the nucleus, while the rest form the surface. For the same reason the model proposed by Delbruck, in which the nucleus is considered to be a crystal, does not have a very well-defined character. But all the models of this type play only a secondary r6le for the interpretation given by the quantum mechanics of the Geiger-Nuttall relation; since this interpretation is determined essentially by the total energy content of the system and its total electric charge.
IX. THE NUCLEAR CONSTITUTION AND NEUTRON CAPTURES UNPUBLISHED MANUSCRIPT [1935?]
See Introduction, sect. 2, ref. 36
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
The folder “Neutron Capture and Nuclear Constitution”, [ 1935-19361, contains two typewritten manuscripts, an outline (1 page) in pencil in Kalckar’s handwriting, and 3 pages, numbered 3 to 5, in pencil in Rosenfeld’s handwriting. Except for a few Danish words it is all in English. The first manuscript, reproduced here, is entitled “The nuclear constitution and neutron Captures” and consists of 4 typewritten pages. The numerous errors in typing and spelling have been retained, since the status of this manuscript is uncertain, and poor typographical quality may contain a clue. The second manuscript, entitled “Nuclear constitution and quantum mechanics”, consists of 2 typewritten pages (with a carbon copy and a second typescript of page 1) with corrections in pencil in Rosenfeld’s handwriting. The handwritten pages by Rosenfeld are apparently a sequel to this. The manuscripts are on microfilm Bohr MSS no. 14.
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The nuclear constitution and neutron Captures. The problem of nuclear constitution presents as wellknown features which differ essentially from the problem of the electronic constitution of atoms. In accounting for the properties of the atom it is justified to speak of individual electrons and even in first approximation characterize the state of atom in ascribing to each electron separately in definite type of binding expressed by quantum numbers referring to the stationary states of a particle bound in a given field of force, determined by the charge on the nuclear charge and the average electronic dencity distribution. As regards the properties of the nucleus we can surely in forst approximation account for its mass by considering it as built up of separate units of masses equal to that of the neutron, but already as regards the unclear [sic] charge we meet with a new aspect of the atomicity of electricity, which cannot simply be accounted for by saying that the nucleus contains a certain number of positions with properties of the kind we know from ordinary electron theory. Also the attempt to consider the neutron and the proton as ultimate constituents of the nucleus would seem arbitrary in the sense that the behaviour of these particles in the nucleus cannot be predicted from properties ascribed to the single particles. Our only source of Information is indeed the study of the nuclear reactions and transmutations of the nucleus in collision with other nuclei or neutrons. Especially the discoveries of the great effectivity of neutrons in producing nuclear transmutations has brought a number of features to light which can hardly be reconciled with the attempts hithers made of constructing models of the nucleus on similar lines as those which have shown themselves so fruitful in accounting for the properties of atoms. Not only the great protons and aparticles by neutron impacts but above all readiness by which neutrons attack themselves to the nucleus in such impacts cannot be reconciled with the view that the neutrons, which penetrate into the nucleus moves in a seperate arbit in the field of the other nuclear particles in a similar way as is assumed for each of the particles in the shell type of nuclear models. already in the early researches of Fermi and his collaboraters on nuclear transmutations by high speed neutrons, it was found that the effective crossections for captures was in several cases found to be of the same order of magnitude of the crossections by which charged particles are expelled. This is much unexpected since in the former case in contrust to the latter, where energy balance is secured by the kinetic energy of hte expelled particles the binding energy has to be cemitted as electromagnetic radiation which in ordinary twobody collisions is generally most improbable. These captures can therefor hardly be explained unless we assume that the kinetic energy of the penetrating neutron is at once shared amond the individual heavy nuclear particles and that
MS,
2
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CIS, p. 3
no particle, charged or uncharged, has sufficient energy to leave the nucleus before, as a consequence of the continuors energy exchange, it happens that a particle finds itself on the surface of the nucleus with sufficient energy to escape. with the great probability of neutrons captures in comparison with neutron scattering observed in such processes. In this threatment the behaviour of the neutron within the nucleus is namely described by a seperate orbit or more accurately wave function, while it would seem that the great probabilityradiative processes can only be explained if the state of the combined system of nucleus and neutron is treated essentially as a manybody problem on the lines of quantum mecanicscorresponding to an ordinary continualexchange of energy between all the nuclear particles. Such a treatment would of couse be very complicatedin detail, but it should be possible in this case just as in the case of high speed nuclear impacts to draw conclusions as regards the duration of the encounter from the impirical data regarding the transition probabilityfor c-ray emission, which gives the lifeelectrostatic energy liberated by such an expulsion. the essential point however is that from the great output of a-particles by neutron impacts on certain nuclei, we can on this view not draw any conclusion as regarding the existence of a-particles in the normal nuclear state. A problem of exstreme interest is afforded by the more recent discovery exstraordinary pacility with which low speed neutrons in certain cases attack themselves to nuclei. Indeed in several cases crossections for such collisions have been found, which exceed the ordinary nuclear crossections by a factor of several thousands. This must of course be explained by a peculiar quantummachanical resonance effect arising from an approximate coinfidence of the total energy of the nucleus and the neutron before the collision with some stationary state of the system formed by a more or less stable combination of the two particles. The very interesting treatment of such resonance effects, given by Bethe, would, however, not seem reconcilable. This would indeed mean, that such an encounterbetween neutron and nucleus has sufficient duration to permit a competition between mechanical and radiation processes to take place. Of course in the closer account of any such processes it is necessary essentially to take the requirements of quantum mechanics into account, which secure us that the nucleus after an encounter finds itself in same stationary state, just as before. the greater the time till energy of the impringing neutron is the more adequate will a simple mechanical consideration be to describe the essential features of the encounter, and if the picture is essentially correct we shall especially expect that the collision will lead to the expulsion of several particles in sted of one as hitherto observed, because it will from simple mechanical arguments clearly be more likely that the superfluos energy in sted of being concentrated on one particle in such a case will be devided among several. The whole process is of course most complicated and
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the preference for the ejection of charged particles by nuclear impacts must naturally be explained by the potential for excited nuclear states of the order of magnitude of l o - * sec. The object of these remarks is, however, primarily emphasize to the essential difference between the problems of atomic and nuclear constitutions, which, in spite of the great success especilly obtained by Gamow of appliation of quantum mechamnics to the general problems of radioactivity-leaves the latter in a situation where rapidly increasing experimental evidence cannot be comprehended by present simple models of nuclear constitution.
MS, P . 4
X. PROPERTIES AND CONSTITUTION OF ATOMIC NUCLEI OM ATOMKERNERNES EGENSKABER OG OPBYGNING Overs. Dan. Vidensk. Selsk. Virks. Juni, 1935 - Maj 1936, p . 39 PROPERTIES AND CONSTITUTION OF ATOMIC NUCLEI Nature 138 (1936) 695 Commuriication to the Royal Danish Academy on 24 January 1936 ABSTRACT
See Introduction, sect. 2, ref. 23.
NIELS BOHR gav e n Meddelelse: O m Atomkeriieriies Egenskaber og Opbygning. De sidste Aars betydningsfulde Opdagelser vedrsrende Atornkernernes Onidannelser liar navnlig belaert 0 s om Kernernes overordentlige Tilbojelighed ti1 at reagere nied liinanden, saa snart d e bringes i indbyrdes Hersring. I Foredraget vil blive vist, hvorledes denne Ornstaendighed kan bringes i nojeste Forbindelse rned Atornkernernes almindelige Egenskaber og ikke rnindst belyser den ejendommelige Forskel mellem ssedvanlige Atomsysterners og selve Atornkernernes Opbygning. Vil blive trykt i Math.-fys. Medd.
Copenhagen Royal Danish Academy of Sciences and Letters, January 24.
NIELS BOHR: Properties and constitution of atomic nuclei. The fundamental discoveries of recent years regarding the transmutation of atomic nuclei, have exhibited the extraordinary facility with which nuclei react, with each other as soon as direct contact is established. This circumstance may be brought into intimate connexion with the general properties of nuclei, when it discloses a characteristic difference between the problems of the ordinary atomic constitution and the structure of nuclei.
XI. NEUTRON CAPTURE AND NUCLEAR CONSTITUTION [ 11 Nature 137 (1936) 344-348 Communication t o the Royal Danish Academy on 24 January 1936
See Introduction, sect. 2, ref. 24.
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FEBRUARY29,
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Neutron Capture and Nuclear Constitution* By Prof, Niels Bohr, F0r.Mem.R.S. MONG the properties of atomic nuclei disA closed by the fundamental researches of Lord Rutherford and his followers on artificial
offering a direct course of information about the mechanism of collision between the neutron and the nucleus. Indeed, the remarkable sharpness of nuclear transmutations, one of the most striking the lines of the characteristic y-ray spectra of is the extraordinary tendency of such nuclei to radioactive elements proves that the lifetime of react with each other as soon as direct contact is the excited nuclear states involved in the emission established. I n fact, almost any type of nuclear of such spectra is very much longer than the reactions consistent with energy conservation periods, circa 10-20 sec., of these lines themselves. I n seems likely to occur in close nuclear collisions. order that the probability of emission of a similar I n collisions between charged particles and nuclei, radiation during a collision between a high-speed contact is, of course, often prevented or made less neutron and a niicleus shall be large enough to probable k)y the mutual electric repulsion ; and account for the experimental cross-sections for the typical features of nuclear reactions are there- these capture processes, it is therefore clear that fore perhaps most clearly shown by neutron the duration of the encounter must be extremely impacts. Already in his original work on the pro- long compared with the time interval, circa perties of high-speed neutrons Chadwick recognised sec., which the neutron would use in simply their great effectiveness in producing nuclear passing through a space region of nuclear dimentransmutations1. Especially after the discovery sions. of artificial radioactivity by Mme and M. JoliotThe phenomena of neutron capture thus force Curie, most instructive evidence regarding nuclear us to assume that a collision between a high-speed reactions has been obtained through the researches neutron and a heavy nucleus will in the first place of Fermi and his collaborators on radioactivity result in the formation of a compound system of produced by bombardment with high-speed neu- remarkable stability. The possible later breaking trons as well as with neutrons of thermal velocities2. up of this intermediate system by the ejection of A typical result of the experiments with high- a material particle, or its passing with emission speed neutrons is the great probability that a of radiation t o a final stable state, must in fact collision with a nucleus of not too large atomic be considered as separate competing processes number will give rise to the ejection of an u-ray which have no immediate connexion with the or a proton, accompanied by the capture of the first stage of the encounter. We have here to do neutron and the formation of a nucleus of a new with an essential difference previously not clearly element which in general will possess P-ray radio- recognised between proper nuclear reactions and activity. The effective nuclear cross-sections for ordinary collisions among fast particles and collisions with such effects are in fact of the same atomic systems, which have been our main order of magnitude as the cross-sections responsible sourcc of information about the structure of for simple scattering of high-sped neutrons by the atom. I n fact, the possibility of counting nuclei, which in turn agree with ordinary estimates by means of such collisions the individual of nuclear dimensions. Another typical experi- atomic particles and of studying their promental result is the surprisingly great tendency perties is due above all to the openness of the even for a fast neutron in collision with a heavy systems concerned, which makes an energy exatom to attach itself to the nucleus with the change between the separate constituent particles emission of y-radiation and the formation of a new during the encounter very unlikely. I n view of isotope which may be stable or radioactive accord- the close packing of the particles in nuclei we ing to the circumstances. I n fact, for processes of must be prepared, however, for just such energy this kind cross-sections are found which although changes t o play a predominant part in typical several times smaller are still of the same order of nuclear reactions. magnitude as nuclear dimensions. If, for example, we consider an encounter Capture processes of high-speed neutrons of the between a high-speed neutron and a nucleus, it is last mentioned type are especially significant in obviously not permissible t o compare the process t o a simple deflection of the path of the neutron * Address dellwred on January 2; bcfore the Copenhagen Acadrmy in the inner nuclear field, possibly combined with (Kgl, Dsnske Vidensk. Selskab.).
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a collision with a separate nuclear particle, resulting in the ejection of the latter. On the contrary, we must realise that the excess energy of the incident neutron will be rapidly divided among all the nuclear particles with the result that for some time afterwards no single particle will possess sufficient kinetic energy t o leave the nucleus. The possible subsequent liberation of a proton or an or-particle or even the escape of a neutron from the intermediate compound system will therefore imply a complicated process in which the energy happens t o be again concentrated on some particle a t the surface of the nucleus. -4t the moment it is scarcely possible t o form a detailed picture of such processes. I n fact, we n u s t recognise that we have no justification even for assuming the existence within nuclei of the particles set free in nuclear disintegrations. I n pnrticular, the well-known difficulties of attributing within a space region of nuclear dimensions an individual existence to charged particles with so small a rest mass as have electrons and positrons, forces us to consider @-raydisintegration as a process by which an electron is created as an entity in a mechanical senses. I n this respect the situation is, of course, essentially different for the heavier particles emitted in nuclear disintegrations, like neutrons, protons and a-rays. Especially the fact that all nuclear maBses in the first approximation are integral multiples of a unit nearly equal t o the neutron mass, makes it very reasonable t o regard particles of such inasses as mechanical entities within nuclei. On account of the small difference between the masses of the neutron and the proton compared with the binding energies in nuclei measured by their so-called mass defect, it would, however, seem more hypothetical to assume the existence in nuclei of particles with the same electric and magnetic properties as those possessed by free neutrons m d protons. I n view of the scarcity of our knowledge of the extraordinary dense state of matter with which we have to do in nuclei, we may ritther regard the integral values of unit electric vharge possessed by nuclei and their disintegration products as a fundamental aspect of the atomicity of electrification, which cannot be accounted for k)y present theories of atomic constitution. Quite apart from the problem of the nature of the nuclear constituents themselves, which is not of direct importance for the present discussion, it is, a t any rate, clear that the nuclear models hitherto treated in detail are unsuited t o account for the typical properties of nuclei for which, as we have seen, energy exchanges between the individual nuclear particles is a decisive factor. In fact, in these models it is, for the sake of simplicity, assumed that the state of motion of each particle
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in the nucleus can, in the first approximation, be treated as taking place in a conservative field of force, and can therefore be characterised by quantum numbers in a similar way to the motion of an electron in an ordinary atom. I n the atom and in the nucleus we have indeed t o do with two extreme cases of mechanical many-body problems for which a procedure of approximation resting on a combination of one-body problems, so effective in the former case, loses any validity in the latter where we, from the very beginning, have to do with essential collective aspects of the interplay between the constituent particles. I n this connexion it is of importance to remember also that the successful quantum mechanical explanation of the simple law combining the lifetime of or-ray products with the energy of the emitted particles, is essentially independent of any special assumption regarding the behaviour of the individual particles in the nucleus. I n fact, on account of the extremely long lifetime of these products compared with all proper nuclear periods, the probability of such disintegration depends in the first approximation only upon the electric field outside the nucleus, which constitutes a so-called potential barrier hindering the escape of the a-rays. It is even very doubtful t h a t a-particles exist in nuclei in the manner assumed in present theories of a-ray decay. Indeed, the frequent appearance of a-rays as a result of natural and artificial nuclear disintegrations may rather be explained by the fact that energy is set free by the very formation of r-particles, and that the liberation of such particles might thus involve a smaller degree of concentration of the excess energy than the liberation of protons or neutrons. So far, the study of the a-ray disintegrations and their intimate connexion with the y-ray spectra, especially cleared up by Gamow, gives us, therefore, information only about the possible values of the energy and to a certain extent of the spin momenta for the stationary states of the nuclear syst,enis concerned. The circumstance that the nuclear states involved in the last mentioned phenomena are found to represent a discrete distribution of very sharp energy levels might perhaps a t first sight seem t o contrast with our assumptions of the existence of a semi-stable intermediate state of the compound system formed by neutron collisions within an apparently continuous range of the kinetic energy of the incident neutron. We must realise, however, that in the impacts of high-speed neutrons we have t o do with an excitation of the compound system far greater than the excitation of ordinary y-ray levels. While the latter at most amounts to a few million volts, the excitation in the former case will considerably exceed the energy necessary
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for the complete removal of a neutron from the normal state of the nucleus. The measurements by Aston of the mass differences of isotopes show that this energy is about ten million volt's. This st'riking difference in the level schemes for low and high excitations of heavy nuclei is, however. just what we would expect according to the view of nuclear reactions here discussed. I n contrast to the usual view, where the excitatim is at'tributed to an elevated quant'um state of an indiridu3.1 part'icle in the nucleus, we must in fact assume that the excitation will correspond to some quantised collective type of motion of all the nuclear particales. On account of the rapid increase of the possibilities of combination of the proper frequencies of such motions for increasing values of the total energy of the nucleus, we should therefore expect that the distance between neighbouring levels would become very much smaller for t'he high excitat'ion concerned in neutron collisions than in the ordinary y-ray levels where we have probably to do with stat'es of collect'ive motions of t'he most simple types. Even for excitations where the levels a,re very close t'oget,her the probability of radiative transition will not, however, on this view be very iiiiich different from that in the lower y-ray states iuid illly material increase in the width of the levels will not arise, unt'il t'he probability of escape of ina,terial particles becomes comparable with t'he radiation probability, Kow, in experiments on high-speed neutron impacts on heavy nuclei, t'he effective croessect ion for scattering is normally several times larger than the cross-section for capture. Accordingly, we must conclude that in t'his case the probabilit'y of the escape of a neutron from the compound system is greater than the probabilit'y of radiative transitions and that the energy levels of the seniist'able stat'e are therefore somewhat broader t'han ordinary y-ray levels. This circuiiistmce, together with the rapidly decreasing nee between neighbouring levels in the energy region concerned, makes it indeed very likely that such levels will not here be separated at all, as is required for t'he explanat'ion of the apparent>ly non-selective character of the capture phenomena. For decreasing velocit'ies of the incident neutrons, however, escape of a neutron from the compnund system will rapidly become very improbable, corresponding to the decreasing probability of t>he necessary concentration of the excess energy of the system on a particular neutron. The sharpness of the levels of the intermediate &ate must therefore be expected t'o approach that of the y-ray levels, as soon as the kinetic energy of t'he free neutrons becomes small compared with t'he total excitation energy in this state.
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FEBRUARY 29, 1936
Most interesting support for these considerations is afforded by the remarkable phenomena of selective capture of neutrons of very small velocities, Working with neutrons of temperature velocity obtained by passing neutron beams through thick sheets of substances containing hydrogen, Fermi and his collaborators found, as is well known, values for the effective crosssections for neutron capture, which vary in a most capricious way from element to element. While for most elements these values were of the same order of magnitude or not much larger than ordinary nuclear cross-sections, values several thousand times larger were found in certain irregularly distributed elements or isotopes. These a t first sight most surprising effects must obviously be attributed to the fact that for such slow neutrons the de Broglie wave-length is very large compared with nuclear dimensions and t h a t , therefore, the simple ideas of path and collision, which can be applied a t any rate approximately to high-speed neutron impacts, here fail completely. Instructive attempts have also been made to explain the phenomenon of selective capture as tt quantum mechanical resonance phenomenon, due to the close coincidence hetween the energy of some almost stable stationary states of the neutron within the nucleus and the siim of the energies of the initial state of the nucleus and of the free iieutron4. These theories, in which the state of motion of the neutron within the nucleus is treated as that of a particle in a conservative field of force, have failed, however, to nccount for the fact that the cross-section for neutron scattering in all selective absorbing elements investigated is much smaller than the cross-section for capture. It is true that the large probability of reflection of the waves describing the behaviour of the neutron in the nncleus-arising from the fact that its wavelength here is very short comp tred with the ivavclength for the free motion of the iieutron-implies that the mean time interval which a neutron may be said to stay in a nucleus is very long compared with the time interval a high-speed neutron on such a model would take in passing through the nucleus. Still, even in the case of complete resonance, the probability of neutron cscaps is in this way found to be larger than the probability for emission of radiation. From the far more intimate interaction between the neutron and the nucleus, which the explanatioii of high-speed neutron capture demands, this remarkable absence of selective scattering of very slow neutrons is, however, just what we should expect for small excess energy, on account of the vanishing probability of neutron escape compared with that of radiative transition.
FEBRUARY29,
1936
NATURE
Moreover, experiments of Fermi and others5 during the last few months have revealed an extreme sensitiveness of the phenomena of selective neutron capture for small variations in the neutron velocity which necessitates a degree of resonance quite incompatible with the above-mentioned nuclear model. I n fact, by the filtration of lowspeed neutron beams through thin sheets of different selective absorbing elements great modifications in the cross-sections of selective capture were obtained, showing that the resonance is restricted to narrow neutron energy regions which are differently placed for different selective absorbers. By using for comparison the capture of neutrons in light elements resulting in the ejection of a-particles, where the selectivity is much less pronounced-and where therefore from general quantum mechanical arguments the probability of capture within the energy region concerned must be expected to be inversely proportional to the neutron velocity-it has even been possible to conclude that the energy region of resonance for certain selective absorbing elements is c o n k e d within a fraction of a volts. From this small breadth of the energy levels of the compound system formed by low-speed neutron capture, we arrive by a simple statistical consideration of the occurrence of selective capture among the heavier elements a t a n estimate of about ten volts for the distance between neighbouring energy levels for the excitation concerned in these phenomena. This is not only in full agreement with the conclusions about the close distribution of energy levels of highly excited nuclei to which we were led through the discussion of the non-selective capture of the high-speed neutrons ; but the extreme sharpness of the levels with which we are concerned in the phenomena of selective neutron capture offers also most interesting support for our primary assumption of the long lifetime of the intermediate state in neutron collisions. I n fact, the narrowness of the levels of the compound system proves in a striking way the extreme smallness of the probability of radiative transitions in nuclei and leads to an estimate for the duration of an encounter between a high-speed neutron and a nucleus as large as a million times the interval which the neutron would use in simply traversing the nucleus. The lack of selectivity in high-speed neutron impacts concerns strictly speaking only the probability of neutron capture by the nucleus and the ejection of a material particle from it. The detailed course of these phenomena will, however, depend in general essentially on the level system of the nucleus h a l l y formed. In fact after the collision process this system must be in some stationary state and if the kinetic energy of the
347
incident neutron is not very large the states between which there can be a choice will all be in the region of ordinary discrete y-ray levels, If then the kinetic energy of the neutrons impinging on a heavy nucleus is smaller thttn the lowest excited level of this nucleus, any neutron escaping from the compound system will necessarily possess the same energy as the incident neutron. In the case, however, of neutron impacts with higher energy there is obviously a certain probability that the nucleus may be left in a n excited state after the escape of a neutron with a correspondingly smaller energy. Actually, the probability of the process following such a course, which implies a smaller concentration of the excess energy of the compound system on the escaping neutron, may often be considerably greater than the probability of neutron escape without excitation. There seems, too, to be experimental evidence for the occurrence of nuclear excitation in neutron collisions, namely in the observation of energy loss of high-speed neutrons traversing substances of high atomic weight', where a direct transfer of translational energy between the neutrons and the nuclei would be expected to be negligibly small. As was mentioned earlier, collisions between high-speed neutrons and the nuclei of elements of small atomic number will in most cases result in the ejection of a n a-ray or a proton. We may conclude here also from the great cross-sections for collision of such effects, that the encounter leads in the first place to the formation of a semistable compound system with a continuous range of energy levels. Even though the lifetime of this system may be very much shorter than that of the y-ray states of heavy nuclei, we must still realise that the subsequent escape of a-rays or protons necessitates a separate concentration process for the excess energy and that in particular we cannot draw any decisive conclusion from these phenomena about the presence of such particles in nuclei under normal conditions. For example, the great probability of emission of a-rays compared with neutron escape from the compound system must, as already indicated, rather be explained by the comparatively small degree of energy concentration involved in the former process. As regards the emission of charged particles we must of course also take into account the repulsion from the rest of the nucleus and in particular the greater d i 5 culty experienced by a charged than by a n uncharged particle with the same final kinetic energy in passing the potential barrier round the nucleus. As has often been pointed out, the last circumstance offers a simple explanation not only of the rapid fall in the output of a-particles and protons as a result of high-speed neutron impacts for
NATURE increasing nuclear charge, but also of the decrease with increasing neutron energy of the ratio between the probabilities of ejection of these two differently charged kinds of particles. The probability of the nucleus being left after the ejection of such particles in the normal or in an excited state depends in each case on the distribution of the energy levels of the final system-which are in general more separated for light than for heavy nuclei-and also on the balanc- between, on one hand, the greater facility of faster particles than of slower ones in penetrating the potential barrier and, on the other hand, the greater demands for energy concentration in the former than in the latter case. Similar considerations will apply for the finer details of the ordinary u-ray disintegrations like the weak groups of long range a-particles and the fine structure of the stronger a-ray lines. In the case also of nuclear transmutation caused by the impact of charged particles as well as for the nuclear disintegration produced by y-rays, the formation of an intermediate semi-stable compound system seems decisive for the explanation of the great variety of the phenomena. Besides typical non-selective effects like the ejection of neutrons and protons by fast a-rays, we meet, as is well known, with pronounced resonance effects for slower a-ray impacts, as well as in the capture phenomena of artificially accelerated protons in light nuclei. On account of the very much shorter lifetime of the intermediate state in such cases the degree of resonance here obtained is, however, much smaller than for selective neutron capture by heavy nuclei. I n this connexion it is perhaps not out of place to note that expressions like a-ray levels or proton levels, such as are used in the ordinary discussion of these effects, based on the attribution of the excitation to a single nuclear particle, lose all meaning on the view of nuclear excitation adopted here. I n fact, the essential feature of nuclear reactions, whether incited by collision or by radiation, may be said to be a free competition between all the different possible processes of liberation of material particles and of radiative transitions, which can take place from the semi-stable intermediate state of the compound system. A detailed discussion from this point of view of the available empirical evidence regarding spontaneous and induced nuclear transmutations will be published shortly8 in collaboration with Mr. F. Kalckar, who has given me most valuable assistance in tracing the consequences of the general argument here developed. There we shall also discuss the limitation of this argument in the case of very light nuclei like the deuteron, where the distinction between the mechanism of the
FEBRUARY 29, 1936
storing of the energy in the nucleus and the mechanism of the liberation of particles, SO pronounced for the reactions of heavy nuclei, gradually loses its significance. Here, however, I should still like briefly to indicate what modifications in the preceding considerations are to be expected even for heavy nuclei should the energy of the intermediate system too far exceed that of its normal state. Even if we could experiment with neutrons or protons of energies of more than a hundred million volts, we should still expect that the excess energy of such particles, when they penetrate into a nucleus of not too small mass, would in the first place be divided among the nuclear particles with the result that a liberation of any of these would necessitate a subsequent energy concentration. Instead of the ordinary course of nuclear reactions we may, however, in such cases expect that in general not one but several charged or uncharged particles will eventually leave the nucleus as a’ result of the encounter. For still more violent impacts, with particles of energies of about a thousand million volts, we must even be prepared for the collision to lead to a n explosion of the whole nucleus. Not only are such energies, of course, a t present far beyond the reach of experiments, but it does not need to be stressed that such effects would scarcely bring us any nearer to the solution of the much discussed problem of releasing the nuclear energy for practical purposes. Indeed, the more our knowledge of nuclear reactions advances the remoter this goal seems t o become. I n concluding this address, I should just like to point out that even if the problem of nuclear constitution does lack the special simplicity in a mechanical respect characteristic of the structure of the atom which has so much facilitated the disentanglement of the relationships of the elements as regards their ordinary physical and chemical properties, it presents, nevertheless, as I have tried to show, peculiar facilities for a comprehensive interpretation of the characteristic properties of nuclei in allowing a division of nuclear reactions into well separated stages to an extent which has no simple parallel in the mechanical behaviour of atoms. J. Chadwick, Proc. Roy. Soc., A, 142, l(1933). * E. F e d , and others, PTOC.Roy. Soe., A, 146,483 (1934); 149, 622 (1935). a Cf.. N. Bohr:‘Faraday Lecture,,J. Chem. Soc., 349 (1932), and W. Heisenberg, Zeeman Verhandehngen”, p. 108. 4 Fermi, and others, Proc. Roy. SOC.,A, 149,622 (1935). Perrin and Elsasser, J . Phys., 6 , 195 (1935). BBthe, Phy.3. Rev., 47, 747 (1936). Fermi and Amaldi, La Ricercio Seientifica, A, 6 , 544 (1935) Szilard, NATURE,136. $49 (1935). Frisch, Hevesy and McKad NATURE,137, 149 (1936). ‘R.Frisch and Q. Placzek, NATURE, 137, 367 (1936). 7 W. Ehrenberg, NATURE,136, 870 (1935) 1 N . Bohr and F. Kalckar, Kgl. Dan. Vid. Selsk. Math-fya. Medd. (in preparation).
XII. NEUTRON CAPTURE AND NUCLEAR CONSTITUTION [2] Nature 137 (1936) 351 Lecture to the Chemical and Physical Society of University College, London, on 11 February 1936
REPORT
See Introduction, sect. 2, ref. 38.
FEBRUARY29,
1936
NATURE
35 1
News and V i e w s Neutron Capture and Nuclear Constitution THE new views of nuclear structure and the processes involved in neutron capture, presented by Prof. Niels Bohr in a n address which appears elsewhere in this issue, were expounded b y him in a lecture to the Chemical and Physical Society of University College, London, on February 11 and were illustrated by two pictures here reproduced. The first of these is intended to convey a n idea of events arising out of a collision between a neutron and the nucleus. Imagine a shallow basin with a number of billiard balls in it as shown in the accompanying figure. If the basin were empty, then upon striking a ball from the outside, it would go down one slope and pass out on the opposite side with its original velocity. But with other balls in the basin, there would not be a free passage of this kind. The struck ball would divide its energy first with one of the balls in the basin, these two would similarly
to the views developed in Prof. Bohr’s address, the levels will for increasing excitation rapidly become closer to one another andwil1,for anexcitation of about 15 million electron volts, corresponding to a collision between a nucleus and a high-speed neutron, be continuously distributed, whereas in the region of small excess energy of about 10 million volts excitation they will still be sharply separated. This is illustrated by the two lenses of high magnification placed over the level-diagram in the two abovementioned regions. The dotted line in the middle of the field of the lower magnifying glass represents zero excess energy, and the fact that one of the levels
FIQ. 1.
share their energies with others, and so on until the original kinetic energy was divided among all the balls. I f the basin and the balls are regarded as perfectly smooth and elastic, the collisions would continue until the kinetic energy happens again to be concentrated upon a ball close to the edge. This ball would then escape from the basin and the remainder of the balls would be left with insufficient total energy for any of them to climb the slope. The picture illustrates, therefore, “that the excess energy of the incident neutron will‘be rapidly divided among all the nuclear particles with the result that for some time afterwards no single particle will possess sufficient kinetic energy to leave the nucleus”. Nuclear Energy Levels THE second figure illustrates the character of the distribution of energy levels for a nucleus of not too small atomic weight. The lowest lines represent the levels with a n excitation of the same order of magnitude as ordinary excited y-ray states. According
FIQ. 2.
is very close to this line (about 3 volt distant) corresponds to the possibility of selective capture for very slow neutrons. The average distance between the neighbouring levels will in this energy region be about ten volts as estimated from the statistics for the occurrence of selective capture. The diagram shows no upper limit to the levels, and these actually extend to very high energy values. If i t were possible to experiment with neutrons or protons of energies above a hundred million volts, several charged or uncharged particles would eventually leave the nucleus as a result of the encounter ; and, adds Prof. Bohr, “with particles of energies of about a thousand million volts, we must even be prepared for the collision to lead to an explosion of the whole nucleus”.
XIII. PROPERTIES OF ATOMIC NUCLEI ATOMKERNERNES EGENSKABER Nordiska (19. skandinaviska) naturforskarmotet i Helsingfors den 11-15 augusti 1936, Helsinki-Helsingfors 1936, pp. 73-81
Address to the Nordic Scientists’ Meeting in Helsinki/Helsingfors given on 12 August 1936 TEXT AND TRANSLATION
See Introduction, sect. 3, ref. 67
P A R T I: P A P E R S A N D MANUSCRIPTS RELATING T O N U C L E A R PHYSICS
This lecture was also published in Fysisk Tidsskrift 34 (1936) 186-194. Apart from correcting a misprint (“the sulphur isotope ;is’’ - conference proceedings, p. 76), Bohr only introduced minor linguistic improvements.
Pohjoismainen (19. skandinaavinen) luonnontutkijain kokous Helsingissa 1936. Nordiska (19. skandinaviska) naturforskarmotet i Helsingfors 1936. Eripaiiios. - SZrtryck.
ATOMKERNERNES EGENSKABER
AV
NIELS BOHR
HELSINKI - HELSINGFORS 1936
This Page Intentionally Left Blank
Professor WIELS BOHR,Kabenhavn:
Atomkernernes Egenskaber. Foredraget indlededes rned en kort Orntale af den Udvikling i Fysiken, der har f m t tii Kendskabet ti1 Atornernes Byggestene, og som tog sin Begyndelse ved Elektronernes Opdagelse ornkring Aarhundredeskiftet og fandt en forelubig ilfslutning ved Lord RUTHERFORDS Opdagelse i 1911 af, a t ethvert Atom indeholder en positivt ladet Kerne af overordentlig srnaa Dirnensioner, hvori Starstedelen af Atomets Masse er koncentreret, og hvorom de rneget lettere negativt ladede Elektroner grupperer sig. Dette simple Billede af Atoniet gjorde det muligt a t skelne skarpt inellem de Egenskaber hos Stofferne, der skyldes Atornkernens indre Bygning, og de der har deres Oprindelse i det ydre Elektronsystems Struktur. hfedens vi ved de szdvanlige fysiske og kemiske Egenskaber ved Stofferne liar a t g0re med Wndringer i det ydre Elektronsystern, skyldes de radioaktive Fznornener hos visse Grundstoffer Processer i Sedenstaaende er en Satnnieniattiing af 1n:iholdet 31 Foredraget, der LIev holdt i nere fri Form rned Benytttlse af e t stort Antal Lysbilleder.
74
selve Atomkernen. Den omtrent samtidige Opdagelse af Isotopernes Eksistens understregede yderligere Forskellen mellem disse t o Grupper af Egenskaber, idet man fandt Grundstoffer, der med iervrigt identiske fysiske og kemiske Egenskaber havde forskellige Atomvagte og ofte tilmed forskellige radioaktive Egenskaber. Det omtaltes dernast, hvorledes den ejendommelige Modsatning mellem Atomernes Stabilitet og sadvanlige mekaniske Modellers Egenskaber har opnaaet en Forklaring gennem Opdagelsen af det PLAxCKske T'irkningskvantum. Medens de T'irkninger, der indgaar i Beskrivelsen af Modeller i sadvanlig Maalestok, er saa store, a t man ganske kan se bort fra Virkningskvantets Eksistens, galder dette ikke mere for Atomerne, hvorfor vi her finder helt nye Lovmaessigheder. Saaledes har det vist sig, a t enhver .endring i e t Atoms Tilstand kan beskrives som en individuel Proces, hvorved Atomet fsres fra en af de saakaldte stationaere Tilstande ti1 en anden af disse, og navnlig har det vzret muligt i vid Udstrakning a t gsre Rede for de optiske Spektres og Rsntgenspektrenes Lovmassigheder ved a t antage, a t Udsendelsen af enhver af Linierne i disse Spektre skyldes en saadan Overgangsproces, hvorved e t Lyskvantum udsendes. De ferlgende Aars gradvise matematiske Trdformning af disse Forestillinger fgrtes ti1 en forelsbig Afslutning gennem Skabelsen af en rationel Kvantemekanik, der fremtrader som en konsekvent Almindeliggerrelse af den klassiske Mekanik. Den Erkendelse, a t enhver med Virkningskvantets Eksistens forenelig Maaleproces medforer en ukontrollerbar Vekselvirkning mellem Maaleobjekt og Maaleinstrument, har endvidere bragt en dybtgaaende Revision af hele Iagttagelsesproblemet med sig, der har f s r t ti1 en fuldstzndig Opklaring af de tilsyneladende Paradoxer, som indeholdes i Kvantemekanikkens principielt statistiske Beskrivelsesmaade. Trods alle disse nye T r a k bevarer imidlertid Problemet om Atombygningen en overordentlig Simpelhed, der ferrst og fremmest skyldes Elektronsystemets aabne Struktur, soin betinger, a t de enkelte Elektroners Bindinger i ferrste Tilnarmelse kan beskrives uafhangigt af hverandre ved H j a l p af en Systematik, der i alle Enkeltheder gOr Rede for Lovmassighederne i Grundstoffernes periodiske System. Ved Problemet om Atonikernernes Opbygning og Egenskaber stilles man derimod paa Grund af den t a t t e Sammenpakning af Partikler i Kernerne overfor en helt ny Situation, hvor man maa vente a t msde vasentlig andre Lovmassigheder end de, der g d d e r for Elektronbindingen i Atomet. Gennem de senere Aars store eksperimentelle Opdagelser indenfor Kernefysiken er imidlertid fremskaffet e t righoldigt Materiale, der allerede paa nuvzrende Tidspunkt aabner Muligheder for en sammenhangende Beskrivelse af Atomkernernes Egenskaber.
75
Grundlaget for hele denne Udvikling skabtes ved det berermte, af RUTHERi 1919 foretagne fsrste Kernespr~engningsforserg,hvor det lykkedes ved Beskydning af Kvalstofatomer med a-Partikler a t udslynge Protoner. Processen kan skrives: FORD
14X 7
+ 4 He-+'JO +
H,
hvor Tallene foroven og forneden angiver hendoldsvis Atonivzgten og Kerneladningen. Dette banebrydende Arbejde efterfulgtes snart af en he1 R a k k e Forserg over Kerneomdannelser, hvor det naste afgerrende Fremskridt bestod i, a t man ti1 Beskydningen af Stofferne ikke som hidtil anvendte de naturligt forekommende a-Straaler, men derimod kunstigt accellererede Protoner. Saaledes lykkedes det COCKROFTog WALTOX i I932 ved Bombardement af Lithium a t sernderdele dette i t o a-Partikler efter Skemaet:
Denne Proces var szrlig interessant, fordi de Protoner, der anvendtes ved Beskydningen, havde en saa ringe Energi, at de ikke efter klassisk-fysiske Forestillinger vilde viere i Stand ti1 a t overvinde den elektrostatiske Frasterdning, som indtil ineget smaa Afstande virker mellem Kernerne. At en saaden Reaktion dog efter Kvanteteorien har en vis Sandsynlighed, var imidlertid allerede tidligere paavist af GAMOW i Forbindelse med hans smukke kvanteteoretiske Forklaring af Lovene for Udsendelse af a-Partikler fra radioaktive Stoffer, hvor det netop drejer sig om en lignende Gennemgang af Partikler gennem Omraader, hvor de iferlge den klassiske Fysik ikke har Mulighed for a t kornnie. Endelig udmarker den omhandlede Proces sig derved, a t man her i alle Enkeltheder kunde gerre Rede for den ved Reaktionen frigjorte kinetiske Energi (ca. 16 Mill. Volt) ved Hjaelp af EINSTEINS Relation for Wquivalens mellem Masse og Energi, idet alle de i Processen optmdende Partiklers Masser var meget nsjagtigt kendt fra ASTOSS massespektroskopiske Maalinger. Vort Kendskab ti1 Atomkernerne er endvidere i overordentlig Grad blevet beriget gennem CHADWICKSOpdagelse i I932 af den saakaldte Neutron, en neural Partikel nied meget n a r samme Masse son1 Protonen, og som fsrst blev iagttaget ved Beskydning af Beryllium med a-Partikler. Reaktionen kan her skrives:
Be
+- 4 He-+':
C $-
Denne Xeutron kunde, som man snart fandt, opstaa ved mange forskellige Kerneprocesser, hvorfor det var naturligt, som navnlig fremhzvet af HEISES-
BERG, a t betragte den som en fundamental Byggesten i alle Kerner. Herefter skulde enhver Atomkerne kun indeholde Protoner og Neutroner, hvis samlede Antal svarer ti1 Atomvzgten, medens Protonantallet er lig med Kerneladningen. Efter denne Opfattelse, hvorved man undgaar de Vanskeligheder, som det efter Kvanteteorien medferrer a t antage Eksistensen af Elektroner i selve Kernen, er de ved b-Straaleomdannelse udsendte Elektroner a t betragte som skabte ved selve Omdannelsesprocessen i lignende Forstand som Lyskvanterne skabes ved Overgange mellem et Atomsystems stationme Tilstande. E n helt ny Epoke indenfor Kernefysiken indlededes allerede Aaret efter ved Wgteparret CURIE-JOLIOTS Opdagelse af, a t visse af de ved Beskydning med a-Partikler dannede nye Grundstofisotoper var ,&Straale-radioaktive, idet de med en vis Periode omdannedes under Udsendelse af enten sedvanlige negative eller i visse Tilfdde positive Elektroner. Disse saakaldte Positroner er a t betragte som en ny Elementarpartikel, hvis Eksistens var forudsagt af DIRACS relativistiske Elektronteori, og som kort forinden var opdaget af ANDERSON og BLACKETT ved Undersergelser over de ved kosmiske Straaler frembragte Sekundzereffekter. Det ferrste Eksempel paa F'rembringelsen af denne saakaldte kunstige Radioaktivitet var den ferlgende Reaktion:
:z
hvorved der under Neutronudsendelsen dannes en radioaktiv Fosforisotop P, der atter med en Halveringstid pan. 3 Minutter omdannes ti1 en Siliciumisotop
30Si under samtidig Udsendelse af en Positron. 14
Navnlig efter FERMISPaavisning af Neutronernes store Evne ti1 ved Sainmensterd med Atomkerner a t frembringe Onidannelser af disse har vi i de allersidste Aar laert et overordentlig stort Antal nye radioaktive Isotoper a t kende. Denne Evne hidrerrer derfra, a t Neutroner paa Grund af deres manglende Ladning ikke kan ionisere og ferlgelig ikke p a samnie Maade soni a-Straaler niiste Energi ved a t passere Stof, nien kun ved Saniniensterd nied Atonikerner, i hvilke de endvidere kan trznge ind chindret af det Kernen omgivende elektriske Felt. Som Eksenipel paa en Kerneonidarinelse nied Neutroner kan anfares: 32 16
S
+ Ln-t
::P +
H,
hvor den dannede Fosforisotop er radioaktiv og omdannes ti1 Svovlisotopen
93 S under Udsendelse af negative Elektroner med en Halveringstid paa ca.
14 Dage. Netop denne usacdvanlig lange Halveringstid har muliggjort en
77
k e k k e vigtige Underswgelser over Posforonisztningen ved kemiske og biologiske Processer ved Hj z l p af den af HEVESY udviklede radioaktive Indikatornietode, der netop ved Opdagelsen af den kunstige Radioaktivitet har faaet et saa overordentlig udvidet og betydningsfuldt Xnvendelsesomraade. Medens alle de hidtil nzttvnte Kernereaktioner er ledsaget af Udsendelsen af niaterielle Partikler, har man genneni FERMIS og h a m Medarhejderes Underbogelser tillige l w t en smlig Cruppe Xeutronreaktioner a t kende, hvor den indfaldende Neutron sinipeltheri indfanges af Atomkernen under 'I'dsendelse af den overskydende Xnergi i Form af elektroniagiietisk Straaling (y-Straalei). Ht t? piik IIksempel er Processen:
hx-or den dannede radioaktive nye Jodisotop har en Halveringstid paa zG Minutter. Ti1 Processer af denne Art knytter der sig den saxlige Interesse, a t de giver 0 s e t nyt Indblik i Nekanisnien ved Kernereaktionerne. Fra en nzrniere Underssgelse af de radioaktive Stoffers y-Straalespektre kan nian nenilig slutte, a t den Tid, en anslaaet Xtonikerne bruger ti1 a t udsende elektromagnetisk Straaling, er nieget lang i Forhold ti1 det 'I'idsruni, en Neutron vilde hrunge on; sinipelthen a t passere igenneni en Xtomkerne. Det betyder, a t hvis der skal v z r e en rimelig Sandsynlighed for Indfangning af Neutronen, niaa dens Samnienstod nied den oprindelige Kerne fare ti1 Dannelsen af e t Melleniprodukt, der fsrst kan ssnderdeles efter forholdsvis lang Tids Forlsb. Dette hanger netop saninien rned den fsr n a v n t e store Tatthed af Partikler i Atomkernen, der niedforer, a t den indfaldende Neutrons Energi ojeblikkelig fordeles mellem samtlige Kernepartikler, saaledes a t ingen af disse faar Energi nok ti1 straks a t forlade Kernen. E n eventuel senere Bortgang af en af Partiklerne vil derfor fordre en tilfzldig Koncentration af Energien paa vedkommende Partikel, hvad der for en tung Kerne paa Grund af det store Antal Partikler i Almindelighed vil k m v e saa lang en Tid, a t der forinden er en betydelig Sandsynlighed for en Straalingsudsendelse. Dette Forhold blev i Foredraget illustreret ved et Lysbillede, der er gengivet i Fig. I , og son1 viser en cirkelforniet Fordybning i en Plade, hvori der befinder sig e t Antal Billardkugler. Hvis en Kugle udefra strirdes ind i Fordybningen, og der ingen andre Kugler befandt sig i denne, vilde Kuglen passere op over Randen paa den modsatte Side og gaa videre med sin oprindelige Hastighed. Paa Grund af de ovrige Kuglers Nmvzrelse vil iniidlertid den ankommende Kugle hurtigt dele sin Xnergi med de svrige Kugler, der forudsat gnidningslss Bevzgelse, under hyppige indbyrdes Saninienstod vil
hevage sig frem og tilbage i Ford! bningen, indtil tilfzldigvis en af deni, tler er i Kxrheden af Kanden,. son1 Folge af Samnienstodene modtager en tilstrzkkelig Energi ti1 a t slippe ud. Fir der selv en ringe Gnidning ti1 Stede nielleni Kuglerne og Pladen eller bIulighed for, a t Kuglens kinetiske Energi ved Saniniestod omsattes i T-arnie, er der derimcd en betydelig Sandsynlighed for, a t ingen af Kuglerne nogensinde slipper Lid af Fordybnirigen, ganske svarende ti1 en Indfangning af en Seutron i en Kerne a n d t r Udsendelse af Straaling . Den oiwordentiige Lethed, hx-ornierl Energi fordeler sig iiielleni Atonikernens enkelte Dele, hetinger en gennenigribende E'orskel nielleni selve
Fig.
I.
Atonikernernes Egenskaber og de Egenskaber hos Xtomet, der vzsentlig a f h m g e r af det ydre Elektronsystem, Dette afspejler sig fmst og fremmest i den meget forskellige Fordeling af Energixzrdirrne for de mulige Tilstande for Kernen og for Blektronsystemet. Medens i det sidste T i l f d d e enhver Xndring af ,4toniets Energi i Slmindelighed kan henfmes ti1 en Z n d r i n g af Rindingsforholdene for en enkelt Elektron, er Kernens Energivzrclier bestemte ved de niulige kollektil-e Bevzgelsesformer for alle Kernens Dele. I Fig. z er der givet en skeniatisk Oversigt over Fordelingen af de saakaldte Energiniveauer for en Kerne nied en Atonivagt onitrent soni Jodets. De laveste Niveauer svarer her ti1 de Tilstande, der er bestenimende for de radioaktive Stoffers y-Straalespektre og har en gennenisnitlig Afstand paa nogle Hundrede Tusinde Elektron Volt. Med voksende Anslagsenergi rykker h'iveauerne meget hurtigt tzettere samnien og lader sig ikke lzngere rent adskille, naar vi komnier op ti1 saadanne Energier, der svarer ti1 Mellenitil-
79
standen for Indfangningen af hurtige Neutroner. Anslagsenergien for disse Tilstande f'indes ved ti1 Keutroneris kinetiske Energi (nogle 3Iillioner T'olt) a t l q g e dens Bitidirigsenergi i Kerrien (ca. 9 Millioner T'olt), der hidrorer fra de s t a r k e Tiltrakningskrafter iiielleni Kernedelene i smaa ;lfstande. Paa E'iguren er den ointrentlige Beliggenhed af de paagzldende Niveauer angivet ved det overste Forstorrelsesglas, der illustrerer, a t Xiveauerne i dette Omraade ligger saa tat, a t de nappe kan skelnes fra hverandre, se!v oili Maalestokken for I:iguren var valgt 100,000 Gange stnrre. De uskarpc Linier, sorii man ser igenneni Classet, skal endvidere illustrere, a t Niveauerne i dette Oiiiraade ikke eiigang kan ventes a t v z r e skarpt adskilte paa Grund af den Fig. 2 . endelige Levetid af de paagaldende Tiistande, der vzsentlig betinges af hluligheder, for en Xeutrons Undslipning fra Kernen. For lavere Anslagsenergier vil Niveauerne v z r e skarpere, idet Tilstandens Levetid alene begrmses af Sandsynligheden for Straalingsprocesser. Dette er illtistreret ved det andet Forstmrelsesglas, der er anbragt saaledes, a t det dzkker over et Energiomraade, der svarer ti1 en Forening af en hvilende Neutron ined den oprindelige Kerne. Deiine Energivzrdi er angivet ved den punkterede Linie i Forstmrelsesglassets Felt, niedens de fuldt optrukne Linier skal antyde Beliggenheden af nogle nzrliggende Kerneniveauer.
80
Et overbevisende Vidnesbyrd om en saadan tzt Fordeling af skarpe Energiniveauer i dette Ornraade har man faaet igennem Undersragelser over Kerners Indfangning af Neutroner med Hastigheder svarende ti1 Brrakdele af en Elektron Volt. Saadanne langsornme Neutroner frembringes, soni FEKMI fmrst har paavist, naar szdvanlige hurtige Neutroner passerer genneni tykke Lag af Paraffin eller andre brintholdige Stoffer. Sorn F d g e af Sarnrnenstmdene ined de disse indeholdende Protoner vil nemlig Neutronerne efterhaanden fordele deres kinetiske Energi nied Protonerne, indtil Neutronerne befinder sig i alniindelig Varrneligevzgt med det Stof, hvorigennern de passerer. I Modsatning ti1 den store Lighed, sorn hurtige Neutroners Reaktioner nied Kerner med ikke altfor forskellige Atornvzgte udviser, har det vist sig, a t Virkningen af Samrnensterd niellem Neutroner med Ternperaturhastigheder og Atomkerner varierer paa den tilsyneladende mest lunefulde Maade, naar man gaar fra e t Grundstof ti1 e t andet. Medens de fleste Stoffer ikke viser nogen specifik Virkning overfor langsomnie Keutroner, har andre Stoffer en overordentlig Evne ti1 a t reagere rned disse. Vi har her a t gerre med et typisk kvantemekanisk Resonansfznomen, der niaa forventes a t optrade, naar Sumnien af den indfaldende Neutrons kinetiske Energi og den oprindelige Kernes Energi i Kormaltilstanden tilfzldigvis falder sanimen med en anslaaet Energitilstand af den Kerne, der vilde dannes ved Keutronens Indfangning. Disse Fznomener laerer os derfor direkte om Energiniveauernes Fordeling og deres Skarphed i det paagaldende Ornraade, og en nzrmere Undersergelse har vist, a t Niveauernes gennernsnitlige Afstand her er omtrent 10 Volt, niedens deres Rredde kun belerber sig ti1 en Brerkdel af en Volt, saaledes sorn det er antydet paa Figuren igenneni Billedet i det paagzldende Forstmrelsesglas. Selv om mange Kernereaktioner paa Grund af den staerke elektriske Frasterdning melleni ladede Partikler ofte frembyder mere indviklede Forhold end Sammenstpd mellem Neutroner og Kerner, har det vist sig a t viere e t for alle Kernereaktioner f d l e s T r a k , a t deres Forlab kan beskrives som foregaaende i t o adskilte Stadier, af hvilke det fmste er en forelrabig Sammensrnelten af de t o sammenst~dendePartikler ti1 et mere eller mindre stabilt Mellemprodukt, medens det sidste bestaar i dette hlelleniprodukts senere Smderdeling under Udsendelse af materielle Partikler eller i en Straalingsudsendelse, hvorved dets endelige Stabilitet sikres. Hvilket Resultat en Kernereaktion giver, er derfor bestemt saavel af Mellemproduktets mulige Energitilstande som af den relative Sandsynlighed for de forskellige Sranderdelings- og Straalingsprocesser, son1 disse Tilstande kan give Anledning til. Ti1 Trods for Kerneproblernernes sterrre Komplikation i rnekanisk Henseende
81
samnienlignet med de szdvanlige Atomproblemer, betyder netop denne Mulighed for en Opdeling af Kernereaktionerne i vel adskilte Stadier en for tlisse ejendominelig Simplifikation, der i h0j Grad letter Oversigten over det baa hastigt voksende experimentelle Materiale vedrmende Atoinkernernes Egenskaher .
Hclsingfors 1936 Finska Litteratursiillskapets T r \ ckeri Ab.
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
TRANSLATION Professor Niels Bohr; Copenhagen: Properties of Atomic Nuclei' The lecture was introduced by a brief review of the development in physics which led to the knowledge of the constituents of the atom, and which started with the discovery of the electron at the turn of the century, and found its temporary completion in Lord Rutherford's discovery in 191 1 that every atom contains a positive nucleus of extremely small dimensions, in which most of the atomic mass is concentrated, and around which the much lighter negatively charged electrons are distributed. This simple picture of the atom made it possible to distinguish clearly between those properties of materials which are due to the internal structure of the atomic nucleus, and those which have their origin in the structure of the outer system of electrons. Whereas the usual physical and chemical properties of materials are concerned with changes in the outer electron system, radioactive phenomena in certain elements are due to processes in the nucleus itself. The discovery of the existence of isotopes at about the same time further emphasised the difference between these two sets of properties, since there were elements with otherwise identical physical and chemical properties which had different atomic weights and often even different radioactive properties. It was then discussed how the peculiar contradiction between the stability of the atom and the behaviour of the usual mechanical models found its explanation in the discovery of Planck's quantum of action. Whereas the actions occurring in the description of models on the everyday scale are so large that one can disregard the existence of the quantum of action, this is no longer true for atoms, and we therefore find here quite new regularities. Thus it turned out that any change in the state of an atom can be described as an individual process, in which the atom passes from one of the so-called stationary states to another, and in particular it has been possible to account to a large extent for the regularities of optical and X-ray spectra by the assumption that the emission of any line in these spectra is due to such a transition, with the emission of a light quantum. In the following years the gradual mathematical formulation of these ideas was brought to a temporary completion by the creation of a rational quantum mechanics, which forms a consistent generalisation of classical mechanics. The realisation that any measurement which is consistent with the existence of the quantum of
'
This is a summary o f the contents of the lecture which was given more informally, with the aid of numerous slides.
P A R T 1: P A P E R S A N D M A N U S C R I P T S R E L A T I N G T O N U C L E A R P H Y S I C S
action is accompanied by an uncontrollable interaction between the measured object and the measuring apparatus, has also brought a fundamental revision of the entire problem of observations, which has led to a complete clarification of the apparent paradoxes contained in the quantum mechanical description, which is fundamentally statistical. However, in spite of all these new features the problem of atomic structure preserves an extraordinary simplicity, which is, above all, due to the open structure of the electron system, which leads to the result that the binding of each individual electron can, to a first approximation, be described independently of the others, with the help of a classification which accounts in all details for the regularities in the periodic system of elements. In the problem of the structure and properties of the nucleus, on the other hand, one faces an entirely new situation, because of the tight packing of particles in the nuclei, and one must expect to meet here essentially different regularities from those valid for the binding of electrons in the atom. In recent years great experimental discoveries in nuclear physics have however provided a wealth of material, which already at this time opens up the possibility of a consistent description of the properties of atomic nuclei. The foundation for this whole development was laid by Rutherford's famous first nuclear disintegration experiment in 1919, where he succeeded in expelling protons by bombarding nitrogen atoms with a-particles. The reaction can be written in the form:
where the upper and lower indices represent the atomic weight and the nuclear charge, respectively. This pioneering work was soon followed by a whole series of experiments on nuclear transmutations, and the next decisive step consisted in using for the bombardment of matter artificially accelerated protons, instead of the naturally occurring a-rays used previously. Thus Cockcrof t and Walton succeeded in 1932 in splitting lithium into two a-particles by proton bombardment according to the scheme: :Li
+
:H
+
$He
+
;He.
This reaction was particularly interesting because the protons used in the bombardment had such a low energy that, by the ideas of classical physics, they would not have been able to overcome the electrostatic repulsion which acts between nuclei down to very small distances. However, in quantum theory such a reaction has a finite probability, as was already shown earlier by Gamow in con-
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
nection with his beautiful quantum theoretical explanation of the emission of aparticles from radioactive substances, where one is concerned just with a similar transition of particles through regions which they could not reach according to classical physics. Finally, the process which we have mentioned was remarkable because one could here in full detail account for the kinetic energy released in the reaction (about 16 MeV) with the help of Einstein’s relation for the equivalence of mass and energy, since the masses of all particles participating in the reaction were very accurately known from Aston’s mass spectroscopic measurements. Our knowledge of the atomic nucleus was further enriched to an extraordinary degree by Chadwick’s discovery in 1932 of the so-called neutron, a neutral particle with very nearly the same mass as the proton, which was first observed in the bombardment of beryllium with a-particles. The reaction can here be written as: :Be
+
:He
+
‘62C
+ 6n
This neutron could, as was soon found, occur in many different nuclear reactions, and it was therefore natural to consider it as a basic constituent of all nuclei, as stressed especially by Heisenberg. Accordingly each nucleus should contain only protons and neutrons, with their total number representing the atomic weight, while the number of protons gives the nuclear charge. According to this view, with which one eliminates the difficulties arising in quantum theory from the assumption of the presence of electrons in the nucleus itself, the electrons emitted in &ray transformations have to be regarded as created in the transformation itself, just as light quanta are created in the transitions between stationary atomic states. An entirely new epoch in nuclear physics was introduced already a year later by the discovery by the Curie-Joliots of the fact that certain new isotopes created by a-particle bombardment were /3-radioactive, and transformed with a certain lifetime with the emission of ordinary negative electrons or, in some cases, positive ones. These so-called positrons have to be regarded as new elementary particles, whose existence was predicted by Dirac’s relativistic electron theory, and which had been discovered a short time previously by Anderson and BIackett in the study of the secondary effects caused by cosmic rays. The first example of the production of this so-called artificial radioactivity was the following reaction:
where the neutron emission leaves a radioactive isotope of phosphorus, ?!P,
PART I: PAPERS A N D MANUSCRlPTS RELATING TO NUCLEAR PHYSICS
which in turn transforms with a half-life of 3 minutes into a silicon isotope, %i, together with the emission of a positron. In particular after Fermi demonstrated the great power of neutrons to cause transmutations in their collisions with nuclei we have learned in the last few years of an extraordinarily large number of new radioactive isotopes. This power results from the fact that neutrons do not ionise because they have no charge, and therefore lose energy not in passing through matter, as d o cx-particles, but only in collisions with nuclei, into which they can penetrate without being prevented by the nuclear electric field. As an example of a nuclear transmutation with neutrons we can quote: 32 16s + 6n ?:P + !H, -+
where the resultant phosphorus isotope is radioactive and transforms into the sulphur isotope with the emission of a negative electron and with a half-life of about 14 days. Precisely this unusually long half-life has made possible a number of important investigations about the transfer of phosphorus in chemical and biological processes, using Hevesy's radioactive indicator method which the discovery of artificial radioactivity has provided with an extraordinarily expanded and meaningful field of application. Whereas all nuclear reactions so far mentioned involve the emission of material particles, the investigations of Fermi and his collaborators have also acquainted us with a particular group of neutron reactions in which the incident neutron is simply captured by the nucleus, with the emission of the excess energy in the form of electromagnetic radiation (y-rays). A typical example is the reaction : 127 531
+
6n
-+
':$I
+
y,
where the resultant new radioactive iodine isotope has a half-life of 26 minutes. Processes of this type are of particular interest, as they give us a new insight into the mechanism of nuclear reactions. Indeed one can conclude from a closer study of the y-ray spectra of radioactive substances that the time needed by an excited nucleus for emitting electromagnetic radiation is very long compared to the time a neutron would take to pass simply through an atomic nucleus. This means that, in order to have a reasonable probability for capture of the neutron, its collision with the original nucleus must lead to the formation of an intermediate product, which can disintegrate only after a relatively long time. This is connected with the above-mentioned great density of particles in the nucleus, as a result of which the energy of the incident neutron is immediately shared with all other nuclear particles, so that none of them have enough energy to escape from the nucleus at once. A possible later escape of one of the particles therefore requires an ac-
[175]
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
cidental concentration of energy on the particle concerned, and for a heavy nucleus this will, because of the large number of particles, generally require so long a time that meanwhile there is an appreciable probability for the emission of radiation. This situation was illustrated in the lecture by a slide, which is reproduced as fig. 1, and which shows a circular well in a board containing a number of billiard balls. If a ball was projected from outside into the well with no other balls in it, the ball would pass over the opposite rim and continue with its original speed. Because of the presence of the other balls the incident ball will rapidly share its energy with the others, which, assuming the motion frictionless, will move back and forth in the well with frequent mutual collisions, until by accident one of them near the edge acquires by the collisions enough energy to escape. If there is even a little friction between the balls and the board, or the possibility that the kinetic energy of the ball will be transformed into heat in the collisions, there will however be a strong probability that none of the balls will ever be able to get out of the well, in complete analogy to the capture of a neutron with the emission of radiation.
Fig. 1.
The extraordinary facility with which the energy gets shared between the individual particles in the nucleus implies a fundamental difference between the properties of the nucleus and the properties of the atom, which depend essentially on the outer electron system. This manifests itself above all in the very different distribution of energy values for the possible states of the nucleus and for the electron system. Whereas in the latter case any change in the energy of the atom can in general be attributed to a change in the quantum numbers of a single electron, the energy levels of the nucleus are determined by the possible forms
P A R T I : PAPERS A N D MANUSCRIPTS RELATING TO N U C L E A R PHYSICS
of collective motion of all its particles. Fig. 2 gives a schematic indication of the distribution of the so-called energy levels for a nucleus with an atomic weight similar to iodine. The lowest levels here correspond to the states which determine the y-spectra of radioactive substances, and have an average spacing of a few hundred thousand electron volts. With increasing excitation energy the levels rapidly accumulate more closely and can no longer be distinguished clearly when we come to those energies which correspond t o the intermediate state for the capture of a fast neutron. To find the excitation energy of these states we have to add t o the kinetic energy of the neutron (a few MeV) its binding energy in the nucleus (about 9 MeV), which results from the strong forces of attraction between nuclear particles at small distances. The figure shows the approximate position of the levels in question by the upper magnifying glass, which indicates that the levels in this region lie so close that they can hardly be separated from each other even on a scale increased 100 000 times. The diffuse lines seen through the glass are intended to illustrate further that the Fig. 2. levels in this region cannot even be expected to be sharply separated because of the finite lifetime of the relevant states, which is essentially due to the possibility of neutron escape from the nucleus. For lower excitation energy the levels become sharper, since the lifetime of the state is limited only by the probability for radiative processes. This is illustrated by the second magnifying glass, which is placed so as to cover the energy region corresponding to the addition of a neutron at rest to the original nucleus. This energy value is indicated by the
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
broken line in the field of the magnifying glass, whereas the full lines are meant to indicate the position of some nearby levels. Convincing evidence of such a dense distribution of sharp energy levels in this region has been obtained from the studies of the capture by nuclei of neutrons at speeds corresponding to a fraction of an electron volt. Such slow neutrons are produced, as was first shown by Fermi, when the usual fast neutrons pass through thick layers of paraffin or other substances containing hydrogen. This is because in the collisions with the protons contained in these, the neutrons will share their kinetic energy with the protons until the neutrons are in thermal equilibrium with the material through which they are passing. In contrast to the great similarity between the reactions of fast neutrons with nuclei of not too different atomic weight, it has turned out that the effect of collisions of neutrons at thermal velocities with nuclei varies in an apparently most capricious manner from one element to another. While most substances show no specific effect for slow neutrons, other substances have an extraordinary power for reacting with them. We are here concerned with a typical quantum-mechanical resonance phenomenon, which must be expected to occur when the sum of the kinetic energy of the incident neutron and the energy of the ground state of the original nucleus happens to coincide with an excited state of the nucleus formed by the capture of the neutron. These phenomena therefore provide direct information about the distribution of energy levels and their sharpness in the region in question, and more detailed research has shown that the average spacing between the levels is about 10 volts, whereas their width amounts to only a fraction of a volt as is indicated in the figure in the view through the appropriate magnifying glass. Although many nuclear reactions often present a more complicated behaviour than the collisions between neutrons and nuclei because of the strong electric repulsion between charged particles, it has been found as a common feature of all nuclear reactions that their course can be described as proceeding in two separate stages of which the first is a temporary fusion of the two colliding particles into a more or less stable intermediate product, whereas the second consists of a later disintegration of the intermediate product with the emission of material particles or in the emission of radiation, ensuring its final stability. The result of the nuclear reaction is therefore determined both by the possible states of the intermediate product, and by the relative probabilities of the various disintegration and radiative processes to which these states can give rise. In spite of the great complexity of the mechanical picture for nuclei, compared to the relevant atomic problems, just the possibility of dividing the nuclear reactions into well separated stages represents for these a peculiar simplification, which greatly facilitates the survey of the so rapidly growing experimental material concerning the properties of atomic nuclei.
XIV. SELECTIVE CAPTURE OF SLOW NEUTRONS UNPUBLISHED MANUSCRIPT [ 19361
See Introduction, sect. 3, ref. 57
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
This manuscript consists of 2 typewritten pages with corrections in ink in Bohr’s handwriting with an amendment in pencil in Kalckar’s handwriting. The manuscript is in English. There is a carbon copy of page 1 with corrections in Bohr’s and Kalckar’s handwritings (not included here). We have reproduced the main (corrected) text including the amendment. The manuscript is on microfilm Bohr MSS no. 14.
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Selective capture of slow neutrons. The fact that certain elements show extraordinary large cross sections for capture of slow neutrons is as [is] well known accounted for by the existence of a semistable stationary state of the compound system formed by the neutron and the nucleus of such elements and possessing an energy closely coinciding with the sum of the energies of the free neutron and this nucleus. In connection with general ideas recently developed about the constitution of atomic nuclei and their reactions it was moreover explained how the lack of similar large cross sections for scattering of slow neutrons can be accounted for by the small probability of neutron escape from the intermediate state of the compound system compared with the probability of emission of radiation from this system resulting in final capture of the neutron. We should like, however, here briefly to point out that it is possible without any detailed theory of the capture mechanism to estimate the absolute values of the probabilities for these processes from direct measurements of the cross sections for capture and their variation with neutron velocity. In fact it follows from simple wave mechanical considerations that in the region where the de Broglie wave length of the incident neutrons is very large compared with nuclear dimensions the capture cross section will always be given by a formula of the same type as that deduced by Bethe by means of a simplified nuclear model. If u is the velocity of the free neutron and a the probability of radiative transition, while b is the probability of neutron escape, this cross section will thus be given by the following formula* Applying the formula to the case of cadmium where the cross section for capture for neutrons of thermal velocities is approximately cm2 and where the selective absorption is practically confined within a region of neutron velocities of a fraction of a volt we get values for a and b of lo-'' sec-' and sec-I respectively. A closer discussion of these results from the view regarding nuclear constitution referred to will be given elsewhere3** together with general discussion of the available experimental evidence regarding nuclear reactions.
* [The formula is missing.]
** [There is no indication in the text where footnotes 1 and 2 occur, and all three footnotes are missing.]
MS.
2
XV. ON THE DISINTEGRATION OF ALUMINIUM BY a-RAYS UNPUBLISHED MANUSCRIPT [1936]
See Introduction, sect. 3, ref. 61.
PART I: PAPERS A N D MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
This manuscript, catalogued as “Disintegration of Atomic Nuclei [II]” , [1937], consists of a carbon copy of 8 typewritten pages with a few corrections and additions in ink in Kalckar’s handwriting. The manuscript is in English. The equations are missing except for the left-hand side of the process labelled (1). The manuscript is on microfilm Bohr MSS no. 14.
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
On the disintegration of aluminium by a-rays. The disintegration of aluminium by impact of a-particles has been subject to a large number of experimental investigations and found to exhibit many properties of great theoretical interest. Already in their original experiments Rutherford and Chadwick observed in the process
the appearance of two distinct proton groups with energies differing by several million volts, and by the subsequent experiments of Pose and of Chadwick and Constable it was found that the yield of protons in both groups showed remarkable sharp maxima for a series of energy values of the a-rays with intervals of a few hundred thousand volts. Later Duncanson and Miller as well as Haxel observed the presence of two further proton groups in the aluminium disintegration while more recent experiments of Haxel have revealed a very interesting variation of the relative intensity of all four proton groups with varying a-ray energy. This is especially pronounced for the highest energies of the a-rays, where the yields of the slowest proton groups increase most markedly. As [is] well known, the disintegration of aluminium by a-rays may also give rise to the emission of a neutron according to the process
where, as discovered by Joliot-Curie, the phosphor isotope formed is radioactive and decays under the emission of positrons with a period of 3 minutes. The variation of the neutron emission with the velocity of the a-rays has recently been investigated in details by Fahlenbrach, who has shown that the neutron yield exhibits maxima for the same a-ray energies as the proton emission, and further found an interesting indication of a decrease of the neutron yield for the largest a-ray energies where as observed by Haxel the proton yield rises so extraordinarily. In the previous attempts of explaining these effects and especially the maxima in the proton yield for certain [a-]ray energies it has been assumed that the incident [a]particle within the nucleus in first approximation moves in a conservative field of force. The quantisation of this motion should therefore exhibit a number of more or less well defined stationary states and according to the idea originally suggested by Gurney the penetration of the [a]particle through the *
[This equation is not completed and the following ones are missing.]
MS,p . 2
PART I : PAPERS AND MANUSCRIPTS RELATING
M5. p 3
To
NUCLEAR PHYSICS
potential barrier around the nucleus would be much facilitated by a quantum mechanical resonance when its energy corresponds to one of these states. In this picture the expulsion of a proton and in particular the appearance of several distinct proton groups should further, according to Gamow, correspond to a process by which the [a] particle falls from its original energy level to one of the lower [a-]ray levels, while a proton is simultaneously raised from its normal level within the nucleus to an energy sufficiently high to allow its escape. By means of such a nuclear model where [a]-particles and protons within nuclei are assumed to move approximately independent of each other in a static field like the electrons in an atom, it is hardly possible, however, to explain a number of the experimental results concerning the process in question. Above all there appear on such a model as remarked by Mott, to be a definite contradiction between the fact clearly brought out by Pose that almost any high speed aparticle, which unhindered of the potential barrier enters the nucleus, expels a proton and the appearance of the remarkably sharp resonance effects for certain smaller a-ray energies. Indeed, the high proton yield for swift a-particles would mean the existence of a coupling between the particle and the proton within the nucleus, which would prevent any resonance of the kind in question to develop for such a-ray energies, where the entrance of an a-particle is essentially hindered by the potential barrier, but where still the proton can pass unhindered over the top of the barrier. Moreover it seems in this way quite impossible to explain Haxel’s later observation of the pronounced increase of [with] increasing [a-]ray energy of the relative probability of the processes by which the slowest protons are ejected. All these difficulties disappear however as soon as we take the extreme facility of energy exchange between the closely packed nuclear particles into account, which, as pointed out in a recent article, is responsible for the characteristic difference between atomic and nuclear reactions. Thus the contact between the aparticle and the aluminium nucleus will in the first place lead to the formation of an intermediate compound system in which the energy may be said to be distributed among all the constituent particles in such a way that none of them will for the next following time possess sufficient energy to escape from the nucleus. Any disintegration of this intermediate system whether it leads to the expulsion of a proton or a neutron or even to the reemission of an [a] particle will therefore claim a subsequent, so to say fortuitous, concentration of the energy on some such elementary or compound particle. From this point of view resonance effects will occur if the sum of the energies of the free a-particle and the Al-nucleus happens to coincide with a stationary state of the intermediate system corresponding to some quantized collective type of motion of all the constituent particles, which has no immediate connection
PART I: PAPERS A N D MANUSCRIPTS RELATING TO PiUCLEAR PHYSICS
with the disintegration mechanism. The sharpness of these stationary states and accordingly of the resonance effects will however depend on the sum of the probabilities of the various possible disintegration processes which this intermediate system can undergo and which are determining for its lifetime. Now in our case the most probable type of disintegration of the compound system is at any rate for fast a-rays the emission of a proton but even if the total energy is large enough to allow one proton to escape without difficulty through the potential barrier the lifetime of the compound system will on account of the necessary preceding energy concentration be very long compared with the time which the incident a-particle or the expelled proton would use in passing through a region of nuclear dimension. This is not only in conformity with the existence of resonance in this energy region but it also explains that the width of the resonance levels in question varies only very little with increasing a-ray energy. A fact which contrasts strikingly to what should be expected if the lifetime of the stationary states concerned was primarily determined by the ease with which the a-ray passes through the potential barrier. Most suggestive evidence regarding the mechanism of disintegration is further obtained by the presence of the proton groups and the way in which their relative intensity varies with the energy of the incident a-ray. The presence of these groups can no longer be said to be due to the existence of some specific a-ray levels in a fixed nuclear field but to a number of stationary states of the collective motion in the Si-nucleus which is left after the escape of a proton from the intermediate compound system. The relative probability that this residual nucleus finds itself in a higher or lower of these states will now depend not only on the greater or smaller difficulty with which the proton passes the potential barrier but also on the probability for the occurrence of the greater or smaller necessary concentration of the excess energy of the proton. In fact, the smaller the energy of the escaping proton, the less demands are evidently put to the energy concentration and we obtain at once an explanation of the marked preference for the expulsion of protons of the lower energy groups as soon as their absolute energy values are large enough to allow also these protons to pass unhindered through the potential barrier. In a more detailed examination of such problems it may be necessary to take the spins of the stationary states of the nuclei concerned into consideration which, as is specially emphasized by Gamow, are often essential in determining the probability of nuclear reactions, but in the particular case of the Aldisintegration by fast a-rays the de Broglie wave lengths of the incident a-particle as well as of the expelled proton groups are sufficiently small to give such spin effects only secondary importance. The different so far observed courses of the collision between a fast a-particle
MS
4
MS,
5
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
and an Al-nucleus are illustrated in the following scheme:
M S , p. h
MS, p . 7
The circle round the compound system formed by the first stage of the process indicates that this system which in its normal state represents a common stable phosphorus isotope is here in an abnormally high excited state. Its excitation energy is in fact given by the sum of the kinetic energy E of the a-ray and the binding energy of an a-particle in an ::P-nucleus, which lies between 8 and 10 M. The first four arrows pointing from the compound system represent the expulsion of the four observed proton groups leaving the residual Si-nucleus in its normal and in three increasingly excited states. The numbers within the brackets attached to the nuclear symbols give the approximate values in millions e.V. of this excitation energy and the energy of the emitted protons respectively, as observed by Duncanson and Miller. The next arrows indicate the disintegration of the compound system by the emission of a proton and the formation of a radioactive phosphorus isotope which is here considered to be left in its normal state, the energy value of which relative to the Si-nucleus is deduced from the positron spectrum as well as from the known difference of the masses of a neutron and a proton. In this case resonance maxima are observed for the same a-ray energies as give rise to maxima in the proton output. So far, however, no resolution of the neutrons in the different energy groups has been observed. Still for sufficiently large a-ray energy such groups must be expected to exist and are probably responsible for the pronounced maximum in the neutron output for a-ray energies of about 7 M.V. observed by Fahlenbrach. The steep fall in the output for still higher energies is presumably an effect of the competition with the proton emission which as mentioned increases so markedly in this energy region. Finally the possible disintegration of the compound system in an Al-nucleus and an a-particle is represented by the last arrow in the diagram. This process is of course not sharply separated from ordinary scattering of a-rays by Alnuclei; it is however probably essential in a detailed investigation of the so called anomalous scattering effect. Also here we shall for sufficiently large energy values expect the presence of groups of a-rays with different energies corresponding to excited states of the Al-nucleus. Due to the large influence of the potential barrier in disintegrations of this type such a course of the process can first be expected to have a considerable probability for the highest a-ray energies. Regarding the relative probabilities of disintegrations of the various types it may further be remarked that a course of the disintegration where the residual nucleus is left in its normal state must for all three types of disintegration be ex-
P A R T I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
pected to have probabilities of the same order of magnitude if the total energy is large enough to allow the particles in question to escape with an energy sufficient to pass freely through the potential barrier. In fact all these processes will demand an energy concentration of a similar character. Due to the comparatively much smaller demand of energy concentration, disintegration where the residual nucleus is left in an excited state will, as explained, often be far more probable and the competition between all the possible processes will in general depend on the distribution of the energy levels for the respective nuclei. For sufficiently large energy however where this distribution will be practically continuous, the expulsion of particles from the compound system with smaller binding energies will always be more probable. In our case it means that the output of protons for such energies will more and more exceed the reemission of a-particles and this again more and more exceed the neutron output. In contrast to the ordinary ideas of resonance by collision it is an immediate consequence of the view-point here discussed that the reversal of any of the disintegration processes of the compound system will give rise to resonance effects if the energy of the incident protons or neutrons relative to the nucleus concerned has the same value as that of the highest energy groups of the emitted particles in case of resonance maximum by bombardment of 27 A1 ,with a-particles. As remarked by Gamow in a recent note such a-resonance by fast neutron impacts might at first sight seem to contrast with the fact that the bombardment of heavier nuclei with fast neutrons generally show no resonance effects. In a former article this fact was explained by the exceedingly close and not even sharply separated level distribution for the compound nuclei concerned, in the energy region which corresponds to the collision with fast neutrons leading to capture. As emphasized there, we shall however expect that the density of the levels by the same excitation energy will diminish rapidly with decreasing atomic weight. In a paper to appear shortly and containing a general discussion of the available evidence regarding nuclear reactions a more detailed quantum mechanical treatment on the lines indicated will be given and especially it will be shown that formulas for resonance phenomena of the same type as that recently deduced by Breit and Wigner by introducing a small coupling between any two nuclear particles with special reference to the explanation of the selective capture of slow neutrons holds also in the case of the intimate coupling between all the nuclear particles claimed for the account of the typical features of nuclear reactions.
MS,p. 8
XVI. EXCITATION AND RADIATION OF ATOMIC NUCLEI UNPUBLISHED MANUSCRIPT [1936]
See Introduction, sect. 3, ref. 58 a n d p. [38]
PART I: PAPERS A N D MANUSCRIPTS RELATIYG TO NUCLEAR PHYSICS
The folder “Excitation and Radiation”, [ 19361, contains various drafts and sheets of calculations. One manuscript, entitled “Excitation and radiation of atomic nuclei”, consists of 3 typewritten pages in English. Formulae and some symbols are missing and there is a gap in the manuscript. There is a carbon copy of this manuscript with a few corrections in pencil in Rosenfeld’s handwriting. This is the version reproduced here. A second manuscript constitutes a draft of the same paper, consisting of 7 numbered pages written in English in pencil in Kalckar’s handwriting. Most pages are dated 10/9. There are two more sheets in Danish, entitled “Ti1 Indledning” (“For the Introduction”). They are dated 8/11 and 11/11. Finally, there are 3 sheets of calculations and drawings in pencil and ink in Bohr’s and Kalckar’s handwritings. One sheet is dated 11/9-36. The manuscript is o n microfilm Bohr MSS no. 14.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Excitation and radiation of atomic nuclei. In a recent article in Nature it has been shown that the typical features of nuclear reactions are determined by the extraordinary facility of energy exchange between the closely packed particles within nuclei, and that also this energy exchange is decisive for the mechanism of excitation of nuclei and the scheme of energy levels corresponding to such excitation. ___
As is well known it has been possible to account for the general way in which the binding energy of atomic nuclei varies with the mass and charge numbers by assuming that the nuclei are built up of neutrons and protons, and especially by introducing exchange forces between proton and neutron pairs of the type proposed by Heisenberg. In a discussion of this problem it is for the sake of simplicity usually assumed that all the nuclear particles in first approximation move independently of each other in a conservative field like the electron in an atom, and that accordingly the state of binding of each proton or neutron is in first approximation determined by a set of quantum numbers in the usual way. Due to the fact that the Pauli exclusion principle which governs the normal distribution of the quantum numbers of the electrons in an atom is assumed to hold also for the protons as well as for the neutrons, this method of approximation gives values for the total binding energy of the nucleus in its normal state which are largely independent of the assumption regarding the binding of the separate particles. In fact the mean kinetic energy of each particle in this state will always come out to be of the same order of magnitude as that of a particle, the motion of which is restricted to a separate cell within the nucleus of a volume equal to the total nuclear volume divided by the particle number. This kinetic energy is in all nuclei of about 20 M.V. pro particle. As soon, however, as we consider the excited states of atomic nuclei it is necessary to take into account the extreme facility of energy exchange between the closely packed nuclear particles which, as shown in a recent article in Nature, is decisive of the typical features of nuclear reactions in collisions which, in several ways, contrast so markedly from the well known features of collisions between ordinary atomic structures and swiftly moving electrified particles. Especially the excitation of nuclei cannot, [as is] done in the usual treatment, be ascribed to an elevated quantum state of the single nuclear particles like the ordinary excited states of atoms, but to some quantized collective type of motion of all the nuclear particles, like the oscillations or pulsations of a liquid drop or an elastic solid body. As indicated in the cited article this view allows a qualitative explanation of the level scheme for the excited states concerned in nuclear reactions as well as for the radiation properties of such states. At this occasion, however, I should like to
MS,
2
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
enter somewhat more closely on the quantitative side of this problem which has been recently subject to interesting discussions in this journal (Bethe and Bloch). In the first place I should like to point out how it is possible to arrive at a more quantitative estimate of the order of magnitude of the lowest excitation energies of nuclei by a simple comparison of the properties of the mentioned macroscopic models. In fact the frequency of the simple vibrations of a drop under the influence of surface tension and the simplest pulsation of an elastic ball will be given by the formulas* V = V =
and
I/ =
respectively, where m is the total mass of the body and 0 and N the surface tension and elastic coefficient respectively. * *
As regards the radiation, it has especially from the study of the so called internal conversion been found that the radiative properties of nuclear states do not in general correspond to those of an oscillating dipole but to those of quadrupoles and higher poles what is possible*** to reconcile with the view that the excitation should be principally due to the motion of a proton or a neutron (or perhaps [a]-particle) relative to the rest of the nucleus. As soon, however, as we compare the motion in an excited nucleus with the oscillations of a homogeneous substance with an evenly distributed charge the situation is completely changed. In fact in any such oscillation the electric center will of course be at rest with the center of gravity and no oscillation dipole moment can occur.
*[The formulae and some symbols are missing.] **[ASindicated, there is a gap in the manuscript here.] ***[It was presumably the intention to say: “which is impossible”.]
XVII. SPIN EXCHANGE IN ATOMIC NUCLEI UNPUBLISHED MANUSCRIPT [1936]
See Introduction, sect. 3 , ref. 65
P A R T I: P A P E R S A N D MANUSCRIPTS RELATING TO N U C L E A R PHYSICS
The folder “Spin Exchange in Atomic Nuclei”, [1936], contains various drafts and calculations. One manuscript, entitled “Spin exchange in atomic nuclei”, consists of a carbon copy of 2 numbered pages and a third typewritten page, all in English. There are a few corrections and additions in pencil and ink in Kalckar’s and Bohr’s handwritings. This manuscript is reproduced here. A separate page of the carbon copy of an earlier version has a handwritten addition by Kalckar, suggesting that the third page is meant as a continuation of page 2. A second manuscript, entitled “Spin exchange between nuclear particles”, consists of 2 typewritten pages (with a carbon copy) in English. There are some corrections in pencil in Rosenfeld’s handwriting. The folder further contains 10 pages of drafts and calculations in English and Danish in Rosenfeld’s, Kalckar’s and an unidentified handwriting. One page is dated 7/4-36. Finally, there is one page of calculations in ink in Dirac’s handwriting, with calculations in pencil on the reverse. None of these calculations seem to be related to the topic of the manuscripts. The manuscript is on microfilm Bohr MSS no. 14.
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Spin exchange in atomic nuclei. In a recent article in “Nature” arguments were given which would seem to prove that the particles within atomic nuclei cannot even in first approximation be treated as moving in separately quantized orbits like the electrons in atoms but that due to the rapid energy exchange between the individual nuclear particles all motions in nuclei are of an essentially collective type and must be quantized as such. These considerations were based on the experimental evidence regarding nuclear reactions by collisions. I should like to point out, however, that additional arguments for the fundamental difference in mechanical respects between nuclei and atoms may be derived from the evidence regarding the spin properties of nuclei in their normal state obtained by the study of the fine structure of optical spectra. The analysis of these fine structures has above all disclosed two quite general rules connecting the spin of an atomic nucleus with its mass number and its charge number. According to the first rule the spin of any nucleus with even or uneven mass number respectively is an even or uneven integral multiple of the unit h/47r. The second rule says that every nucleus with even charge number as well as even mass number will in its normal state moreover have the spin value zero. As often remarked the first of these rules is an immediate consequence of quantum mechanics if we consider all nuclei as composed of protons and neutrons and to each of these particles ascribe the spin value h / 4 ~In . particular this rule is quite analogous to that which holds for the total spin of the electronic configurations in atoms where each electron moves with quantized angular momentum regulated by the Pauli exclusion principle in the well known manner. The many interesting attempts to account for the spin of nuclei on a similar basis have failed, however, to offer a reasonable explanation for the far more frequent absence of spin in the normal states of nuclei than in electronic configurations, as expressed by the second rule. This rule suggests in fact that protons as well as neutrons in nuclei have a marked tendency to combine in pairs with opposite spin values far greater than any such tendency of electrons in atoms. This difference is obviously connected with the same close packing in nuclei which is responsible for the predominant part which the energy exchange between nuclear particles play in collision phenomena. The origin of such pair-combinations between the protons and the neutrons in nuclei may also be looked for in a spin exchange between two particles with the same charge but with opposite spin, similar to the charge exchange within [each] neutron-proton pair in nuclei assumed by Heisenberg to explain the strong forces which seem to bind the members of any such pair to one another.
MS, p. 2
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
\IS.
p.
]!I
Moreover the existence of strong orienting couplings between the nuclear particles means that we cannot consider the protons and neutrons in nuclei as mechanical entities in the sense demanded by the usual applications of the exclusion principle. In the first approximation only pairs of these particles may be considered as such entities, and their relative motions may therefore be treated like that of spinless atoms in a gas or liquid. According to the general views of nuclear constitution proposed in the cited article this motion may in fact even in highly excited nuclei only exert a small influence on the average state of binding of the nuclear particles. The absence of total spin in the normal state of nuclei composed of even numbers of protons as well as even numbers of neutrons is now simply explained by assuming that the total angular momentum of the collective motions in this state is equal to zero. All kinetic energy of such nuclei in the normal state may in fact be ascribed to the normal vibrations of the system as a whole, and due to the decrease of the frequencies of these vibrations by increase of the nuclear mass this energy will for heavy nuclei be only of small importance for the estimate of the total nuclear energy and its variation by nuclear disintegrations.
XVIII. ON THE TRANSMUTATIONS OF LITHIUM BY PROTON IMPACTS UNPUBLISHED MANUSCRIPT [ 19361
See Introduction, sect. 3, ref. 66.
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
This manuscript consists of a main manuscript, reproduced here, and some additional pages, suggesting a partial re-wording. All are in English. The main manuscript consists of a carbon copy of 4 pages, with some numbers and a small correction added in ink in Bohr’s handwriting. There is an earlier version of a part of page 1. The references have all been added by the editor, as indicated. There are two additional pages written in ink in Kalckar’s handwriting and 2 parts cut out from carbon copies with corrections and deletions in ink. The manuscript is on microfilm Bohr MSS no. 14.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
On the transmutations of lithium by proton impacts. The transmutation of lithium by the impact of artificially accelerated protons presents a variety of different phenomena, which have raised problems of great interest. The fast a-rays observed in the original experiments of Cockcroft and Walton' were ascribed by them to the process
and this interpretation was convincingly supported by consideration of the conservation of energy and momentum during this process. In fact, the a-rays were found to appear in pairs with almost opposite directions and equal kinetic energy and the sum of these energies, about 17 MV, was found to correspond closely to the energy released in the process as estimated from the measurements by Aston and Bainbridge of the masses of the nuclear particles involved. The slower particles observed in such collisions were ascribed by Kinsey, Oliphant and Rutherford' to the process
and the correctness of this interpretation was proved in subsequent experiments by Oliphant, Shire and Crowther3 by separation of the two lithium isotopes. The kinetic energy released in process (2) was found to be about 3 MV, which corresponds to a mass of the isotope ?He in close agreement with that obtained from its formation by collisions of two deuterons. As observed by Crane and Lauritsen4 the bombardment of Li by protons is also accompanied by the emission of penetrating y-rays with energies between 4 and 16 MV, within which interval there apparently could be detected a number of separate spectral lines. The larger maximum energy of these y-rays clearly shows that they originate from impact on the isotope :Li, and it was suggested
' [J.D. Cockcroft and E.T.S. Walton, Experiments with High-Velocity Positive Ions II. The Disintegration of Elements by High-Velocity Protons, Proc. Roy. SOC.A137 (1932) 229-242.1 [M.L. Oliphant, B . B . Kinsey and Lord Rutherford, The Transmutation of Lithium by Protons and by Ions of the Heavy Isotope of Hydrogen, Proc. Roy. SOC.A141 (1933) 72,2-733.] ' [M.L. Oliphant, E.S. Shire and B.M. Crowther, Separation o f t h e Isotopes of Lithium and some Nuclear Transformations Observed with them, Proc. Roy. SOC.A146 (1934) 922-929.1 [H.R. Crane, L.A. Delsasso, W.A. Fowler and C.C. Lauritsen, Cloud Chamber Studies of the Gamma-Radiation from Lithium Bombarded with Protons, Phys. Rev. 48 (1935) 125-133.1
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
by Crane and Lauritsen that they were due to a disintegration process like ( l ) , where one of the a-particles after the disintegration, instead of being in its normal state, was in an excited state from which it returned after the separation to its normal state with emission of y-radiation. From general arguments concerning nuclear reactions developed in a recent article5, it seems, however, more likely, as we shall see, that the y-rays in question are emitted from an excited Be-isotope formed by the process
MS.P 2
According to these arguments, the first stage in any reaction caused by collisions between nuclei is the formation of an intermediate compound system in which the energy is divided among all the composing particles to an extent which prevents the immediate escape of any of them against the attractive forces which act between nuclear particles at close distances. The subsequent course of the collision is therefore the outcome of a competition between the various disintegration and radiation processes which the compound system may undergo and the relative probabilities of which will depend on the total energy of this system as well as of its spin, but not on the way in which it is formed. While in heavy nuclei the probability of the radiation processes are for many reactions of the same order of magnitude as the probability of disintegration processes, for light nuclei the latter processes will generally be far more probable than the former. In this respect the compound system formed by a proton and a :Li-nucleus presents, however, an exceptional case, because the symmetry conditions of quantum mechanics imply, as pointed out by Beck6, that a nucleus of the type $Be can not disintegrate into two a-particles unless its total spin is equal to an even multiple of the unit h/27r. Now the spin of 3Li is equal to 3/2 and that of the proton 1/2 of this unit, and since for the comparatively slow protons in question a contribution to the spin of the compound system arising from an orbital angular momentum is improbable, the values of the total spin of this system which chiefly come into consideration are 1 and 2. The latter value would correspond to the process (l), while the appearance of the former might give rise to the emission of a y-radiation of considerable intensity. The assumption that the y-rays observed by Crane and Lauritsen originate in this way is also strongly supported by the fact that they found a pronounced maximum of intensity of the radiation for an energy of the incident proton of [N.Bohr, Neutron Capture and Nuclear Constitution, Nature 137 (1936) 344-348. Reproduced on P. [1511.1 [ G . Beck, in: Handbuch der Radiologie, 2nd ed., 6 (1933) 390.1
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
about 7/2 MV 7 , in striking contrast with the steady increase of the yield of the disintegration processes (1) and (2) for increasing proton energies. While this rise closely corresponds to the theoretical expectations as regards the probability for the penetration of the protons through the potential barrier round the Li nuclei, the maximum of the y-ray intensity is obviously a resonance effect due to the presence of a semistable stationary state of the compound system with a life time much longer than that involved in the processes (1) and (2). Such a long life time, however, is hardly compatible with the view, that the y-radiation is due to an excitation of one of the a-particles formed by a process of the type (1). It is true that an a-particle excitation of about 16 MV would leave very little kinetic energy to be released in the disintegration, making this very highly improbable, but the spectral distribution observed by Crane and Lauritsen would on this view mean that an a-particle besides an excited stationary state at about 16 MV, would also have a number of other such states of much lower excitation energy which much easier might be formed directly by disintegration of the compound system with the simultaneous release of a large amount of kinetic energy. These disintegration processes should therefore have probabilities of the same order of magnitude as the processes (1) and ( 2 ) , in contradiction with the long life time demanded by the resonance effect. Excluding any disintegration process with a-ray excitation, the only process which competes with the radiation transitions in the intermediate state of the ,8Be nucleus with spin 1 is the escape of a proton; but on account of the small energy released the probability of this process will be comparatively small and the radiative processes will therefore have an appreciable chance in this competition. It seems therefore quite natural to assume that the y-radiation observed by Crane and Lauritsen is emitted from a highly excited :Be-nucleus with spin 1 formed by the process (3) and that the spectral lines into which this radiation can apparently be analyzed form an integral part of the y-ray spectrum of this Be isotope. The circumstance that this spectrum involves well-separated levels at an excitation as high as 16 MV is in no way contradictory to the close accumulation of the nuclear levels of heavy elements for much smaller excitation, since the separation of the levels must be expected to decrease rapidly with increasing nuclear mass. Another much discussed feature of the lithium-proton reactions is the fact that under similar conditions the probability of the process (1) is about 30 times smaller than the probability of process (2). An explanation such as that suggested [H.R. Crane, L.A. Delsasso, W.A. Fowler and C.C. Lauritsen, High-Energy Gamma-Rays f r o m Lirhium and Fluorine Bombarded with Protons, Phys. Rev. 46 (1934) 531-533; also, C.C. Lauritsen and H . R . Crane, Evidence of un Excited State in the Alpha-Particle, ibid., 46 (1934) 537-538.1
MS, p . 3
P A R T I: PAPERS A N D MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
M , ,I 4
by Goldhaber' resting on the assumption that any change of spin direction of the individual protons and neutrons in nuclei is unlikely to occur in nuclear reactions, is however hardly possible to uphold in view of the extremely rapid exchange of energy and probably also of spin in close nuclear collisions. Moreover, if it were attempted to apply this argumentation to the behaviour of the intermediate compound system involved in the nuclear reactions in question, it would mean that the probability of a-ray emission from the !Be-nucleus of spin 2 would be even smaller than the probability for proton escape, which would again involve that we had to do with a marked resonance phenomenon contrasting with the apparently constant ratio of the yields of the processes (1) and (2) for varying proton energies. In order to explain the small value of this ratio there is also no necessity for assuming that the probability of disintegration of the compound system :Be with spin 2 into two a-particles is abnormally low, but the effect is rather due to the small probability of the formation of this system resulting from the extreme rapidity with which it disintegrates, and which prevents resonance. In fact, we have here to do with a quantum mechanical effect analogous to optical problems of induced excitation of spectra by illumination of atoms with monochromatic light, where as well known the intensity of the excited radiation increases with the probability of the corresponding radiative transitions only as long as these transitions do not materially shorten the life time of the excited atomic states. The yield of a nuclear disintegration such as that in question will therefore have a maximum value if the life time of the compound system is of the same order of magnitude as that which corresponds to proton escape only, and will decrease proportionally to the life time of this system if it has a considerably smaller value. The small yield of the process (1) compared with that of process (2) may therefore be simply explained by the much smaller life time of the compound system in the former case due to the far greater kinetic energy released.
[ M . Goldhaber, discussion contribution in: International Conference on Physics, London 1934, Camb. Univ. Press (for The Physical Society), 1935, Vol. 1, Nuclear Physics, pp. 163-168.1
XIX. TRANSMUTATIONS OF ATOMIC NUCLEI Science 86 (1937) 161-165
See Introduction, sect. 3, ref. 68.
SCIENCE FRIDAY, AUGUST20, 1937
VOL. 86
Transmutataons of Atomzc h'uelea: PROFESSOR NIELS BOAR
161
Physacs Teachang an the S o u t h : PROFESSOR L. L. I~ENDREN 165 Sczentafic Events: Report of the Bratash Forestry Commissaon; T h e Proposed Reancorporatzon o f the Ameracan Chemacal Soczety; T h e Faeld Museum o f Natural Hast o r y ; Recent Deaths and Memorials 169 Scientafic ATotes and News
171
Discussaon: AMahomet and the Mountaan: PROFESSOR G. R. WIELAND.Proposed Chemical Mechanasms f o r the Productton o f Sloan Erythema and Pagmentatzon b y ARNOW.A MacroRadaant E n e r g y : DR. L. EARLE b iologacal Test f o r Carcinogenzc Hydrocarbons: DR. SANUELGOLDSTEIN. Drought and the Fungous Flora of Colorado: DR. P. F. SHOPE. Agaan F l y L. TROXELL ang Fashes: DR. EDWARD 174
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Special Articles: A Latent V i r u s of L i l y : DR. FRANK P. McWHORTER.A Response of A l f a l f a t o B o r a x : P R O FESSOR L. G. WILLIS and J. R. PILAND. Enzymic Synthesis of Go-carbosylase: DR. HENRYTAUBER.. 179 Science N e w s ...................................................................................
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TRANSMUTATIONS O F ATOMIC NUCLEI' By Professor NIELS BOHR INSTITUTE O F THEORETICAL PHYSICS, UNIVERSITY OF COPENHAGEN
IThas been pointed out on a n earlier occasion2 that in order to understand the typical features of nuclear transmutations initiated by impacts of material particles it is necessary to assume that the first stage of any such collision process consists in the formation of a n intermediate semi-stable system composed of the original nucleus and the incident particle. The excess energy must in this state be assumed to be temporarily stored in some complicated motions of all the particles in the compound system, and its possible subsequent breaking u p with the release of some elementary or complex nuclear particle may from this point of view be regarded as a separate event not directly connected with the first stage of the collision 1 Abstract of lectures given in the spring of 1937 at various universities in the United States. The illustrations are reproductions of three slides shown in these lectures. 2 N. Bohr, Nature, 137 : 344, 1936.
process. The final result of the collision may therefore be said to depend on a competition between all the various disintegration and radiation processes from the compound system consistent with the conservation laws. A simple mechanical model which illustrates these features of nuclear collisions is reproduced in Fig. 1, which shows a shallow basin with a number of billiard balls in it. I f the bowl were empty, then a ball which was sent in would go down one slope and pass out on the opposite side with its original energy. When, however, there are other balls in the bowl, then the incident one will not be able to pass through freely but will divide its energy first with one of the balls, these two will share their energy with others, and so on until the original kinetic energy is divided among all the balls. If the bowl and the balls could be regarded as perfectly
SCIENCE
162
smooth and elastic, the collisions would continue until a sufficiently large part of the kinetic energy happened again to be concentrated upon a ball close to the edge. This ball would then escape from the basin, and if the energy of the incident ball mere not very large, the remainder of the balls would be left with insufficient total energy f o r any of them to climb the slope. If, however, there were even a very small friction between the balls and the basin or if the balls were not perfectly elastic, it might very well happen that none of the balls would have a chance to escape before so much of the kinetic energy were lost as heat through friction that the total energy would be insufficient f o r the escape of any of them.
FIG.1
Such a comparison illustrates very aptly what happens when a fast neutron hits a heavy nucleus. On account of the large number of particles which in this case constitute the compound system and their strong interaction with one another, we must in fact expect from this simple mechanical analogy that the lifetime of the intermediate nucleus is very long compared with the time taken by a fast neutron to cross a nucleus. This explains, first of aI1, that although the probability f o r a heavy nucleus to emit electromagnetic radiation in such a time is extremely small, nevertheless there is on account of the long life of the compound nucleus a not quite negligible probability that the system instead of releasing a neutron will emit its excess energy in the form of electromagnetic radiation. Another experimental fact, which is easily understood from such a picture, is the surprisingly large probability of inelastic collisions, resulting in the emission of a neutron with a much smaller energy than the incident one. Indeed from the above considerations it is clear that a disintegration process of the compound system, which claims a smaller amount of energy concentrated on one single particle, will be much more likely to occur than a disintegration, in which all the excess energy has to be concentrated on the escaping particle. A t first sight such simple mechanical considerations might be thought to contradict the fact, so well established from the study of the radioactive y-ray spectra, that nuclei like atoms possess a discrete distribution of energy levels. For in the above discussion it was
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VOL. 86, No. 2225
essential that the compound system would be formed f o r practically any kinetic energy f o r the incident neutron. We must realize, however, that in the impacts of high-speed neutrons we have to do with an excitation of the compound system f a r greater than the excitation of ordinary y-ray levels. While the latter at most amounts to a few million volts, the excitation in the former case will considerably exceed the energy necessary f o r the complete removal of a neutron from the normal state of the nucleus, which from mass defect measurements can be estimated to be about eight million electron volts. Fig. 2 then illustrates in a schematic way the general character of the distribution of energy levels f o r a heavy nucleus. The lower levels, which have a mean energy difference of some hundred thousand volts, correspond to the y-ray levels found in radioactive nuclei. For increasing excitation the levels will rapidly come closer to one another and will f o r an excitation of about 15 million volts, corresponding to a collision between a nucleus and a high-speed neutron, probably be quite continuously distributed. The character of the upper part of the level scheme is illustrated by the two lenses of high magnification placed over the level diagram, one in the above-mentioned
FIG.2
region of continuous energy distribution and the other in the energy region corresponding to the excitation which the addition of a very slow neutron to the original nucleus would give f o r the compound system thus formed. The dotted line in the middle of the field of the lower magnifying glass represents the excitation energy of the compound nucleus when the kinetic energy of the incident neutron is exactly zero, and the distance from this line down to the ground state is therefore just the binding energy of the neutron in the compound system.
AUGUST 20, 1937
SCIENCE
Information a.bout the level distribution in the energy region near this line can be obtained from experiments on the capture of very slow neutrons with energies of a fraction of a volt. Thus if the kinetic energy of the incident neutron just corresponds to the energy of one of the stationary states of the compound system, quantum mechanical resonance effects mill occur, which may give effective cross sections f o r capture of the neutrons several thousand times larger than ordinary nuclear cross sections. Such selective effects have actually been found for a number of elements, and it has further been found that the breadth of the resonance region in all these cases is only a small fraction of a v0lt.3 From the relative incidence of selective capture among the heavier elements and from the sharpness of the resonances, it can be estimated that the mean distance of levels in this energy region is of the order of magnitude of about 10-100 electron volts. I n the field of the lower magnifying glass in Fig. 2 there are indicated a number of such levels, and the circumstance that one of these levels is very close to the dotted line corresponds to the possibility of selective capture f o r very slow neutrons in this particular case. The distribution of energy levels indicated in Fig. 2 is of a very different character from that with which we are familiar in ordinary atomic problems where on account of the small coupling between the individual electrons bound in the field round the nucleus the excitation of the atom can in general be attributed to an elevated quantum state of a single particle. The nuclear level distribution is, however, just of the type to be expected for, a n elastic body, where the energy is stored in vibrations of the system as a whole. For, on account of the enormous increase in the possibilities of combina.tion of the proper. frequencies of such motions with increasing values of the total energy of the system, the distance between neighboring levels will decrease very rapidly f o r high excitations. Indeed, considerations of the above character are well known from the discussion of the specific heat of solid bodies a t low temperatures. Thermodynamical analogies can also be applied in a fruitful way for the discussion of the disintcgrat,ion of the compound system with release of material particles. Especially the case of emission of neutrons, where no forces extend beyond proper nuclear dimensions, exhibits a very suggestive analogy to the evaporation of a liquid or solid body a t low temperature. 3 The phenomenon of selective capture of slow neutrons, which shows a n interesting formal analogy with optical resonance, has especially been studied in a paper of G. Breit and E. Wigner ( P h y s . Rev., 4 9 : 642, 1 9 3 6 ) . Estimates from experimental evidence of the breadth of the levels were first given by 0. R. Frisch and G. Plaezek ( N a t u r e , 1 3 7 : 357, 1936) and have been discussed in details in a recent paper by H. Bethe and G. Placzek ( P h y s . Rev., 51: 450, 1 9 3 7 ) .
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I n fact, it has been possible from the approximate knowledge of the level system of nuclei at low excitations to get a n estimate of the “temperature” of the compound nucleus, which leads to evaporation ‘probabilities f o r neutrons consistent with the lifetimes f o r the compound system in fast neutron collisions derived from the analysis of experiments.4 Fig. 3 illustrates the course of a collision between a fast neutron and a heavy nucleus. To follow the simple trend of the arguments, an imaginary thermometer has been introduced into the nucleus. As the figure shows, the scale on the thermometer is in billions of degrees centigrade, but in order to get a more familiar measure f o r the temperature energy, one has also added another scale to the thermometer showing the temperature in millions of electron volts. The figures give the different stages of the collision process. To begin with, the original nucleus is in its normal state and the temperature is zero. After the nucleus has been struck by a neutron with about ten million volts kinetic energy, a compound nucleus is formed with 18 million volts energy, and the temperature is raised from zero to
I
I
FIG.3
roughly one million volts. The irregular contour of the nucleus symbolizes the oscillations in shape corresponding to the different vibrations excited at the temperature in question. The next figure shows how a neutron escapes from the system and the excitation, and accordingly the temperature, is somewhat lowered. I n the last stage of the process the remaining part of the energy is emitted in the form of electromagnetic radiation and the temperature drops down to zero. The course of the collision described above is the 4 The idea of applying for the probability of neutron escape from compound nuclei the usual evaporation formula was first proposed by J. Frenkel (Sow. Phys., 9 : 533, 1 9 3 6 ) . A more detailed investigation on the basis of general statistical mechanics is given in a paper by V. Weisskopf ( P h y s . Review, in print).
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SCIENCE
most probable one if the energy of the incident neutron is large, but f o r lower energies of the neutron the probabilities of escape and of radiation will bceome of the same order of magnitude, giving rise to a considerable probability f o r capture. I f we finally go down to the region of very slow neutrons it is known experimentally that the probability f o r radiation is even very much larger than the probability of escape. It will, however, be clear that in this case the analogy between neutron escape and evaporation will be quite inadequate, because the mechanism of escape, like the formation of the compound syskem, involves here specific quantum mechanical features which can not be analyzed in such a simple way. A quantitative comparison between ordinary evaporation and neutron escape can in fact be carried through only in case of excitation energies of the compound system, very large compared with the energy necessary for the removal of a single neutron, f o r only in this case will the excitation of the residual nucleus left after the escape of a neutron be nearly equal to that of the compound system, as is assumed in the usual evaporation phenomena where the change in the heat content of the bodies concerned during the escape of a single gas molecule is negligibly small: The above considerations can therefore be applied in this simple form only when the change in the temperature in going from the second to the third stage in Fig. 3 is comparatively small. Although the conditions f o r the application of the evaporation analogy are in general not strictly fulfilled in the experiments on fast neutron impacts so f a r carried out, there are still a great number of more qualitative consequences derivable from the analogy, which are very useful in the discussion of such collision processes. F o r instance, the above-mentioned large probability of energy loss in collisions between fast neutrons and nuclei just corresponds to the fact, that the molecules released in ordinary evaporation do not take the whole energy of the hot body, but that they in general come off with the much smaller energy per degree of freedom corresponding to the temperature of the evaporating body. It should further be expected from the thermodynamic analo,T that the released particles would have a n energy distribution around this mean value which corresponds to the Maxwellian distribution. If the energy of the incident neutron is several times larger than the binding energy per particle, it can moreover be predicted that not one single particle but several particles, each with a n energy small compared to that of the incident particle, will leave the compound system in successive separate disintegration processes. Nuclear reactions of this type have actually been experimentally found to take place in a number of cases.
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The above considerations can also be applied to the release of charged particles like protons and a-particles from the compound system, but i t must be kept in mind that in this case the latent heat of evaporation is not simply the binding energy of the charged particle, but that we have to add to this the electrostatic energy due to the mutual repulsion of the escaping particle and the residual nucleus. This repulsion will moreover have the effect of speeding u p the particles after their escape from the nucleus, and the mean kinetic energy of the charged particles will thus be larger than that of the neutrons by a n energy amount corresponding to this repulsion. W e should, therefore, expect that the most probable energy of the emitted particles would be approximately equal to the sum of the temperature energy and the electrostatic repulsion, and that the probability f o r the emission of charged particles with still larger energies would, as in the case of neutrons, decrease exponentially according to a Maxwellian distribution. This preference f o r nuclear processes, where the escaping charged particle takes only a p a r t of the available energy, leaving the residual nucleus in an excited state, is in fact one of the most striking features of a great number of reactions in which protons or a-particles are emitted from the compound system. So f a r we have mainly been concerned with nuclear processes initiated by impacts of neutrons. Similar considerations concerning the formation of a n intermediate state will, however, apply f o r collisions between charged particles and nuclei; but in this case it must be taken into account that the repulsive electric forces acting between the positively charged nuclei may often f o r small kinetic energies of the incident particle prevent or make less probable the contact necessary f o r the establishment of the compound nucleus. The combined action of this electrostatic repulsion of nuclear particles a t great distances and their strong attraction a t small distances can in fact be simply described by saying that the nucleus is surrounded by a so-called “potential barrier” which the incident charged particles have to pass in order to come in contact with the nucleus. As is well known from the explanation of the laws governing the spontaneous a-ray disintegration of radioactive nuclei, a charged particle may in quantum mechanics have a probability of penetrating through such a potential barrier, even in cases where the particle on classical mechanics, on account of its insuficient energy, would be stopped at the surface of the barrier. This quantum mechanical effect gives also a familiar explanation of the experimental fact that slow protons, when striking not too heavy nuclei, have been found to have a considerable probability of producing nuclear disintegrations, even f o r energies where classically the particles would be prevented by the
.kVGKST
20, 1937
SCIENCE
electric repulsion from coming in contact with the bombarded nucleus. Another interesting feature in collisions between charged particles and lighter nuclei is the remarkable resonance effects found f o r disintegrations caused by impacts of protons and a-particles. As in the case of selective effects of slow neutrons, such resonances must be ascribed to the coincidence of the sum of the energies of the incident particle and the original nucleus with a stationary state of the compound system corresponding to some quantized collective type of motion of all its constituent particle^.^ Especially in case of a-partide impacts, much information concerning the distribution of highly excited levels in lighter nuclei has been derived from such resonance effects. I n contrast to the dense distribution of levels found in heavier nuclei, the spacing of the levels in this case is as large as several hundred thousand volts f o r an excitation considerably higher than ten million volts. This result can, however, be readily understood if one realizes that the lowest excited levels are farther away from each other f o r light nuclei than f o r heavier and that therefore the number of possible combinations of these levels in a given energy region is much smaller in the first case than in the second. Not only the distances between the resonance levels, but also their half value breadths, are in general much larger in lighter nuclei than in heavier, indicating that the lifetime of the compound system is very much 5 Besides the total energy of the compound system also its spin and other symmetry properties may, as often pointed out, be of importance for the analysis of resonance phenomena. How such considerations can be brought into connection with the general picture of nuclear reactions here presented is discussed in a paper by F. Kalckar, I. R. Oppenheimer and R. Serber to appear shortly in Physical Revieu.
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shorter in the former case than in the latter. This comes first of all from the circumstance that the resonances in heavy nuclei are found only f o r very slow particles, where the probability f o r escape is extremely small, so that the lifetime of the compound system is only limited by the probability of emission of electromagnetic radiation, whereas in lighter nuclei the lifetime is in general entirely determined by the possibility of releasing comparatively fast particles. Quite a p a r t from this, we should, however, expect that the lifetime of a heavy nucleus-even if the nucleus were highly enough excited to emit fast particleswould be much longer than of a light nucleus on account of the lower temperature to be ascribed to a heavy nucleus than to a lighter one f o r a given excitation energy. I n fact, it would appear that quite simple considerations such as those here outlined enable us to account in a general way f o r the peculiar features of nuclear reactions initiated by collisions. Likewise it seems possible to explain the characteristic differences between the radiation properties of nuclei and those of atoms by means of similar considerations based also essentially on the extreme facility of energy exchange between the closely packed nuclear particles as compared to the approximately independent binding of each electron in the atom. The closer discussion of such problems will, however, claim more detailed considerations, which lie outside the scope of the present brief report.6
6 A more comprehensive account of the development of the ideas here presented will be published shortly in the Proceedings of the Copenhagen Academy by Mr. F. Kalckar and the writer.
XX. ON THE TRANSMUTATION OF ATOMIC NUCLEI OM SPALTNING AF ATOMKERNER 5 . nordiske Elektroteknikerm~de,J . H . Schultz Bogtrykkeri,
Copenhagen 1937, pp. 21-23 Lecture to a Meeting of Nordic Electrical Engineers on 27 August 1937 TEXT AND TRANSLATION
See Introduction, sect. 3, ref. 70
This Page Intentionally Left Blank
OM SPALTNING AF ATOMKERNER’) Af Professor N . Bohr, Kmbenhavn. Foredraget indlededes m ed en kort Oversigt over den Udvikling af Fysiken, som har fmrt ti1 vort nuvarende Kendskab ti1 Atomernes Opbygning og karakteristiske Egenskaber, og som indlededes ved Elektroneriies Opdagelse omkring Aarhundredeskiftet og navnlig tog Fart efter Rutherfords Opdagelse i 1911 af den saakaldte Atomkerne. Som bekendt forte disse Opdagelser ti1 den Forestilling, at ethvert Atom indeholder en positivt ladet Kerne af overordentlig smaa Dimensioner, hvori Storstedelen af Atomets Masse er koncentreret, og hvorom de meget. lettere negativt ladede Elektroner grupperer sig. Dette simple Billede af Atomet gjorde det muligt at drage en skarp Skillelinie mellem de Egenskaber hos Stofferne, der skyldes Atomkernens egen Struktur, og de der har deres Oprindelse i det ydre Elektronsystem. Saaledes er Stoffernes sadvanlige fysiske og kemiske Egenskaber betingede af den Maade, hvorpaa Elektronerne er bundne i Atomet, og vil derfor praktisk talt alene vare bestemt ved Kernens elektriske Ladning og kun i overordentlig ringe Grad af Kernens Masse og indre Bygning. Derimod skyldes de radioaktive Fanomener hos visse Grundstoffer Processer, hvorved selve Atomkernen undergaar Forandringer under Udsendelse af ladede Partikler med stor Energi - de saakaldte a- og 3-Straaler. Forskellen mellem disse to Grupper af Egenskaber understregedes paa szerlig tydelig Maade gennem Opdagelsen af StoHer - de saakaldte Isotoper -. der med iovrigt identiske fysiske og kemiske Egenskaber har forskellige A t o m v q t e og ofte tilmed forskellige radioaktive Egenskaber. Den narmere Undersmgelse a € det ydre Elektronsystems Opbygning frembod dog uventede Vanskeligheder, idet det viste sig, at den szdvanlige Mekaniks Regler anvendt paa Kerneatoniet ikke var i Stand ti1 at forklare den for Atomsystemer karak-
teristiske Stabilitet. Et Udgangspunkt for Lasningen af disse Vanskeligheder fandtes imidlertid i Plancks Opdagelse af Vjrkningskvantet, hvorefter de klassiske mekaniske Love kun har deres fulde Gyldighed i det Omraade, der indbefatter vore dagligdags Erfaringer, og hvor alle i Betragtning kommende Virkninger er overordentlig store i Forhold ti1 et enkelt Kvantum. Efter en langere Udvikling, der Skridt for Skridt har fort ti1 stadig mere vidtgaaende Endringer i vore wdvanlige fysiske Forestillinger, er det paa dette Grundlag i de senere Aar lykkedes at udvikle en ny mere omfattende Mekanik - den saakaldte Kvantemekanik - der paa fuldt konsevent Maade er i Stand ti1 at beskrive alle de Lovmassigheder, der er knyttede ti1 det ydre Elektronsystems Opbygning og Reaktioner. Trods de mange nye Traek, der komnier ind i Problemet om Atomhygningen, bevarer dette Problem imidlertid en overordentlig Simpelhed paa Grund af Elektronsystemets aabne Strulttur, der tillader i farste Tilnzrmelse at beskrive de enkelte Elektroners Bevagelsesforhold uafhaengigt af hinanden. Ved Problemet om Atomkernernes Opbygning og Egenskaber stilles man derimod paa Grund af den uhyre t a t t e Sammenpakning af Partikler i Kernerne overfor en Situation af en helt ny Art, hvor man mader vasentlig andre Lovmassigheder end dem, der gelder for Elektronbindingen i Atomet. Gennem de senere Aars store eksperimentelle Opdagelser indenfor Atomfysiken er imidlertid fremsltaffet et righoldigt Materiale, der allerede paa nuvarende Tidspunkt aabner Muligheder for et samlet Overblik over Atomkernernes vigtigste Egenskaber. Grundlaget for hele denne Cdvikling skabtes ved Rutherfords bermmte Forsog fra 1919, hvor det lykkedes ham, ved -4nvendelse af a-Partikler fra radioaktive Kerner som Projektiler, at frembringe
I) Nedenstaaende er en Sammenfatning af Indholdet af Foredraget, der blev holdt i mere fri Form med Benyttelse af et stort Antal Lysbilleder.
22
en Sanderdeling af Kvalstofkerner under Fraspaltning af Brintkerner. Dette banebrydende Arbejde efterfulgtes snart af en he1 Rakke Forseig over Kerneonidannelser, hvor det naste afgeirende Fremskridt bestod i, at man ikke som hidtil anvendte de natu1ligt forekommende a-Strxaler, men derimod kunstigt accelererede Brintkerner ved Beskydningen af Stofferne. De feilgende Aar bragte en Rakke nye opsigtsvaekkende Opdagelser indenfor Kernefysiken. Saaledes opdagede Chadwick i 1932 den saaltaldte Neutron, en neutral Partikel med omtrent samme Masse som Brintkernen. Denne nye Kernebyggesten, som viste sig at opstaa ved mangfoldige Kerneprocesser, kunde endvidere selv anvendes som Projektil ved Kernebeskydningen, og da den paa Grund af sin manglende elektriske Ladning havde langt steirre Evne ti1 at trange gennem Stof end de hidtil anvendte ladede Kerneprojektiler, lykkedes det ved Hj a l p af den at frembringe en stor Mangde nye Former for Kerneomdannelser. En helt ny Epoke indenfor Kernefysiken indlededes i Aaret 1933, da det lykkedes Egteparret JoliotCurie at vise, at talrige af de Grundstofisotoper, der dannedes ved kunstige Kerneomdannelser, var pstraaleradioaktive, idet de med en vis Halveringstid omdannedes under Udsendelsen enten af sadvanlige negative eller i visse Tilfalde positive Elektroner. Disse sidstnzvnte Partikler, de saakaldte Positroner, der er at betragte som en ny Slags Elementarpartikler, var iavrigt allerede opdaget Aaret forud af Anderson og Blackett ved Unders~gelserover de ved kosniiske Straaler frembragte Virkninger. De Kerneprocesser, der resulterer i Dannelsen af radioaktive Slutprodukter, er sarlig simple at analysere, idet man paa Grund af den Straaling, der udgaar fra det dannede Stof let kan undersecge dets kemiske Egenskaber og saaledes bestemme Omdannelsesprocessens Forbb, medens man tidligere for dette Formaal var henvist ti1 et ofte meget vanskeligt Studium af de udjagede Partiklers Natur. I den Forbindelse maa ogsaa henvises ti1 de store Muligheder, som Anvendelsen af de mange nye radioaktive Isotoper som Indikatorer ved kemiske og i s m biologiske Processer aabner. Paa det biologiske Omraade er saadanne Undersggelser navnlig udfort her i K~be nha vnaf Professor Hevesy i Samarbejde med en Rakke danske Biologer. Det store eksperimentelle Materiale, der i Leibet af de sidste Aar er blevet indsamlet paa Kernefysikens Omraade, har ogsaa bidraget ti1 Klarlaggelsen af visse karakteristiske T r a k ved selve Kerneomdannelsernes Forlob. Det har saaledes vist sig, at enhver saadan Omdannelse foregaar i to Stadier, bvoraf det farste bestaar i en midlertidig Sammen-
[2 161
smeltning af den indfaldende Partikel og den oprindelige Kerne, medens det andet Stadium bestaar i dette Mellemprodukts S~nderdelingunder Udsendelse af ladede eller uladede Kernepartiltler. Den forholdsvis store Stabilitet af Mellemproduktet beror derpaa, at Energien ved Sammensteidet paa Grund af Kernepartiklernes store Tathed straks fordeles saa ligeligt mellem alle disse, at ingen enkelt Partikel faar Energi nok til umiddelbart at forlade Kernen. En eventuel senere Bortgang af een af Kernepartiltlerne vil derfor fordre en saa at sige tilfaldig Koncentration af den n~dvendigeEnergi paa vedkommende Partikel, paa ganske tilsvarende Maade som Fordampningen af et Molekyle fra en Vadskedraabe kraever, at en vis Del af Varmeenergien i Draaben koncentreres som kinetisk Energi paa vedkommende Molekyle. Ved Hjalp af saadanne simple termodynaniiske .4nalogier har det virkelig varet muligt at gore Rede for flere af de mest karakteristiske Lovmassigheder ved Frigeirelsen af materielle Partikler ved kunstige Kerneomdannelser . Den store Mangde af eksperimentelle Erfaringer, der saaledes har givet 0s et Indblik i Atomkernernes Natur, har det kun varet muligt at opnaa ved Anvendelse af de vidunderlige eksperimentelle Hjalpeniidler, den moderne Elektroteknik har frembragt. Feirst og fremniest har Svagstreimselektrotekniken forsynet 0s med Forstxkeranordninger, der tillader 0 s at registrere eller talle Enkeltpartikler, som udsendes i Atomkerneprocesser, hvad enten det drejer sig om de fra kunstigt radioaktive Stoffer udsendte @-Partikler eller om Brintkerner eller a-Partikler, der udsendes under Atoms~nderdelinger. Men ogsaa Accelerationen af Brintkerner ti1 Brug som Projektilef ti1 .4toms~nderdeling har jo varet en Opgave af rent elektroteknisk Art. Ved de f ~ r s t eForseig i Rutherfords Laboratorium i Cambridge, der i 1932 u d f ~ r t e saf Cockcroft og Walton, anvendtes Udladningsreir, hvorved Brintioner opnaaede tilstrzkkelig Hastighed ti1 a t trange ind i lettere Atomkerner ved at gennemleibe et Spzndingsfald paa ca. M Million Volt, frembragt ved et System af Transformatorer forbundet med Ensrettere. En anden Type af H0jspandingsanlag, der er indfrart af van de Graaff ved Massachusetts Institute of Technology, er baseret paa en dristig Anvendelse af det gammelkendte Princip, der ligger ti1 Grund for Elektricermaskinens Virkning. Ved F o r s ~ gmed Spaltninger af tungere Atomkerner, der ogsaa altid har storre elektrisk Ladning, niaa de kunstiqt accelererede Projektiler have rneget store Hastigheder for at kunne overvinde den elektrostatiske Frastmdning, der modsatter sig deres I n d t r m gen i Kernen. Da det imidlertid frembyder store
Vanskeligheder og kraver uhyre Dimensioner at drive Hajspandingsanlaeggenes Spmding h ~ j e r eend ti1 I B z Millioner Volt, har det varet af stgrste Betydning, at det er lykkedes Amerikaneren E. 0. Lawrence at konstruere en elektromagnetisk Accelerator eller ))Cyclotron((,hvori man ved a t lade Brintionerne bevage sig i lukkede Baner i et stsrkt Magnetfelt ved Hjalp af et hajfrekvent Vekselfelt kan give dem en Rakke Accelerationer efter hinanden. TilTrods for, at de enkelte Accelerationer opnaas gennem Spandingsfald af nogle faa tusind Volt, kan den endelige Hastighed blive lige saa stor, som hvis Ionen havde gennemlobet et Spsendingsfald paa 10 Millioner Volt.
23 Begge de gmtalte Typer af Anlag ti1 Acceleration af Brint kerner har fundet udstrakt Anvendelse i Atomkerneforskningen, og flere saadanne -4nlag er under Bygning forskellige Steder i Verden. Det er gladeligt, at vi ogsaa i Danmark, paa Universitetets Institut for teoretisk Fysik, har kunnet paabegynde Opforelsen af et H0jspandingsanlag og en Cyclotron, takket vare storstilede TJnderstattelser fra Carlsbergfondet og Rockefellerfondet, samt fra Thomas B. Thriges Fond, der har skrenket Instituttet en sarlig konstrueret Elektromagnet af meget store Dimensioner, udfgrt paa Thriges Fabriker i Odense.
P A R T 1: P A P E R S A N D M A N U S C R I P T S R E L A T I N G T O N U C L E A R P H Y S I C S
TRANSLATION
On the Transmutation of Atomic Nuclei' By Professor N. Bohr, Copenhagen. The lecture began with a brief review of the development of physics which has led to our present knowledge of the structure of the atom and its characteristic properties. This started with the discovery of the electron at the turn of the century and got under way particularly after Rutherford's discovery of the so-called atomic nucleus in 191 1. It is well known that these discoveries led to the idea that every atom contains a positively charged nucleus of extremely small size, in which the major part of the mass of the atom is concentrated, and around which the much lighter negatively charged electrons are arranged. This simple picture of the atom made it possible to draw a sharp distinction between those properties of matter which depend on the proper structure of the nucleus, and those which have their origin in the outer electron system. Thus the ordinary physical and chemical properties of matter are dependent on the way in which the electrons are bound in the atom, and will therefore in practice be determined only by the electric charge of the nucleus, and only to an extremely small degree by its mass or internal structure. The radioactive phenomena in certain elements, on the other hand, are due to processes in which the nucleus itself undergoes transformations with the emission of charged particles of high energy - the so-called aand 6-rays. The distinction between these two groups of properties was underlined particularly clearly by the discovery of substances - the so-called isotopes - which, with otherwise identical physical and chemical properties, have different atomic weights and often in addition different radioactive properties. The further study of the structure of the outer electron system presented unexpected difficulties, because it turned out that the rules of ordinary mechanics, when applied to the nuclear atom, were unable to explain the stability characteristic of atomic systems. A basis for the solution of these difficulties was, however, found in Planck's discovery of the quantum of action, according to which the classical mechanical laws have their full validity only in the region, including our day-to-day experience, in which all relevant actions are extremely large compared to a single quantum. After a long development, which led step by step to ever more far-reaching changes in our normal physical ideas, the development of a new and more comprehensive mechanics - the so-called quantum mechanics - was achieved on this basis in recent years. This is capable of
'
Summary of the contents of the lecture which was given more informally with the aid of a large number of slides.
P A R T I : P A P E R S A N D M A N U S C R I P T S RELATING TO N U C L E A R PHYSICS
describing in a fully consistent manner all the regularities related to the structure and reactions of the outer electron system. However, in spite of the many new features which arise in the problem of the structure of the atom, this problem retains an extraordinary simplicity because of the open structure of the electron system, which allows, in first approximation, a description of the behaviour of individual electrons independently of each other. In the problem of the structure and properties of the nucleus, o n the other hand, one faces a situation of an entirely new kind, because of the extremely tight packing of particles in the nucleus, so that one here meets essentially different regularities from those valid for the binding of electrons in the atom. In the past few years great experimental discoveries in atomic physics have, however, created a wealth of material, which already at this time offers the possibility of an overall review of the most important properties of the nucleus. The basis for this whole development was created by Rutherford’s famous experiment in 1919, where he succeeded, by using a-particles from radioactive nuclei as projectiles, in splitting nitrogen nuclei with the ejection of hydrogen nuclei. This pioneer work was soon followed by a whole series of experiments on nuclear transmutations, and the next decisive step consisted in using, instead of natural a-rays as hitherto, artificially accelerated hydrogen nuclei for the bombardment of matter. The following years brought a number of sensational discoveries in nuclear physics. Thus Chadwick discovered in 1932 the so-called neutron, a neutral particle with about the same mass as the hydrogen nucleus. This new nuclear constituent, which was found to appear in a variety of nuclear processes, could in its turn be used as a projectile for bombarding nuclei. Since, because of its lack of electric charge, it has a far greater power to penetrate matter than the charged nuclear projectiles used before, it was possible to produce, with its help, a great number of new forms of nuclear transmutations. A new epoch for nuclear physics was introduced in 1933, when the JoliotCuries succeeded in showing that numerous isotopes created by artifical nuclear transmutations were /3-radioactive and transformed with a certain half-life with the emission of either negative or, in certain cases, positive electrons. These latter particles, the so-called positrons which have to be regarded as a new type of elementary particles, had actually already been discovered the year before by Anderson and Blackett in investigations of the effects of cosmic radiation. The nuclear reactions which result in the creation of radioactive end products are particularly simple to analyse, since by means of the radiation emitted by a given substance one can easily study its chemical properties, and thus determine the course of the transmutation, whereas previously one had for this purpose to rely on the often difficult study of the nature of the emitted particles. In this connection one should also mention the great possibilities opened up by the application
PART I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
of the many new radioactive isotopes as indicators for chemical and biological processes. In the field of biology such investigations are carried out particularly here in Copenhagen by Professor Hevesy in collaboration with a number of Danish biologists. The extensive experimental material which has been built up in the course of recent years in the field of nuclear physics has also contributed to the clarification of certain characteristic features of the course of the nuclear transmutations themselves. Thus it has been found that any such reaction proceeds in two stages, of which the first consists in a temporary fusion of the incident particle with the original nucleus, whereas the second stage consists in the disintegration of this intermediate product with the emission of charged or neutral particles. The relatively great stability of the intermediate product is due to the fact that in the collision the energy is shared immediately between all nuclear particles, because of their great density, and no single particle receives enough energy to leave the nucleus at once. A possible later departure of one of the particles will therefore require a, so-to-speak accidental, concentration of the necessary energy on the particle in question, in entire analogy with the way in which the evaporation of a molecule from a liquid drop requires that a certain amount of the thermal energy of the drop gets concentrated as kinetic energy on that molecule. With the help of such simple thermodynamic analogies it has actually been possible to account for many of the most characteristic regularities in the liberation of material particles in artificial nuclear transmutations. The great quantity of experimental results which have thus given us an insight into the nature of the atomic nucleus was made possible only by the application of the wonderful experimental facilities which modern electrical engineering has created. Primarily the weak-current techniques have provided us with amplifying arrangements which have allowed us to register or count single particles emitted in nuclear reactions, whether one is dealing with P-particles from artificially radioactive substances, or with hydrogen nuclei or a-particles emitted in atomic disintegrations. But also the acceleration of hydrogen nuclei for use as projectiles in atomic transmutations has, after all, been a purely electrotechnic task. The first experiments carried out by Cockcroft and Walton in Rutherford’s laboratory in Cambridge in 1932 used a discharge tube in which hydrogen ions acquired sufficient speed to penetrate into the lighter nuclei by passing through a potential difference of about 1/2 million volts, generated by a system of transformers connected with rectifiers. Another type of high-voltage installation, introduced by van de Graaff at the Massachusetts Institute of Technology, is based on a daring application of the long-known principle of the action of the electric induction machine. For experiments with the disintegration of heavier nuclei, which always have
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
also a higher electric charge, the artificially accelerated projectiles must have very high speeds to overcome the electrostatic repulsion which opposes their entry into the nucleus. However, since an increase of the tension in a high voltage set beyond 1 to 2 million volts meets serious difficulties and requires enormous dimensions, it was of the greatest importance when the American E.O. Lawrence succeeded in building an electromagnetic accelerator, or “cyclotron”, in which one makes the hydrogen ions move in closed orbits in a strong magnetic field with the help of a high-frequency alternating electric field, which can give them a series of accelerations in succession. Although each single acceleration occurs only in a potential difference of a few kilovolts, the final speed can be as large as if the ions had traversed a potential difference of 10 million volts. Both the described types of installations have found extensive applications in nuclear physics research and many such sets are being built in various places all over the world. It is pleasant that also here in Denmark, in the Institute for Theoretical Physics of the University, work has started on the erection of a highvoltage set and a cyclotron, thanks to the generous support from the Carlsberg Foundation, the Rockefeller Foundation, and also from the Thomas B. Thrige Foundation, which has given to the Institute a specially constructed electromagnet of very large dimensions, built in the Thrige factory in Odense.
[221]
XXI. ON THE TRANSMUTATION OF ATOMIC NUCLEI BY IMPACT OF MATERIAL PARTICLES I. GENERAL THEORETICAL REMARKS
(WITH F. KALCKAR)
Mat.-Fys. Medd. Dan. Vidensk. Selsk. 14, no. 10 (1937)
See Introduction, sect. 3, ref. 46.
Det Kgl. Danslte Videnskabernes Selsl
ON T H E TRANSMUTATION OF A T O M I C NUCLEI BY IMPACT O F MATERIAL PARTICLES I. G E N E R A L T H E O R E T I C A L REMARKS BY
N. B O H R
AND
F. KALCKAR
KBBENHAVN LEVIN & MUNKSGAARD I'JNAI1 hlL"I<S(;AAIII)
1937
Printed in Denmark. Bianco Lunos Bogtrykkeri AIS.
PREFACE
A
s indicated by the title the present paper was intended to form the first part of a treatise consisting of three parts to appear in immediate succession. The second part was planned as a more detailed elaboration of the theory of nuclear collisions on the general lines discussed here while the third part should contain an analysis on such lines of the available experimental evidence about nuclear transmutations. The publication of the present paper which was in print in January 1937 was, however, postponed and the completion of the other parts of the treatise delayed due to a visit of the authors to American universities in order to attend a number of conferences where nuclear problems were discussed. In the meantime the subject has been in rapid development due to the publication of several important papers during the last few months. Moreover a n admirable complete report of the present state of nuclear dynamics has been published by H. BETHEin “Reviews of Modern Physics”, 9, 69, (1937), in which are included detailed comments on some of the considerations here presented, based on verbal communications from the authors at a conference in Washington, February 1937. Under these circumstances the plan of publishing a more comprehensive treatise has been temporarily abandoned, and in order to bring the present paper up to date it has been completed by a n addendum written in October 1937 and containing references and brief comments of the most important recent contributions to the subject.
1*
TABLE O F C O N T E N T S Page
8 1. 8 2.
Basic i d e a s . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Nuclear level distribution . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5 3.
Radiative properties of nuclei.
8 4.
...........
13
Escape of neutrons from excited n u c l e i . . . . . . . . . . . . . . . . . . . . . 16
Q 5. Slow neutron collisions
8 6. 0 7.
5 8
20
.............................
Release of charged part Collisions between charged particles and n u c l e i . . , , , . . , . , , , ,
.......................
,
28
.
34
8
1.
Basic Ideas.
I
n a recent paper1 it was pointed out that the extreme facility of energy exchanges between the densely packed particles in atomic nuclei plays a decisive role in determining the course of nuclear transmutations initiated by impact of material particles. In fact, the assumption underlying the usual treatment of such collisions, that the transmutation consists essentially in a direct transfer of energy from the incident particle to some other particle in the original nucleus leading to its expulsion, cannot be maintained. On the contrary, we must realize that every nuclear transmutation will involve an intermediate stage in which the energy is temporarily stored in some closely coupled motion of all the particles of the compound system formed by the nucleus and the incident particle. On account of the strong forces which come into play between any two material particles at the small distances in question, the coupling between the particles of this compound system is N. BOHR, Neutron capture and nuclear constitution, Nature 137, 344 and 351, (1936), cited for brevity in the following as (A). A d d e d i n p r o o f . In a more recent article (Science 86, 161, 1937) a brief account of the later developments of t h e views presented i n the paper cited is given. A fuller account with more detailed references to the previous litterature on the subject is further contained in an address a t the International Physical Congress in Paris, October 1937, which will soon appear in t h e congress communications.
6
Nr. 10. N. BOHR and F. KALCKAR:
in fact so intimate that its eventual disintegration - whether it consists in the release of an “elementary” particle like a proton or a neutron, or of a “complex” nuclear particle like a deuteron or an a-ray - must be considered as a separate event, independent of the first stage of the collision process. The final result of the collision may thus be said to depend on a free competition between all the various disintegration and radiation processes of the compound system consistent with the general conservation laws. From this point of view the treatment of nuclear transmutations initiated by collisions will imply in the first place a n examination of the balance between the separate processes involved in the formation and disintegration of the semistable intermediate system. Notwithstanding the suggestiveness of simple mechanical analogies (A, p . 351) the discussion of this problem obviously demands proper quantum theoretical considerations. In fact, not only are the possible energy states of the compound system generally restricted by the laws of quantum mechanics, but also the formation or disintegration of this system will often involve characteristic quantum mechanical effects of the kind well known from the successful explanatibns of the laws of radioactive decay due to CONDONand GURNEY,and especially to GAMOW. Considerable modifications in the usual treatment of such problems, which rest upon the assumption that the incident particle within the nucleus to a first approximation moves in a fixed field of force, are necessitated, however, by the intimate coupling here assumed between the motion of the particles in nuclei. Still we shall see that the extreme thoroughness of this coupling actually introduces certain simplifications which permit one to draw a number of simple conclusions of a comprehensive character about nuclear reactions.
Transmutation of Atomic Nuclei by Impact of Material Particles. I.
7
Results of great interest on the constitution of atomic nuclei have been obtained, as is well known, by treating such nuclei as quantum mechanical systems built up entirely of neutrons and protons. This offers not only an explanation of the fact revealed by the study of band spectra and of the hyperfine structure of series lines that the intrinsic spin of the nucleus of any isotope is an odd or even multiple of the unit h / 4 n , according as its mass number is odd or even respectively, but also allows a general understanding of the way in which the stability of nuclei, and hence the occurrence of isotopes and the values of their mass defects, vary with mass and charge number. In this connection it may be especially noted that the important information about the forces between nuclear particles at and his close distances obtained in this way by HEISENBERG collaborators rests essentially upon an estimate of the average kinetic energy of these particles in the normal state of nuclei. Since protons as well as neutrons obey the Pauli exclusion principle, this kinetic energy will in fact be nearly independent of the conditions of motion assumed for the nuclear particles and, as regards its order of magnitude, will always be comparable with what would be obtained if each particle was assumed to move in a separate cell within the nucleus. Any closer examination of the constitution of atomic nuclei based on the usual procedure in which, like the extranuclear electrons in atoms, each particle is assumed in the first approximation to move independently in a conservative field of force cannot, however, on account of the far more intimate coupling between nuclear particles, be expected to yield results which may be directly compared with the actual properties of nuclei. Notwithstanding the
8
Nr. 10. N. BOHR and F. KALCKAR:
promising attempts at a more rigorous treatment of the constitution of very light nuclei, we must for the moment be content to consider atomic nuclei as a state of matter of extreme density and electrisation, whose properties can only be explored by the analysis of the experimental evidence on nuclear reactions. Still, the circumstance that the excitation energy of the compound nucleus involved in ordinary experiments on nuclear transmutations is very small compared with the total energy necessary for the complete separation of all its constituent particles permits, as we shall see, a simple comparison to be made between many properties of nuclear matter and the properties of ordinary liquid and solid substances.
5 2. Nuclear Level Distribution. As shown in (A), the distribution of energy levels of excited nuclei exhibits a striking difference from what would be expected if such excitations, as ordinarily assumed, were due to a n abnormally high energy state of a single nuclear particle. Thus the experimental evidence concerning the capture of fast and slow neutrons by heavy nuclei with emission of radiation shows that the distance between the energy levels of such nuclei decreases rapidly with increasing excitation, with the result that the distribution of energy levels becomes practically continuous, even for excitation energies which - although sufficient for the escape of a neutron with great kinetic energy - are far too small to alter essentially the semistable character of the compound system. Even within the region of continuous distribution the mean life time of the compound system is probably more than a hundred thousand times as long as the time interval which a fast neutron would use in passing through a region
Transmutation of Atomic Nuclei by Impact of Material Particles. I.
9
of nuclear dimensions. The typical features of the nuclear level distribution are easily understood, however, if we realize that the stationary states of a nucleus must correspond to some quantized collective type of motion of all its constituent particles. In fact the rapid approach of neighbouring nuclear levels with increasing energy resembles (comp. A p. 346) the characteristics of the multitude of the linear combinations which may be formed by a number of independent quantities (see Addendum I). The nuclear level distribution has therefore very much the same character as that of the quantum states of a solid body, well known from the theory of specific heats at low temperatures (see Addendum 11). This analogy suggests a more direct comparison between the excitation of a nucleus and the vibrations of elastic substances, a comparison which is much simplified by the circumstance that apart from the very lightest nuclei the density of matter and energy is practically the same in all nuclei. Denoting by N the total number of protons and neutrons in such a nucleus, the volume will in fact be approximately given by
V
=
NP,
(1)
where 6 is about 3.10-l3 and may be taken as the diameter of the cell occupied by a n individual nuclear particle. Further the average kinetic energy of each particle in such nuclei will be given approximately by the simple formula
where h is Planck's constant, and ,u the nearly equal mass of a proton or a neutron. This gives for K approximately
10
Nr. 10. N . BOHRand F. KALCKAR:
20 M. e. V. and, since from measurements of mass defects the average binding energy of a neutron or a proton in a nucleus is found to be approximately 10 M. e. V., the average potential energy loss per nuclear particle becomes nearly 30 M . e. V. Just as 6 may be considered as a characteristic unit of length in nuclear problems, a suitable unit of time in such problems is given by the interval z, which a n elementary particle of kinetic energy K would use in covering the distance 6. This time interval which is approximately given by
sec is of the order of magnitude of The circumstance that the excitation energy of heavier nuclei is always very small compared with the total kinetic energy NK in the normal state of the nucleus invites us now to compare the nuclear excitations with the oscillations in volume and shape of a sphere under the influence of an elasticity E or surface tension w given by expressions of the type of e = C,K6-3; o = C,KdF2, (4) where the dimensionless factors C , and C , must be expected to be approximately constant for all but the lightest nuclei. Thus the frequences vE and vg of the oscillations of the simplest character of a sphere of volume V and density o are given by the familiar formulas y
E
E -
&l/av-io-&;vm
E
-
wl/sv-io-i,
(5)
which are easily tested by dimensional considerations. Putting o = p 6 - 3 we obtain from ( 5 ) by means of (l), ( a ) , and (4)
Transmutation of Atomic Nuclei by Impact of Material Particles. I.
11
for the energy differences between successive quantum states of the nucleus corresponding to such oscillations
A C E = h v , CS I / S x N - - b K ; A W E = h v ,
I/=,
N - h K . (6)
Due to the difficulty of estimating the numerical values of the constants C, and C, the main interest of these formulas is the variation of the energy differences with N . Thus the fact that the average energy differences between the lower excited states of nuclei varies decidedly faster than N-b and even somewhat more rapidly than N - 6 shows that, at any rate for heavier nuclei, simple elastic vibrations corresponding to A C E are not responsible for the lowest excited states and can only be expected to be present for higher excitations. The circumstance, however, that d,E corresponds more closely to the way the average distance of the lower levels decreases with N , suggests a more direct comparison of surface oscillations with the fundamental modes of nuclear excitation responsible for the main features of the level distribution. Still the fact that the proper surface energy of nuclei estimated from the mass defect curves1 give, when introduced in (4) and (6), values for d,E of more than a million volts even for heavy nuclei, where the average level distance is certainly not more than a few hundred thousand volts, shows the great difficulty involved in such a comparison (see Addendum 111). Obviously any such simple considerations can at most serve as a first orientation as regards the possible origin of nuclear excitations. In a closer discussion of this problem more detailed considerations regarding the specific character of the interactions between the individual nuclear particles on the stability as well as of the excicf. C. F. v. WEIZSACKER, Die Atomkerne, Leipzig 1937.
12
Nr. 10. N. BOHRand F. KALCKAR:
tation mechanism of nuclei are needed. This is in fact not only indicated by the well known periodicities in the mass defect curve but also by the marked difference observed between the distances of the ground level and the excited levels for nuclei with even and odd mass and charge numbers. These effects must obviously be ascribed to the different degrees of saturation of the forces between pairs of nuclear particles obtainable in such nuclei on account of the restrictions implied by the Pauli principle in a more rigorous quantum mechanical treatment of the many body systems concerned. Due to the close coupling of the motion of the nuclear particles it would seem difficult, however, at the moment to discern to what extent conclusions concerning the exchange character or the spin dependence of the specific nuclear forces are reliable, when based on considerations of nuclear models with weak coupling between the particles. In particular any attempt of accounting for the spin values by attributing orbital momenta to the individual nuclear particles seems quite unjustifiable. We must in fact assume that any orbital momentum is shared by all the constituent particles of the nucleus in a way which resembles that of the rotation of a solid body. Denoting by J the moment of inertia. we obtain
as an estimate of the energy differences between the lowest quantum states of such rotations. For heavy nuclei ( 7 ) gives values small compared with the average level distance and may therefore possibly explain the fine structure observed for many energy levels of such nuclei. Part of
Transmutation of Atomic Nuclei by Impact of Material Particles. I .
13
this fine structure and perhaps many other of the characteristic features of the structure of the lower level distribution may, however, be attributed to the orientations of the intrinsic spins of the nuclear particles relative to each other and to the resulting angular momentum of the nuclear motions (see Addendum IV).
g
3. Radiative Properties
of Nuclei.
As first revealed from the study of so-called internal conversion of y-rays, the radiation emitted from excited nuclei will often show polarity properties differing essentially from that of an excited atom containing an electron in an abnormally high quantuni state. While in the atomic case the intense radiations are always of dipole type, nuclear radiations corresponding to poles of higher order are found to be relatively intense. It is true that this is just what should be expected if nuclei could be considered as composed entirely of constituents like a-particles, all having the same charge and the same mass, because in that case the electric center would always coincide with the mass center and exclude the appearance of any dipole moment1. In the more general case, however, where nuclei must be considered to be built up of protons and neutrons, the appearance of dipole moments must - quite independent of the character of the forces between the particles -- obviously be expected to appear, if the coupling is assumed to be so small that the state of the nucleus can be described by attributing well defined quantum states to each particle. If, on the contrary, the coupling between the motions of the individual particles is assumed to be so intimate that we have only to do with collectively quantized states of the Comp. N. BOHR,Journ. Chem. SOC. p. 381 (1932).
14
Nr. 10. N. BoHn and F.
KALCKAn:
whole nucleus, the situation will obviously be very different. In fact, unless the excitation is so high that the relative position of neighbouring particles is essentially affected, the radiative properties of the nucleus must be expected to show a close resemblance with that of a rotating or oscillating body with practically uniform electrisation and, due to the approximate coincidence of the charge and the mass center, dipole moments will under such conditions be absent or at any rate much suppressed. Such a comparison also makes possible a quantitative estimate of the probabilities of the radiative processes responsible for neutron capture. In fact, for an oscillation of the nuclear matter with frequency v and relative amplitude a the quadrupole radiation emitted per unit time will be approximately
R
E2 ( 2 7 ~ -~a)2 ~d 4 , C5
where E = Ze is the total electric charge, and d =; 6 the diameter of the nucleus. Further we have for a low quantum state hv (2nv)' ct2 d 2 M , (9) "'8
where M = N p is the total mass of the nucleus. Eliminating a from (8) and (9) we get for the probability of a radiative transition in unit time
Now the life time of the excited nuclear states formed by slow neutron impact on heavy nuclei corresponds to a value of f r about z-' lo-' and this agrees with ( l o ) , if h v for the most probable radiative transition is of the order of a million volts, as would seem consistent with general experimental evidence.
Transmutation of Atomic Nuclei by Impact of Material Particles. I.
15
Formula (10) holds of course only in the case of a transition actually accompanied by a quadrupole radiation. For nuclear excitations corresponding to radial pulsations or to simple rotations even the quadrupole moment will, however, disappear and radiative transitions will become still more improbable1. As regards the question of radiative transitions between any two levels of a n excited nucleus, it must also be noted that the various possible types of oscillations can generally not be expected to be independent of each other. In fact a n estimate by means of (9) of the amplitudes of these oscillations shows that even for heavy nuclei such amplitudes will be small compared with nuclear dimensions only for the lowest quantum states. In general there will therefore probably be a close coupling between the elastic vibrations of the different types, which may explain the observation of the frequent appearance of comparatively hard radiation from excited nuclei corresponding to transitions between distant nuclear levels2. In this connection it may be hoped that further experiments on the radiation emitted from excited nuclei as well as on nuclear disintegrations produced by y-rays will help to clear u p the question of the mechanisms of the excitation of nuclei (see Addendum V). C. F. v. W E I Z S ~ C K Naturwiss. EH, 24, 813, (1936) has recently suggested that the appearance of so-called isomeries among the artificial radioactive elements may be explained by the extremely small probabilities which radiative transitions with a change of angular momentum of several times h / 2 n would have on a n y nuclear model. In this connection it may be of interest to call attention to the possibility t h at the uniformity of the electrisation of the densely packed nuclear matter may also make the probabilities of radiative transitions as well as of internal conversion processes between certain other pairs of nuclear states extremely small. * Cornp. esp. S. K I K U C H I , K. HUSIMIand H. AOKI, Nature 1:{7, 992. (1936).
16
Nr. 10 N. BOHHand F. KALCKAR:
8 4. Escape of Neutrons from Excited Nuclei. As already mentioned in 0 1, the disintegration of
the compound system involved in nuclear transmutations must be considered as a n event depending only on the state of this system and not on the way in which it is formed. Such disintegrations demand in fact a so to speak fortuitous concentration on the individual particle released of a n essential part of the energy temporarily stored in intrinsic motions of the nuclear matter. These characteristic features of nuclear dynamics appear especially clearly in the case of the disintegration of the compound system which results in neutron escape. In fact, in the case of release of charged particles the electric repulsion extending beyond the range of the proper nuclear forces may under certain circumstances have a considerable influence on the probability of the disintegration, and this essentially quantum mechanical effect cannot always, as we shall see in 8 6 be unambiguously seperated from the kinematical conditions for the liberation of a particle from the nuclear matter. Even in the case of neutron collisions classical mechanical considerations cannot be unambiguously applied to the motion of the neutrons outside the nucleus, unless the de Broglie wave length
is shorter than or at any rate comparable with nuclear dimensions. Strictly we cannot speak of a definite estakrlishment of interaction between a free neutron and some particle within the nucleus, unless 2 is comparable with 6. The formaticn of a semistable compound system, which under such conditions will in almost every case result from contact
Transmutation of Atomic Nuclei by Impact of Material Particles. I. 17
between the incident neutron and the surface of the nucleus, closely resembles in fact the adhesion of a yapour molecule to the surface of a liquid or solid body. Conversely the disintegration of the compound system with neutron release exhibits a suggestive analogy to the evaporation of such substances at low temperatures. This analogy has been emphasized by F R E N K E L in a recent paper1 in which he has derived, by a comparison with the well-known evaporation formula, a n expression for the probability of neutron escape from a n excited nucleus which, in our notation, can b e written
\\.here W is the work necessary for the liberation of a neutron from the nuclear matter, T the effective temperature and lc Boltzmann's factor. This temperature energy of estimates by assuming that the the nucleus FRENKEL excitation energy is distributed according to Planck's formula over a multitude of oscillators equal in number with the intrinsic degrees of freedom of a system consisting of N particles. If U is the total excitation energy of the nucleus, this gives
where the summation is extended over all the oscillators. Assuming further that the frequencies of these oscillators are all comparable with the lowest frequencies of the radiation emitted from excited nuclei, he obtains for the
'
J. FRENKEL,Sow. Phys. 9, 533, (1936).
Vidensk.Selsk. Math.-fys. Medil. XIV. 10.
2
IS
Nr. 10. N . BOHR and F. KALCKAR:
compound system formed by the collision between a neutron and a heavy nucleus values for k T of a few hundred thousand electron volts. Introduced in (12), this gives values for r,, considerably smaller than the probability of neutron escape estimated from experiments. Since W is about 10 M. e. V. the formula is, however, very sensitive to the estimate of T and a far better agreement with experimental values is actually obtained, if we take into account that the possible oscillations of the nuclear matter have very different frequencies varying from the values given by formulas like ( 7 ) u p to values of the same order of magnitude as K l h . Practically all the excitation energy of the compound system is therefore stored in a few oscillations of the nuclear matter of smallest frequencies and accordingly the temperature of the nucleus calculated by (13) will be several times as high as that estimated by FRENKEL, and becomes quite sufficient to secure an approximate agreement with the observed disintegration probabilities in the cases where a reasonable accuracy of formula (12) can be expected. A quantitative comparison between ordinary evaporation and neutron escape from the compound system is in fact limited not only by the difficulty involved in a n accurate estimate of the effective temperatures of this system but also by the circumstance that the excitation of the residual nucleus left after the escape of a neutron will generally be much smaller than that of the compound system, in contrast with usual evaporation phenomena where the change in the heat energy of the bodies concerned, during the escape of a single vapour molecule, is negligibly small. A formula like (12) can therefore only be expected to give approximately correct results when the average excitation of the
Transmutation of Atomic Nuclei by Impact of Material Particles. I . 19
residual nucleus, although always smaller than that of the compound system, is still of the same order of magnitude. (See Addendum VI). In such cases a comparison between neutron escape from the compound system and ordinary evaporation offers, too, a simple explanation of the relative probabilities of different disintegration processes leading to different excited states of the residual nucleus. In fact, formula (12) gives primarily a n estimate of the probability of those disintegration processes in which the energy of the escaping neutron is approximately the same as that of a gas molecule at the temperature concerned, and the relative probabilities of the escape of neutrons with higher velocities must be expected to be smaller in approximate conformity with Maxwell’s velocity distribution of gas molecules. Actually such a comparison offers a simple explanation of the observation that i n nuclear reactions resulting in neutron release the probability of a neutron leaving the nucleus with the total energy available is generally very small, if this energy is large compared with the temperature energy. (See Addendum VII). Similar considerations are also in qualitative agreement with the observed great probability of energy transfer in collisions between nuclei and neutrons of kinetic energy greater than the energy difference between the normal and the lowest excited states of the nucleus. While this effect contrasts so strikingly with the usual ideas of nuclear collisions it is (compare (A), p. 347) nevertheless readily explained by the smaller demands on the concentration of the energy stored in the nuclear matter necessary for neutron escape in such disintegrations of the compound system as leave the residual nucleus in an excited state 2*
20
Nr. 10. h'. B O H Hand E'.
I
than in such as leave it in its normal state. I n ver? violcnt collisions, where the energy of the compound system is comparable or even larger than I<, \ve should further expect that several particles would leave this system in successive separate disintegration processes l. If such a disintegration process results in the escape of a neutron its most probable energy \vill be of the same order of magnitude as the teniperature energy of the compound system, \vhile, if a charged particle is released, its energy will h e higher o n account of the additional effect of the electrical repulsion beyond the nuclear surface, which in a case like this h a s only a minor influence on the liberation process itself. (See 5 6 ) .
5
5 . Slow Neutron Collisions.
I n the case of collisions between nuclei a n d neutrons with such small kinetic energies that the de Broglie \yave length (1 1) is very long compared with nuclear dimensions we cannot, as h as been mentioned, speak in a n unambiguous way about contact between the neutron a n d the nucleus. Accordingly every simple basis is evidently lost for a n ordinary mechanical description of the formation of the compound system or its disintegration. This is also sho\vn most strikingly b y the remarkable phenomena of capture of slow neutrons for which effective cross sections have been found amounting to several thousand times of simple nuclear cross sections. In these highly selective phenomena we have obviously to do with a typical q u a n tu m mechanical resonance effect where, although the collision process can The escape of more than one neutron in nuclear collision has recently been observed in fast neutron collisions by F. HEYH, Nature 138, 723, (1936).
Transmutation of Atomic Nuclei by Impact of Material Particles. I. 21
still be separated in well defined stages, the probabilities of successive stages cannot be estimated independently of each other. In the first attempts to explain the appearance of such resonance the neutron was supposed to move within the nucleus in a fixed field forming a so-called potential hole. On account of the great fall in potential, the kinetic energy of the neutron within the hole would in fact be so large that its wave length became smaller than the diameter of the hole, although the wave length outside was much larger. This great change in wave length therefore effects an almost complete reflection of the neutron wave from the inner walls of the hole, allowing a standing wave of considerable intensity to be built up for suitable energy values of the neutron. As a consequence of the existence of such a semistable state of motion of the neutron within the nucleus there will appear for these energy values both an abnormally large scattering effect corresponding to the reemission of the neutron from this state and a considerable probability of capture of the neutron resulting from a radiative transition to a lower energy state within the potential hole. Although this picture in a very instructive way illuminates essential features of the resonance effect, it was soon found quite insufficient to account for the details of the phenomena observed. In particular an estimate of the probability of radiative effects in such simple collision processes shows that the probability of scattering will always be greater than or comparable with the probability of capture in contrast with the experimental results, according to which the often extraordinarily large capture probability of slow neutrons is in no case found to be accompanied by a n excessively high scattering effect.
22
Nr. 10. N. BOHRand F. KALCKAR:
To overcome this difficulty. G. BREITand E . W I G N Ehave R~ proposed a modification of the explanation of the resonance effects in slow neutron collisions according to which, in the intermediate state another nuclear particle through its interaction with the incident neutron is lifted from its normal state to a higher quantum state at the same time as the neutron becomes itself bound in some stationary state in the nuclear field with an energy too low to allow its immediate escape. On account of the small power of penetration of the incident neutron wave into a potential hole of nuclear dimensions even a relatively small probability of energy transfer from the neutron to another particle bound in the nucleus is in fact, as they showed, sufficient to reverse the balance between the scattering and the radiative processes in such collisions. Still, as was already pointed out in (A), the observed extraordinary sharpness of the resonance phenomena and their comparatively frequent occurrence demand a much longer life time of the intermediate system and a much closer distribution of its energy levels than any nuclear model with weak coupling between the individual particles can give. The decisive progress in the treatment of the resonance problems by BREIT and WIGNER consists, however, in the establishment of general formulas for the variation of the cross sections of neutron scattering and capture in the resonance region, which are of great value for the analysis of the experimental evidence. Denoting by r, and I; the probabilities of neutron disintegration and of radiative transitions of the compound system respectively these cross section formulas can be written BREITand WIGNER,Phys. Rev. 49, 519, (1936).
Transmutation of Atomic Nuclei by Impact of Material Particles. 1.
23
where 1 and E are the wave length and kinetic energy of the incident neutron respectively, and E , is the energy value to be ascribed to the semistable stationary state of the compound system. The remarkable resemblance of (14) and (15) with well known optical dispersion formulas is most suggestive and illustrates in particular the difficulties of separating simply in resonance collisions the probability of the formation of the compound system from the probabilities of the competing disintegration and radiation processes of this system. While the ratio between the latter probabilities as always alone determines the relative yields of scattering and capture, we see from the dependence of the absolute values of these yields on r, and r,. how these probabilities also influence the degree of resonance obtainable and thereby the probability of the formation of the compound system. As regards the discussion of the experimental evidence by means of (14) and (15). it is especially important that it in principle is possible from measurements of the breadth of the resonance region /3
= I1
(rn+ rr.)
(16)
and of the maximum capture cross section
to determine r, as \veil as
r,..The closer
analysis of the phenomena shows that for heavier elements I-,. is of the order of
24
N r . 10. N. BOHR and F. KALCKAR:
sec-l, and that the ratio of r, and r, for neutrons of temperature velocity is about lo3. While r, over a considerable energy region must be expected to vary only slowly with energy, r, will, as follows from quite simple quantum mechanical arguments, be directly proportional to the velocity of the incident neutron in the energy region, where the neutron wave length is large compared with nuclear dimensions, because in such a case the balance between the processes will depend only on the probability of the presence of a neutron close to the nucleus'. \Ye shall therefore expect that rn and r, will be of the same order of magnitude for neutron energies of about l o 5 volts. For still higher energies I n must be expected to increase still more rapidly and soon become much greater than r, in conformity with the experimental evidence regarding fast neutron collisions 2. In the formulas (14) and (15) it is presumed that only one semistable state of the compound system is responsible for the anomalous variation of the cross sections for capture As pointed out by 0. R. FRISCHand G. PLACZEK, Nature 13i, 357, (1936), and by P. WEEKES,M . LIVINGSTONE and H. BETHE,Phys. Rev. 49, 471 (1936), such simple arguments offer a direct method of gauging small neutron velocities. In fact the cross section for nuclear disintegrations initiated by slow neutron impacts and resulting in the release of fast a-rays will over a large energy region with high approximation be inversely proportional to the neutron velocity, since in such a case t h e life time of the compound system will be very small and all typical resonance effects will disappear as also shown by formula (15), if B given by (16) is very large compared with the energy of the incident neutrons in t h e whole region concerned. In a recent paper by H. BETHEand G. PLACZEK, Phys. Rev. 61, 450, ( I 937), a detailed discussion of the expcrirnental evidence regarding slow
neutron collisions is given. In this paper formulas of somewhat more general type than (14) and (15) are developed, in which an explicit account is taken of the influence on the resonance phenomena of the spin properties of the nuclei concerned.
Transmutation of Atomic Nuclei by Impact of Material Particles. I.
25
and scattering. Just as in the case of optical dispersion it is possible, however, to account for the combined effects of several resonance levels, if only the breadth of each level is small compared with the distance between neighbouring levels. In case the compound system in the energy region concerned has a continuous level distribution such an analysis cannot be unambiguously performed, but - if in this region the wave length of the incident neutron is still large compared with nuclear dimensions - the cross section for scattering and capture will be given by the simple expression (17), if the Z”s are identified with the slowly varying probabilities of disintegration and radiation of the compound system. In fact, in contrast to the case of collisions with fast neutrons, the cross sections will in this region be determined by a balance between the processes of formation and disintegration of the compound system which quite resembles that in complete resonance. (Addendum VIII).
5
6 . Release
of Charged Particles from Nuclei.
As is well known from the quantum mechanical explanation of u-ray disintegration of radioactive nuclei, a charged particle may escape from a nucleus even if its potential energy in the region just outside the proper nuclear surface would be larger than its kinetic energy at great distances. In fact, a most instructive explanation of the characteristic relation between the energy with which a-rays are expelled from radioactive nuclei and the average life time of such nuclei has been obtained by comparing these disintegrations with the escape of a particle through a fixed potential barrier around the nucleus formed by the combined action of the attraction between the nuclear particles at small distances and their electrostatic repulsion
26
Nr. 10. K. B O H Rand F. KALCKAR:
beyond the range of these forces. As well known from GAMOW’Stheory, we get in this way for the probability of disintegration per unit time
where ni and E are the mass of the particle and the energy with which it is expelled, P ( r ) is the potential of the particle at the distance r from the center of the nucleus, a is the inner radius of this barrier, and b the classical distance of closest approach. Formula (18) has in particular been used as a basis for estimates from the known disintegration constants of the radii of radioactive nuclei. The recognition of the decisive influence of energy exchanges between the individual nuclear particles on the probability of the release of uncharged particles from the compound system formed by nuclear collisions raises, however, the question to what extent such estimates are reliable. In fact we have to consider that the a-particle before its expulsion does in no way move freely in a fixed potential hole but that its escape from the nucleus must rather be considered as composed of two more or less sharply separated steps, of which the first consists in the release of the a-particle from the nuclear matter, and the second in its penetration as a free particle through a potential barrier. Comparing the first step of this process with the escape of fast neutrons from highly excited nuclei, BET HE^ has in a recent paper concluded that the penetrability of the a-particle barrier must be many times larger than hitherto assumed and has thus arrived at values for nuclear radii which are considerably larger than those H. BETHE, Phys. Rev. 60, 977 (1936).
Transmutation of Atomic Nuclei by Impact of Material Particles. I.
27
ordinarily adopted and which would require a radical change in all estimates of the effect of the extranuclear electric forces in charged particle reactions. As regards such a n argumentation it must be remembered, however, that while the outer slope of the barrier is determined entirely by the electric repulsion between the nuclear particles at large distances, its inner rise is essentially due to the peculiar nuclear forces at small distances. The disintegration of the imaginary nucleus, which would remain after the complete elimination of the barrier, would therefore not be opposed by the nuclear forces in the same way as the escape of neutral particles from real nuclei, and the difference between two such processes will obviously be the larger the more the top of the potential barrier is raised over the energy of the escaping particle. In the particular case of radioactive nuclei in their normal state, where the height of the a-ray barrier is of the same order of magnitude as K , the instability of the nuclear system which remains after the eliniination of this barrier would thus seem to be so large that the probability of disintegration of the nucleus would be practically determined by the barrier effect alone. Notwithstanding the ambiguity inherent in all estimates of nuclear radii without a closer discrimination between various possible types of nuclear reactions, it would therefore seem that estimates of the radii of radioactive nuclei by means of formulas of the type of (18) can hardly be changed greatly by taking the many body aspects of the problem into account. (See Addendum IX.) Compared with a-ray decay of radioactive nuclei in their normal state the relative influence of the repulsive forces and the energy exchange between the individual nuclear particles on the disintegration probabilities is com-
28
Nr. 10. N. BOHRand
F. KALCKAR:
pletely reversed in the highly excited compound nuclei formed by collisions where, as already remarked in 8 4, the direct effect of the repulsive forces will often simply be a subsequent acceleration of the charged particles evaporating from the nuclear matter. This effect is especially clearly shown in the much studied nuclear transmutations initiated by a-ray impact on light nuclei and resulting in the expulsion of high speed protons. Resembling the circumstances of neutron escape from excited nuclei it is found that, as soon as the energy is large enough, it is more likely that the nucleus after the proton expulsion is left in an excited state than in its normal state. The only difference between the relative abundance of the various proton groups appearing in such transmutations and that of the corresponding neutron groups is, in fact, that due to the repulsion even the slowest protons have energies markedly higher than the temperature of the compound nucleus. Still, as regards the estimate of the absolute values of the disintegration probabilities by means of evaporation formulas of the type (12), it must be remembered that the latent heat of evaporation cannot be simply identified with the energy necessary to remove a proton in the normal state of the compound nucleus to infinite distance, but that the potential of the proton just outside the nuclear surface must be added to this energy. § 7 . Collisions between Charged Particles and Nuclei.
In nuclear transmutations initiated by impacts of charged particles we can, if the energy of these particles is sufficiently large as in fast neutron collisions, consider the formation of the compound system as a direct consequence of a contact between the incident particle and the original nucleus. In case of charged particles, however, the energy
Transmutation of Atomic Nuclei by Impact of Material Particles. I .
29
must of course be so large that even after the penetration through the electrostatic repulsive field around the nucleus the wave length of the incident particle is still small compared with nuclear dimensions. For impacts of high speed a-particles on lighter nuclei the approximate fulfilment of these conditions for a simple treatment of the formation of the compound system is proved by the fact that the total yield of the disintegration processes is nearly independent of the velocity of the incident particles. This is particularly clearly shown in certain cases where as well protons as neutrons can be released in comparable abundance as a result of the collision, and where it is found that the sum of the yield of protons and neutrons is remarkably constant over a large region of u-ray energy, even if their relative abundance may vary considerably within this region1. At the same time this observation shows most strikingly that in such collisions we have not to do with any direct coupling between the individual protons and neutrons expelled and the incident a-ray, but that the proton and neutron release represents competing disintegration processes of the compound system2. In a-ray impacts with smaller energies we meet with a more complicated situation, partly because the energy levels of the compound system are no longer continuously distributed but more or less sharply separated and partly because the establishment of contact between the incident particle and the original nucleus presents in itself a typical quantum mechanical problem. As regards the latter question it is See 0. HAXEL, 2. f. Phys. 93, 400, (1935). A d d e d i n p r o o f . This point has recently also been emphasized by W. D. HARKINS,Proc. Nat. Acad. of Sci. 23, 120, (1937), who, without entering more closely on the question of the mechanism of nuclear reactions, already several years ago has advocated the view t h at nuclear transmutations are always initiated by the formation of a compound system.
30
Nr. 10. N. BOHRand F. KALCKAR:
well known that GAMOW'Stheory for the penetration through the potential barrier around the nucleus allows one, in many cases of nuclear disintegrations initiated by a-ray impact, to account satisfactorily for the variation of the output with increasing a-ray energy. It is, however, obvious that the remarkable maxima for certain a-ray energies observed in several nuclear disintegrations giving rise to the expulsion of high speed protons cannot be explained in the usual way by attributing such maxima to the presence of a semistable quantum state of the incident a-particle within the barrier, from which it may fall to some lower quantum state accompanied by the rise of the proton from its normal energy level within the nucleus to a level sufficiently high to allow its escape. In fact, no such explanation of the resonance effects, where in the first approximation the a-particle as well as the proton is supposed to move in a fixed nuclear field, can be reconciled with the large probability of proton emission by impact of faster a-particles, which may be assumed easily to penetrate into the interior of the nucleus. Indeed, as remarked incidentally by MOTTI already some years ago, this fact implies a coupling between the a-particle and a proton, which would be far too close to permit a resonance to develop even for lower a-ray energies, where the penetration of the a-particle into the nucleus is assumed to be essentially influenced by the potential barrier, but where the excess energy is still sufficient to permit the proton to pass unhindered over the top of the barrier. The resonance effect in question must clearly be attributed to a coincidence of the sum of the energies of the free a-particle and the original nucleus with that of a stationary state of the compound system corresponding to some quanN . F.
hfOTT,
Proc. Roy.
SOC.
133, 228, (1931).
Transmutation of Atomic Nuclei by Impact of Material Particles. I.
31
tized collective type of motion of all its constituent particles. The sharpness of these states and accordingly of the resonance effects will depend on the life time of the compound system, which will be determined by the sum of the probabilities of the various competing disintegration processes of this system. Apart from exceptional cases the release of protons will be far the most probable and will, as clearly shown by the velocity distribution of the emitted protons mentioned in 5 6, depend on an evaporation like process of the nuclear matter which only indirectly will be influenced by the presence of the repulsive forces outside the nucleus. This is not only in conformity with the existence of resonance in the energy region, where a proton would be able to escape without difficulty from the potential barrier, but also explains the fact that the width of the resonance levels for not too fast a-rays varies only slowly with increasing a-ray energy, although the ease with which an a-particle passes through the potential barrier should increase very rapidly with increasing a-ray energy. In a more detailed discussion of nuclear transmutation initiated by a-ray impacts it must further be taken into account that the wave length of the a-particle even in the resonance region is generally of the same order as nuclear dimensions and that therefore special attention must be paid to the possibilities of different values of its angular momentum relative to the nucleus and their influence on the absolute values of the effective cross sections for the disintegration process. This circumstance will in particular influence an estimate of the relative importance of the potential barrier and of energy exchange within the nucleus on the release probability of a-particles in the region concerned. It is in this connection also of interest to note that the
32
Nr. 10. N.
BOHR a n d F. KALCKAH:
phenomenon of so called anomalous scattering of a-rays in close nuclear collisions may not, as in the usual treatment, be entirely attributed to a deflection of the a-ray in a fixed field of force but may be essentially influenced by the possibility that a n a-particle is temporarily taken u p in the compound nucleus and subsequently emitted by a separate disintegration process. In nuclear transmutations initiated by artificially accelerated protons the repulsive forces will on account of the comparatively small energy of the incident particle have a preponderent influence on the whole phenomenon. This is also shown by the great accuracy with which the relative variation of the output with proton energy, apart from cases of exceptional sharp resonance, is given by GAMOW’S theory. Simple calculations of the probability of penetration of the protons through the potential barrier can, however, not explain the often remarkably large differences between the absolute values of thc output of transmutation processes by impact on different nuclei. These specific effects show in fact in a striking way the great extent to which the probability of the formation of the compound system in the proper quantum mechanical region may depend on the probabilities of disintegration processes of this system itself, which probabilities may again depend largely on the spin properties of the original nucleus and the disintegration pr0ducts.l In the particular case of highly selective capture of slow protons by certain light nuclei we meet, as regards the way in which the capture cross section depends on the probabilities of proton escape and of radiative transitions, Compare M. GOLDHABER, Proc. Camb. Phil. SOC. 30, 361 (1934); H E Y D E N B U R G and M. A. TUVE, Phys. Rev. 60, 504 (1936). (See also Addendum IV).
L. R. HAFSTAD, N. P.
33
Transmutation of Atomic Nuclei by Impact of Material Particles. I.
with a n especially instructive analogy to slow neutron capture, at the same time as the two phenomena exhibit extreme differences in mechanical respects. In fact the cross section for proton capture and the breadth of the resonance region can obviously be expressed by general formulas of the same type as (15) and (16), but while the probability of neutron release r, depends solely on energy exchanges within the nuclear matter the corresponding probability for proton escape will also largely depend on the extranuclear repulsion. Still due to the high excitation of the compound system the situation is essentially different from a-ray disintegration of radioactive nuclei in their normal state, discussed in paragraph 6, and the influence on of the mechanism of release of the proton from the nuclear matter will here be comparable with the barrier effect. Essential new features are exhibited by transmutations initiated by deuteron collisions where the output over larger energy regions is often very much greater than estimated by the quantum mechanical probability of a material point with charge and mass like that of the deuteron in reaching the surface of the nucleus. As pointed out by OPPENHEIMER and PHILLIPSwe must, however, here take into consideration that on account of the comparatively large size and small stability of the deuteron it may be disrupted during the collision with the result that the neutron is captured by the nucleus and the proton repelled by the extra nuclear field. For the smallest deuteron velocities this view seems actually to offer a satisfactory explanation of the experimental evidence. For larger deuteron velocities, where still the energy is too small to allow a sufficiently probable penetration of a charged mass point into the interior of the nucleus,
r,
r,
J . K. OPPENHEIMER and M. PHILLIPS, Phys. Rev. 48, 500 (1935). Vidensk. Selsk. Math.-fys. Medd. XIV. 10.
3
34
N r . 10. N. BOHRand F. KALCKAR:
it is, however, necessary to assume that even a partial overlapping of the regions, to be ascribed to the motions of the elementary particles of which the nucleus and the deuteron respectively are composed, may result in a complete fusion of the two systems into a semistable compound nucleus. On account of the weak binding energy of the deuteron the excitation of the compound nucleus will here be almost double as high as that which results from a neutron or proton impact. Still - except in the extreme case of mutual collisions between deuterons where the total energy approaches that of two free protons and two free neutrons too closely to allow a n intermediate state of sufficient stability - the excitation energy of the compound system will be so small compared with the total binding energy of its particles that, like in other nuclear transmutations, the collisions can be separated into two well defined stages. In fact just the great variety of the disintegration processes of the compound system made possible by the high excitation in deuteron collisions offers many instructive examples of the competition responsible for the final result of nuclear reactions.
Addendum. I. Under the simplifying assumption that each level represents a combination of a number of nearly equidistantly distributed quantities the density of nuclear levels for high excitation can be simply estimated by means of an asymptotic formula for the number of possible ways p(n) any integer may be written as a sum of smaller positive integers which has been derived by G. H. HARDYand S. RAMANUJAN (Proc. London Math. SOC.(2) XLII, 7 5 , 1918) and to which
Transmutation of Atomic Nuclei by Impact of Material Particles. I.
35
our attention has recently b e drawn. This formula can for large values of n be approximately written
If now for the unity we assume an energy value of 2*1O5 e. V. corresponding approximately to the average distance between the lowest levels of heavier nuclei, we get for the number of combinations with which an excitation energy of 8 * 1 0 6e. V. can he obtained p(40) S 2.104, meaning an average level distance of about 10 e. V. which roughly corresponds to the densities of the level distribution estimated from slow neutron collisions. 11. A closer theoretical discussion of the characteristic
features of the nuclear level distribution has been given by H. BETHE (Phys. Rev. 50, 332, 1936, and Rev. mod. Phys. 9, 69, 1937) who, on the basis of general theorems of statistical mechanics connecting the entropy of a thermodynamical system with the average energy, has estimated the density of energy levels of a highly excited nucleus for two different simplified models of nuclear excitation. In the first of these the coupling between the motion of the individual particles is entirely neglected for the sake of simplicity and the excitation energy is compared with that of a so called Fermi gas at low temperatures; in the second model the coupling is assumed to be close and the excitation energy is supposed to have its origin entirely in capillarity oscillations of the nuclear matter of the type discussed briefly in the text. Although none of these models can be assumed to reproduce the actual conditions in nuclei correctly, the calculations of BETHE offer instructive examples of the ways in which the typical character of the level scheme of nuclei 3*
36
Nr. 10. N. B O H Rand F. KALCKAR:
follows from the assumption that the excitation energy is shared by the nuclear particles in a way corresponding to a thermal equilibrium. Further interesting contributions to this problem have been given by L. LAXDAU (Sow. Phys. 11, 556, 1937) and V. W E I S S I ~ O P (Phys. F Rev. 52, 295, 1937) who, without introducing any special assumptions as regards the origin of nuclear excitation, have calculated the nuclear level density by thermodynamical methods, assuming that the mean value of the excitation energy for a heavy nucleus is proportional to the square of its absolute temperature. This condition, which also is fulfilled in the first of the two special cases discussed by BETHE, does actually mean that the fundamental modes of motion in nuclei have energy values which are nearly equidistant. It is therefore interesting to note that the formulas for the nuclear level density derived from thermodynamical analogies are - at any rate as regards the exponential dependence on the total excitation energy of the nucleus - practically identical with the expression for p(n) in Addendum I, if we by the number n understand the measure of the total energy with the energy differences between the lowest stales, as unit.
111. The question of the origin of nuclear excitation involves great difficulties due not only to the scarcity of our knowledge of the specific nuclear forces but also to the complications of the quantum mechanical problem concerned. The aim of the simple remarks in the text is therefore in the first line to discuss certain possibilities of a simplified semi-empirical treatment. While in this respect the existence of quasi elastic oscillations of nuclei suggests itself by a straightforward correspondence argument, it is,
Transmutation of Atomic Nuclei by Impact of Material Particles. I.
37
however, very doubtful whether such an argument can be legitimately applied to an analogy of nuclear excitation with capillary oscillations. In fact the comparison with a non viscous fluid involved in this analogy can hardly be maintained in view of the close coupling between the motions of the individual nuclear particles. Besides such a comparison would -- as kindly pointed out to us by Prof. PEIERLSat a recent discussion in Copenhagen - force us to consider other types of inner nuclear motions as well, which in particular would be inconsistent with the comparison mentioned in the text of the rotational motion within a nucleus and that of a rigid body. IV. The problem of the interaction between the orbital momenta and spin vectors of the nuclear particles has often been discussed not only in connection with the spin values of nuclei but also in attempts of accounting for the remarkable selection rules for various nuclear transmutations. Usually these effects are ascribed to a loose coupling between the orbital momenta of the individual particles and their spin vectors like that in atoms. In a recent paper by F. KALCKAR, J. R. OPPENHEIMER and R. SERBER (Phys. Rev. 62, 279, 1937) it is shown, however, that it seems possible to explain these rules merely by assuming that the total angular momentum and the resulting intrinsic spin of the nuclear particles are coupled sufficiently loosely to allow a well defined quantum mechanical specification of their relative orientations. V. A treatment of the nuclear photoeffect consistent with the views on nuclear excitation and radiation here discussed is attempted in a recent paper by F. KALCKAR, J. R, OPPENHEIMER and R. SERBER,(Phys. Rev. 62, 273,
38
Nr. 10. N. BOHRand F. KALCKAR:
1937). In particular it is shown how it is possible from the remarkable experiments by W. BOTHEand W. G E N T N E R with high energy y-rays (Naturwiss., 25, 90, 126, 191, 1937), to estimate the probabilities of radiative transitions from excited states to the normal state of the nucleus. For nuclei of medium atomic weight and 1 7 M. e. V. excitation these probabilities are in certain cases found to be of the order zrl* 1OW9 sec-l, i. e., about of the most probable radiation probabilities for such nuclei. This comparatively large probability of such distant transitions contrasts strikingly with what might at first sight be expected from a simple comparison (see L. L A N D A USow. , Phys. 11, 556, 1937) of the radiation froni an excited nucleus and a black body with the temperature of about a million volt per degree of freedom (see 9 4). Still it may be remarked that such a comparison involves difficulties due to the high degree of polarity of nuclear radiation and the close coupling between the various modes of excitation mentioned in the text. Moreover the apparently capricious way in which the yield of the nuclear photoeffects varies from element to element suggests that we have in transitions from these highly excited nuclear states to the normal state to do with some peculiar features of the radiative mechanism connected perhaps with the appearance of dipole moments. VI. A closer examination of the conditions for the application of an evaporation formula of the usual type to nuclear disintegration problems is given by V. WEISSKOPF in a recent paper cited in Addendum 11. On the basis of general methods of statistical mechanics a detailed discussion is given there not only of the limitation of simple thermodynamical analogies in nuclear problems due to
Transmutation of Atomic Nuclei by Impact of Material Particles. I.
39
the comparatively few degrees of freedom of the system concerned, but also of the generalisations of the usual thermodynamical procedure required for the proper treatment of such systems. VII. The energy distribution of neutrons escaping from highly excited nuclei has been especially closely studied in the case of the usual neutron source of Beryllium bombarded with a-rays. While here the distribution of the fast neutrons is found to agree closely with the theoretical expectations, a n apparent deviation is exhibited by the relative abundance of neutrons with energies far below the estimated temperature of the compound nucleus. This apparent difficulty disappears, however, if we assume that the slow neutrons in question must, as first suggested by P. AUGER(Journ. de Physique, 4, 719, 1933), be ascribed to a more complex process, the first stage of which is the escape of an a-ray from the compound system leaving a beryllium nucleus in an excited state, while the second stage consists in the subsequent breaking u p of this nucleus into two a-particles and a slow neutron. This view is further strongly supported by a recent experimental investigation by T. BJERGE(Proc. Roy. SOC.,in print). VIII. The question of the quantum mechanical resonance effects in case of continuous level distribution has recently been more closely discussed by F. KALCICAR,J. R. OPPENH E I M E R and R . S E R B E R in the paper cited in Addendum V, on the nuclear photoeffect, which presents special features analogous to the problem of nuclear transmutations initiated by impact of slow particles. A more comprehensive quantum mechanical treatment of nuclear reactions will further be given in a paper by F. KALCKARto appear shortly and
40
N r . 10. N . BOHRand F. KALCKAR:
in which it will especially be attempted to develop general arguments resembling the correspondence treatment of atomic radiation problems. IX. The question of the proper estimate of the nuclear radii to be derived from the analysis of a-ray disintegration of radioactive nuclei is further discussed by BETHE in his recent report on nuclear dynamics (Rev. of Mod. Phys., 9, 69, 1937), where he makes extensive use of the enlarged values of such radii which he has proposed in the paper cited on page 26. In this connection BETHE also comments on the criticism of this procedure of estimating nuclear radii given in the text and presented at the Conference in Washington (see Preface). Meanwhile an important contribution to this problem has been given by LANDAU in his paper cited in Addendum 11, where he has succeeded from very general arguments in deducing a comprehensive formula for the dependence of the probability of nuclear disintegrations under release of charged particles on the external repulsion as well as on the density of the level distribution of the nucleus in the energy region concerned. In the case of radioactive decay, where the levels are widely formula leads to values for the nuclear separated, LANDAU’S radii which differ only little from those derived from ordinary potential barrier formulas but which are essentially different from those proposed by BETHE. The closer connection between L A X D A l j ’ S treatment and the argumentation given in the text will be discussed in the forthcoming paper of KALCKARwhich was mentioned above.
Frerdig fra Trykkeriet den 27. November 1937.
XXII. NUCLEAR MECHANICS [l] MECANIQUE NUCLEAIRE
Actuulites scientifiques et industrielles: Reunion internutionale de physique-chimie-biologie, Congres du Palais de la decouverte, Paris, Octobre 1937, Hermann et Cie, Paris 1938; II - Physique nucleuire, pp. 81-82 Address to the International Congress of Physics, Chemistry and Biology in Paris, 30 September - 7 October 1937 TEXT AND TRANSLATION
See Introduction, sect. 3, ref. 71.
P A R T I: PAPERS A N D MANUSCRIPTS RELATIKG TO NUCLEAR PHYSICS
A report of this conference was given in Nature 140 (1937) 710-714. There is a summary of Bohr’s address on p. 71 1.
I
Mhanique nuckaire N . BOHR
Le but de la conference est de mettJre en relief les differences essentielles qui existent entre les proprietes dynamiques des noyaux et celles des systbmes atomiques, et d’indiquer les principales consbquences qui en resultent pour l’interpretation des &actions nuclbaires. Ces diff Brences decoulent du fait que les particules constituantes des noyaux sont concentrees dans des domaines beaucoup plus rbduits que ce n’est le cas pour les atomes. I1 suit de la, tout d’abord, que les forces determinant la constitution des atomes ne sont autres que celles que 1’0n peut dbduire de 1’Btude des particules lihres tandis que la structure des noyaux est conditionnee par des forces n’agissant qu’a trbs petites distances : ainsi l’explication de la constitution des atomes est basbe sur l’utilisation d’une loi d’interactjon bien connue, tandis que le problbme de la structure des noyaux ne peut &re ainsi &pare de celui de la forme des lois de forces nuclkaires. De plus dans les atomes, les mouvements des particules constituantes peuvent &re traites en premiere approximation comme independants les uns des autres : c’est justement sur cctte particularitit que repose l’explication du systbme pbriodique des elements ; dans les noyaux, au contraire le couplage entre les particules est si fort qu’aucune approximation de ce genre n’est possible. C’est pour comprendre les lois des transmutations nucleaires provoqubes par des coIIisions que Yon doit tenir compte essentiellement de cet etat de choses. On est conduit a imaginer, comme stade intermeCOWGBPB DE L A D 8 C O U V ~ T B ,11
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diaire d’une telle reaction, la formation d’un systeme compose dans lequel 1’Bnergie totale est distribude entre tous les constituants, et qui ne peut se desintegrer que lorsqu’une Bnergie suffisante se concentre sur l’un de ces constituants. Le rQsultat final de la reaction est donc determine par une concurrence entre les diverses possibilites de desintkgration e t de rayonnernent du systeme compose. De ce point de vue, la capture et I’expulsion de particules rapides peut 6tre traitee par analogie avec le phknomene de l’haporation. On arrive ainsi a definir une temperature du systeme compose, qui determine la vitesse des particules expulsees. Dans le cas o h les particules sont chargees, il faut en plus tenir compte des grandes forces electrostatiques de repulsion. Dans le cas des neutrons, au contrkre, ces forces n’existent pas, et l’on peut alors Qtudier la formation de systemes composes par chocs de neutrons tres lents, phenomene qui donne lieu A d’intkressants effets de resonance, et presente une grande analogie avec la dispersion optique. De ces effets on a pu deduire sur la densite des niveaux du systeme compose e t sur les probabilitks des differents processus de dksintbgration des renseignements detaillea, qui cadrent parfaitement avec la conception genbrale de la mecanique nuclkaire qui fait l’objet de la confQrence. ((
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PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
TRANSLATION
Nuclear Mechanics. The aim of the lecture is to bring out the essential differences which exist between the dynamical properties of nuclei and those of atomic systems, and to indicate the main consequences of this for the interpretation of nuclear reactions. These differences stem from the fact that the particles which constitute the nucleus are concentrated into much smaller domains than is the case for atoms. From this it follows, in the first place, that the forces which determine the structure of atoms are the same as those which one can deduce by studying free particles, whereas nuclear structure is governed by forces acting only over very short distances; thus the explanation of atomic structure is based on the use of a very well-known law of interaction, whereas the problem of nuclear structure cannot similarly be separated from that of the form of the nuclear law of force. Moreover, the movements of the constituent particles in the atom can in first approximation be treated as independent of each other: this is just the particular feature on which rests the explanation of the periodic system of elements; in the nucleus, on the other hand, the coupling between the particles is so strong that no approximation of this kind is possible. For the understanding of the rules of nuclear transmutations caused by collisions it is very essential to allow for this state of affairs. One is led to visualising, as an intermediate state of such a reaction, the formation of a “compound system” in which the total energy is distributed among all constituents, and which can disintegrate only when sufficient energy is concentrated on one of the constituents. The final result of the reaction is therefore det.ermined by a competition between the various possible disintegration modes and the emission of radiation from the compound system. From this point of view the capture and emission of fast particles can be treated in analogy with the phenomenon of evaporation. One is led to define a “temperature” of the compound system, which determines the velocities of the emitted particles. In the case of charged particles one has further to allow for the strong electrostatic repulsion. In the case of neutrons, however, these forces do not exist, and one can therefore study the formation of compound systems by the impact of very slow neutrons, a phenomenon which gives rise to interesting resonance effects, and presents a close analogy with optical dispersion. From these effects one has been able to derive detailed information about the level density of the compound system and about the probabilities of various disintegration processes, which agree perfectly with the general concept of nuclear mechanics which forms the purpose of the lecture.
XXIII. NUCLEAR MECHANICS [2] UNPUBLISHED MANUSCRIPTS 1937
See Introduction, sect. 3, ref. 7 2 .
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The folder “Nuclear Mechanics”, 1937, contains various drafts and notes in English, Danish and French, related to Bohr’s address at the International Congress of Physics, Chemistry and Biology in Paris, 30 September - 7 October 1937 (see document XXII). Except where otherwise indicated, the handwriting is Rosenfeld’s. 1 page, a carbon copy in French, contains two short addresses given by Bohr at the opening and closing of the conference. 2 handwritten pages in English in pencil are probably notes taken at the lecture. However, they bear little resemblance to the published version. 4 pages in Danish in pencil in Rosenfeld’s and Jacobsen’s handwritings apparently constitute outlines and lists of slides for the lecture. 7 numbered handwritten pages in English apparently constitute a detailed outline of the lecture or of a subsequent paper. 1 handwritten page in English in pencil, entitled “Nuclear Mechanics” seems to be an early draft of an outline of the lecture. 1 handwritten page in Danish (title in German: “Kerne und Atome”) in ink seems to represent the beginning of an early outline. 1 typewritten page in English, with corrections in pencil, entitled “Nuclear Mechanics”, may be intended as part of a paper for publication. It is dated 31 August, 1 handwritten page in Danish in pencil, dated 3 October 1937, seems to be a brief outline. 5 handwritten pages in Danish in pencil, dated 15-17 November 1937, may be notes for a published version of the lecture or the plan of a paper. There are two versions, entitled “Nuclear Mechanics” and “Nuclear Mechanics - New Plan”. 4 handwritten pages in English contain various alterations and additions. They are in pencil and ink in Kalckar’s and Rosenfeld’s handwritings. Finally there are 5 more or less complete drafts of the paper in English (one amendment in Danish), all entitled “Nuclear Mechanics”: Draft I : 10 typewritten pages (two pages mistakenly numbered 4). There is a carbon copy of this draft, where the second page 4 is missing and some pages are re-numbered in pencil. Draft 2: carbon copy of Draft 1 with numerous amendments in pencil in Rosenfeld’s and Kalckar’s handwritings. The numbering of the last pages has been corrected in pencil. There are 3 more pages in English and Danish in pencil, 2 in Rosenfeld’s handwriting and 1 in Kalckar’s handwriting, representing further amendments. This is the version reproduced here as Draft A . We have reproduced the corrected text, omitting a section on page 1 and the beginning of page 2 as was probably the intention (in any event the substance occurs in Draft B, described below). The last paragraph on page 2 has been cut off in the course
PART I: PAPERS AND MANUSCRIPTS RELATING TO KUCLEAR PHYSICS
of re-drafting, but this was not completed and we have included it in its original position. The last of the preceding part of page 2 has been replaced by a handwritten page which apparently was intended to supersede the original typescript. However, another handwritten page, indicated as a correction to page 3, has not been used because the typed text seemed more informative. The page in Kalckar’s handwriting has not been used since it is in the nature of notes for amendment rather than an amended text. Finally, there are 4 handwritten pages which probably represent further modifications, but which have not been included. They are dated 29 November and 1 December. Draft 3: 3 pages of which the first is a carbon copy, dated 1 December 1937, and the following two are typewritten. Draft 4 : Carbon copy, dated 3 December 1937, of 5 pages with minor handwritten corrections. It is considerably enlarged, using only the beginning of Draft 3. Draft 5 : 6 typewritten pages, dated 3 December 1937. It represents a re-typing of Draft 4 with the alterations made there on the first 4 pages included. There is an additional page. This version is reproduced here as Draft B . The manuscripts are on microfilm Bohr MSS no. 14.
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[Draft A]
Nuclear Mechanics.
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In the nuclei of atoms we have to do with matter in an extreme degree of concentration and we are presented with essentially new problems of atomic mechanics concerning the extent to which nuclei can be considered as systems built up of more elementary particle as well as the development of adequate methods of dealing with the mechanical properties of such systems. Fundamental for the problem of nuclear constitution are of course the discoveries that not only the electric charges of nuclei are integers when measured in terms of the elementary unit of electricity, but that also the mass of any nucleus is with high approximation an integral multiple of the mass of the lightest nucleus, the proton. The early attempt suggested by these facts at treating nuclei as systems of protons and electrons was at once confronted, however, with the impossibility of understanding the great stability and compactness of nuclei. Moreover the discrepancy between the symmetry and spin properties of such systems and the dependence of these properties on the mass and charge number as observed for actual nuclei means difficulties which could obviously not be removed by any simple modification of the laws of force between the electric particles at very small distances. Not only is it impossible, within the frame of quantum mechanics, to understand that systems containing light particles like electrons could possess the stability and compactness of nuclei, but also the observation that all nuclei of even or odd mass number have even or odd spin values respectively, quite independently of the parity properties of the charge number, is in direct contradiction to such a picture of nuclear constitution. The liberation of electrons from nuclei in many radioactive disintegrations must therefore be regarded as a process by which these electrons are created as mechanical entities. In this situation, the discovery of the neutron was therefore of the utmost importance; for, assuming that the neutron has the same spin properties as the proton and also satisfies the exclusion principle, it immediately became clear that a model of the nucleus consisting of an assembly of protons and neutrons in suitable numbers would in no case exhibit symmetry and spin properties incompatible with the empirical evidence. A great advance in the treatment of nuclei as systems of protons and neutrons was due to HEISENBERG, who showed how the quantum mechanical fornalism could be rationally extended to include forces between protons and neutrons with similar saturation properties as those which constitute the homopolar valence bonds between atoms. Even the spontaneous disintegration with emission of negative or positive electrons of natural radioactive bodies as well as such artificially generated nuclei, which are unstable
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due to a defect or an excess of positive electric charge, could be brought in connection with the proton-neutron model through a remarkable theory proposed by FERMI. According to FERMI’s fundamental assumption, a transformation of a neutron into a proton, as well as the reverse process, can take place within the nucleus, accompanied respectively by the creation of a negative or a positive electron, together with a neutrino, i.e., a neutral particle of small or even vanishing rest-mass, and having the same spin as an electron. The assumption of this latter particle is necessary, as was first remarked by PAULI, to account, at least formally, for the conservation of spin and above all for the conservation of energy during the process, since the electron, as revealed by the energy spectra of 0-ray disintegrations, may carry with it any fraction of the well-defined energy difference between the initial and final stages of the transformation. A further important consequence of HEISENBERG’s and FERMI’s theories is that, in accordance with the general scheme of quantum mechanics, they establish in principle a relation between the probabilities of the processes just considered, the order of magnitude of which is given by the empirical data on 0-ray disintegration periods, and the magnitude of the forces between proton and neutron. Owing to mathematical difficulties connected with the divergence of the usual perturbation theory of quantum mechanics, no rigorous conclusions in this respect can, however, be obtained at the present stage of the theory, but the very fact of the necessity of such a relation remains one of the most promising features of the present method of approach to the difficult problem of the part played by light particles in nuclear constitution and nuclear reactions. Quite apart from its theoretical importance just discussed, for the problem of nuclear constitution, the neutron proved a most powerful tool, especially in the hands of FERMI and his collaborators, to initiate nuclear reactions, and the analysis of the results so obtained led to a more definite insight into the mechanism of nuclear reactions and the typical features of the structure of nuclei. Especially collision processes between high speed neutrons and nuclei, resulting in the capture of the neutron and in the release of either material particles or electromagnetic radiation, is significant in offering a direct course of information about the mechanism of collision between the neutron and the nucleus. In fact, as pointed out at an earlier occasion, the frequent occurrence of such processes and their great variety fall quite outside the scope of the usual treatment of atomic collision processes, where, on account of the weak interaction between all the particles concerned, the incident particle can be assumed to a first approximation to move independently of the other constituents in a fixed field of force, On the contrary, we must realize that every nuclear transmutation
*
[Pagination corrected in pencil.]
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will involve an intermediate stage in which the energy is temporarily stored in some closely coupled motion of all the particles of the compound system formed by the nucleus and the incident particles. On account of the strong forces which come into play between any two material particles at the small distances in question the coupling between the particles of this compound system is in fact so intimate that the accompanying release of some particle or a y-ray must be considered as a separate event independent of the first stage of the collision process. The final result of the collision may thus be said to depend on a free competition between all the various disintegration and radiation processes of the compound system consistent with the general conservation laws. Moreover, on account of the close coupling b e t w e n the nuclear particles the distribution of energy levels will for a nucleus be very different from what it is for an ordinary atomic system, and will rather resemble that to be expected for an elastic body where the energy is stored in vibrations of the system as a whole. As a consequence of the enormous increase in the possibilities of combination of the proper frequencies of such motions with increasing values of the total energy, the distance between neighbouring levels will decrease very rapidly for high excitations. This is in fact in comformity with the general experimental evidence as regards the distribution of energy levels for the highly excited compound nuclei formed by impacts of slow and fast neutrons on heavier elements. For a more detailed discussion of the properties of such highly excited nuclear systems and especially their disintegration with release of material particles, a suggestive analogy with the phenomenon of evaporation from a liquid or solid body at low temperature has proved most fruitful. In fact, it has been possible by an application of PLANCK’s formula for a system of harmonic oscillators, making use of the approximate knowledge of the level system of nuclei at low excitations to get an estimate of the “temperature” of the compound nucleus, which leads to evaporation probabilities for neutrons consistent with the life times for the compound system in fast neutron collisions derived from the analysis of experiments. It must be noted, however, that a quantitative comparison between ordinary evaporation and neutron escape can be carried through only in case of excitation energies of the compound system, very large compared with the energy necessary for the removal of a single neutron, for only in this case will the excitation of the residual nucleus left after the escape of a neutron be nearly equal to that of the compound system, as is assumed in the usual evaporation phenomena where the change in the heat content of the bodies concerned during the escape of a single gas molecule is negligibly small. A further necessary condition for the application of the evaporation analogy is that any incident particle hitting the proper nuclear surface will give rise to the formation of a compound system, a condi-
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
tion which can only be expected t o be fulfilled when the incident particle is so fast that its de Broglie wave length is of the order of or smaller than nuclear dimensions. In this case the collision process can in fact to a sufficient approximation be described on purely classical considerations. Although the conditions for the application of the evaporation analogy are in general not strictly fulfilled in the experiments on fast neutron impacts so far carried out, there are still a great number of more qualitative consequences derivable from the analogy, which are very useful in the discussion of such collision processes. For instance, the observed large probability of energy loss in collisions between fast neutrons and nuclei just corresponds to the fact, that the molecules released in ordinary evaporation do not take the whole energy of the hot body, but that they in general come off with the much smaller energy per degree of freedom corresponding to the temperature of the evaporating body. It should further be expected from the thermodynamic analogy that the released particles would have an energy distribution around this mean value which corresponds to the Maxwellian distribution. If the energy of the incident neutron is several times larger than the binding energy per particle, it can moreover be predicted that not one single particle but several particles, each with an energy small compared to that of the incident particle, will leave the compound system in successive separate disintegration processes. Nuclear reactions of this type have actually been experimentally found t o take place in a number of cases. The above considerations can also be applied to the release of charged particles like protons and a-particles from the compound system, but it must be kept in mind that in this case the latent heat of evaporation is not simply the binding energy of the charged particle, but that we have to add to this the electrostatic energy due to the mutual repulsion of the escaping particle and the residual nucleus. This repulsion will moreover have the effect of speeding up the particles after their escape from the nucleus, and the mean kinetic energy of the charged particles will thus be larger than that of the neutrons by an energy amount corresponding to this repulsion. We should, therefore, expect that the most probable energy of the emitted particles would be approximately equal to the sum of the temperature energy and the electrostatic repulsion, and that the probability for the emission of charged particles with still larger energies would, as in the case of neutrons, decrease exponentially according to a Maxwellian distribution. This preference for nuclear processes, where the escaping charged particle takes only a part of the available energy, leaving the residual nucleus in an excited state, is in fact one of the most striking features of a great number of reactions in which protons or a-particles are emitted from the compound system. When we now pass to the consideration of collisions with slow particles having wave lengths large compared with nuclear dimensions, we must expect that the
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formation and disintegration of the compound system will involve specific quantum mechanical features. This is most strikingly shown in experiments on the radiative capture of quite slow neutrons, where abnormally large cross sections amounting to more than thousand times of ordinary nuclear cross sections is found for certain elements. Although the occurrence of such selective capture phenomena can be accounted for in a simple way as a quantum mechanical resonance effect resulting from the diffraction of the neutron wave by any suitable attractive field of force, a closer understanding of all the observed features of the process can also in this case only be obtained if we take essentially into account the strong coupling between the nuclear particles, which excludes any treatment based on the simple assumption that the neutron were moving inside the nucleus more or less independently of the other nuclear constituents. In fact, while on account of the great complication of the mechanical problem concerned a complete treatment of the processes involved is at present impossible, a general formalism resembling that of optical dispersion theory can nevertheless be obtained, which gives the general dependence of the cross sections for the various processes on the energy of the incident particle. Another interesting resonance effect has been found for disintegrations caused by impacts of protons and a-particles on light nuclei. As in the case of selective effects of slow neutrons, such resonances must be ascribed to the coincidence of the sum of the energies of the incident particle and the original nucleus with a stationary state of the compound system corresponding to some quantized collective type of motion of all its constituent particles. The strong coupling between the individual nuclear particles will not only be essential for the mechanical properties of nuclei but will also strongly influence the way in which electromagnetic radiation is emitted. While in the case of usual atomic systems, where the radiative process corresponds to a transition of a single particle from one quantum state to another, the most intense radiation will always be of dipole type, radiations corresponding to poles of higher order are found to be relatively intense in the case of nuclei. This is in fact readily explained by realising that in the complicated collective types of motion characteristic of nuclear excitation the electric charges will probably be so uniformly distributed over the nucleus that the mass and charge centers will almost coincide and consequently the dipole moments will be absent or at any rate much suppressed. Such considerations also make possible a quantitative estimate of the probabilities of the radiative processes responsible for neutron capture and yields in fact results in good agreement with general experimental evidence. If we try, however, to account for finer details of the radiation process such as the spectral composition of the emitted y-rays we meet with the great difficulty that, due to the scarcity of our knowledge of the forces between the individual nuclear parti-
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
cle[s], we are unable to predict the nature of the fundamental modes of motion in nuclei. Thus any comparison of nuclear motions with the oscillations of ordinary solid or liquid substances would not seem justifiable in view of the radical different dynamical and statical conditions in the two cases. In this respect it is to be hoped that the rapidly increasing experimental material as regards the distribution of the lower nuclear levels as well as of their radiative properties may help to throw some light on the still open questions in nuclear structure.
[Draft B] 3.12.37
NUCLEAR MECHANICS. Rutherford’s discovery, that all charge and mass in the atom, apart from that carried by electrons, is concentrated within a nucleus of an extension exceedingly small compared with that of the whole atom, lent an extreme simplicity to our picture of atomic structure, since it allowed an exhaustive description of the atom as a mechanical system defined by simple characteristics of the separate atomic particles, the nucleus and the extranuclear electrons. On this fundamental feature rests indeed the whole quantum mechanical treatment of the problem of atomic constitution, the development of which has further been greatly facilitated by the possibility of regarding in first approximation each electron in the atom as bound independently in a field of force representing the attraction of the nucleus and the average repulsion of the other electrons. As is well known, it is just the possibility of such an approximate procedure which allows the familiar classification of the electron bindings by means of quantum numbers, which has given so complete an explanation of the periodic system of the elements and in particular brought to light the Pauli principle of exclusion. Essentially new problems of atomic mechanics arise, however, in connection with intranuclear constitution concerning as well the extent to which nuclei can be identified with systems built up of more elementary particles as the development of adequate methods of dealing with the mechanical properties of such systems. In fact, not only does the explanation of the stability and compactness of nuclei obviously claim the assumption of peculiar forces acting between atomic particles within distances of the order of nuclear dimensions, but it has even been gradually recognised that it is not possible to consider all material particles which are released from nuclei in natural or artificial disintegration processes as proper nuclear constituents. In particular, such light particles as elec-
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trons cannot be treated, within the frame of quantum mechanics, as bound in regions of nuclear dimensions, and we are therefore forced to regard the liberation of positive or negative electrons from radioactive nuclei as a creation of these particles as mechanical entities. In order to account for the conservation of energy and momentum in such processes, it is, as is well known, even necessary to assume that together with the electron also a light neutral particle is created. Although the development of these ideas, especially by Pauli, Heisenberg, and Fermi, has opened promising outlooks for the attack on fundamental problems of atomic theory, their more immediate consequence for the problem of nuclear constitution is the recognition of the necessity of regarding nuclei as mechanical systems composed entirely of heavy particles. A basis for the realisation of this program was, of course, supplied by the discovery of the neutron. In fact, a nuclear model consisting of an assembly of protons and neutrons not only gives an immediate interpretation of the charge and mass numbers of nuclei but, assuming that the neutron has the same spin properties as the proton and like it satisfies the exclusion principle, its general symmetry and spin properties will also in no case be incompatible with the empirical evidence. Moreover, it suggests a simple explanation of the remarkable variation of stability of nuclei according to the odd or even character of the mass and charge number, especially emphasized by Harkins. It is interesting to remember that just in this connection the hypothesis of a heavy neutral particle as a nuclear constituent has been discussed several years before the neutron was detected as an isolated particle, and before the contradictions between the spin properties of nuclear models containing electrons and those of actual nuclei were clearly recognized. A more detailed treatment of the proton-neutron model was, however, first initiated by Heisenberg who pointed out that the quantum mechanical formalism could be rationally generalised to include novel types of forces between neutrons and protons capable of accounting in a general way for the characteristic stability properties of nuclei in their dependence of the mass and charge nnmbers. Still, the great complication of a quantitative treatment of such compact systems - where no simple procedure of approximation like that so successfully used in the exploration of the extranuclear electronic configurations in atoms can be applied - has as yet made it impossible to arrive in this way at conclusions of unique character as regards the laws of force between nuclear particles. More direct information about these laws is, however, to be expected from the continuation of the very promising recent investigations on close collisions between free protons and neutrons. In spite of these deep-rooted difficulties inherent in the problem of nuclear constitution it has been possible on the general principles of quantum mechanics t o develop to a considerable extent an analysis of the experimental evidence
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regarding the properties of nuclei disclosed in their reactions as well with material particles as with radiation. The first decisive step in this direction was the well known theory of [a]-ray emission from radioactive nuclei brought forward independently by Gurney and Condon, and by Gamow. In this theory, the action exerted on the [a]-particle by the rest of the nucleus is compared with that of a fixed potential field representing an attraction at a distance of the order of nuclear dimensions, and the ordinary electrostatic repulsion at larger distances. While on ordinary mechanics such a field would represent an impenetrable barrier for [a]-particles with the energies observed, it is a typical feature of quantum mechanics that there will be a certain probability for the escape through the barrier within a given time interval of an [a]-particle of any positive energy. These simple considerations were indeed sufficient t o obtain a most instructive explanation of the fundamental law of radioactive decay as well as of the characteristic empirical relation between the life time of a radioactive nucleus and the energy of the emitted [a]-rays. Essentially the same quantum mechanical effect accounts, as is well known, also for the possibility of producing nuclear disintegrations of lighter nuclei by impact of [a]-rays with energies less than the repulsive potential at the surface of the nucleus, and especially allows a quantitative analysis of the disintegrations initiated by impact of protons of relatively small velocities, a phenomenon so paradoxical from the point of view of classical mechanics. The possibility of accounting by means of such a simple model for the essential features of these phenomena lies, however, in the circumstance that, due to the predominant influence of the barrier effect, the features are only to a secondary degree dependent on the mechanism of interaction between the nuclear particles at close distances. In particular, it must be observed that the remarkable connection pointed out by Gamow, between the long range [a]-particles and the fine structure of [a]-ray spectra on the one hand, and the existence of discrete excited states of nuclei, as revealed by the analysis of [?]-ray spectra on the other hand, is a direct consequence of the general quantum postulates and offers no evidence of any independent state of motion of [a]-particles, nor even of their separate existence, in the interior of the nucleus. * The closer examination of the apparently so successful simple quantum mechanical treatment of the typical resonance effects in [a]-ray and proton collisions shows also, as we shall see, the essential insufficiency of any nuclear model in which the particles in first approximation are assumed [to move] independently in a fixed field of force. First the study in recent years of nuclear transmutations initiated by neutron impacts - where, due to the absence of electrostatic * [A section superseded by the following paragraph has been omitted here.]
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repulsion, circumstances are much simpler than in charged particle collisions has, however, clearly revealed the decisive role which the great facility of energy exchanges between the closely packed particles in nuclei plays in determining the course of all nuclear reactions. Above all the observation that collision processes between high speed neutrons and heavy nuclei frequently result in the capture of the incident neutron with emission of electromagnetic radiation shows that the duration of such collision processes is extremely long compared with the time which a neutron uses in simply passing through a region of nuclear dimensions. In fact, as pointed out at an earlier occasion, this forces us to assume that such collision processes involve an intermediate state in which the energy is temporarily stored in some closely coupled motion of all the particles of the compound system formed by the initial nucleus and the incident neutron. In this stage no single particle will possess a kinetic energy sufficient to liberate itself from the strong attractive forces of the other nuclear particles and any subsequent disintegration process of the compound system will therefore claim a so to speak fortuitous concentration of the available energy on the particle released. Such a disintegration must thus be considered as a separate event quite independent of the first stage of the collision process and the final course of the collision between the neutron and the nucleus may be said to depend on a free competition between the different possible disintegration and radiation processes of the compound system. Such considerations offer also an immediate explanation of the great facility with which nuclear disintegrations are produced by neutron impacts on lighter nuclei and the great variety of such processes the account of which falls quite [outside] the scope of the usual treatment of atomic collision[s].
XXIV. UNPUBLISHED NOTE ABOUT (n, 2n) REACTIONS [ 1937-1938?] FROM FOLDER, VARIOUS NOTES, CATALOGUED AS OF [ 1935- 19371
See Introduction, sect. 3, ref. 77
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The folder “Various Notes”, catalogued as of [1935-19371, contains drafts in English as well as calculations. There are 3 numbered pages and a 4th page, being a summary of the other 3, written in pencil in Kalckar’s handwriting. This is the part reproduced here. There are further two carbon copies of 1 page, entitled “Interaction between neutrons and nuclei”, possibly the beginning of a different paper on the same subject. One copy has a few corrections in pencil in Kalckar’s handwriting. Finally, there are 6 pages of rough calculations in pencil, not relating to the manuscript. They seem to be in Rosenfeld’s, Kalckar’s and possibly Bohr’s handwritings. The manuscript is on microfilm Bohr MSS no. 14.
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Ordinarily the nucleus wil! from such an excited state return to the normal state with emission of radiation because the excitation energy will not be sufficient for the liberation of another material particle. As indicated in the article we shall, however, if we could experiment with neutrons of sufficiently large energy, expect that several particles will leave the nucleus as the result of the impact, since such a course of the process will be far more probable than the escape of a neutron with the total excess energy or the emission of part of this energy as electromagnetic radiation. Now ((*processes of this type seem actually to occur already in collisions of ordinary high speed neutrons with very heavy nuclei, where the binding energy of a neutron, as shown by Aston’s measurements of the mass differences of isotopes, are comparatively small) ) the beautiful recent experiments of Meitner and Hahn about the production of new radioactive series by bombardment of uranium with neutrons seem actually to show that processes of this type occur in collisions between ordinary high speed neutrons and very heavy nuclei. In fact these authors conclude from the experiments that in certain cases the collision between the neutron and the uranium nucleus leads instead of the attachment of the neutron to the nucleus with the formation of a heavier uranium isotope to the disruption of the neutron from the nucleus resulting in the formation of a lighter isotope. The beautiful recent discoveries of Meitner and Hahn of new radioactive series produced by bombardment of Uranium with neutrons have brought to light a new feature of nuclear reactions showing that a collision between a neutron and a heavy nucleus may not only result in the capture of a neutron with the formation of a heavy isotope but may under circumstances also result in the attachment of the neutron.
* [This part was deleted in the manuscript.]
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XXV. ON NUCLEAR REACTIONS OM ATOMKERNEREAKTIONER Overs. Dan. Vidensk. Selsk. Virks. Juni 1937 - Maj 1938, p. 32 Communication to the Royal Danish Academy on 19 November 1937 ABSTRACT TEXT AND TRANSLATION
See Introduction, sect. 3, ref. 73.
P A R T I: PAPERS A N D MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
In the report in Nature 141 (1938) 91, this abstract was condensed into a single sentence (under the title, “Mechanism of nuclear reactions”): “A discussion of the applications of thermodynamical analogies for the analysis of nuclear reactions”.
NIELS BOHR giver en Meddelelse: O m Atomkernereaktioner. Paa Grund af den taette Sanimenpakning af Partiklerne i Atomkernerne og d e staerke Krsfter, d e r virker mellem d e enkelte Kernebestanddele, frembyder Kernernes Reaktioner forskellige karakteristiske T r s k , der afviger vssentligt fra saedvanlige Atomreaktioner. Medens disse Forhold i en tidligere Meddelelse h a r vaeret diskuteret ved H j s l p af kvalitative Betragtninger, vil det i Foredraget blive vist, hvorledes en mere kvantitativ Analyse af Kernereaktionernes Forlrab kan opnaas ved Anvendelse af termodynainiske Analogier.
TRANSLATION Niels Bohr presents a communication: On Nuclear Reactions. Due to the close packing of the particles in atomic nuclei and the strong forces acting between the individual constituents of nuclei, nuclear reactions exhibit various characteristic features, which deviate considerably from those of usual atomic reactions. While these circumstances in an earlier communication were discussed by means of qualitative considerations, it will be shown in the lecture how a more quantitative analysis of the processes of nuclear reactions can be obtained by thermodynamical analogies.
XXVI. NUCLEAR EXCITATIONS AND ISOMERIES UNPUBLISHED MANUSCRIPT 1937
See introduction, sect. 3, ref. 74.
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
The folder “Nuclear Excitations and Isomeries”, 1937, contains 3 typewritten pages in English and the top part of the 4th page, reproduced here together with a sheet of data in Danish in ink in Placzek’s handwriting. The manuscript is dated 7 December 1937. The footnotes are missing. There is a carbon copy with a few corrections in pencil, probably in Rosenfeld’s handwriting. The manuscript is on microfilm Bohr MSS no. 14.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
7.12.37.
Nuclear excitations and isomeries. Due to the strong coupling between the closely packed particles in nuclei we have in nuclear excitations not to d o with abnormally high quantum states of a single or a few particles like in excited atoms, but with some higher stationary state corresponding to motions of an essentially collective type of all the nuclear particles.' The simplest comparison which presents itself is with the elastic vibrations of a solid body, which in fact on quantum mechanics give rise to a distribution of energy levels similar to that of nuclei, the characteristic feature of which is that the distance between neighbouring levels decreases very rapidly with increasing excitation. On such a comparison, the high nuclear excitations correspond in general to combinations of a large number of fundamental modes of vibration of comparatively small frequencies and energy quanta. Still, we shall also expect the occurrence of certain states corresponding to the excitation of a few or even a single mode of vibration with a large energy quantum. Now such two different modes of excitation of about the same energy will obviously correspond to quite different radiative properties. In the former case, we must in fact expect a close resemblance between the radiation of the nucleus and that of a black body of a temperature estimated on the lines of the well-known specific heat theory of solid bodies; while in the second extreme case we will have to do with the emission of a single radiation quantum. Moreover, we may expect that final states of the nucleus resulting from the radiative processes initiated by the two different types of excitation can be essentially different. Thus in the case of the single mode excitation, the radiation will lead directly to a return to the normal state of the nucleus; while the cascade-like radiation processes initiated by the multiple mode excitation might have a large probability to lead to some metastable nuclear state of comparatively low excitation energy, such as those which have been revealed by the discovery of isomeric radioactive nuclei. Quite apart from the interesting still unsolved question of the quantum mechanical specification of such metastable nuclear states', the above considerations would offer a simple interpretation of the important observation3 that certain radioactive nuclear isomers are only produced by capture of neutrons of definite velocities, while others result from impacts of neutrons of very different velocities. In fact, this would be explained if in the former case we had to do with a single mode excitation leading to the normal state of the new radioactive product, and in the latter cases with multiple mode excitations leading practically I
*,
[Probably the paper reproduced on p. [1511.1 [Footnotes left blank.]
MS, p. 2
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
MS, p. 4
always through cascade processes to some higher metastable states of this product. The assumption used so far for the sake of simplicity, that in nuclear excitations we have merely to do with pure elastic vibrations is in no way essential for the argument which would just as well apply if, besides such vibrations, we take account of the possibility of nuclear rotations specified by different spin values. In particular, it will be seen that the cascade radiation processes may just lead to the probable occurrence of large spin differences between the initial and final states, which would provide a simple interpretation of the metastability, already pointed out by Weizsacker. It needs also hardly be emphasized that the assumption, that the excitation processes leading with great probability to a return to the normal state involve a single mode of vibration, shall not be taken literally, but that the argument will also hold for multiple mode excitations involving one or more exceptionally large vibrational quanta. A specification of the different types of excited states as that in question can of course only be unambiguously upheld in the region where the nuclear energy levels are more or less sharply separated. In the region of continuous level distribution we must indeed reckon with the possibility of a transition from one type of vibrational motion to another within time intervals short in comparison with the mean life times of the energy states concerned, determined by the possible disintegration or radiation processes. Still, also in this region a certain degree of stability of specific modes of excitation arising under special conditions would seem to be indicated by experiments on nuclear disintegrations produced by high frequency radiation. In fact, the pronounced selectivity of these effects even for heavy elements and for radiation quanta of an energy sufficient to raise the nucleus into the region of continuous level distribution, can hardly be understood otherwise than by assuming that the first step of the process is the excitation of a single mode of vibration, limited to separate energy intervals. In order to explain the comparatively large size of these intervals, we have to assume that the duration of this type of excitation is many times shorter than the mean life time of the excited nucleus. At the same time, this duration would seem to be quite long enough to account for the fact, disclosed by the quantum mechanical discussion of the experimental effects, that the probability of radiative transitions leading back from the excited state to the normal state of the nucleus is much larger than could be explained if we had to do, as we hitherto assumed, with an excitation in which the various modes of vibration were represented in a similar way as in thermodynamical equilibrium, leading to a radiation of the black body type.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Isornerie. 1) Brom, 2 stabile Isotoper i?Br og $iBr. Ved langsomme Neutroner dannes 3 Perioder: 18mi",5h, 36h Ved y-Straaler dannes ogsaa 3 Perioder: gmin, l P i " , 5h. Derfor er 6"'" . . . = "Br 18"'" og 5h . . . = *'Br To Isomerer
36h . . .
=
82Br
2) Rhodium, 2 stabile Isotoper 'SiRh (kun 0.08%!) og '::Rh. Langsomme Neutroner: 2 kraftige Perioder: 40SeC og 4'"'". Begge viser pracis den samme O p f ~ r s e m.H. l ti1 Resonanz. Saa godt som sikkert har '!$Rh to Isomerer
3) Indium, 2 stabile Isotoper ';?In (5070) og ';$In. Langsomme Neutroner: 3 Perioder: 13SeC,l h , 4h. Gammastraaler: 1 ny Periode af lmin. 1min 121n 4h 'I41n Sandsynligvis 13SeCog l h 11% to Isomerer
'
4) Uran Langsomme Neutroner: Der dannes 3 Familier. En af dem viser udpraget Resonanzindfangning, de to andre ikke Spor. Altsaa &' J har -~ 3 Isomerer, - og de to af dem nedarver sig gennem flere 0-Udsendelser.
TRANSLATION
Is0 rn erisrn . 1) Bromine, 2 stable isotopes i?Br and !iBr. Slow neutrons yield 3 periods: 18 min, 5 h, 36 h. y-rays also yield 3 periods: 6 min, 18 min, 5 h. Therefore 6 min . . . = ''Br Two isomers 18 min and 5 h . . . = "Br 3 6 h . . . = 82Br
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
2) Rhodium, 2 stable isotopes '%Rh (only 0.08'70!) and '%Rh. Slow neutrons: 2 strong periods: 40 sec and 4 min. Both show precisely the same behaviour with respect to resonance. Practically certain that '%Rh has two isomers 3) Indium, 2 stable isotopes ':?In (5'70) and ':;In. Slow neutrons: 3 periods: 13 sec, 1 h, 4 h. Gamma rays: 1 new period of 1 min. 1 min Il2In 4h '141n Probably 13 sec and 1 h I161n Two isomers
4) Uranium Slow neutrons: There are 3 families. One of them shows pronounced resonance capture, the two others no trace of this. It follows that '??U has 3 isomers and that the progeny of two of them include several &emitters.
XXVII. NUCLEAR PHOTO-EFFECTS Nature 141 (1938) 326-327
See Introduction, sect. 4, ref. 79
FEB. 19, 1938,
NATURE
326
VOL.
141
Letters to the Editor The Editor does not hold himself responsible f o r opinions expressed by his c w r q o n d e n t a . H e cannot undertake to return, or to correspond w i f h the writers of, rejected manuscripts intended for this or any other part of NATURE.N o notice is taken of anonymous communications.
SOTES ox POINTS IN CORRESPONDENTS ARE INVITED
SOME OF THIS WEEK'S LETTERS APPEAR ON P. TO ATTACH
SIMILAR
Nuclear Photo-effects Tm beautiful experiments of Bothe and Gentner' on the ejection of neutrons from heavier nuclei by means of y-rays with energy of about 17 M.v. resulting from impact of protons on lithium, have revealed a remarkable selectivity of these nuclear photoeffects. Thus a few elements, apparently irregularly distributed, were found to possess cross-sections for such effects of the order while for the large majority of the elements investigated no measurable effects could so far be detected. At first sight this selectivity might, as pointed out from various sides, seem difficult to reconcile with the views on the mechanism of nuclear reactions to which one has been led through the study of the effects initiated by neutron impacts2. I n fact, the distribution of the energy levels of the compound nucleus formed in such collisions must for all heavier elements be expected to be practically continuous for excitation energies above 10 M.v., while the nuclear photoeffects obviously demand a special sensitivity for much higher excitations confined within well-separated energy regions. This apparent contradiction disappears, however, if we realize that the level distribution of the compound nuclei, which form the intermediate stage in nuclear transformations initiated by collisions, represents the ensemble of stationary states corresponding to the more or less coupled modes of vibration of the nucleus, while the response to the photo-effects is primarily conditioned by certain special vibratory motions with singular radiation properties. Thus, in nuclear transformations initiat,ed by high-frequency radiation, wo have not to do with a simple competition of the disintegration and radiation probabilities of a well-defined intermediate state, but rather with the balance between the radiative processes and the effect of the coupling of the corresponding specific vibrations of the nucleus and the other possible modes of nuclear vibrations. This coupling will tend to the rapid extinguishment of any special features of the initial type of excitation and to its replacement by a more stable state of the excited nucleus, where the energy is distributed among all modes of vibration in a way analogous to the heat motions of a solid.body at low temperature. As soon as such a state of nuclear excitation is established, the course of the photoeffect is practically determined. In fact, the radiative properties of the nucleus in this state will resemble that of a black body with a temperature of a few million volts, and the probability that the whole energy is emitted in a single radiation quantum of 17 M.v. will accordingly be negligibly small. Moreover, for the high excitations concerned, the total probability of the radiative processes of the nucleus will be very much smaller than the probability of its disintegration, which increases exponentially with the temperature like in a usual evaporation process.
SUMMARIES
TO THEIR
334.
COMMUNICATIONS.
This argument implies that the cross-section for nuclear photo-effects in the energy region concerned will be given by a formula of the type well known from the theory of optical selective absorption :
where h and v are the wave-length and frequency of the y-rays respectively, and vi one of the sequence of such frequencies corresponding to maximum resonance. Further, r R and r c are the probabilities in unit time, respectively, for the re-emission of a quantum hv from the initial special state of excitation of the nucleus and for the conversion of this transitory state to the ordinary state of nuclear excitation with the same energy. This latter process will be seen t o correspond closely to the effect of collisions in diminishing the resonance in absorption of light in gases a t high pressures. Present experimental evidence does not directly disclose for any given element the variation of the cross-section of the selective photo-effect with the frequency of the y-rays. Still, from the way in which this cross-section varies among the elements for rays with hv = 17 M.v., it would appear that the distance between the resonance maxima in this energy region is probably some million volts and that the breadth of each of these maxima is roughly comparable with the variation of hv in the incident y-rays due to natural width of the line and the Doppler effect in the proton-lithium collision which amounts If, further, the largest to about 50,000 volts. cross-sections observed are assumed to correspond to maximum resonance, we get from the above formula values for I'R and Fc of the order of magnitude 10'5 see.-' and 1 0 1 9 sec.-* respectively. Both these values appear quite reasonable. In fact, on account of the high frequency of the y-rays concerned, we should expect r R t o be several times as large as the probability of emission of ordinary y-rays in nuclear transmutations, estimated from neutron captures to be about 1014 see.-'. Further, the value for l?c is much smaller than the frequency l o z 1see.-' of the initiating y-rays, while it is much larger than the probability of disintegration of the excited nucleus, estimated by the evaporation analogy to be of the order 10'6 sec.-l for energies of about 17 M.v. The proportion between the duration of the initial transitory state and the whole lifetime of the excited nucleus, which for 17 M.v. is thus probably of the order should for lower energies be still smaller, since the coupling between the different modes of vibration will presumably decrease much more slowly than the probability of neutron escape. At the same time the ratio between the chances of re-emission of a quantum hv from the initial state of excitation and from the more stable state of the excited nucleus will rapidly decrease. Still this ratio,
N o . 3564,
FEB. 19, 1938
NATURE
which for 1 7 M.v. is extremely large, will scarcely approach unity before we have come well within the energy region of discrete nuclear levels. Even in the upper part of this region, we must therefore be prepared to find a selectivity of the nuclear photoeffect similar to that found in the continuous energy region, but in experiments with sufficient monochromatic y-rays each resonance maximum will here resolve itself into a fine band of sharp absorption lines corresponding to the separate levels. With the vanishing predominance of the initial state of excitation with regard to the radiation processes, this kind of selcctivity, however, will soon disappear and be replaced by a line absorption spectrum of the usual type, which of course will he accompanied by a niiclear photo-effect only so long as hv is large enough to cause a disintegration of the nucleus. In the discussion of these problems, of which a more detailed account will be given in a forthcoming paper in the communications of the Copenhagen Academy of Sciences, I am indebted t o my collaborators of the Institute of Theoretical Physics for valuable help, especially t o Mr. Fritz Kalckar, .whose sudden death a few weeks ago means a most regrettable loss to us all*. N. BOHR. Universitetet,s Institut for Teoretisk Fysik, Copenhagen, 0 Jan. 31. * Cf. p. 319 of this issue. Bothe, W., a n d Gentner, M'., 2 . Phys., 106, 2% (1937). Cf. Bohr, N., NATURE, 137, 344 (1936) ; a n d also Bohr, N. and Kalckar, F., Math. Phys. Comm., Copenhagen Acad. Sci., 14, 10 (193i).
327
XXVIII. QUANTUM OF ACTION AND ATOMIC NUCLEUS WIRKUNGSQUANTUM UND ATOMKERN Ann. d. Phys. 32 (1938) 5-19 TEXT AND TRANSLATION
See Introduction, sect. 3, ref. 7 5 .
P A R T I : P A P E R S A N D MANUSCRIPTS RELATING TO N U C L E A R PHYSICS
There is a Danish version of this paper, “Virkningskvantum og Atomkerne”, published in Fys. Tidsskr. 36 (1938) 69-84. Although the Danish version on the whole follows the German version rather closely, it is nevertheless re-phrased in many places, probably reflecting the rapid development of the subject as well as the fact that Bohr obviously had to meet a well-defined deadline for the German version, to be included in the Planck Festschrift. For a closer comparison the reader is referred to the original publication. It may, however, be mentioned here that “nur etwa 10 Volt” (p. 13, line 10 from below) in the Danish version was changed into “kun . . . faa Volt” (“only . . . a few Volts”), “etwa 1 MV” (p. 15, line 8) was changed into “nogle faa Mill. Volt” (“a few MeV”), and that a major part of the third paragraph from the end (pp. 17-18) was completely revised. There is an English abstract of the paper, along with several others from the Festschrift, in Nature 141 (1938) 981-982.
Sonderabdruck aus Annalen
d e r Physilc
.
-
6. Folge Bd.32 Heft1 u.2.1938
V E R L A G V O N J O H A N N A M B R O S I U S B A R T R IK L E I P Z I G .
Printed in Qermanp
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Wirkungsquantum und Atomkern Von N i e l s Bohr
Man kann sich wohl kaum grogere Unterschiede im Wesen und in der Vorgeschichte zweier entscheidender physikalischer Errungenschaften denken als zwischen P l a n c k s Entdeckung des elementaren Wirkungsquantums und der Entdeckung des Atomkerns durch R u t h e r f o r d . Wahrend die erstere das SchluBergebnis der auf den allgemeinen Prinzipien der Thermodynamik fuBenden Analyse des schon von K i r c h h o f f als von allen speziellen Eigenschaften der materiellen Korper vollig uuabhangig erkannten Wiirmestrahlungsgesetzes darstellt , bedeutet die letztere die Vervollstandigung der detaillierten Vorstellung vom atomaren Aufbau der Materie, die wir der ErschlieBung ganz neuer Erfahrungsgebiete durch die wunderbare Entwicklung der Experimentierkunst unserer Zeit verdanken. Eben die gegenseitige Erganzung dieser beiden so grundsatzlich verschiedenen Erweiterungen unserer physikalischen Erkenntnis ist auch der Hintergrund f u r das rasche Bufbluhen der Erforschung atomarer Erscheinungen gewesen, die wir im Laufe des letzten Menschenalters erlebt haben. Welchen unentbehrlichen Schlussel zur Aufklarung der ratselhaften Stabilitat der Atome uns das Wirkungsquantum darbot, wurde ja erst vollig klar durch die E,rfahrungen uber die Bausteine der Materie, die im Model1 des Kernatoms zusammengefaBt sind und die einen so tiefen Einblick in den Ursprung allgemeiner physikalischer und chemischer GesetzmaBigkeiten vermittelten, besonders was die Verwandtschaften der Elemente und ihre Uniwandelbarkeit betrifft. I n der Tat entschleierte die auBerordentliche Einfachheit dieses Modells die Notwendigkeit, eine neuartige Grundlage fur die Atomstabilitat zu suchen und sogar auf einen unmittelbaren Zusammenhang zwischen der Beschaffenheit der von den Atomen ausgesandten Strahlung und irgendwelchen Bewegungen der Elektronen zu verzichten, und gab daher den AnlaB sowie die Freiheit, dem durch das Wirkungsquantum bedingten, der klassischen Naturbeschreibung fremden Zug von Individualitat gerecht zu werden durch die Annahme der Existenz stationarer Zustande und des elementaren Charakters der die fjbergangsprozesse begleitenden
6
Annalen der Physik. 5. Folge. Band 32. 1938
Strahlung. Diese sogenannten Quantenpostulate, die die E i n s t e i n sche Deutung des Photoeffekts einschlossen und bald durch die Stohersuche von F r a n c k und H e r t z eine direkte Bestatigung bekamen, erlaubten nicht nur eine einfache Deutung der Spektralgesetze , sondern ergaben zugleich die Moglichkeit, auf rationelle Weise die spektroskopischen Ergebnisse a n Hand des Atommodells zu vemerten. Die ersten Schritte auf diesem TTege wurden durch die Forderung geleitet, daB die Behandlung sich in der Grenze, wo die gesamte in Frage kommende Wirkung groB ist gegeniiber dem einzelnen Quantum, der klassischen Beschreibungsart anschlieBt. Entscheidend f u r die Anwendbarkeit dieser sogenannten Korrespondenzforderung war vor allem die infolge der Kleinheit des Kerns gegeniiber dem ganzen Atom gegebene Moglichkeit, das gewohnliche Kraftgesetz f u r elektrische Punktladungen mit groBer Annaherung aufrecht zu erhalten. Diese lockere Struktur des Kernatoms bedeutet auch dadurch eine groBe Erleichterung des uberblicks, daW sie in weitem Umfang erlaubt, die Bindung jedes einzelnen Elektrons im Atom als unabhangig von den anderen zu betrachten , deren Anwesenheit in erster Naherung einfach eine teilweise Abschirmung der Kernladung verursacht. Mit Hilfe des standig wachsenden Reichtums an spektroskopischen Erfahrungen und der besonders von S o m m e r f e l d entwickelten Systematik der Quantenzahlen der Atomzustande wurde auf diese R e i s e allmahlich eine korrespondenzmaBige Beschreibung der Bindung jedes einzelnen Elektrons im Atom erzielt, die eine jedenfalls in den Hauptziigen vollstandige Erklarung ergab f u r die im periodischen System dargestellten Verwandtschaften der Elemente , was ihre physikalischen und chemischen Eigenschaften betrifft. Obwohl kurz nachher die Erkenntnis der Spineigenschaften des Elektrons durch U h l e n b e c k und G o u d s m i t , und vor allem die Aufstellung des Paulischen AusschlieBungsprinzips f u r die Elektronenbesetzung der Quantenzustande, eine vorlaufige Xbrundung der primitiven Korrespondenzmethode ergab, zeigte sich jedoch die Unzulanglichkeit des fortdauernden , wenn auch eingeschrankten Gebrauchs klassischer mechanischer Vorstellungen immer deutlicher, im besonderen f u r die Eeriicksichtigung der feineren Ziige der Wechselwirkung der Elektronen im Atom. Eine harmonische Verschmelzung der quantenhaften und der klassischen Ziige der Theorie des Atombaus wurde bekanntlich erst erreicht durch die Ausbildung rationeller quantenmechanischer Methoden, die wir, einerseits der gliicklichen Einfiihrung der neuartigen intuitiven Icleen von Licht-
N. Bohr. Wirkungsquantum und Atomkern
7
quant und Materiewelle durch E i n s t e i n , d e B r o g l i e und S c h r o d i n g e r , anderseits der fortschreitenden Ausbildung der Korrespondenzbehandlung uber K r a m e r s Arbeiten zu ihrer glanzenden Durchfuhrung von H e i s e n b e r g , B o r n , J o y d a n und D i r a c , verdanken. Als Hohepunkt dieser Entwicklung kann wohl die relaticistische Elektronentheorie von D ir a c angesehen werden, die nicht nur die feinsten Ziige der Spektren zwangslaufig aufzuklaren Permochte, sondern zugleich die experimentell bestatigte Voraussage der Umwandlungsmoglichkeit von Strahlungsenergie in Paare von positiven und negativen Elektronen enthielt. F u r unseren Zweck braucht j a auch nur kurz daran erinnert zu n-erden, dab die Quantenmechanik es nicht allein ermoglicht hat, die Reschreibung der Eigenschaften der einzelnen Atome zu einem gewissen AbschluB zu bringen, sondern daB sie auch ganz neue und fruchtbare Gesichtspunkte geliefert hat zum Verstandnis der verschiedenartigen chemischen Bindungen in Molekulen sowie die Erklarung mancher typischen Eigenschaften der festen Korper, insbesondere der Metalle, For denen man bisher ratlos stand. E s handelt sich j a iiberhaupt nicht allein urn die Vervollstandigung der theoretischen Methoden der Atomphysik, sondern um eine derartig tiefgehende Umgestaltung unserer begriff lichen Hilfsmittel zur Beschreibung der Natur, da6 sogar eine durchgreifende Revision des Beobachtungsbegriffes selber erforderlich war. Vor allem bedeutet die durch das Wirkungsquantum bedingte unvermeidliche Wechselwirkung zwischen den betreffenden atomaren Objekten und den fur die Definition der Phanomene notigen Mebinstrumenten, daB die unter verschiedenen Versuchsbedingungen gewonnenen Resultate nicht in der ublichen, auf der Vorstellung des selbstandigen Verhaltens der Objekte fu6enden Beschreibungsart zusammengefaBt werden konnen, sondern in einem neuartigen komplementaren Terhaltnis zueinander stehen. Der in den H e i s e n b e r g s c h e n Unbestimmtheitsrelationen ausgedriickte prinzipiell statistische Charakter der Quantenmechanik ist in der Tat keinerlei vorlaufige Einschrankung der Analyse der atomaren Erscheinungen, sondern er entspricht in sinngema6er Weise dem Gesichtspunkt der Komplementaritat, der umfassender als das Kausalitatsideal ist, und notwendig, um der Reichhaltigkeit der durch die Existenz des Wirkungsquantums bedingten Erfahrungen Rechnung zu tragen. Wenn wir uns nach diesen einleitenden Bemerkungen unserem eigentlichen Thema, der Bedeutung des Wirkungsquantums f u r das Problem des Aufbaus und der Stabilitat der Atomkerne, selber zuwenden, so wird es zunachst auffallen, dab die Fragestellung in wesentlichen
8
Annalen der Physik. 5. Folge. B a d 32. 1938
Punkten genau die umgekehrte ist wie diejenige, die beim Angriff auf die oben besprochenen Atomprobleme vorlag I). Wahrend wir dort von einer jedenfalls weitgehenden Kenntnis der Bausteine der Atome und der zwischen ihnen wirkenden Krafte ausgehen konnten, ist es ohne weiteres klar, da% die groBe Dichte und der starke Zusammenhalt der Kerne Krafte zwischen den Kernteilchen verlangen, die nur in Bbstanden von der GroBenordnung der Kerndimensionen wirken, deren genaues Gesetz aber yon vornherein Follig unbekannt ist. AuBerdem stellte es sich bald heraus, daB es wegen der Existonz des Rirkungsquantums sogar unmoglich ist, alle materiellen Teilchen , die in naturlich vorkommenden oder kiinstlich hervorgerufenen Kernzerfallsprozessen freigemacht werden konnen, als selbstandige Kernbausteine anzusehen. Schon die ersten durch die fundamentale A s t o n sche Eutdeckung - daB nicht nur die elektrischen Ladungen der Kerne Vielfache der Elementarladung sind, sondern daB auch die Masse jedes Kerns mit hoher Naherung ein ganzes Vielfaches der Masse des leichtesten Kerns, des Protons, ist - angeregten Versuche, Kerne als Systeme von Protonen und Elektronen anzusehen, enthiillten Widerspruche prinzipieller Art. Ganz abgesehen von den Schwierigkeiten, auf Grund dieser Auffassung den Zusammenhalt der Kerne zu erklaren, zeigten sich namlich Unvertraglichkeiten zwischen den Symmetrie- und Spineigenschaften solcher Systeme und den spektroskopisch beobachteten Eigenschaften der Kerne in ihrer Abhangigkeit von den Ladungs- und Massenzahlen. Eine nahere Untersuchung zeigte auch, daB es im Rahmen der Quantenmechanik, ganz unabhangig von jeder Annahme iiber die in Kernen herrschenden Krafte, unmiiglich ist, solchen leichten Partikeln wie Elektronen eine selbstandige Existenz im Kernbereich zuzuschreiben. Die Auslosung positiver oder negativer Elektronen in radioaktiven Kernprozessen mu8 daher mit einer Erzeugung dieser Partikel als 1) Eine ausfuhrlichere Darstellung der Entwicklungsgeschichte der Theorie des Atombaus, wo auch auf den hier betonten Unterschied der Atom- und Kernprobleme hingewiesen wurde, findet sich in der Faraday Lecture des Verf. (Journ. Chem. SOC.S. 381. 1932). Die unten dargestellten Gesichtspunkte zur ErklSirung der typischen Merkmale der Kernreaktionen wurden zuerst in einem in Nature 137. S. 344. 1936 und in Die Naturwissenschaften XXIV. H. 16. 1936 erschienenen Artikel entwickelt. Eine weitere Ausfuhrung dieser Gesichtspunkte ist in einer Abhandlung von N. B o h r u. F. K a l c k a r (Danske Videnskabernes Selskab XIV. H. 10. 1937) gegeben, wo auch ausfuhrliche Literaturhinweise zu finden sind. Die am SchluB des vorliegenden Artikels erwahnten Kernphotoeffekte wurden nnlangst in einer kurzen Mitteilung in Nature 141. S. 326. 1938 behandelt.
N . Bohr. Wirkungsquantum und Atomkern
9
mechanische Einheiten verglichen werden , ahnlich der Emission eines Lichtquants von einem Atom. Um die Erhaltung von Energie und Impuls in p-radioaktiven Prozessen zu bewahren, ist es bekanntlich sogar notwendig anzunehmen, dab auBer dem Elektron noch ein leichtes, bisher nicht beobachtetes, neutrales Partikel bei solchen Prozessen erzeugt wird. Obwohl die Entwicklung dieser Qesichtspunkte, insbesondere durch P a u l i , F e r m i und H e i s e n b e r g , noch keinen befriedigenden AbschluB errreicht hat, hat sie nichtsdestoweniger neue aussichtsreiche Angriffsmoglichkeiten auf Grundprobleme der Atomtheorie eroffnet und fuhrt vor allem zur Erkenntnis der Notwendigkeit, Atomkerne als mechanische Systeme, die nur aus schweren Partikeln bestehen, aufzufassen. Bekanntlich lieferte C h a d w i c k s Entdeckung des Neutrons eine Grnndlage f u r die Ausfuhrung dieses Programms. I n der T a t ergibt ein aus Protonen und Neutronen bestehendes Kernmodell nicht nur eine unmittelbare Deutung der Ladungs- und Massenzahlen der Kerne, sondern auch seine allgemeinen Symmetrieeigenschaften werden unter der Annahme, daB das Neutron denselben Spin wie das Proton besitzt und wie dieses dem BusschlieBungsprinzip gehorcht, in keinem Fall mit den Beobachtungen unvertraglich. Aut3erdem deutet ein solches Model1 eine einfache Erklarung an f u r die eigentumliche, fruhzeitig von H a r k i n s hervorgehobene Abhangigkeit der Stabilitat der Kerne von der Gerad- oder Ungeradzahligkeit der Ladungs- und Massenzahlen. Es ist interessnnt, sich daran zu erinnern, daB in dieser Verbindung die Annahme eines schweren neutralen Kernbausteins melirere Jahre vor der Isolierung des Neutrons diskutiert wurde, und zwar noch bevor a n Hand der Quantentheorie die Widerspruche zwischen den Eigenschaften der wirklichen Kerne und denen jedes Kernmodells, das Elektronen enthalt, klar erkannt wurden. Ein entscheidender Fortschritt in der Behandlung des ProtonNeutron-Kernmodells wurde von H e i s e n b e r g erzielt, der zeigte, wie der quantenmechanische Formalismus mittels einer einfachen Verallgemeinerung die Einfuhrung von neuartigen Xraften zwischen Proton und Neutron erlaubt, die ahnliche Sattigungseigenschaften besitzen wie die Valenzkrafte chemischer Verbindungen, und deren Vorhandensein notwendig scheint, um die typische Variation der Massendefekte der Kerne mit den Nassenzahlen zu erklaren. I n den spateren Jahren ist vielfach versucht worden, derartige Ansatze uber Kernkrafte naher in ihren Konsequenzen zu prufen ; abgesehen aber von der aussichtsreichen Behandlung der allerleichtesten Kerne ist dieser Weg schon darum sehr schwierig, weil die starke
10
Annalen der Physik. 5. Folge. Band 32. 1938
Kopplung der Bewegungen der einzelnen Kernteilchen die Benutzung aller solcher Approximationsmethoden , die die Erforschung der Elektronenbindungen im Atom so erleichtert haben, ausschliebt. Ganz abgesehen von der Frage der Kraftgesetze darf aber auch nicht vergessen werden, daB der Umstand, daB die Kerne adiabatisch in Neutronen und Protonen zerlegt werden konnen, keine Sicherheit dafur bietet, da6 eine genauere Beschreibung ihrer Eigenschaften in ahnlicher T e i s e wie die der gewohnlichen Atomsysteme - allein mit Hilfe der bisher fur die Charakterisierung der isolierten Teilchen benutzten Merkmale durchgefuhrt werden kann. Besonders 'klar kommt auch der Gegensatz in der Problemstellung bei Erforschung des Atombaus und des Kernbaus, was Ausgangspunkte und Hilfsmittel betrifft, zum Ausdruck in der Weise, wie die Deutung des sich rasch anhaufenden experimentellen Materials iiber die Reaktionen der Kerne allmahlich fortgeschritten ist. Der Ausgangspunkt dieser Entwicklung war die erst durch die Quantenmechanik ermoglichte Erklarung des radioaktiven Zerfallsgesetzes, das seit seiner Aufstellung durch R u t h e r f o r d und S o d d y der unfehlbare Leitfaden bei der Entwirrung des groBen Gebietes der Radioaktivitat gewesen ist. Obwohl schon E i n s t e i n in seiner beruhmten einfachen Herleitung des P l a n c k s c h e n Warmestrahlungsgesetzes auf Grund der Quantenpostulate die Analogie zwischen dem radioaktiven Zerfall und den atomaren Strahlungsprozessen hervorgehoben hatte, blieb das Zerfallsgesetz lange ratselhaft , insbesondere nachdem R u t h e r f o r d darauf aufmerksam machte, daB die AbstoBungsenergie zwischen Atomkern und ausgeschleudertem a-Teilchen im allgemeinen wesentlich groBer ist als die kinetische Energie dieses Teilchens. Kurz nach der Klarung der Prinzipien der Quantenmechanik wurde aber bekanntlich von G u r n e y und C o n d o n , und unabhangig von G a m o w , gezeigt, daB wir es hier eben mit einem besonders lehrreichen Beispiel des Versagens der gewohnlichen mechanischen Vorstellungen zu tun haben. I n der Tat bietet nach der Quantenmechanik ein riiumlich beschranktes Kraftfeld kein absolutes Hindernis selbst fur Teilchen, deren kinetische Energie kleiner ist als das Potentialmaximum; und schon ein einfacher Vergleich des Kraftgesetzes zwischen a-Teilchen und Kern mit einer kugelsymmetrischen Potentialbarriere genugt, urn eine unmittelbare Erklarung der belrannten G e i g e r - N u t t a l s c h e n Relation zwischen der mittleren Lebensdauer eines radioaktiven Elements und der kinetischen Energie der ausgeschleuderten a-Teilchen zu liefern. Dieser groBe Erfolg war der Auftakt zu einer auBerst fruchtbaren Entwicklung, die einen umfassenden nberblick uber die
N . Bohr. Wirkungsquantum und Atomkern
11
naturlichen und kunstlichen Kernumwandlungsprozesse und die begleitenden elektromagnetischen Strahlungserscheinungen herbeifuhrte. Vor allem ist hier G a m o w s Erklarung der feineren Strukturen der a-Strahlspektren zu erwahnen, durch die, nach dem Vorbild der Deutung der optischen Spektren, die Orundlage f u r eine nahere Kenntnis der diskreten Quantenzusthde der Kerne geschaffen wurde. Zunachst handelte es sich jedoch - im Gegensatz zur korrespondenzmabigen Analyse der Atomspektren - eigentlich nur urn die sinngemaBe Anwendung der klassischen Erhaltungssatze und der Quantenpostulate. Insbesondere erwies sich allmahlich die schematische Darstellung des Kernfeldes als ein Potentialloch, in dem sich die Tejlchen annahernd unabhangig voneinander bewegen, als unzulanglich, urn die naheren Einzelheiten der Kernreaktionen und besonders die oft damit verbundenen charakteristischen Resonanzphanomene zu erklaren. I n der T a t hat es sich, wie wir sehen werden, herausgestellt, dab das typische Merkmal der Kernreaktionen gegenuber den Atomreaktionen eben in der im Vergleich mit der Kopplung der Elektronenbewegungen im auBeren Bereich des Atoms uberaus engen Kopplung zwischen den Bewegungen der Teilchen irn Kern und dem dadurch bedingten auBerordentlich leichten Energieaustausch zwischen den einzelnen Kernteilchen besteht. Dieser Sachverhalt wurde vor allem klargelegt durch das von der Entdeckung der kunstlichen Radioaktivitat durch F. und I. J o l i o t angeregte nahere Studium der von NeutronenstoBen hervorgerufenen Kernurnwandlungen. Wegen der Abwesenheit von AbstoBung augerhalb des eigentlichen Kernbereichs sind die letzteren Phanomene vie1 einfacher zu ubersehen als ZusammenstoBe zwischen Kernen und positiv geladenen Teilchen wie Protonen und u-Partikeln, bei denen die Anwesenheit der Potentialbarriere oft von uberwiegendem EinfluB ist. Aus dem Umstand, dab die Wirkungsquerschnitte f u r unelastische StoBe zwischen schnellen Keutronen und schweren Kernen von der gleichen GroBenordnung sind wie die Kerndurchmesser, 1aBt sich in der Tat sofort schlieBen, daB die Kopplung zwischen dem eindringenden Neutron und den im Kern rorhandenen Teilchen sehr eng sein muB. Noch weitergeheide Schlusse erlaubt die von F e r m i zuerst nachgewiesene Tatsache, daB solche StoBe sogar mit betrachtlicher Wahrscheinlichkeit zum Einfangen des Neutrons fuhren konnen unter Bildung eines neuen stabilen Kerns, der zwar oft ,9-radioaktiv ist, aber immer eine Lebensdauer von ganz anderer GroBenordnung als die bei den StoBprozessen in Betracht kommenden Zeiten besitzt. Ein derartiger Neutroneinfang muB namlich notwendig mit einer Ausstrahlung der OberschuBenergie verknupft sein,
12
Annalen der Physik. 5. Folge. Band 32. 1938
und aus der beobachteten Wahrscheinlichkeit eines solchen Verlaufs des ZusammenstoBes kann man daher schlieBen, daB die StoBdauer auberordentlich lang ist im Vergleich zu den Zeitintervallen, die f u r den einfachen Durchgang des Neutrons durch den Kernbereich erforderlich sind. Schon die .Ton der Ladung und den Dimensionen der Kerne gesetzte obere Grenze der Wahrscheinlichkeit der y-Strahlemission bedeutet in der T a t , daB das Verhaltnis zwischen StoBdauer und den letzteren Zeitintervallen von der GroBenordnung eine Million sein muB. Die ubliche, den ZusammenstoBen zwischen schnellen Elektronen und Atomen angepaBte Behandlungsweise der atomaren StoBerscheinungen, wobei in erster Naherung mit der Bewegung in einem festen Kraftfelde gerechnet wird, versagt daher vollig bei der Beschreibung eines ZusammenstoBes zwischen einem Neutron und einem Kern. Vielmehr mussen wir uns vorstellen, dab das Eindringen des Neutrons in den Kernbereich sofort zu einem Energieaustausch mit den Kernteilcheu AnlaB gibt, der zur Folge hat, daB die Energie sehr schnell uber samtliche Teilchen des vom Neutron und dem ursprunglichen Kern gebildeten Gesamtsystems so gleichma6ig verteilt wird, daB kein einzelnes Partikel in der nachsten Zeit geniigend Energie besitzt, urn den Kern gegen die Anziehungen der Nachbarteilchen zu verlassen. Die Beschaffenheit dieses Zwischenzustandes bedingt weiter, daB das SchluBresultat des ZusammenstoBes durch eine sozusagen freie Konkurrenz zwischen allen moglichen Zerfallsund Strahlungsprozessen des Gesamtsystems bestimmt ist, was eine unmittelbare Erklarung liefert f u r die auffallende Reichhaltigkeit der Kernumwandlungsphanomene, in welchen fast alle mit der Energieerhaltung zu vereinbarenden Verlaufe der StoBprozesse zum Vorschein kommen. Eben in dieser Verbindung ist schon bald nach R u t h e r f o r d s ersten Zertriimmerungsversuchen mit a-Strahlen die Annahme eines Zwischenzustandes bei Kernumwandlungen verschiedentlich diskutiert worden; vor den Neutronenexperimenten war jedoch nicht nur der EinfluB der Barriereneffekte schwierig zu uberblicken, sondern es fehlte auch jede Grundlage f u r eine Abschatzung der Lebensdauer des Zwischenzustandes und f u r die nahere Beurteilung seiner Eigenschaften. Ein besonders lehrreiches Resultat der Diskussion uber Kernumwandlungen bei NeutronenstoBen ist au6erdem die Aufdeckung eines grundsatzlichen Unterschiedes zwischen der Verteilung der Energiezustande bei Kernen und derjenigen bei Atomen. I n der Tat verlangt die Bildung eines langlebigen Zwischenzustandes bei ZusammenstGRen zwischen Kernen und Neutronen beliebiger, ge-
N . Bohr. Wirkungsquantum und Atornkern
13
nugend hoher Energie einen ausgedehnten kontinuierlichen Energiebereich des Gesamtkerns, der zuniichst in direktem Widerspruch zu stehen schien mit dem Nachweis der diskreten Energiezustande der Kerne durch die Analyse der y-Strahlspektren. U'ir mussen aber bedenken, daB wir es bei solclien ZusanimenstoBen mit einer Anregungsenergie des Gesamtkerns zu tun haben, die vie1 groBer ist als die Energie der angeregten Zustande, die f u r die gewohnlichen y-Strahlerscheinungen in Retracht kommen. Wahrend wir es im letzteren Fall mit einer Xnregung yon hiichstens einigen Millionen Volt zu tun haben, wird j a im ersteren Fall die Anregungsenergie gleich der Sumnie der kinetischen Energie des freien Neutrons und der Bindungsenergie eines Keutrons im Sormalzustand des Gesamtkerns, welche fur Massenzahlen mittlerer GroWe fast 10 MV betragt. Tatsiichlich beginnt fur. solche Massenzahlen der kontinuierliche Energiebereich erst bei etwa 12 MV Anregungsenergie, und er schliefit sich dem Gebiet der diskreten Kernzustiinde ganz gleichmiiiwig an, indem die Abstiinde henachbarter Zustande, die f u r die tiefsten Zustande von des GrGBenordnung 1 M V sind, sehr rasch mit zunehmender Energie abnehmen. Einen direkten Einblick in die aufierordentlich dichte TTerteilung der Kernzustiinde bei hohen Anregungsenergien haben die Untersuchungen uber Einfang ganz langsamer Neutronen gegeben , die - im Gegensatz zu den StoBversuchen mit schriellen Neutronen ausgepriigte Unterschiede der Reaktionen von Kernen niit nur wenig verschiedenen Ladungs- und Massenzahlen aufweisen. Diese Selektivitat ist offenbar eine quantenmechanische Resonanzerscheinung, die von einer sozusagen zuf'alligen Koinzidenz der Bindungsenergie des Neutrons in dem bei der Einfangung gehildeten neuen Kern und einern Quantenzustand dieses Kerns bedingt ist. Aus der Scharfe der Resonanz und dem Vorkommen der Selektivitat, unter den Elementen laBt sich tatsachlich, auf Grund einfacher statistischer cberlegungen, schlieBen, da6 f u r mittlere Massenzahlen der Niveauabstand bei ungefahr 10 MV nur etwa 10 Volt betragt. Die Resonanzerscheinungen bei StoBen lmgsamer Neutronen sind iiberhaupt von gs6Btem Interesse, und vor allem liefert die Beobachtung von Wirkungsquerschnitten, die in einzelnen Fallen mehr als 1000 ma1 so groB wie die geonietrischen Querschnitte der Kerne sein konnen, ein schlagendes Beispiel fur das vollige Versagen des klassischen Bahnbegriffes innerhalb von Dimensionen, die klein sind im Vergleich zu der d e B r o g l i e s c h e n Wellenlange. Unter solchen Umstanden zeigt in der T a t das StoBproblem eine weitgehende Ahnlichkeit rnit akustischen und optischen Resonanzphanomenen, uad
14
Annalen der Physik. 5 . E'olge. Band 32. 1938
besonders kann, wie zuerst B r e i t und W i g n e r , und nachher ausfiihrlicher B e t h e und P l a c z e k gezeigt haben, die Weise, in der die Wirkungsquerschnitte eines Kerns f u r Streuung und Einfangung mit der Energie des Neutrons variieren, durch F'ormeln von ganz ahnlichem Typus wie die wohlbekannten Dispersionsformeln der Optik dargestellt werden. Wahrend diese Folgerungen sich auf sehr allgemeine Betrachtungen griinden, verlangt dagegen die Erklarung der Verteilung der Energiezustande der Kerne sowie die hbschatzung der f u r den Verlauf der Kernreaktionen maBgebenden Wahrscheinlichkeiten der individuellen Zerfalls- und Strahlungsprozesse eine nahere Untersuchung der bezuglichen mechanischen Probleme. Wohl laBt sich zur Zeit keine strenge Behandlung dieser Probleme durchfuhren ; jedoch konnen viele charakteristische Eigenschaften der Kerne, f u r die eben die enge Kopplung der Kernteilchen von ausschlaggebender Bedeutung ist, weitgehend aufgeklart werden durch einen Vergleich mit wohlbekannten Eigenschaften von festen und flussigen Korpern. Vor allem erklart sich der typische Unterschied zwischen den Verteilungen der Anregungszustande von Atomen und Kernen sofort durch die Bemerkung, daB wir in angeregten Atomen es im allgemeinen mit der Anderung eines Quantenzustandes eines einzelnen Elektrons zu tun haben, wahrend es sich bei der Kernanregung urn die Qiiantisierung von Bewegungen skmtlicher Teilchen handelt, die an die Rotationen und Schwingungen eines festen Korpers erinnern. Die Gesamtheit der Energiezustande eines elastischen Korpers wird in der Tat, wenn wir zunachst von Rotationen absehen, aus allen moglichen Kombinationen der mit ihren Grundschwingungen korrespondierenden Quantenzustande gegeben und hat daher, infolge des uberaus raschen Anwachsens der Kombinationsmoglichkeiten mit der Energie, genau denselben allgemeinen Charakter wie das Zustandsspektrum der Kerne. Auch in quantitativer Hinsicht gibt dieser Vergleich eine annahernd richtige Darstellung der Verteilung der Kernzustande, indem es sich zeigt, dab wir aus den Kombinationen von ungefahr aquidistant verteilten Eigenwerten rnit Abstanden von ungefahr 1 MV schon bei 10 MV eine Zustandsdichte bekommen von derselben Grobenordnung wie jene , welche aus den Versuchen mit langsamen Neutronen erschlossen ist. Diese Vorstellung von der Anregung eines Kerns zeigt offenbar eine weitgehende Analogie zu den Warmebewegungen eines festen Korpers bei tiefen Temperaturen, und in diesem Sinne kann man von der Erwarmung der Kernsubstanz bei der Bildung des Gesamtkerns durch einen Zusammenstob sprechen. Die dabei in Frage
N . Bohr. Wirkungsquantum und Atomkern
15
kommende Temperatur ist zwar ungeheuer hoch im ublichen MaBstabe (von der GroBenordnung loll Grad), aber sie ist im KernmaBstab sehr klein, da bei einem StoB mit nicht besonders schnellen Partikeln im allgemeinen nur eine geringe Anzahl der Schwingungsmoglichkeiten angeregt w i d . Abgeschatzt mittels der Quantentheorie der spezifischen Warme entspricht f u r mittlere Massenzahlen die Temperatur des Gesamtkerns bei gewohnlichen StoBversuchen etwa 1MV pro Freiheitsgrad. Fur sehr schnelle StijBe wird sie naturlich hoher, wachst aber nur langsam, weil die angeregten Freiheitsgrade sich rasch vermehren, und sogar bei einem ZusammenstoB zwischen einem Kern und einem Partikel mit 100 MV wird die Temperatur nur wenige Millionen Volt betragen. Dieser Begriff der Kerntemperatur ist nicht niir sehr bequem zur Charakterisierung der Kernanregung, sondern er ist vor allem eine groBe Hilfe gewesen bei der Beschreibung der mit den Kernumwandlungen verbundenen Zerfalls- und Strahlungsprozessen , die nach unserer Vorstellung nahe Analogien zu einer Verdampfung und einer Warmestrahlung nufweisen. Vor allem erinnert, wie zuerst F r e n k e l bemerkt hat, die Aussendung von Neutronen durch hochangeregte Kerne weitgehend an einen gewohnlichen VerdampfungsprozeB , auf den die bekannte Formel der Reaktionskinetik fur die Abhangigkeit der Verdampfungsgeschwindigkeit von der Temperatur und der Bindungswarme jedenfalls annaherungsweise angewandt werden kann. Auch liefert dieser Vergleich eine unmittelbare Erklarung dafur, daB die bei Kernreaktionen freigelassenen Neutronen ini allgemeinen niclit die ganze Uberschugenergie mitnehmen , sondern eine Energieverteilung aufweisen, die auffallende Ahnlichkeit mit dem M a x w ellschen Verteilungsgesetz f u r die entsprechenden Kerntemperaturen besitzt. L)er Befund, daB ZusammenstoBe mit schnellen Neutronen anstatt zur Einfangung zu einem LosreiBen von einem oder mehreren Neutronen fuhren konnen, l a & sich nuch ungezwungen als ein stufenweiser Zerfall des Gesamtkerns auffassen, der f u r immer hohere Anregungsenergien mehr und mehr der allmahlichen Verdampfung eines Fliissigkeitstropfens ahnlich wird. F u r kleinere Anregungen muR j edoch bei Anwendung eines solchen Vergleichs mit gewisser Vorsicht vorgegangen werden, indeni - im Gegensatz zu den ublichen Verdampfungsprozessen, wo die gesamte Warmeenergie der Korper uberaus groB ist im Vergleich zu der zur Freilassung eines einzelnen Molekuls notigen Energie - bei den StoBversuchen die Anregungsenergie des Gesamtkerns gewohnlich von derselben GroBenordnung wie die Bindungsenergie eines Neutrons
16
dnnalen der Physik. 5 . Folye. Band 32. 1938
ist. Wie besonders L a n d a u und W e i B k o p f gezeigt haben, lassen sich jedoch auch f u r die Behandlung solcher Prozesse Nethoden der statistischen Mechanik anwenden, die eine konsequente Verallgemeinerung der rein thermodynainischen Betrachtungsweise darstellen. Auch wenn das stoBende oder ausgeschleuderte Partikel geladen ist, verlaiuft die Kernumnandlung als ein stufenweiser ProzeB. bei dern erst ein Gesamtkern gebildet wird, dessen Energie in iihnlicher Weise wie in einem erwarmten Kiirper verteilt ist uncl dessen Zerfall sich danach als ein verdampfungsahnlicher ProzeB vollzieht. I n solchen Fiillen kann Ljedoch die bbstoBung, besonders venn die Energie der Partikel gering ist, grol3en Einflui3 auf die Wahrscheinlichkeit sowohl der Bildung des Gesamtkerns wie seines Zerfalls ausuben. Nicht nur sind dabei die quantenrnechanischen Barriereneffekte zu berucksichtigen, sondern auch f u r Energien der Partikel, die groBer sincl als ihr Potential in der Nalie der Kernoberfliiclie, ist es wesentlich zu bemerken, daB bei Sbsch$tzung der Temperatur des Zwischenzustandes und der fur ihre Zerfdlswahrscheinliclikeit maBgebenden Verdampfungswiirme diese Potentiale von der Gesamtenergie abgezogen werden mussen. Eine einfache Folge der AbstoWung ist auch. daB die kinetische Energie des freigelassenen geladenen Partikels im allgemeinen groBer wird als die der ungeladenen, weil in ersterem Fall die potentielle Energie wieder zur eigentlichen Temperaturenergie zu addieren ist. Wenn die kinetische Energie des stoBenden Partikels nicht groR genug ist, uni den Gesamtkern in den ltontinuierlichen Energiebereich zu bringen, treten, ebenso TI ic bei den StoBen mit langsamen Neutronen, auch bei geladenen Partikeln typische Resonanzerscheinungen auf. Der Umstand, daB solche Resonanzen ofters f u r Energien des stoBenden Partikels auftreten, die groB genug sind, um den freien Durchgang durch die Potentialbarriere zu gestatten, zeigt deutlich das Versagen der friiheren Auffassung, nach der es sich urn einen quasistationken Zustand des Partikels innerhalb der Barriere handelte. DaB wir es dagegen mit einer Koinzidenz der Gesamtenergie mit einem Quantenzustand der kollektiven Bewegungen der Kernteilchen zu tun haben, wird auch besonders schlagend gezeigt durch die neuen Reobachtungen von Bo t h e und seinen Mitarbeitern , wonach Resonanzen bei StoBen z wischen Kernen und Partikeln verschiedener Ladung, die zu demselben Gesamtkern fuhren , fur genau dieselben Werte der Gesamtenergien auftreten. Die uberaus enge Kopplung zwischen den Bewegungen der Kernteilchen, die fur die Kernreaktionen beim StoB entscheidend ist, bewirkt auch, daB die Strahlungseigenschaften der Kerne wesentlich
N . Bohr . Wirkungsquantum und Atomkern
17
verschieden von denen der Atome sind. Wahrend die Strahlung der letzteren im allgemeinen ubergangsprozessen entspricht, bei welchen nur die Bindung eines einzelnen Elektrons geandert wird, und die mit Dipolschwingungen korrespondieren , ist die Strahlung der Kerne - wie sich aus der Untersuchung der yon der y-Strahlung hervorgerufenen Photoeffekte in der augeren Elektronenhulle desselben Atoms herausgestellt hat - im allgemeinen vom Quadrupoltypus. Nach unserer Vorstellung von der Kernanregung ist dies auch unmittelbar verstandlich, da eine Strahlung dieses Typus eben mit der Schwingung eines elastischen Korpers mit angenahert gleichmagiger Massen- und Ladungsverteilung korrespondieren wird. Bei solchen Schwingungen konnen j a in erster Naherung keine Dipolmomente auftreten, weil der elektrische Mittelpunkt stets mit dem Schwerpunkt zusammenfallen muB. Eine auf der GroBe der Kerne und den Amplituden der quantisierten Kernschwingungen basierte Abschatzung der in Frage kommenden Quadrupolmomente fuhrt auch zu einer annahernden ubereinstimmung mit den aus der Scharfe der Resonanz bei Einfangung langsamer Neutronen berechneten Wahrscheinlichkeiten der Strahlungsprozesse. Was die Intensitatsverteilung der Strahlung f u r hoch angeregte Kerne betrifft, sollten wir eine gewisse xhnlichkeit mit der Warmestrahlung bei der betreffenden Temperatur erwarten. Das schnelle Anwachsen der Emissionswahrscheinlichkeit mit der Frequenz fur Strahlung hoherer Polaritat wird jedoch eine relativ hohe R a h r scheinlichkeit f u r die groBeren Quantenspriinge bewirken, die sich besonders bei der Anregung leichter Kerne bemerkbar macht und in gewissen Fallen sogar zu einem fjberwiegen der Strahlungskomponente fuhrt, die einem direkten ubergang Zuni Normalzustand des Kernes entspricht. Besonders interessant in dieser Hinsicht ist die beim StoB von Protonen an Lithium erzeugte Strahlung, die fast nur eine Komponente mit einer. Energie von nahezu 1 7 MV enthalt. Die verhaltnismafiig groBe Intensitat dieser Strahlung ruhrt iibrigens daher, daB wir es bei solchen StoBen mit einer ausgepragten Resonanz zu tun haben, bei welcher der betreffende Zustand des Gesamtkerns infolge allgemeiner quantenmechanischer Symmetrieforderungen nicht in zwei a-Partikel zerfallen kann , und die Strahlungsprozesse daher lediglich mit der Freilassung eines verhaltnismagig langsamen Protons, das nur schwer durch die Potentialbarriere dringen kann, konkurrieren. Weitere interessante Aufschlusse uber die Strahlungseigenschaften der Kerne versprechen neuerdings die schonen Untersuchungen von B o t h e und G e n t n e r zu ergeben iiber die Auslosung Annalen der Physik. 5 . Folge. 32.
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Annalen der Physik. 5. Folge. Band 32. 1938
von Neutronen aus schweren Kernen durch Bestrahlung mit der eben erwahnten Proton-Lithium y-Strahlung. Der Befund, daB die einzelnen bestrahlten Eiomente ein ganz verschiedenes Verhalten bei solchen Kernphotoeffekten zeigen, schien zwar im ersten Augenblick schwierig vereinbar mit den allgemeinen Vorstellungen von Kernanregungen, zu denen die Kernumwandlungen bei SttiBen gefiihrt haben. Nach diesen sollen j a alle die betreffenden Elemente bereits f u r Anregungsenergien weit unterhalb 17 MV eine kontinuierliche Energieverteilung besitzen, und wir konnen daher keinen gewiihnlichen Resonanzeffekt erwarten. Wir miissen aber bedenken, daB die Verhaltnisse bei Kernumwandlungen durch StoB- und Strahlungserscheinungen ganz verschieden liegen. Wahrend beim StoB der Verlauf der Prozesse wesentlich von einer Konkurrenz der moglichen Zerfalls- und Strahlungswahrscheinlichkeiten des langlebigen Zwischenzustandes bestimmt ist, wird der Verlauf der Photoeffekte dagegen von dem Verhaltnis zwischen der Kopplung und dem Strahlungsfelde mit den damit korrespondierenden spezifischeii Schwingungsbewegungen des Kerns einerseits und der Kopplung dieser Schwingungen mit den anderen moglichen Schwingungstypen andererseits abhangen. Das Vorhandensein der letzten Kopplung bewirkt, daB die Energie sich schnell auf alle Schwingungen, ahnlich wie in einem erwarmten Korper, verteilt, und daB somit die Wahrscheinlichkeit pro Zeiteinheit der Emission der Anregungsenergie in Form eines einzelnen Quants von dem Wert, den sie in der Anfangsstufe der Anregung hat, sehr bald auf einen iiberaus kleinen, dem Warmestrahlungsgesetz entsprechenden MTert herabsinkt. Der Kernphotoeffekt wird nun auch im kontinuierlichen Gebiet eine selektive Frequenzabhangigkeit aufweisen , sofern dieser nbergang noch nicht rasch genug ist, um den EinfluB der anfanglichen Anregungsart auf die Gesamtwahrscheinlichkeit der Wiederausstrahlung des Quants zum Verschwinden zu bringen. Nach dieser Auffassung, wonach die durch die genannten Versuche angedeutete Selektivitat der Kernphotoeffekte im kontinuierlichen Zustandsgebiet eine nahe Analogie zum Vorhandensein scharfer ultraroter Absorptionsgebiete eines festen Korpers bei gewiihnlicher Temperatur zeigt, wiirde sich offenbar die Moglichkeit bieten , die Kopplungsstarke der Kernschwingungen aus den Photoeffekten zu ermitteln. D a wegen des im Vergleich rnit dem Fall eines Kristalls vie1 groBeren Einflusses der quantenhaften Nullpunktsenergie der Kernsubstanz diese Kopplungaverhaltnisse theoretisch schwer zu beurteilen sein diirften, muB der Weiterfiihrung der Versuche mit grobem Interesse entgegengesehen werden.
N . Bohr. Wirkungsquantum und Atomkern
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Eine andere Erscheinung wollen wir noch kurz erwahnen, die neue Einblicke in den Anregungsmechanismus der Kerne verspricht, namlich die Entdeckung yon sogenannten Kernisomeren, d. h. langlebigen Produkten mit denselben Ladungs- und Massenzahlen, die verschiedene radioaktive Eigenschaften besitzen. I n den letzten Jahren ist das Vorkommen solcher Kernisomerien bei der Umwandlung vieler Elemente festgestellt worden, und im besonderen haben sich sehr interessante Falle ergeben aus den Untersuchungen Ton H a h n und M e i t n e r uber die durch Neutronenstobe an TJran erzeugten neuen radioaktiven Familien. Wie W e i z s a c k e r zuerst bemerkt hat, IaBt sich die Existenz langer Lebenszeiten angeregter Kerne durch die Annahme erklaren, daB die bezuglichen Kernzustande besonders groBe Drehimpulsquantenzahlen besitzen, und daB daher die Strahlungsprozesse, die dem flbergang in den Normalzustand entsprechen wurden, iiberaus kleine Wahrscheinlichkeiten haben. Diese Auffassung, die an die Metastabilitat gewisser Atomzustande erinnert, ist sehr ansprechend; es kann aber zur Zeit noch schwerlich uberblickt werden, ob sie geniigt, um die speziellen Bedingungen , unter denen die verschiedenen Kernisomerien erscheinen, zu erklaren, oder ob noch bisher nnbekannte, fur die Kernprozesse eigentiimliche Auswahlregeln hier eine Rolle spielen. Beim AbschluB dieser kurzen Zusammenfassung, deren Absicht vor allem war, einen Eindruck Y O U der wundervollen Fruchtbarkeit des neuen Forschungsgebietes zu geben, das durch das Zusammenspiel der grundsatzlichen Entdeckungen yon P l a n ck und R u t h e r f o r d entstanden ist, braucht kaum besonders betont zu werden, da6 wir in der eigentlichen Kernphysik erst am Anfang einer Entwicklung stehen. Was uns aber zii den grogten Hoffnungen auf weitere Fortschritte berechtigt, ist die innige Verbindung von experimentellen und theoretischen Untersuchungen, die die Forschung auf diesem Gebiete auszeichnet. K o p e n h a g e n , Institut fur theoretische Physik. (Eingegangen 27. Februar 1938)
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TRANSLATION
Quantum of Action and Atomic Nucleus By Niels Bohr One can hardly imagine two decisive achievements in physics differing more in their nature and in their origin than Planck’s discovery of the elementary quantum of action and Rutherford’s discovery of the atomic nucleus. Whereas the former represents the final result of the analysis, on the basis of the general principles of thermodynamics, of the law of thermal radiation, recognised already by Kirchhof f as completely independent of all specific properties of material bodies, the latter implies the completion of the detailed representation of the atomic constitution of matter, which we owe to the opening-up of completely new areas of experience by the wonderful development of the art of experimentation in our time. It is just the mutual fulfilment of these so fundamentally different extensions of our physical understanding which is also the background to the rapid prospering of the exploration of atomic phenomena, which we have experienced in the last generation. How indispensable a key for the elucidation of the puzzling stability of atoms the quantum of action provided for us, was shown with complete clarity only in the light of experience with the constituents of matter, combined in the model of the nuclear atom, which enables us to gain such a deep insight into the origin of general physical and chemical regularities, particularly as regards the relations between the elements as well as their immutability. In fact the extraordinary simplicity of this model revealed the necessity to seek a new basis for atomic stability, and to renounce any direct connection between the nature of the radiation emitted by the atoms and any particular movement of the electrons; it therefore gave us both the motivation and the freedom to do justice to the individuality, a feature dependent on the quantum of action and foreign to the classical description of nature, by the assumption of the existence of stationary states and of the elementary character of the radiation accompanying the transition processes. These so-called quantum postulates, which included Einstein’s interpretation of the photoelectric effect, and which soon received their direct confirmation by the collision experiments of Franck and Hertz, permitted not only a simple interpretation of the laws of spectra, but at the same time gave us the possibility of evaluating the spectroscopic results rationally in terms of the atomic model. The first steps of this development were guided by the postulate that in the limit in which the total action involved is large compared to a single quantum, the treatment must approach the classical description. The applicability of this
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so-called correspondence postulate depended decisively on the possibility of retaining the ordinary law of force for electric point charges to a good approximation, because of the small size of the nucleus compared to the whole atom. This loose structure of the nuclear atom facilitates the understanding also by making it possible, to a large extent, to regard the binding of each electron in the atom as independent of the others, whose presence in a first approximation simply causes a partial screening of the nuclear charge. With the help of the steadily increasing wealth of spectroscopic data and of the systematics of the quantum numbers of the atomic states, developed in particular by Sommerfeld, one gradually achieved in this way a description, in terms of correspondence, of the binding of each individual electron in the atom, and therefore an explanation, complete at least in its major features, for the relations between the elements, represented in the periodic system, as regards their physical and chemical properties. Although soon afterwards the recognition of the spin properties of the electron by Uhlenbeck and Goudsmit, and above all the establishment of Pauli’s exclusion principle for the occupation of the quantum states by electrons, provided a provisional completion of the primitive correspondence method, nevertheless the inadequacy of the continued, even though restricted, use of classical mechanical concepts made itself felt more and more, particularly as regards the account of the finer features of the interaction of the electrons in the atom. A harmonic fusion of the quantum theoretical and classical features of the theory of atomic constitution was, as is well known, achieved only by the development of rational quantum mechanical methods, which we owe, on the one hand, to the fortunate introduction of the novel intuitive ideas of light quanta and matter waves by Einstein, de Broglie and Schrodinger, and on the other hand to the continuing elaboration of the correspondence treatment by way of Kramers’ papers to its brilliant perfection by Heisenberg, Born, Jordan and Dirac. The high point of this development is perhaps Dirac’s relativistic electron theory, which was able not only to explain rigorously the finest features of spectra, but also contained the prediction of the possibility of transmutation of radiant energy into pairs of positive and negative electrons, which was confirmed by experiment. For our purposes it is sufficient to recall briefly the fact that quantum mechanics not only enabled the description of the properties of individual atoms to reach a certain finality, but that it also supplied entirely new and fruitful points of view for the understanding of the various types of chemical bonds in molecules, and the explanation of many typical properties of solids, in particular of metals, which one previously had faced without any understanding. This was by no means only a matter of perfecting the theoretical methods of atomic physics, but of such a deep reformulation of the conceptual means of our
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description of nature that even a profound revision of the very concept of observation was required. Above all, the unavoidable interaction between the atomic objects in question and the measuring instruments required for the definition of the phenomena, resulting from the quantum of action, means that the results obtained under various experimental conditions cannot be combined in the usual form of description based on the idea of the independent behaviour of the objects, but are in a novel, complementary relation to each other. The fundamentally statistical character of quantum mechanics which is expressed in Heisenberg’s uncertainty relations is indeed not a temporary restriction of the analysis of atomic events, but it corresponds in an appropriate manner to the point of view of complementarity, which is more comprehensive than the ideal of causality, and necessary in order to account for the wealth of experiences depending on the existence of the quantum of action. When we now turn from these introductory remarks to our specific theme, the significance of the quantum of action for the constitution and stability of the atomic nuclei, it will be noticed at once that the basic problem is precisely the reverse of that which was met in the attack on the atomic problems mentioned above’. Whereas we could there start from an extensive knowledge of the constituents of the atom and the forces of interaction between them, it is immediately clear that the high density and the strong binding of nuclei require forces between the nuclear particles which act only over distances of the order of nuclear dimensions, but whose precise law is completely unknown in advance. It also soon turned out that, because of the existence of the quantum of action, it is even impossible to assume that all the material particles which are liberated in natural or artificial nuclear decay processes are actual nuclear constituents. Already the first attempts to consider nuclei as systems of protons and electrons, prompted by Aston’s discovery - that not only the electric charges of nuclei are multiples of the elementary charge, but that also the mass of each nucleus is, to a good approximation, an integral multiple of the mass of the lightest nucleus, the proton - met fundamental contradictions. Apart from the
’
A more detailed account of the development of the theory of atomic structure, in which the difference between atomic and nuclear problems stressed here is also pointed out, can be found in the author’s Faraday Lecture (J. Chem. SOC., 1932, p. 381). The points of view quoted below for the explanation of the typical characteristics of nuclear reactions were first developed in an article published in Nature 137 (1936) 344 and in Naturwiss. 24 (1936) 241. A further extension of these points of view is contained in an article by N. Bohr and F. Kalckar (Mat.-Fys. Medd. Dan. Vidensk. Selsk. 14, no. 10, 1937) which also gives extensive references to the literature. The nuclear photoeffect mentioned at the end of the present article has been discussed recently in a brief note in Nature 141 (1938) 326.
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difficulties in trying to explain the stability of nuclei on this basis, there appeared incompatibilities between the spin and symmetry properties of such systems and the spectroscopic results on the properties of nuclei in their dependence on atomic and mass number. In addition, a closer study showed that within the framework of quantum mechanics, regardless of any assumption about the forces acting within the nucleus, it is impossible to attribute to particles as light as eiectrons an actual existence within the nuclear volume. The emission of positive or negative electrons in radioactive decay of nuclei must therefore be considered as the creation of these particles as mechanical units, similar to the emission of a light quantum by an atom. In order to retain the law of conservation of energy and momentum in radioactive 0-decay it has even become necessary, as we know, to postulate that in addition to the electron a light neutral particle, not so far observed, is emitted. Although the development of these points of view particularly by Pauli, Fermi and Heisenberg, has not yet reached a satisfactory conclusion, it has nevertheless opened new promising possibilities of dealing with the fundamental problems of atomic theory, and above all has disclosed the necessity of regarding nuclei as mechanical systems consisting only of heavy particles. It is well known that Chadwick’s discovery of the neutron provided a basis for the implementation of this programme. Indeed a nuclear model consisting only of protons and neutrons provides not only an immediate interpretation of the charges and mass numbers of nuclei; moreover the general symmetry properties predicted by the model under the assumption that the neutron possesses the same spin as the proton, and, like the latter, obeys the exclusion principle, are in all cases compatible with the observations. In addition, such a model provides a simple explanation for the peculiar dependence of the stability of nuclei on the odd or even character of the charge and mass number, which was pointed out very early by Hurkins. It is interesting to recall that in this connection the assumption of a heavy neutral nuclear constituent was discussed several years before the neutron was identified, and this was even before quantum theory had led to a clear recognition of the contradictions between the properties of real nuclei and those of any nuclear model containing electrons. A decisive step in the treatment of the proton-neutron model of the nucleus was achieved by Heisenberg, who showed how the quantum mechanical formalism made it possible, by means of simple generalisation, to introduce novel types of force between proton and neutron which have saturation properties like the valence forces in chemical compounds, and whose existence seems necessary to explain the typical variation of the mass defect of nuclei with their mass number, In the last few years there have been many attempts to explore more closely the consequences of such assumptions about the nuclear forces; but,
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apart from the promising treatment of the very lightest nuclei, this approach is very difficult because the strong coupling of the motion of the individual particles excludes the use of all those approximations which in such great measure facilitated the study of the binding of atomic electrons. Quite apart from the question of the law of force, it should also not be forgotten that the fact that nuclei can be decomposed adiabatically into neutrons and protons offers no guarantee that the detailed description of their properties - similarly to those of the usual atomic systems - can be carried out using solely the variables used so far for the characterisation of isolated particles. The difference between the problems in the study of atomic and nuclear structure, as regards starting points and tools, is also brought out particularly clearly by the manner in which the interpretation of the rapidly accumulating experimental material on nuclear reactions has gradually progressed. The starting point of this development was the explanation, possible only on the basis of quantum mechanics, of the law of radioactive decay which, since its formulation by Rutherford and Soddy, has been the infallible guide in disentangling the large field of radioactivity. Although Einstein had already stressed the analogy between radioactive decay and radiative processes in atoms in his famous simple derivation of Planck’s law of radiation, the law of decay remained a mystery for a long time, particularly after Rutherford had pointed out that the energy of repulsion between the nucleus and the emitted a-particle is usually much greater than the kinetic energy of that particle. Shortly after the principles of quantum mechanics were formulated, it was shown, as is well known, by Gurney and Condon, and independently by Gamow, that we are dealing here just with a particularly instructive example of the failure of ordinary mechanical concepts. Indeed in quantum mechanics a field of force which is limited in space does not represent an absolute barrier even for particles with a kinetic energy less than the maximum of the potential; and even a simple comparison of the law of force between a-particle and nucleus with a spherically symmetric potential barrier is adequate to yield an immediate explanation of the well-known Geiger-Nuttall relation between the mean life of a radioactive element and the kinetic energy of the ejected a-particle. This great success was the beginning of a most productive development which led to a comprehensive account of the natural and artificial nuclear transmutations and the accompanying electromagnetic radiation phenomena. Above all one should mention here Gamow’s explanation of the fine structure of a-spectra, which created, with the interpretation of optical spectra as a model, the basis for a more intimate knowledge of the discrete quantum states of nuclei. In the first place this consisted - contrary to the analysis of atomic spectra using correspondence - only of the appropriate use of the classical conservation laws and
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the quantum postulates. In particular the schematic representation of the nuclear field as a potential well in which particles move nearly independently, was gradually recognised to be inadequate to explain the details of nuclear reactions and particularly the characteristic resonance phenomena often associated with them. It turned out indeed, as we shall see, that the typical feature of nuclear reactions, as opposed to atomic reactions, consists just in the exceeding!y close coupling between the motions of individual particles in the nucleus, compared with the coupling between the electron motions in the outer region of the atom, and the resulting extraordinarily easy exchange of energy between the individual nuclear particles. This state of affairs was demonstrated in particular by the detailed study of the transmutations caused by neutron impact, which was stimulated by the discovery of artificial radioactivity by the Curie-Joliots. Because of the absence of repulsive forces outside the nuclear region proper, neutron collisions are much easier to study than the impact on nuclei of positively charged particles such as protons and a-particles, in which the presence of the potential barrier often has an overwhelming influence. Indeed the fact that the cross section for inelastic collisions between fast neutrons and heavy nuclei is of the same order of magnitude as the diameter of the nucleus, immediately leads to the conclusion that the coupling between the incident neutron and the particles in the nucleus must be very close. Further conclusions can be drawn from the fact, first demonstrated by Ferrni, that such impacts lead with appreciable probability to capture of the neutron, with the formation of a new stable nucleus, which may often be 0-radioactive, but always has a mean life of a very different order of magnitude from the times involved in the collision process. This is significant because such a neutron capture must necessarily involve the radiative emission of the excess energy; from the observed probability of such a course of the collision process one may therefore conclude that the duration of the collision is extremely long compared to the time intervals necessary for a simple passage of the neutron through the nuclear volume. Even the upper limit on the rate of yemission set by the charge and the dimensions of nuclei implies indeed that the ratio between the duration of the collision and the latter time interval must be of the order of a million. The normal method of treatment of atomic collisions appropriate for the collisions between fast electrons and atoms, which uses in first approximation the motion in a static field of force, therefore fails completely for the description of the collision between a neutron and a nucleus. Instead, we must imagine that the penetration of the neutron into the nucleus leads immediately to an exchange of energy with the nuclear constituents, with the result that the energy is spread very rapidly over all particles of the compound system formed by the neutron and the
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target nucleus, so uniformly that over a short time no particle will have sufficient energy to escape from the nucleus against the attraction of its neighbours. The existence of this intermediate state further implies that the final result of the collision is determined by an essentially free competition between all possible disintegration and radiation processes of the compound system, and this provides an immediate explanation for the striking wealth of nuclear transmutation phenomena, in which almost all processes consistent with the conservation of energy actually appear. Precisely in this connection the idea of an intermediate state in nuclear transmutations was discussed on various occasions, already shortly after Rutherford’s first experiments on nuclear disintegration by aparticles; however, prior to the neutron experiments it was not only difficult to assess the influence of barrier effects, but one completely lacked any basis for estimating the lifetime of the intermediate state and for a more detailed determination of its properties. Another particularly instructive result of the discussion on nuclear transmutations by neutron impact is the disclosure of a fundamental difference between the distribution of energy levels in nuclei and those in atoms. The formation of a long-lived intermediate state in the collisions between nuclei and neutrons of any sufficiently high energy indeed requires an extensive continuous energy spectrum of the compound nucleus, which at first appears to be in direct contradiction with the evidence for discrete energy levels in nuclei from the analysis of y-ray spectra. We must remember, however, that in such collisions we are dealing with excitation energies of the compound nucleus far above those of the excited states relevant for the usual y-ray phenomena. Whereas in the latter case we are dealing with excitations of at most a few MeV, the excitation energy in the former case is the sum of the kinetic energy of the incident neutron and the binding energy of a neutron in the ground state of the compound nucleus, which for medium mass number amounts to nearly 10 MeV. Actually the continuous energy spectrum begins for such a mass number only at about 12 MeV excitation, and it follows on continuously from the region of discrete nuclear levels, while the distance between adjacent levels, which for the lowest states is of the order of 1 MeV, decreases very rapidly with increasing energy. Direct insight into the extremely dense distribution of energy levels of highly excited nuclei has been provided by the investigations of the capture of very slow neutrons which give - contrary to the experiments with fast neutrons - pronounced differences in the reactions of nuclei with only slightly differing charge and mass numbers. This selectivity is evidently a quantum mechanical resonance phenomenon, conditioned by an, as it were accidental, coincidence of the binding energy of the neutron in the new nucleus formed by its capture, with a quantum state of this nucleus. From the sharpness of the resonance and the occur-
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rence of the selectivity amongst the elements one can in fact conclude by means of simple statistical considerations that the level spacing for medium mass number at approximately 10 MeV excitation amounts to only about 10 eV. Altogether the resonance phenomena occurring in the impact of slow neutrons are of the greatest interest; above all the observation of cross sections amounting in some cases to more than 1000 times the geometrical cross section of the nucleus provides a striking example of the complete failure of the classical concept of an orbit within regions small compared to the de Broglie wavelength. Indeed the collision problem shows in such circumstances an extensive resemblance to acoustic and optical resonance phenomena; in particular, as was shown first by Breit and Wigner, and later in more detail by Bethe and Placzek, the manner in which the scattering and capture cross sections of a nucleus vary with the neutron energy can be represented by formulae of a quite similar type to the wellknown dispersion formulae of optics. Whereas these conclusions are based on very general considerations, the explanation of the energy distribution of nuclear levels and the estimate of the probabilities of the individual disintegration and radiation processes, which determine the course of the reaction, require a closer study of the relevant mechanical problems. At present a rigorous treatment of these problems does not seem feasible; yet many characteristic properties of nuclei, which are dominated by just the close coupling of the nuclear particles, can be clarified to a large extent by a comparison with well-known properties of solids and liquids. Above all, the typical difference between the distributions of excited levels of atoms and nuclei is immediately explained by the remark that in an excited atom we are in general dealing with a change in the quantum state of a single electron, whereas the nuclear excitation is concerned with the quantisation of the motion of all particles, reminiscent of the rotations and vibrations of a solid. Indeed, if in the first place we ignore rotation, the totality of energy levels of an elastic solid is given by all possible combinations of quantum states corresponding to its normal modes; because of the extremely rapid increase with energy of the possibility of combinations, this has exactly the same general character as the nuclear level spectrum. This comparison gives even quantitatively an approximately correct picture of the distribution of nuclear levels. It is found that from the combinations of approximately equidistant eigenvalues with distances of about 1 MeV we get already at 10 MeV a level density of the same order of magnitude as that derived from the experiments with slow neutrons. This picture of the excitation of a nucleus evidently shows a far-reaching analogy with the thermal motion of a solid at low temperatures, and in this sense one can speak of the nuclear matter being heated by the formation of a compound nucleus in a collision. While the relevant temperature is enormously high
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on the usual scale (of the order of 10" degrees), it is very low on the nuclear scale, since a collision with not extremely fast particles usually excites only a small number of vibrational degrees of freedom. Estimates using the quantum theory of specific heats give, for medium mass number, the temperature of the compound nucleus in ordinary collision experiments as about 1 MeV. For very fast impact it is of course higher, but it grows only slowly, because the number of excited degrees of freedom grows rapidly, and even in a collision of a nucleus with a particle of 100 MeV the temperature would amount to only a few MeV. This concept of nuclear temperature is not only very convenient for characterising the nuclear excitation, but above all it has been most helpful in the description of the disintegration and radiation processes involved in the nuclear transmutations, which in this picture show close analogies with evaporation and thermal radiation. Above all, as was first pointed out by Frenkel, the emission of neutrons by highly excited nuclei reminds one in many respects of ordinary evaporation, to which the well-known formula of reaction kinetics giving the dependence of the evaporation rate on temperature and latent heat is applicable at least approximately. This comparison also provides an immediate explanation of the fact that the neutrons liberated in nuclear reactions in general do not carry away all of the excess energy, but show an energy distribution strikingly reminiscent of the Maxwell distribution at the corresponding nuclear temperature. The fact that collisions with fast neutrons produce, instead of capture, the ejection of one or more neutrons, can be understood naturally as a decay of the compound nucleus in stages, which for higher and higher excitation energy gradually becomes more like the gradual evaporation of a drop of liquid. At lower excitations one must however apply such a comparison with some caution, because - contrary to the usual evaporation processes, in which the total heat content of the body is extremely large compared to energy required to release a single molecule - the excitation energy of the compound nucleus in the collision experiments is usually of the same order of magnitude as the binding energy of one neutron. However, as shown in particular by Landau and Weisskopf, one can treat such processes also by methods of statistical mechanics which form a consistent generalisation of the purely thermodynamic reasoning. Even when the incident or emitted particle is charged the transmutation takes place in stages, in which first a compound nucleus is formed with an energy distribution similar to that of a hot body, and afterwards there is a decay similar to evaporation. However in such cases the repulsion can have a major influence on the probability both of the formation and of the decay of the compound nucleus, particularly when the energy of the particle is low. Here one must not only allow for the quantum mechanical barrier effects, but, even for particle
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energies above the value of the potential near the nuclear surface, it is essential to subtract this potential from the total energy in estimating the temperature of the intermediate state, and the heat of evaporation, which influences the decay probability. Another simple consequence of the repulsion is that the kinetic energy of an emitted charged particle is in general greater than that of a neutral one, since in the former case the potential energy must again be added to the thermal energy proper. If the kinetic energy of the incident particle is not sufficient to carry the compound nucleus into the region of continuous energies, there appear typical resonance phenomena also for charged particles, just as in the case of collisions with slow neutrons. Such resonances appear often for incident energies which would allow the particle to pass freely through the potential barrier, and this fact shows clearly the failure of the earlier interpretation according to which this involved a quasi-stationary state of the particle inside the potential barrier. Instead we are dealing with a coincidence between the total energy and a quantum level of the collective motion of the nuclear particles, and this was demonstrated strikingly by the new observations of Bothe and his collaborators, showing that resonances in collisions of nuclei and particles of different charges, which lead to the same compound nucleus, occur at exactly the same values of the total energy. The very strong coupling between the motions of the nuclear particles, which is decisive for the nuclear reactions in collisions, also leads to radiative properties of nuclei which are very different from those of atoms. The radiation of the latter generally corresponds to transitions in which the binding of only one electron changes, and which correspond to dipole vibrations; the radiation from nuclei - as shown by the study of the photo-effect caused by the y-rays in the outer electron cloud of the same atom - is generally of the quadrupole type. Our picture of nuclear excitation makes this immediately intelligible, since the emission of radiation of this type is comparable to the vibration of a n elastic body with approximately uniform mass and charge distributions. In such vibrations dipole moments d o not appear in first approximation, since the centre of electricity will always coincide with the centre of mass. An estimate of the relevant quadrupole moments, based on the nuclear dimensions and the amplitude of the quantised nuclear vibrations leads to approximate agreement with the probability of radiative processes estimated from the sharpness of the resonance in the capture of slow neutrons. As regards the intensity distribution of the radiation from highly excited nuclei, we should expect some resemblance to thermal radiation at a corresponding temperature. However, as a result of the rapid rise of the emission probability with frequency for radiation of higher multipolarity, there will be a relatively high probability of the larger quantum jumps, which becomes particularly noticeable in the excitation of light nuclei; in certain cases this even
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makes that component of the radiation dominant which corresponds to a direct transition to the ground state of the nucleus. In this respect there is particular interest in the radiation produced by the impact of protons on lithium, which consists almost exclusively of one component with an energy of nearly 17 MeV. Incidentally, the relatively high intensity of this radiation is due to the fact that in such collisions we are dealing with a pronounced resonance, in which the relevant state of the compound nucleus cannot decay into two a-particles, because of general quantum mechanical symmetry requirements, so that the radiative processes compete only with the emission of a relatively slow proton, which does not easily penetrate through the potential barrier. Presently the beautiful investigations of Bothe and Gentner about the release of neutrons from heavy nuclei by the bombardment with the above-mentioned proton-lithium y-rays promise to yield further interesting clues about the radiative properties of nuclei. Different elements show, under such bombardment, a very different behaviour of the nuclear photo-effect, and this result seems at first difficult to reconcile with the general ideas about nuclear excitations to which one had been led by the transmutation by collisions. According to these ideas all the elements concerned should have a continuous energy spectrum even at excitation energies well below 17 MeV, and we therefore cannot expect any ordinary resonance effect. We must realise, however, that the condition for nuclear transmutations by collisions and by radiation are completely different. In the case of a collision the course of the process is determined essentially by the competition between the possible disintegration and radiation probabilities of the long-lived intermediate state; the course of the photo-effect on the other hand will depend on the ratio of the coupling of the radiation field with the corresponding specific modes of vibration of the nucleus to the coupling of these vibration modes with other possible types of vibration. The presence of the latter type of coupling has the effect that the energy spreads very rapidly to all vibrations, just as in a heated body, so that the probability per unit time of the emission of the excitation energy in the form of a single quantum decreases rapidly from its value in the first stage of excitation to a much smaller value corresponding to thermal radiation. The nuclear photo-effect will then show, also in the continuous energy region, a selective frequency dependence, provided this change is not rapid enough to suppress completely the influence of the initial excitation type on the total re-emission probability of the quantum. This interpretation, by which the selectivity of the nuclear photo-effect in the continuum, which is suggested by the mentioned experiments, shows a close analogy with the presence of sharp infrared absorption bands of solids at ordinary temperatures, would evidently open the possibility of determining the strength of coupling between the nuclear vibrations from the photo-effect. Since the quantum
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
mechanical zero-point energy of nuclear matter has a much greater influence than in the case of a crystal, the behaviour of this coupling is very hard to judge theoretically, and the continuation of these experiments must be awaited with great interest. We shall also mention briefly another phenomenon which promises new insights into the mechanism of nuclear excitation: the discovery of so-called nuclear isomers. These are long-lived products with the same charge and mass numbers, but with different radioactive properties. In the last few years the occurrence of such nuclear isomerisms has been found in the transmutations of many elements, and in particular very interesting examples have resulted from the investigations of Hahn and Meitner on the new radioactive families generated by the impact of neutrons on uranium. Weizsacker was the first to point out that the existence of very long lifetimes of excited nuclei can be explained by the assumption that the relevant nuclear states have particularly large angular momenta, so that the radiative processes corresponding to transitions to the ground state have an extremely small probability. This interpretation, which is reminiscent of the metastability of certain atomic states, is very appealing; however, at the present it is still difficult to judge whether this is sufficient to explain the special conditions in which the various nuclear isomerisms appear, or whether a part is played by hitherto unknown selection rules characteristic of nuclear processes. In concluding this brief review, which was intended mainly to give an impression of the wonderful fertility of the new field of research which has arisen from the interplay of the fundamental discoveries of Planck and Rutherford, it is hardly necessary to emphasise that in nuclear physics proper we are only at the beginning of its development. However, we may be encouraged to place great hopes in further progress by the intimate connection between experimental and theoretical investigations which characterises the research in this field.
Copenhagen, Institute for Theoretical Physics. (Received 27 February 1938)
XXIX. RESONANCE IN NUCLEAR PHOTO-EFFECTS Nature 141 (1938) 1096-1097
See Introduction, sect. 4, ref. 80
Resonance in Nuclear Photo-Effects Is connexion with the remarkable selectivity of
nuclear photo-effects of heavy elements indicated by experiments, it was pointed out in a recent note in X A T U R Ethat ~ such photo-effects might provide a means of examining certain features of the mechanism of excitation of atomic nuclei not disclosed by ordinary experience about nuclear reactions by collisions. In fact, the probability of excitation of a nucleus by monochromatic radiation depends on the degree to which forced oscillations of given frequency of the nuclear matter can be produced, and experiments on the variation of the yield of the photo-effects with radiation freynency would therefore allow a direct estimate of the strength of coupling between the different modes of oscillation into which the collective motion of the nuclear particles ma)- approximately be resolved. I n view of the L-ery incomplete experimental evidence, I would like, however, t o emphasize the preliminary character of any such estimates as attempted in the note referred to, and at the same time t o direct attention to a possible misunderstanding of the argument regarding the separation of the course of the photo-effects into successive stages. Such a separation into the initial excitation of a certain mode of oscillation and its subsequent quenching due t,o the coupling cannot, of course, be carried oiit in the case of strictly monochromatic radiation. Nevertheless, a well-defined meaning can be attached to the argument as soon as we, instead, consider the effect of a timelimited irradiation with a corresponding frequency uncertainty. I n particular it follows from such a treatment that, so far as we are concerned only with mean values of the yield of the photo-effects over energy regions wide compared with the distance of the nuclear levels, all typical resonances will be essentially the same whether the level distribution is discrete or continiions. It follows also that, contrary to an assertion in the note, the selectivity is completely independent of the ratio between the chances of the re-emission of the whole energy as a single radiation quantum in the initial and in the subsequent stage of t h e excitation process. All such conclusions are in fact in complete harmony with a treatment on the lines of the ordinary theory of dispersion of monochromatic radiation, according to which the selective phenomena would be attributed t o an abnormally large radiative transition probability to the normal state from certain energy regions. For the clarification cf these points I am indebted to discussions with Prof. Peierls and Prof. Placzek, in collaboration with whom a paper about nuclear resonance phenomena with special regard to the abovementioned arguments is being prepared for publication in the communications of the Copmhagcn Academy of Sciences. N . BOHR. Institute of Theoretical Physics, Copenhagen. >lay 28. I
c'f. B0Ill', S . , S A T C R E , 141, $26 (1938).
XXX. SYMPOSIUM ON NUCLEAR PHYSICS INTRODUCTION Address to the British Association for the Advancement of Science on 18 August 1938 ABSTRACT Brit. Ass. Adv. Sci., Report of the Annual Meeting, 1938 (108th Year), Cambridge, August 17-24, London 1938, p. 381 REPORT Nature (Suppl.) 142 (1938) 520-521
See Introduction, sect. 4, ref. 81.
PART I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
From the way in which the symposium was reported in Nature it is not quite clear where the report of Bohr’s talk stops.
SECTIONAL TRANSACTIONS. SECTION A. MATHEMATICAL AND PHYSICAL SCIENCES.
Thursday, August 18. SYMPOSIUM o n Nuclear physics
(10.0).
Prof. N. BoHR.-Introduction. D u e to t h e extreme facility of energy exchange between t h e closely packed particles in atomic nuclei, nuclear reactions show certain typical features which differ strikingly from those of ordinary atomic reactions. I n particular nuclear transmutations initiated by collisions with heavy particles take place in two well-separated stages of which t h e first consists in the formation of a semi-stable compound nucleus, where t h e excitation energy is distributed among the nuclear particles i n a similar way to that in a heated body, and t h e second in t h e subsequent disintegration of this system or its de-activation by emission of radiation, exhibiting instructive analogies to evaporation or thermal radiation respectively. Similarly t h e excitation of nuclei by radiation, resulting i n the release of heavy particles, sugqests a comparison with the well-known phenomena of selective absorption of infra-red radiation by solid or liquid substances. I t is shown how thcse views combined with simple arguments of quantum theory account in a comprehensive way for t h e experimental evidence regarding such nuclear phenomena.
520
Supplement t o N A T U R E of September 17, 1938
Nuclear HE discussion on nuclear physics arranged to take place in Section A (Mathematical and Physical Sciences) on August 18 was introduced by Prof. Niels Bohr, of Copenhagen, who gave an account of the new ideas in nuclear theory which have developed under his guidance during the last few years. The old nuclear theory a t tempted to explain the interactions of fast particles with nuclei by considering the behaviour of single particles inside the nucleus rather on the same lines as in the theory of the outer electronic system. This picture gave a satisfactory account ot the penetration of charged particles into light naclei but failed to account for many phenomena, in particular the large probability of capture of slow neutrons by nuclei relative to the probability of elastic scattering. These difficulties have been removed by the realization that owing to the tight packing of particles within the nucleus, there is a great facility of energy exchange between the particles. I n consequence, when a particle penetrates a nucleus its energy is rapidly distributed amongst all the particles, resulting in a general increase in ‘nuclear temperature’. The nucleus then remains in the excited state until sufficient energy is again concentrated on one particle for ’eraporation’ or escape to occur. Alternatively, the state of excitation may decay by emission of radiation, but owing to the high symmetry of rharge distribution. dipole radiation is in general unlikely and the decay period consequently long. The ‘intermediate nucleus’ thus exists for a period long compared with the time which would have been taken for the incident particle to traverse the system unhindered. The study of the properties of this intermediate nucleus, its states of excitation and rates of decay, is the point of greatest interest to-day in nuclear physics. Prof. Bohr showed how much guidance as t o its properties can be obtained from simple
Physics mechanical models. Thus the system behaves in many respects like a drop of fluid, and the states of excitation can be compared with the oscillations in volume and shape of a sphere under the influence of its elasticity and surface tension. The experimentally established result t h a t the distance between excited levels diminishes rapidly with increasing excit,btion energy suggests also t h a t nuclear frequencies can be formed from a linear combination of a few fundamental frequencies, The level distribution is therefore of a similar character to t h a t of the quantum states of a solid body, and suggestive analogies occur between the absorption of infra-red radiation in solids and the absorption of high-energy y-rays by nuclei. I n such a way the results of Prof. Bothe on the wide variations in eEciency of disintegration of different elements by such -rays might be explained. The energies of the stationary states can be obtained from experiments of the type described by Mr. P. I. Dee and Prof. W. Bothe. It is observed that many nuclear processes show resonance effects -that is, they occur with maximum intensity for a particular range of energy of the incident particle. This resonance is explained by the sum of the energy of the incident particle and the original nucleus coinciding with the energy of a stationary state of the compound nucleus. The compound nucleus may decay either by the emission of charged particles, neutrons or y-rays, and in consequence the intensity of the emission of such radiations will show resonance maxima as the energy of the bombarding particle is changed. The Cavendish Laboratory experiments determined the intensity and energy of the y-rays emitted when beryllium, boron, carbon and fluorine are bombarded b y protons. Resonance maxima were observed for beryllium a t 350 and 670 kilovolts ; for boron a t 180, 650, 850 and 950 kilovolts ; for the
Supplement t o N A T V R E of September 17, 1938 c u b o n isotope of mass 12 a t 480 kilovolts ; for thc carbon isotope of mass 13 a t 570 kilovolts and for fluorine a t 330, 470, 590, 670, 860, 920 kilovolts. The fluorine experiments are particularly interesting in shouing the closeness of the levels of 2oXe uhen excited t o 13.5 million volts A further point of interest is the 'breadth' of the different nuclear states. Sharply defined energy states and sharp resonances occur when the lifetime of the Ytnte is long, that is, when the probability of decay is s mdl I n the above cases, the resonance occurs because decay of the excited nucleus bj7 particle einisyion is improbable. The experiments determine only an upper limit t o the breadth of the states owing to the spread in the energy of the incident particles (about 20 kilovolts). Prof Bothe's experiments measured the intensity of emission of 2-particles, neutrons and y-rays from the same intermediate nucleus. He found that although some resonance levels are observed for all the radiations, others occur only for one type of decay, a result which introduces some difficulty for the view that the different radiations are competing methods of decay from the same nuclear state Another method of determining energy levels of nuclei depends on observing the energies of the different groups of particles emitted when an excited nucleus returns to stability. Thus when fluorine is bombarded by deuterons, the compound nucleus *1Ne emits four groups of 2-particles, the most energetic group occurring in a transition to the ground state of 1 7 0 and the other groups in transition to excited states of 170. Thus excited states in 1 7 0 a t 0.83, 2.95, 3.77 and 4.49 million volts are found. One of these was already known to be produced when oxygen is bombarded by deuterons ; two have been determined from experiments by Gilbert and by Bothe on the disintegration of neon b y neutrons. Thus different methods of formation of a nucleus show in general the same excited states. I n some nuclear reactions the residual nucleus may be left in a metastable excited state in which it has only a small chance of decay by y-ray emission. This may occur when the angular momentum of the metastable state differs by several units of h 2 x from that of the ground stdte We may then have two nuclei of the Same mass and charge but with different properties.
52 1
XXXI. REACTIONS OF ATOMIC NUCLEI OM ATOMKERNERNES REAKTIONER Overs. Dan. Vidensk. Selsk. Virks. Juni 1938 - Maj 1939, p. 25 REACTIONS OF ATOMIC NUCLEI Nature 143 (1939) 215 Communication to the Royal Danish Academy on 21 October 1938 ABSTRACT
See Introduction, sect. 4, ref. 83
NIELS B O H R giver e n Meddelelse: On1 Atoi~ikeriieriies Reaktioner. I Forbindelse med Forelz!ggelsen af en Af handling, skrevet i Samarbejde med G. PLACZEK og R . PEIERLS, bliver der i Foredraget gjort Rede for, hvorledes (let e r miiligt ud fra enkelte mekaniske Synspunkter og Benyttelse af simple termodynamiske hnalogier at forklare mange karakteristiske T r z k v e d r ~ r e n d eAtomkernernes Keaktioner. Vil blive t r y k t i Math.-fys. Medd.
Copenhagen Royal Danish Academy of Sciences and Letters, October 21.
NIELS HOHR : Reactions of atomic nuclei. 1 1 1 connexion with the communication of a paper. writtjen in collaboration with G. Placzek and R . Peierls, a general survey is given of the use of simple mechanical ideas and thermodynamic analogies to explain several characteristic features of nuclear reactions.
XXXII. DISINTEGRATION OF HEAVY NUCLEI [l] Nature 143 (1939) 330
See Introduction, sect. 5 , ref. 99
NATURE
330
FEB.25, 1939,
VOL.
143
Letters to the Editor The Editor does not hold himself responsible for opinions expressed by his correspondents. He cannot undertake to return, or to correspond with the writers of, rejected manuscripts intended fo. this or any other part of NATURE. N o notice is taken of anonymous communications. NOTESON
POINTS
IN SOME OF THIS WEEK’S LETTERS APPEAR
ON P.
(‘ORRESPONDEXTS ARE INVITED TO ATTACH SIMILAR SUMMARIES TO THEIR
Disintegration of Heavy Nuclei THROUGH the kindness of the authors I have been informed of the content of the letters‘ recently sent to the Editor of NATUREby Prof. Meitner and Dr. Frisch. I n the first letter, these authors propose an intcrpretation of the remarkable findings of Hahn and Strassmann as indication for a new type of disintegration of heavy nuclei, consisting in a fission of the nucleus into two parts of approximately equal masses and charges with release of enormous energy. In the second letter, Dr. Frisch describes experiments in which these parts are directly detected by tho very large ionization they produce. Due to the extreme importance of this discovery, I should be glad to add a few comments on the mechanism of the fission process from the point of view of the general ideas. developed in recent years, to account for the main features of the nuclear reactions hitherto observed. According to these ideas, any nuclear reaction initiated by collisions or radiation involves as an intermediate stage the formation of a compound nucleus in which the excitation energy is distributed among the various degrees of freedom in a way resembling the thermal agitation of a solid or liquid body. The relative probabilities of the different possible courses of the reaction will therefore depend on the facility with which this energy is either released as radiation or converted into a form suited to produce the disintegration of the compound nucleus. I n the case of ordinary reactions, in which the disintegration consists in the escape of a single particle, this conversion means the concentration of a large part of the energy on some particle a t the surface of the nucleus, and resembles therefore the evaporation of a molecule from a liquid drop. In the case of disintegrations comparable to the division of such a drop into two droplets, it is evidently necessary, however, that, the quasi-thermal distribution of energy be largely converted into some special mode of vibration of the compound nucleus involving a considerable deformation of the nuclear surface. In both cases, the course of the disintegration may thus be said to result from a fluctuation in the statistical distribution of the energy between the various degrees of freedom of the system, the probability of occurrence of which is essentially determined by the amount of energy to be concentrated on the particular type of motion considered and by the ‘temperature’ corresponding t o the nuclear excitation. Since the effective cross-sections for the fission phenomcno, for neutrons of different velocities seem to be of about the same order of magnitude as the cross-sections for ordinary nuclear reactions, we may therefore conclude that, for the heaviest nuclei the deformation energy sufficient for the fission is of
[342]
337.
COMMUNICATIONS.
the same order of magnitude as the energy necessary for the escape of a single nuclear particle. For somewhat lighter nuclei, however, where only evaporationlike disintegrations have so far been observed, the former energy should be considerably larger than the binding energy of a particle. These circumstances find their straightforward explanation in the fact, stressed by Meitner and Frisch, that the mutual repulsion between the electric charges in a nucleus will for highly charged nuclei counteract to a large extent the effect of the short-range forces between the nuclear particles in opposing a deformation of the nucleus. The nuclear problem concerned reminds us indeed in several ways of the’ question of the stability of a charged liquid drop, and in particular, any deformation of a nucleus, sufficiently large for its fission, may be treated approximately as a classical mechanical problem, since the corresponding amplitude must evidently be large compared with the quantum mechanical zeropoint oscillations. Just this condition would in fact seem to provide an understanding of the remarkable stability of heavy nuclei in their nonnal state or in the states of low excitation, in spite of the large amount of energy which would be liberated by an imaginable division of such nuclei. The continuation of the experiments on the new type of nuclear disintegrations, and above a11 the closer examination of the conditions for their occurrence, should certainly yield most valuable information as regards the mechanism of nuclear excitation. At the Institute for Advanced Study, Princeton, N.J. Jan. 20. [NATURE, 143, 239 and 275 (1939)l.
N. BOHR.
XXXIII. RESONANCE IN URANIUM AND THORIUM DISINTEGRATIONS AND THE PHENOMENON OF NUCLEAR FISSION Phys. Rev. 55 (1939) 418-419
See Introduction, sect. 5, ref. 115.
Reprinted from THE PHYSICAL REVIEW, Vol. 5 5 , No. 4, 418-419, February 15, 1939 Printed in U. S. A.
Resonance in Uranium and Thorium Disintegrations and the Phenomenon of Nuclear Fission The study of the nuclear transmutations by neutron bombardment in uranium and thorium, initiated by Fermi and his collaborators, and followed up by Meitner, Hahn and Strassmann, and by Curie and Savitch, has brought to light a number of most interesting phenomena. Above all, as pointed out by Meitner and Frisch,' the recent discovery of Hahn and Strassmann of the appearance of a radioactive barium isotope as the product of such transmutations offers evidence of a new type of nuclear reaction in which the nucleus divides into two nuclei of smaller charges and masses with release of a n energy of more than a hundred million electron volts. The direct proof of the occurrence of this so-called nuclear fission was given by Frisch2 for thorium as well as for uranium by the observation of the very intense ionization produced in a gas by the high speed nuclear fragments. In a recent note3 commenting on the ingenious suggestions put forward for the explanation of the fission phenomenon by Meitner and Frisch, the writer has stressed that the course of the new type of reactions, just as t h a t of ordinary nuclear reactions, may be assumed to take place in two well-separated stages. The first of these is the formation of a compound nucleus, in which the energy is stored in a way resembling that of the heat motion of a liquid or solid body; the second consists either in the release of this energy in the form of radiation or in its conversion into a form suited t o produce the disintegration of the compound nucleus. In the case of ordinary reactions, resulting in the emission of a proton, neutron or a-particle from this nucleus, we have to do with a concentration of a considerable part of the excitation energy on some particle a t the nuclear surface, sufficient for its escape, which resembles the evaporation of a molecule from a liquid drop. In the case of the fission phenomena, the energy has to be largely converted into some special type of motion of the whole nucleus causing a deformation of the nuclear surface sufficiently large to lead t o a rupture of the nucleus comparable to the division of a liquid drop into two droplets. From considerations of statistical mechanics analogous to those applied to the evaporation-like nuclear disintegrations, it follows indeed that the probability of occurrence of fission becomes comparable t o t h a t of ordinary nuclear
reactions when, with increasing nuclear charge, the deformation energy concerned has decreased to values of the same order of magnitude as that demanded for the escape of a single particle. Here I should like to show how such considerations would seem to offer a simple interpretation of the peculiar variation with neutron velocity of the cross sections of the different transmutation processes of uranium and thorium observed by Meitner, Hahn and S t r a s ~ r n a n nIn . ~ the light of the new discoveries, the great variety of processes obtained, which could not be disentangled on the ordinary ideas of nuclear disintegrations, would seem, according to Meitner and Frisch, to be reduced to only two types of transmutations. Of these the one consists in an ordinary radiative capture of the incident neutron, resulting in the formation of the normal state of the compound nucleus, which is subsequently transmuted by 8-ray emission into a stable nucleus. T h e other consists in the fission of the excited compound nucleus, which may take place in a large number of different ways, in which a wide range of mass and charge numbers of the fragments may occur. This last point, which makes i t impossible without a closer study of the statistical distribution of the fragments to trace a product of given chemical properties and radioactive period back to its origin from some particular isotope of the original element, is, as we shall see, of especial importance for the understanding of certain striking peculiarities in the case of uranium. F o r the capture processes, which lead to the radioactive uranium and thorium isotopes of periods 24 and 33 minutes, respectively, Meitner, Hahn and Strassmann found evidence of resonance phenomena for neutrons of comparatively small velocities. In uranium, where the phenomenon was more completely investigated, they found for neutron energies of about 25 volts a capture cross section a t least 30 times larger than that for thermal neutrons. Since in this resonance region the cross section amounts to about 10-21 cm2, i t is, as they pointed out, obviously necessary from simple arguments of dispersion theory to ascribe the phenomenon to the abundant uranium isotope of mass number 238. From the fact t h at neither for uranium nor thorium is the resonance capture accompanied
L E T T E R S
T O
I)y a n y large increase of t h e cross section for t h e fission pi-occsses, \ye m a y further conclude t h a t the probability of irntiiation by t h e compound nucleus in t h e excited s t a t e s coricernt:tl is consitlcrably larger t h a n t h e fission probability, and t h a t t h e noriiial s t a t e s of these nuclei, a p a r t froin their P-ray radioactivity, a r e essentially stable. A s regards all other transmutation processes, which a r e now to lie ascribed t o fission, marked differences between uraiiiuiii and thorium were found i n t h e investigations of lleiliier, I l a h n a n d Strassniann a s well a s in t h e direct csperiiiicnts of Frisch. With fast neutrons, fission cross sections of t h e same order of magnitude were found for uraniuiii a n d thorium, b u t with neutrons of thermal ~ e l o c i t i e sa large increase of t h e fission cross section was observed for uranium a n d not for thorium. T h e results for fast neutrons a r e simply explained on the basis of the general picture of nuclear processes outlined above, accordiiig t o which we should expect t h e fission probability to increase much more rapidly with excitation than t h e ratliation probability, and t o become considerably larger than t h e latter for t h e high excitations of t h e coiiipountl nucleus concerned. T h e peculiar effect in uranium for slow neutrons could obviously, however, not be reconciled with the above considerations if it were t o be attributed t o the formation of the compound nucleus of niass number 239; hut since, as already indicated, t h e periods of the most frequent radioactive fragments should be independent of the isotope undergoing fission, Lye have t h e possibility of attributing the effect concerned t o a fission of t h e excited nucleus of mass 236 formed b y t h e impact of t h e neutrnns o n the rare isotope of mass 235. Froni the fact t h a t the binding energy of a neutron in a nucleus of even charge number should be appreciably larger if the niass nuniber is even than if it is o d d , we should actually expect for a given neutron velocity a higher cscitation energy for the compound nucleus 236 t h a n for 239, ant1 accordingly a much denser distribution of resonance levels antl a much larger probability of fission in t h e
T H E
E D I T O R
419
former t h a n in t h e latter case. E v e n for excitations produced by impacts of sloa neutrons, Lye niay therefore expect t h a t t h e probability of fission of t h e nucleus 236 will be larger t h a n t h a t of radiative c a p t u r e ; antl d u e t o t h e corresponding broadening of t h e levels, t h e level (listribution of 236 in this region might even be continuous. I n a n y case, provided t h e fission probability is high enough, we shall expect for small neutron energies cross sections inversely proportional t o the velocity, allowing us t o account both for t h e obscrvecl yields of t h e process concerned for thermal neutrons a n d for the absence of a n y appreciable effect for neutrons of soniewhat higher velocities. For fast neutrons t h e cross sections c a n , of course, never exceed nuclear dimensions, a n d because of t h e scarcity of t h e isotope concerned t h e fission yields will be much smaller t h a n those obtained from neutron impacts on the a b u n d a n t isotope. I t would t h u s seeni t h a t all t h e known experimental facts receive a simple explanation without a n y assumption of peculiarities of special levels. Such assumptions a s have hitherto been thought necessary t o account for these phenoiiiena would in fact seeni difficult t o reconcile with general ideas of nuclear excitation. I n a forthcoming paper i n collaboration with Professor J o h n A. Wheeler, a closer discussion will be given of t h e fission mechanism a n d of t h e stability of heavy nuclei in their normal and excited states.
N. B O H K Institute for Advanced Study. Princeton, New Jersey, February i . 1Y3Y. 1 L. Meitner a and 1 n R . Frisch. Nature (in . .press), where references to the previous literature are given. 2 I<. Frisch. Nature (in press). T h e riianuscript of this note as uxll a s t h a t of Professor Lleitner and D r . Frisch have kindly been coiiimunicated to me by the authors. As I have learned froin other friendly communications, further most inte interesting evidence regarding the fission phenomenon has in the meantime been obtained in several laboratories in America and Europe 3 N. Bohr, Nature (in press). 4 L. Meitner, 0. Hahn and F. Strasslnann. Zeits. f. Physik 106, 2.49
(1937): 109, 538 (1938).
XXXIV. SUMMARY ON FISSION MANUSCRIPT WITHOUT TITLE (1 939) DANISH TEXT AND TRANSLATION
See Introduction, sect. 5 , ref. 116
P A R T I: PAPERS A N D MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
This manuscript consists of a carbon copy of 2 pages in Danish, written on a typewriter without Danish letters, with a few amendments in ink in Rosenfeld’s handwriting. There are two carbon copies (3 pages each) of the same manuscript, including the amendments, typed on a typewriter with the Danish alphabet. We have used the latter version and the page references in the margin refer to it. The manuscript has not yet been microfilmed.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Ud fra de Forestillinger, der er udviklede i NATURE- og PHYS. REV.Noterne* bestemmes Fission Udbyttet alene ved Konkurrencen imellem NeutronFordampningen (Sandsynlighed F N ) , Straalingsudsendelse (Sandsynlighed r s ) og Fission af Kernen (Sandsynlighed r F ) . For Uran (Kompound-Kerne 239) og Thorium (Kompound-Kerne 233) vil l7lv r s r F variere med Energien af de indfaldende Neutroner paa den Maade, som det skematisk er vist paa Fig. 1. Dette Forlab forklarer, at der ingen Fission af disse Kerner findes for Temperatur-Neutroner og CD-Neutroner, men kun for DD-Neutroner og a Be-Neutroner, samt at Fission ikke, eller i hvert Tilfzelde med overmaade ringe Sandsynlighed, kan frembringes af D med 5 MEV.Hastighed, fordi disse paa Grund af den Energi, Protonen tager bort, kun vil give et ringe Anslag af Kompound-Kernen, maaske endda endnu mindre end Anslaget for Temperatur-Neutroner. Vigtigt at undersage er primzert: Forholdene mellem Tvzersnittene for Fission og uelastisk Neutron-Spredning for forskellige Hastigheder baade i Uran og Thorium, eller sekundzrt: hvad der maaske er lettere, undersage Endringen af Forholdet mellem Fission-Tvzersnit for Uran og Thorium for forskellige Neutron-Hastigheder. For Uran (Kompound-Kerne 236) maa Sandsynlighedskurverne kvalitativt ventes at forlabe relativt som paa Figur 2, hvad der forklarer, at der i dette Tilfzlde kun findes meget ringe Neutron-Capture selv for langsomme Neutroner, og at Fission i dette Tilfzlde er szrlig udprzeget for smaa NeutronHastigheder, hvor Fission-Tvzersnittet skulde variere som 1/ u , hvad der ogsaa er paavist ved B-Absorption i Columbia-Instituttet, og som vil udkomme i en Note i Phys. Rev. af Marts 1**. Endvidere forklarer Kurverne, at Neutron-Capture er meget usandsynlig i Uran 235; det vil imidlertid v z r e af starste Interesse, om saadan Capture kunde paavises ved en svag Radioaktivitet med en ny Periode, fordi det vilde give en kvantitativ Bestemmelse af Forholdet imellem r F og r s for smaa Neutron-Hastigheder. Alle Snitpunkter paa Kurverne er naturligvis endnu meget ubestemte. ** *
hlS, p . 2
r Fig. 1
* [See the Introduction, ref. 99 and ref. 115.1 * * [See the Introduction, ref. 110.1 * * * [Added in the version typed with Danish alphabet.]
P A R T 1: P A P E R S A N D M A N U S C R I P T S R E L A T I N G T O N U C L E A R P H Y S I C S
Fig. 2
\4\,
11.
3
Sperrgsmaalet om Rigtigheden af Forklaringen af de to Uranisotopers Rolle ved Fission-Fzenomenet er blevet meget ivrigt bestridt fra forkellig Side, hvor man har gjort gzldende, at man, hvis Forklaringen er rigtig, skulde vente en meget forskellig statistisk Fordeling af Fission-Produkterne for hurtige og langsomme Neutroner. Ud fra simple teoretiske Betragtninger forekommer det mig imidlertid, at Antagelsen af meget store Forskelle er overdrevet, og at man kun burde vente smaa Forskelle i den statistiske Fordeling. Det vilde v a r e meget vigtigt, om dette Punkt kunde underserges nzermere, og navnlig om man kunde finde Forskellen for Sandsynligheden af Fremkomsten af Spaltningsprodukter med szerlig store eller szrlig smaa Ladnings- og Massetal. Iervrigt burde man i denne Henseende finde smaa Forskelle for forskellige Neutron-Energier, idet Kerneanslaget for een og samme Isotop kunde have en Indflydelse paa Produktfordelingen. Man maa i denne Henseende endda vzere forberedt paa, at Fordelingen for Uran (Kompound-Kerne 236) med langsomme Neutroner kunde ligge imellem Fordelingen for Uran (Kompound-Kerne 239) for Neutroner af 1 MEV. og 3 MEV., udsendte efter D-D Sammenstcad i forskellige Retninger. Det vilde for den teoretiske Diskussion v a r e af allersterrste Betydning, dersom der kunde gerres Fission-Forserg med Mesothorium, hvor man vel kun terr vente Fission for store Neutron-Energier. Forserget er naturligvis vanskeligt og eventuelt kostbart, men dersom det overhovedet kan lade sig gerre, vilde en Undersergelse v z r e af afgerrende Betydning, da man jo desvzrre ikke raader over andre Kerner end Uran og Thorium i det omhandlede kritiske Omraade. Man har vel allerede paa Instituttet set de mange forskellige Noter, der er offentliggjorte i Phys. Rev. af 15. Februar og i Comptes Rendus af 30. Januar. Om Forserg i Amerika, som endnu ikke er offentliggjorte i Phys. Rev., har jeg dels herrt, at man i saavel Berkeley som i Columbia har taget smukke WilsonFotografier af Spaltningsprodukternes Baner, men jeg har endnu ikke set saadanne, og endvidere at man i Washington har fundet, at der med en Forsinkelse af ca. 20 Sek. efter Fissionen udsendes Neutroner fra Spaltningsprodukterne. Jeg har skrevet ti1 Tuve for at herre nzermere om disse Undersergelser, som jeg tror kan forklares simpelthen som en Neutron-Fordampning hos anslaaede Kerner efter 0-Straaleudsendelsen. For szrlig store Maksimal
PART I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
6-Straale Energier kan man nemlig hos saadanne forholdsvis tunge Kerner paa Grund af den t=tte Niveaufordeling vente, at et Kerneanslag efter pStraaleudsendelsen vil have en betydelig Sandsynlighed. Hvis den hele Energi er 12 MEV., vil Rest-Kerneanslaget let kunne overstige de 8 MEV., n~dvendigefor en Neutron-L~srivelse.For de szrlige Kerner, det drejer sig om, med anomale Forhold mellem Ladningstal og Masse, er endda L~srivningsenergienrimeligvis betydelig mindre, ca. 5 MEV. Hvis man i K ~ b e n h a v nhar iagttaget noget saadant Fznomen, vil jeg meget gerne h ~ r enzrmere derom, og hvis Arbejdsplanerne tillader det, vil det jo v m e rart, om man i alle Tilfzlde kunde bekrEfte Tuves Iagttagelse, og navnlig u n d e r s ~ g eNeutronernes Forsinkelse nzrmere, da det j o let kan dreje sig om forskellige Spaltningsprodukter med forskellig Periode, ja endda om et Antal successive p-Straale-Omdannelser af Produkterne; dette er dog maaske ikke rimeligt, da Neutron-Udsendelser vil nedsztte Energiforskellen for den n m t e B-Straale.
TRANSLATION According to the ideas developed in the notes in Nature and Phys. Rev.* the fission yield is determined only by the competition between neutron evaporation (probability r N), emission of radiation (probability r s ) and fission of the nucleus (probability r F ) . For uranium (compound nucleus 239) and thorium (compound nucleus 233) r N , r s , r F will vary with the energy of the incident neutron as shown in fig. 1. This behaviour explains that there is no fission of these nuclei for thermal or for C + D neutrons, but only for D + D and for Q + Be neutrons, and also that 5 MeV deuterons produce no fission, or in any case only with an extremely small probability, because, as the protons carry away energy, there will be only a low excitation of the compound nucleus, perhaps even lower than for thermal neutrons. It is important to study primarily: the ratio between the fission and inelastic scattering cross sections for different velocities both in uranium and in thorium, or secondarily: which is perhaps easier, to study the change with neutron velocity in the ratio of the fission cross sections between uranium and thorium. * [See the Introduction, ref. 99 and ref. 115.1
P A R T I: PAPERS A N D MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
For uranium (compound nucleus 236) the curves for the probabilities must be expected to run relatively as in fig. 2 , which explains that in this case little neutron capture is found even for slow neutrons, and that the fission is in that case particularly pronounced at small neutron velocities, for which the fission cross section should vary as l / u , as is also demonstrated at Columbia by the B absorption, as will appear in a note in Phys. Rev. of 1 March*. The curves also show that neutron capture is very improbable in uranium 235; it would, however, be of the greatest interest whether such a capture could be found through a weak radioactivity with a new period, because this would give a quantitative determination of the ratio between r F and I's for low neutron velocities. \IS, p 2
The positions of all intersections between curves are of course still very uncertain.**
p< I__
r Fig. 1
Fig. 2
The question of the validity of this explanation of the roles of the two uranium isotopes in the fission phenomenon is being strenuously disputed from various sides. It has been argued that, if the explanation is correct, one should expect very different statistical distributions of the fission products for fast and slow neutrons. However, it seems to me from simple theoretical considerations, that the assumption of great differences is an exaggeration, and one ought to expect only small differences in the statistical distribution. It would be very important if this point could be investigated further, and especially if one could find the difference in the probability of producing fission products with very high or particularly low charge or mass number. Actually one ought in this respect to find small differences for different neutron energies even in the same isotope, since
* [See the Introduction, ref. 110.1 * * [Added in the version typed with
Danish alphabet.]
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
the degree of excitation might have an influence on the distribution of products. On this question one has to be prepared to find even that the distribution for uranium (compound nucleus 236) with slow neutrons could lie between the distribution for uranium (compound nucleus 239) for neutrons of 1 MeV and 3 MeV, emitted in different directions after D-D collisions. It would be of the highest significance for the theoretical discussion if one could do a fission experiment with mesothorium, where one presumably could expect fission only at high neutron energies. The experiment is of course difficult and possibly expensive, but if it can be done at all it would be of decisive importance, since one has unfortunately no other nuclei at one’s disposal in the critical region under discussion besides uranium and thorium. Presumably the many different notes published in Phys. Rev. of 16 February and in the Comptes Rendus of 30 January have already been seen in the Institute. I have heard about an American experiment done both at Berkeley and at Columbia, but not yet published in Phys. Rev., in which they have taken pretty cloud chamber photographs of fission product tracks, but I have not seen these yet. I have also heard that people in Washington have found that neutrons are emitted from the fission products with a delay of about 20 sec after the fission. I have written to Tuve to hear more details of these investigations, which, I believe, can be explained simply as neutron evaporation from a nucleus in an excited state after 0-emission. For particularly high maximum P r a y energy one can indeed expect that the usual behaviour of relatively heavy nuclei with their dense level distribution will lead to a significant probability of excitation after 0emission. If the total energy is 12 MeV, the excitation of the residual nucleus can easily exceed the 8 MeV necessary for the release of a neutron. For those particular nuclei with which we are concerned, with an anomalous relation between charge and mass, the separation energy is even likely to be considerably lower, about 5 MeV. If such a phenomenon has been noticed in Copenhagen I would like to hear about it in detail and, if the programme permits, it would be very nice if one could in any case confirm Tuve’s observation and in particular study the neutron delays in detail since this can easily involve different fission products with different periods and even a number of successive 0-ray transmutations of the products; but this is perhaps not plausible since the neutron emission will reduce the energy difference for the next 0-ray.
MS,
3
XXXV. RESIDUAL EXCITATION O F HEAVY NUCLEI AFTER P-RAY EMISSION UNPUBLISHED MANUSCRIPT FROM FOLDER, NOTES FROM BOHR’S STAY IN PRINCETON, 1939
See Introduction, sect. 5 , ref. 118.
P A R T I : P A P E R S A N D M A N U S C R I P T S RELATING TO N U C L E A R PHYSICS
The folder “Notes from Bohr’s Stay in Princeton”, 1939, contains various drafts and lecture notes. Unless otherwise indicated, the handwriting is Rosenfeld’s. One manuscript, entitled “Residual excitation of heavy nuclei after P-ray emission” is reproduced here. It consists of 2 pages in English written in ink. Many things have been deleted and changed in presentation, but not in substance. We have reproduced the revised text. There are a further 8 pages of lecture notes in English and Danish, dated 20 March 1939, and 27 March. They are written in ink; there are a few additions by Bohr. 4 pages in English and Danish in pencil and ink are loose notes on various aspects of nuclear physics, including spin. Finally, there is one page of figures in ink with the caption (in Danish) “Resonance in a Plate with a Large Dielectric Constant” in Erik Bohr’s handwriting. The manuscript is on microfilm Bohr MSS no. 16.
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Residual excitation of heavy nuclei after P-ray emission. The observation of neutron emission following fission processes of Uranium with a delay of several seconds' suggests that the heavy nuclear fragments have a considerable probability of being left after a P-ray disintegration in a state with an excitation energy sufficient for the subsequent escape of a neutron. The occurrence of this phenomenon should be connected with the exceptionally large ratio between mass and charge of the nuclear fragments as compared with the stable isotopes of similar charge and mass numbers. This means in fact that for these fragments the total energy available for the P-ray process is exceptionally large, and the neutron binding energy of the end products anomalously low. Thus, it follows from a simple estimation based on the well-known semi-empirical formula for nuclear energy in its dependence on mass and charge numbers, that the total energy available for the process may well be of the order of magnitude of 10 MeV, while the neutron binding energy may be as low as 5 MeV. Moreover, a relatively large probability of P-ray emission with sufficiently small energy release to allow the subsequent neutron escape should just be expected from the rapid increase of the density of level distribution with excitation energy for such heavy nuclei. In fact, if we provisorily assume that the relative probability of a certain P-ray process will increase as the fifth power of the energy released, as suggested by a simple comparison with the empirical laws of usual P-ray processes, involving only transitions to the normal state or some state of low excitation of the final nucleus, we shall expect a statistical distribution of resulting excitation given by
W ( E )d E prop. (E, - E ) 5 D ( E dE, ) where E, is the total energy available and D ( E ) the density of level distribution for an excitation E. Now, for heavy nuclei, we have approximately
where f? is of the order of magnitude of a million volts. The maximum value of W ( E ) will according[ly] be
' [This reference
is presumably R.B. Roberts, R.C. Meyer a n d P. Wang, Further Observations on Splitting of Uranium and Thorium, Phys. Rev. 55 (1939) 510-511 (submitted 18 February 1939, published 1 March 1939).] the
~
~
p
.
2
XXXVI. MECHANISM OF NUCLEAR FISSION [l] (WITH J.A. WHEELER)
Phys. Rev. 55 (1939) 1124 Abstract of Paper Presented at the 227th Regular Meeting of the American Physical Society in Washington, 27-29 April, 1939
See Introduction, sect. 5 , ref. 120.
P A R T I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Bohr also reported on this work in the discussion following a lecture by Hahn in the Royal Institution, London, on 23 June 1939. See Nature 144 (1939) 46.
71. Mechanism of Nuclear Fission. N . BOHR,Institute f o r Advanced Study, A N D J O H N A. WHEELER,Princeton L7niuersity.-.4n estimation of the energy required to separate the nuclei of thorium and uranium into two or more parts of comparable mass and charge shows conclusively that the fission process cannot be attributed t o a quantum mechanical effect analogous t o alpha-particle emission from the ground state of a heavy nucleus but t h at we have t o do with a n essentially classical effect arising from the possibility of comparatively large deformations of the excited compound nucleus.* T h e electrostatic repulsion of the nuclear particles will, in fact, for the heaviest nuclei nearly compensate the effect of the short range forces in opposing such deformation and a simple calculation shows t h at the energy required for a critical deformation is of the same order as the neutron binding energy. From the arguments familiar from the theory of monomolecular reactions, the disintegration constant for th e system when excited with the energy E is given by, N*(E-E,)/hp(E), where p is the density of energy levels in the original state of the excited nucleus, E, is the potential energy of deformation in the critical state, and N*(E*) is the number of energy levels in that state with energy less than E*. On these lines the dependence of fission probability on energy, and the statistical distribution in size and mass of the fragments and their initial excitations, are estimated.
* L. Meitrier and R. Frisch. Nature 143, 239 (1939). See also N . Bohr, Nature 143, 330 (1939) and Phys. Rev. 55, 418 (1939).
XXXVII. THE MECHANISM OF NUCLEAR FISSION [2] (WITH J.A. WHEELER)
Phys. Rev. 56 (1939) 426-450
See Introduction, sect. 5 , ref. 121.
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
There is a mistake in Table 111, as indicated in the handwritten addition, probably in the handwriting of Miss S . Hellmann (Bohr’s secretary).
SEPTEMBER
1.
PHYSICAL REVIEW Printed in U. S. A.
1939
VOLUME 56
The Mechanism of Nuclear Fission NIELSBOHR University of Copenhagen, Copenhagen, Denmark, and The Institute for Advanced Study, Princeton, New Jersey AND
JOHNARCHIBALD WHEELER Princeton University, Princeton, New Jersey (Received June 28, 1939)
On the basis of the liquid drop model of atomic nuclei, an account is given of the mechanism of nuclear fission. In particular, conclusions are drawn regarding the variation from nucleus to nucleus of the critical energy required for fission, and regarding the dependence of fission cross section for a given nucleus on energy of the exciting agency. A detailed discussion of the observations is presented on the basis of the theoretical considerations. Theory and experiment fit together in a reasonable way to give a satisfactory picture of nuclear fission.
INTRODUCTION
Just the enormous energy release in the fission process has, as is well known, made it possible to observe these processes directly, partly by the great ionizing power of the nuclear fragments, first observed by Frisch3 and shortly afterwards independently by a number of others, partly by the penetrating power of these fragments which allows in the most efficient way the separation from the uranium of the new nuclei formed by the f i ~ s i o nThese .~ products are above all characterized by their specific beta-ray activities which allow their chemical and spectrographic identification. In addition, however, it has been found that the fission process is accompanied b y an emission of neutrons, some of which seem to be directly associated with the fission, others associated with the subsequent beta-ray transformations of the nuclear fragments. I n accordance with the general picture of nuclear reactions developed in the course of the last few years, we must assume that any nuclear transformation initiated b y collisions or irradiation takes place in two steps, of which the first is the formation of a highly excited compound nucleus with a comparatively long lifetime, while
THEd
iscovery by Fermi and his collaborators that neutrons can be captured by heavy nuclei to form new radioactive isotopes led especially in the case of uranium to the interesting finding of nuclei of higher mass and charge number than hitherto known. The pursuit of these investigations, particularly through the work of Meitner, Hahn, and Strassmann as well as Curie and Savitch, brought to light a number of unsuspected and startling results and finally led Hahn and Strassmann’ to the discovery that from uranium elements of much smaller atomic weight and charge are also formed. The new type of nuclear reaction thus discovered was given the name “fission” by Meitner and Frisch,2who on the basis of the liquid drop model of nuclei emphasized the analogy of the process concerned with the division of a fluid sphere into two smaller droplets as the result of a deformation caused by an external disturbance. In this connection they also drew attention to the fact that just for the heaviest nuclei the mutual repulsion of the electrical charges will t o a large extent annul the effect of the short range nuclear forces, analogous to that of surface tension, in SO. R. Frisch, Nature 143, 276 (1939); G. K. Green and opposing a change of shape of the nucleus. T o Luis W. Alvarez, Phys. Rev. 55, 417 (1939); R. D. Fowler R. W. Dodson, Phys. Rev. 55, 418 (1939); R. B. produce a critical deformation will therefore and Roberts, R. C. Meyer and L. R. Hafstad, Phys. Rev. 55, require only a comparatively small energy, and 417 (1939); W. Jentschke and F. Prankl, Naturwiss. 27, 134 (1939); H. L. Anderson, E. T. Booth, J . R. Dunning, by the subsequent division of the nucleus a very E. Fermi, G. N. Glasoe and F. G. Slack, Phys. Rev. 5 5 , 511 (1939). large amount of energy will be set free. and F. Strassmann, Naturwiss. 27, 11 (1939); see, also, P. Abelson, Phys. Rev. 5 5 , 418 (1939). L. Meitner and 0. R. Frisch, Nature 143, 239 (1939). 10. Hahn
4 F. Joliot, Comptes rendus 208, 341 (1939); L. Meitner and 0. R. Frisch. Nature 143, 471 (1939); H. L. Anderson, E. T. Booth, J. R. Dunning, E. Fernii, G. N. Glasoe and F. G. Slack, Phys. Rev. 55, 511 (1939).
426
42 7
MECHANISM OF NUCLEAR
FISSION
the second consists in the disintegration of this siderations lead to an approximate expression for compound nucleus or its transition to a less the fission reaction rate which depends only on excited state by the emission of radiation. For a the critical energy of deformation and the propheavy nucleus the disintegrative processes of the erties of nuclear energy level distributions. T h e compound system which compete with the general theory presented appears to fit together emission of radiation are the escape of a neutron well with the observations and to give a satisand, according to the new discovery, the fission factory description of the fission phenomenon. For a first orientation as well as for the later of the nucleus. While the first process demands the concentration on one particle a t the nuclear considerations, we estimate quantitatively in surface of a large part of the excitation energy of Section I by means of the available evidence the the compound system which was initially dis- energy which can be released by the division of a tributed much as is thermal energy in a body of heavy nucleus in various ways, and in particular many degrees of freedom, the second process examine not only the energy released in the requires the transformation of a part of this fission process itself, b u t also the energy required energy into potential energy of a deformation of forsubsequent neutron escape from the fragments and the energy available for beta-ray emission the nucleus sufficient to lead to division.6 Such a competition between the fission process from these fragments. In Section I1 the problem of the nuclear and the neutron escape and capture processes seems in fact to be exhibited in a striking manner deformation is studied more closely from the by the way in which the cross section for fission point of view of the comparison between the of thorium and uranium varies with the energy nucleus and a liquid droplet in order to make an of the impinging neutrons. T h e remarkable estimate of the energy required for different difference observed by Meitner, Hahn, and nuclei t o realize the critical deformation necesStrassmann between the effects in these two sary for fission. In Section I11 the statistical mechanics of the elements seems also readily explained on such lines by the presence in uranium of several stable fission process is considered in more detail, and an isotopes, a considerable part of the fission approximate estimate made of the fission probaphenomena being reasonably attributable to the bility. This is compared with the probability of rare isotope U235 which, for a given neutron radiation and of neutron escape. A discussion is energy, will lead to a compound nucleus of then given on the basis of the theory for the higher excitation energy and smaller stability variation with energy of the fission cross section. In Section IV the preceding considerations are than that formed from the abundant uranium applied to an analysis of the observations of the isotope.6 In the present article there is developed a more cross sections for the fission of uranium and detailed treatment of the mechanism of the thorium by neutrons of various velocities. In fission process and accompanying effects, based particular it is shown how the comparison with on the comparison between the nucleus and a the theory developed in Section I11 leads to liquid drop. The critical deformation energy is values for the critical energies of fission for brought into connection with the potential thorium and the various isotopes of uranium energy of the drop in a state of unstable equilib- which are in good accord with the considerations rium, and is estimated in its dependence on of Section 11. In Section V the problem of the statistical nuclear charge and mass. Exactly how the excitation energy originally given to the nucleus distribution in size of the nuclear fragments is gradually exchanged among the various degrees arising from fission is considered, and also the of freedom and leads eventually to a critical questions of the excitation of these fragments and deformation proves to be a question which needs the origin of the secondary neutrons. not be discussed in order to determine the fission Finally, we consider in Section VI the fission probability. In fact, simple statistical con- effects to be expected for other elements than thorium and uranium at sufficiently high neutron N. Bohr, Nature 143, 330 (1939). velocities as well as the effect to be anticipated in N. Bohr, Phys. Rev. 55, 418 (1939).
W61
N.
BOHR A N D J. A.
428
WHEELER
M ( Z , A ) = C,+3B,4’(Z-$A)’ +(Z-3A)(M,-M,)+3Z2e2/jroAt.
thorium and uranium under deuteron and proton impact and radiative excitation.
(3)
Here the second term gives the comparative masses of the various isobars neglecting the influence of the difference M , - M , of the proton and neutron mass included in the third term and of the pure electrostatic energy given by the fourth term. In the latter term the usual assumption is made t h a t the effective radius of the nucleus is equal to roAt, with r o estimated as 1.48 x lO-’3 from the theory of alpha-ray disintegration. Identifying the relative mass values given by expressions (2) and ( 3 ) , we find
I . EKERGYRELEASED B Y NUCLEAR DIVISION T h e total energy released by the division of a nucleus into smaller parts is given b y
A E = (Mo-BMi)c2,
(1)
where M o and M i are the masses of the original and product nuclei a t rest and unexcited. We have available no observations on the masses of nuclei with the abnormal charge to mass ratio formed for example by the division of such a heavy nucleus as uranium into two nearly equal parts. T h e difference between the mass of such a fragment and the corresponding stable nucleus of the same mass number may, however, if we look apart for the moment from fluctuations in energy due to odd-even alternations and the finer details of nuclear binding, be reasonably assumed, according to an argument of Gamow, to be representable in the form
i%f(z,A ) - M ( Z A , A ) = $ B A ( Z - 2 , 4 ) ’ ,
(2)
where 2 is the charge number of the fragment and ZA is a quantity which in general will not be an integer. For the mass numbers A = 100 to 140 this quantity Z A is given by the dotted line in Fig. 8, and in a similar way it may be determined for lighter and heavier mass numbers. B.4 is a quantity which cannot as yet be determined directly from experiment but may be estimated in the following manner. Thus we may assume that the energies of nuclei with a given mass A will vary with the charge Z approximately according to the formula TABLE I. Values of the quantities which appear in Eqs. (6) and (7), estimated for various values of the nuclear mass number A . Both B A and 6~ are in M a .
50 60 70 90 8o
140
1 I 23.0 27.5 31.2
3.6 3.8
39.4 35.0
2.0 2.2
I I 1 58.0 I
2.6
2.7 2.7 2.6 2.4
2.1
1.2
1.9
1.8
180 190
72.9 76.4
1.0 1.0
200 210 220 230 240
80.0
0.96 0.92
83.5 87.0 90.6 93.9
0.88 0.86 0.83
1.2 1.1
1.1 1.1
1.1
1.0 1.0
BA’= ( M , - M M , + 6 Z ~ e 2 / 5 r o A f ) / ( -4 A2 ~ ) (4) and
B A= B ~ ’ + 6 e ~ / j r o A t = ( h f p - &In 3A 3e2/5ro)/ (3-4 - 2,). (5)
+
T h e values of B Aobtained for various nuclei from this last relation are listed in Table I . On the basis just discussed, we shall be able to estimate the mass of the nucleus (2, A ) with the help of the packing fraction of the known nuclei. Thus we may write
M ( Z ,A ) = A ( l + f a )
I
+ $ B A ( Z - Z A ) ~ - $ B AA even, Z even , (6) ++SA +O
[ OA d d even,
Z odd
where f A is to be taken as the average value of the packing fraction over a small region of atomic weights and the last term allows for the typical differences in binding energy among nuclei according to the odd and even character of their neutron and proton numbers. In using Dempster’s measurements of packing fractions we must recognize t h a t the average value of the second term in (6) is included in such measurements.’ This correction, however, is, as may be read from Fig. 8, practically compensated by the influence of the third term, owing to the fact t h a t the great majority of nuclei studied in t h e mass spectrograph are of even-even character. From (6) we find the energy release involved in electron emission or absorption by a nucleus unstable with respect to a beta-ray ’A. J. Dempster, Phys. Rev. 53, 869 (1938).
W71
429
OF
MECHANISM
transformation : Es=B.t{,Zn-Z1-~)-6A
I
Aeven,Zeven
++O 6 ~[ OAd d even, Z odd
.
NUCLEAR FISSION
(7)
T h i s result gives us the possibility of estimating 6.1 by an examination of the stability of isobars of even nuclei. In fact, if an even-even nucleus is sralile 01- unstable. then 6’1 is, respectively, greater or less than B.,t { lZ.,l - A 1-3). For nuclei of medium atomic weight this condition brackets 6‘1 \.cry closely; for the region of very high mass numbers, on t h e other hand, we can cstimate 6~ tlii-cctly from the difference i n energy release of the successive beta-ray transformations
U X , - + ( U X I , ,VZ)-tU,I, 1 1sTh-+\ZsThII-iRaTh, RaD+RaE-+RaF. The estimated values of 6n are collected in Table I . Applying the available measurements on nuclear masses supplemented by the above considerations, we obtain typical estimates as shown in Table I1 for the energy release on division of a nucleus into tivo approximately equal parts.* Reloiv mass number A--100 nuclei are energetically stable with respect to division ; above this limit energetic instability sets in with respect TAIII,I$ 11. Estimates f o r the energy release on division of typical nuclei iizto two fragments are given in the third column. I n the fourth i s the estimated value of the total additional energy release associated w’ith the subsequent beta-ray transformatio?zs. Energies are in MeV. - .i8NiG1 6oSn117 G8Er1G7 8 2 P b2O0 02u230
14Si30,31 25Mnbs>59 34Se83, 84 41Nb103.103 ,,pd119, 120
-11 10 94
120 200
2 12 13 32 31
FIG. 1. The difference in energy between the nucleus
e2U23gin its normal state and the possible fragment nuclei
44Ru100and 48Cd139(indicated by the crosses in the figure) is estimated to be 150 Mev as shown by the corresponding contour line. In a similar way the estimated energy release for division of U2a9into other possible fragments can be read from the figure. The region in the chart associated with the greatest energy release is seen to be at a distance from the region of the stable nuclei (dots in the figure) corresponding to the emission of from three to five betaravs.
energy associated with the separation overcompensates the desaturation of short range forces consequent on the greater exposed nuclear surface. T h e energy evolved on division of the nucleus U239into two fragments of any given charge and mass numbers is shown in Fig. 1. I t is seen that there is a large range of atomic Inasses for which the energy liberated reaches nearly the maximum attainable value 200 M e v ; b u t t h a t for a given size of one fragment there is only a small range of charge numbers which correspond to an energy release a t all near the maximum value. Thus the fragments formed by division of uranium in the energetically most favorable way lie in a narrow band in Fig. 1, separated from the region of the stable nuclei by an amount which corresponds to the change in nuclear charge
N.
associated with the emission of three to six betaparticles. The amount of energy released in the beta-ray transformations following the creation of the fragment nuclei may be estimated from E q . ( 7 ) , using the constants in Table I. Approximate values obtained in this way for the energy liberation in typical chains of beta-disintegrations are shown on the arrows in Fig. 8. The magnitude of the energy available for beta-ray emission from typical fragment nuclei does not stand in conflict with the stability of these nuclei with respect to spontaneous neutron emission, as one sees a t once from the fact t h a t the energy change associated with an increase of the nuclear charge by one unit is given by the difference between binding energy of a proton and of a neutron, plus the neutron-proton mass difference. A direct estimate from Eq. (6) of the binding energy of a neutron in typical nuclear fragments lying in the band of greatest energy release (Fig. 1) gives the results summarized in the last column of Table 111. T h e comparison of the figures in this table shows t h a t the neutron binding is in certain cases considerably smaller than the energywhich can be released by beta-ray transformation. This fact offers a reasonable explanation as we shall see in Section 1 7 for the delayed neutron emission accompanying the fission process.
11. NUCLEARSTABILITY WITH RESPECT TO
DEFORMATIONS
According to the liquid drop model of atomic nuclei, the excitation energy of a nucleus must be TABLE 111. Estimated values of energy release in beta-ray transformations and energy of neutron binding in final nucleus, in typical cases; also estimates of the neutron binding in the dividing nucleus. Values in MeV. BETA-TRANSITION
I
430
BOHR AND J. A. WHEELER
RELEASE
BINDING
Compound
5
5.4 6.4 5.2 5.2 Ar4
w}
a.
b
u C
FIG.2. Small deformations of a liquid drop of the type 6r(B) =anPn(cos 0 ) (upper portion of the figure) lead to characteristic oscillations of the fluid about the spherical form of stable equilibrium, even when the fluid has a uniform electrical charge. If the charge reaches the critical value (10Xsurface tension Xvolume)t, however, the spherical form becomes unstable with respect to even infinitesimal deformations of the type n = 2. For a slightly smaller charge, on the other hand, a finite deformation (c) will be required to lead t o a configuration of unstable quiZibrium, and with smaller and smaller charge densities the critical form gradually goes over (c, b, a ) into that of two uncharged spheres an infinitesimal distance from each other ( a ) .
expected to give rise to modes of motion of the nuclear matter similar to the oscillations of a fluid sphere under the influence of surface tension . 9 For heavy nuclei the high nuclear charge will, however, give rise to an effect which lvill to a large extent counteract the restoring force due to the short range attractions responsible for the surface tension of nuclear matter. This effect, the importance of m-hich for the fission phenomenon was stressed by Frisch and Meitner, will be more closely considered in this section, \vhere we shall investigate the stability of a nucleus for small deformations of various typesloas Xvell as for such large deformations that division may actually be expected to occur. Consider a small arbitrary deformation of the liquid drop with which we compare the nucleus such that the distance from the center to an arbitrary point on the surface with colatitude 0 is changed (see Fig. 2) from its original value R N. Bohr, Nature 137, 344 and 351 (1936); N. Bohr and F. Kalckar, Kgl. Danske Vid. Selskab., Math. Phys. Medd.
14, KO.10 (1937). 10 After the formulae given below were derived, expressions for the potential energy associated with spheroidal deformations of nuclei were published by E. Feenberg (Phys. Rev. 5 5 , 504 (1939)) and F. Weizsacker (Naturwiss. 27, 133 (1939)). Further, Professor Frenkel in Leningrad has kindly sent us in manuscript a copy of a more comprehensive paper on various aspects of the fission problem, to appear in the U.S.S.R. "Annales Physicae," which contains a deduction of Eq. (9) below for nuclear stability against arbitrary small deformations, as well as some remarks, similar to those made below (Eq. (14)) about the shape of a drop corresponding to unstable eauilibriurn. A short abstract of this paper-has sirice appeared in Phys. Rev. 5 5 , 957 (1939).
P691
431
MECHANISM
OF
NUCLEAR
r; = R N * F IG . 3. The potential energy associated with a n y arbitrary deformation of the nuclear form may be plotted as a function of the parameters which specify the deformation, thus giving a contour surface which is represented schematically in the left-hand portion of the figure. T h e pass or saddle point corresponds to the critical deformation of unstable equilibrium. To the extent to which we may use classical terms, the course of the fission process may be symbolized by a ball lying in the hollow at the origin of coordinates (spherical form) which receives a n impulse (neutron capture) which sets it to executing a complicated Lissajous figure of oscillation about equilibrium. If its encrgy is sufficient, it will in the course of time happen to move in the proper direction to pass over the saddle p i n t (after nhich fission will occur), unless it loses its energy (radiation or neutron re-emission). At the right is a cross section taken through the fission barrier, illustrating the calculation in the text of the probability per unit time of fission occurring.
FISSION
beyond which the nucleus is no longer stable with respect to deformations of the simplest type. T h e actual value of the numerical factors can be calculated with the help of the semi-empirical formula given by Bethe for the respective contributions to nuclear binding energies due to electrostatic and long range forces, the influence of the latter being divided into volume and surface effects. A revision of the constants in Bethe's formula has been carried through by Feenberg" in such a way as to obtain the best agreement with the mass defects of Dempster ; he finds YO+
1 . 4 X 10-13 cm, 4nr0~0.i.14 MeV. (12)
From these values a limit for the ratio Z 2 / A is obtained which is 1 7 percent greater than the ratio (92)2/238 characterizing U238.Thus we can conclude t h a t nuclei such as those of uranium and thorium are indeed near the limit of stability set by the exact compensation of the effects of to the value electrostatic and short range forces. On the other hand, we cannot rely on the precise value of the r ( 0 ) =R[l+ao+cYzPz(cos 6 ) limit given by these semi-empirical and indirect +WP3(CoS 0) * -1, (8) determinations of the ratio of surface energy to electrostatic energy, and we shall investigate where the a,, are small quantities. Then a below a method of obtaining the ratio in question straightforward calculation shows that the from a study of the fission phenomenon itself. surface energy plus the electrostatic energy of the Although nuclei for which the quantity Z 2 / Ais comparison drop has increased to the value slightly less than the limiting value (11) are stable with respect to small arbitrary deforma& + E = ~ T ( ~ O A * ) ~+ 2O~[ ~~2 ~ / 5 + 5 a 3 ~ / *7* +* tions, a larger deformation will give the long ( n- 1)(n+2)a7b2/2(2n+ 1) * range repulsions more advantage over the short range attractions responsible for the surface +3(Ze)2/5roAi[l - a z 2 / 5 - 10a32/49tension, and i t will therefore be possible for the --5(%-- l)a,2/(2n+1)2-. (9) nucleus, when suitably deformed, to divide spontaneously. Particularly important will be where we have assumed that the drop is comt h a t critical deformation for which the nucleus is posed of an incompressible fluid of volume just on the verge of division. T h e drop will then (47r/3)R3= (4a/3)ro3A, uniformly electrified to a possess a shape corresponding to unstable equilibcharge Ze, and possessing a surface tension 0. rium: the work required to produce a n y infiniExamination of the coefficient of aZ2in the above tesimal displacement from this equilibrium expression for the distortion energy, namely, configuration vanishes in the first order. T o 4~ro~OAf(2/.5) { 1- ( Z 2 / A ) examine this point in more detail, let us consider x[e2/10(4a/3)rosO]) (10) the surface obtained by plotting the potential energy of an arbitrary distortion as a function of makes it clear that with increasing value of the the parameters which specify its form and magniratio Z 2 / A we come finally to a limiting value tude. Then we have t o recognize the fact t h a t the
+.
+
+. *I
-
(Z2/A)l,m,t,ng= 10(4n/3)ro30/e2,
a],
(11)
l1
E. Feenberg, Phys. Rev. 55, 504 (1939).
N.
B O H R A N D J . A . WHEELER
432
potential barrier hindering division is to be compared with a pass or saddle point leading between two potential valleys on this surface. The energy relations are shown schematically in Fig. 3, where of course we are able to represent only two of the great number of parameters which are required t o describe the shape of the system. The deformation parameters corresponding to the saddle point give us the critical form of the drop, and the potential energy required for this distortion we will term the critical energy for fission, E f . If we consider a continuous change in the shape of the drop, leading from the original sphere to two spheres of half the size a t infinite separation, then the critical energy in which we are interested is the lowest value which we can a t all obtain, by suitable choice of this sequence of shapes, for the energy required to lead from the one configuration to the other. Simple dimensional arguments show t h a t the critical deformation energy for the droplet corresponding to a nucleus of given charge and mass number can be written as the product of the surface energy by a dimensionless function of the charge mass ratio :
equal the total work done against surface tension in the separation process, i.e.,
\ire can determine Ef if we know the shape of the nucleus in the critical state ; this will be given by solution of the well-known equation for the form of a surface in equilibrium under the action of a surface tension 0 and volume forces described by a potential cp :
Ef = 2 .47r020(A/2)8 - 4 r r o 2 0 A j
KO+ p = constant,
(.11)
= 2 . 4aro20(A/2) 3 - 47rro20Af
E
.
(15)
From this it follows t h a t f(O)=2~--1=0.260.
(16)
(2) If the charge on the droplet is not zero, but is still very small, the critical shape will differ little from t h a t of two spheres in contact. There will in fact exist only a narrow neck of fluid connecting the two portions of the figure, the radius of which, rn, will be such as t o bring about equilibrium ; to a first approximation (1 7 )
2 r r n 0= (Ze/2)2/(2ro(A/2)1)2
or
rn/roA+= 0.66(
f> / (f)
I i mi t i n g
.
(18)
T o calculate the critical energy to the first order in Z2/A, we can omit the influence of the neck as producing only a second-order change in the energy. Thus we need only compare the sum of surface and electrostatic energy for the original nucleus with the corresponding energy for two spherical nuclei of half the size in contact with each other. We find
$2
*
*
3(Ze/2)2/5r0(A/2)
+(Ze/2)2/2r0(A/2)t - 3(Ze)2/5roAt, (19)
from which E , / 4 r r o 2 0 A f =f(x) =0.260-0.215~, (20)
where K is the total normal curvature of the provided surface. Because of the great mathematical difficulties of treating large deformations, we are = (charge) 2/surface I im i t ing however able to calculate the critical surface and x = the dimensionless function f in (13) only for tensionXvolumeX 10 (21) certain special values of the argument, as follows : ( 1 ) if the volume potential in (14) vanishes is a small quantity. (3) In the case of greatest altogether, we see from (14)t h a t the surface of actual interest, when Z2/A is very close t o the unstable equilibrium has constant curvature ; we critical value, only a small deformation from a have i n fact to deal with a division of the fluid spherical form will be required to reach the into spheres. Th'us, when there are no electrostatic critical state. According to Eq. (9), the potential forces at all t o aid the fission, the critical energy energy required for an infinitesimal distortion for division into two equal fragments will just will increase as the square of the amplitude, and
(f> / (4)
433
MECHANISM
OF
NUCLEAR
FISSION
With the helpof (23) we obtain the deformation energy as a function of a2 alone. B y a straightforward calculation we then find its maximum value as a function of CQ, thus determining the energy required to produce a distortion on the verge of leading to fission :
E , / ~ TZ0A Y f =f(x) = 98 (1 - x ) ~ 135 / - 1 1 3 6 8 ( 1 - ~ ) ~ / 3 4 4 2 5 +. * FIG.4. The energy Ej required to produce a critical deformation leading t o fission is divided by the surface energy 4?rR20 to obtain a dimensionless function of the quantity x = (charge)2/(10XvolumeXsurface tension). The behavior of the function f(x) is calculated in the text for .r=O and x = 1, and a smooth curve is drawn here to connect these values. The curve y ( ~ determines ) for comparison the energy required t o deform the nucleus into two spheres in contact with each other. Over the cross hatched region of the curve of interest for the heaviest nuclei the surface energy changes but little. Taking for it a value of 530 Mev, we obtain the energy scale in the upper part of the figure. In Section IV we estimate from the observations a value El-6 Mev for P9. Using the figure we thus find (Z2jA)li,,t,,,=47.8 and can estimate the fission barriers for other nuclei, as shown.
will moreover have the smallest possible value for a displacement of the form P2(cos 0 ) . T o find the deformation for which the potential energy has reached a maximum and is about to decrease, we have to carry out a more accurate calculation. \Ye obtain for the distortion energy, accurate to the fourth order in CYZ, the expression
+
AEs+~=4aro~OAt[2cr2~/5116c~2~/105 101(u24/35+2az2ar4/35+a42]
-3(Ze)2/5roAt[a22/5+64cu23/105 + 5 8 ~ ~ ~ ~ / 3 5 + 8 a z ~ c u 4 / 3 5 + 5 ~ u 4 ~ / 2 7(22) ], in which i t will be noted t h a t we have had to include the terms in a? because of the coupling which sets in between the second and fourth modes of motion for appreciable amplitudes. Thus, on minimizing the potential energy with respect to a 4 ,we find c ~ 4 =
- (243/595)~~2~
(23)
in accordance with the fact t h a t as the critical form becomes more elongated with decreasing Z2/A, it must also develop a concavity about its equatorial belt such as to lead continuously with variation of the nuclear charge to the dumbbell shaped figure discussed in the preceding paragraph.
P721
(24)
for values of Z 2 / A near the in-stability limit. Interpolating in a reasonable way between the two limiting values which we have obtained for the critical energy for fission, we obtain the curve of Fig. 4 for f as a function of the ratio of the square of the charge number of the nucleus to its mass number. T h e upper part of the figure shows the interesting portion of the curve in enlargement and with a scale of energy values a t the right based on the surface tension estimate of Eq. (12) and a nuclear mass of A=235. T h e slight variation of the factor 4aro20Af among the various thorium and uranium isotopes may be neglected in comparison with the changes of the factor f ( x ) . In Section IV we estimate from the observations t h a t the critical fission energy for U239is not far from 6 MeV. According to Fig. 4, this corresponds t o a value of x=0.74, from which we conclude that ( Z 2 / A )l i m i t i n g = (92)2/239X0.74 =47.8. This result enables us to estimate the critical energies for other isotopes, as indicated in the figure. I t is seen t h a t protactinium would be particularly interesting as a subject for fission experiments. As a by product, we are also able from Eq. (12) to. compute the nuclear radius in terms of the surface energy of the nucleus; assuming Feenberg's value of 14 Mev for 4aro20,we obtain ro = 1.47 X cm, which gives a satisfactory and quite independent check on Feenberg's determination of the nuclear radius from the packing fraction curve. So far the considerations are purely classical and any actual state of motion must of course bd described in terms of quantum-mechanical concepts. T h e possibility of applying classical pictures to a certain extent will depend on the smallness of the ratio between" the zero point amplitudes for oscillations of the type discussed above and the nuclear radius. A simple calcu-
N.
BOHR A N D J. A.
lation gives for the square of the ratio in question the result (av,*)~v; zero p u l n t = A - 7 ' 6
X ( ( h 2 / 1 2 M p 7 0 * ) ! 4 r 7 0 * O $) W i ( 2 W + I ) $ X { (w- 1 ) (w+ 2 ) ( 2 ~ +1) - 2 0 ( ~ -1)xI-i.
(25)
Since { ( h 2 / 1 2 ~ p 7 ~ 2 ) / 4 r $,7 ~this 0 ~ $ratio ~ is indeed a small quantity, and it follows that deformations of magnitudes comparable with nuclear dimensions can be described approximately classically by suitable wave packets built up from quantum states. In particular we may describe the critical deformations which lead to fission in an approximately classical way. This follows from a comparison of the critical energy E f - 6 Mev required, as we shall see in Section I V , to account for the observations on uranium. with the zero point energy qhwz= A-i { 4 ~ , ? 0 . 2 ( 1- x ) h 2 / 3 M p 7 2 )
-0.4 Mev
(26)
of the simplest mode of capillary oscillation, from which i t is apparent that the amplitude in question is considerably larger than the zero point disturbance : ( C ~ * * ) A ~ / ( ~ U Zm ~ r)oA p~o;i n t
=Ef/ihuz- 15. (27)
The drop with which we compare the nucleus will also in the critical state be capable of executing small oscillations about the shape of unstable equilibrium. If we study the distribution in frequency of these characteristic oscillations, we must expect for high frequencies to find a spectrum qualitatively not very different from that of the normal modes of oscillation about the form of stable equilibrium. T h e oscillations in question will be represented symbolically in Fig. 3 by motion of the representative point of the system in configuration space normal to the direction leading t o fission. T h e distribution of the available energy of the system between such modes of motion and the mode of motion leading to fission will be determining for the probability of fission if the system is near the critical state. T h e statistical mechanics of this problem is considered in Section 111. Here we would only like to point out that the fission process is from a practical point of view a nearly irreversible process. In fact if we imagine the fragment nuclei resulting from a fission t o be
WHEELER
434
reflected without loss of energy and to run directly towards each other, the electrostatic repulsion between the two nuclei will ordinarily prevent them from coming into contact. Thus, relative to the original nucleus, the energy of two spherical nuclei of half the size is given by Eq. (19) and corresponds to the values f*(x) shown by the dashed line in Fig. 4. T o compare this with the energy required for the original fission process (smooth curve for f(x) in the figure), we note t h a t the surface energy 4 r r o 2 0 A * is for the heaviest nuclei of the order of 500 Mev. We thus have to deal with a difference of -0.05 X 500 Mev = 25 Mev between the energy available when a heavy nucleus is just able to undergo fission, and the energy required to bring into contact two spherical fragments. There will of course be appreciable tidal forces exerted when the two fragments are brought together, and a simple estimate shows t h a t this will lower the energy discrepancy just mentioned by something of the order of 10 MeV, which is not enough to alter our conclusions. T h a t there is no paradox involved, however, follows from the fact that the fission process actually takes place for a configuration in which the sum of surface and electrostatic energy has a considerably smaller value than that corresponding to two rigid spheres in contact, or even two tidally distorted globes ; namely, by arranging t h a t in the division process the surface surrounding the original nucleus shall not tear until the mutual electrostatic energy of the two nascent nuclei has been brought down to a value essentially smaller than that corresponding to separated spheres, then there will be available enough electrostatic energy to provide the work required to tear the surface, which will of course have increased in total value to something more than that appropriate to two spheres. Thus it is clear t h a t the two fragments formed by the division process will possess internal energy of excitation. Consequently, if we wish to reverse the fission process, we must take care that the fragments come together again sufficiently distorted, and indeed with the distortions so oriented, that contact can be made between projections on the two surfaces and the surface tension start drawing them together while the electrostatic repulsion between the effective electrical centers of gravity of the two parts is
P731
435
MECHANISM OF NUCLEAR
still not excessive. The probability that two atomic nuclei in any actual encounter will be suitably excited and possess the proper phase relations so that union will be possible to form a compound system will be extremely small. Such union processes, converse to fission, can be expected to occur for unexcited nuclei only when \ve have available much more kinetic energy than is released in the fission processes with which we are concerned. The above considerations on the fission process, based on a comparison between the properties of a nucleus and those of a liquid drop, should be supplemented by remarking t h a t the distortion which leads to fission, although associated with a greater effective mass and lower quantum frequency, and hence more nearly approaching the possibilities of a classical description than any of the higher order oscillation frequencies of the nucleus, will still be characterized by certain specific quantum-mechanical properties. Thus there will be an essential ambiguity in the definition of the critical fission energy of the order of magnitude of the zero point energy, h w 2 / 2 , which however as we have seen above is only a relatively small quantity. More important from the point of view of nuclear stability will be the possibility of quantum-mechanical tunnel effects, which will make it possible for a nucleus to divide even i n its ground state by passage through a portion of configuration space where classically the kinetic energy is negative. An accurate estimate for the stability of a heavy nucleus against fission in its ground state will, of course, involve a very complicated mathematical prob!em. In natural extension of the well-known theory of a-decay, we should in principle determine the probability per unit time of a fission process, A,, by the formula A,( = r j / h ) = 5 ( ~ , / 2 ~ )
Xexp - 2
L:
{ 2 ( V - E ) C m , ( d ~ , / d a ):da/h. ~) i
(28)
The factor 5 represents the degree of degeneracy of the oscillation leading to instability. T h e quantum of energy characterizing this vibration is, according to (26), ha-0.8 MeV. The integral in
FISSION
the exponent leads in the case of a single particle to the Gamow penetration factor. Similarly, in the present problem, the integral is extended in configuration space from the point P1 of stable equilibrium over the fission saddle point S (as indicated by the dotted line in Fig. 3) and down on a path of steepest descent to the point Pz where the classical value of the kinetic energy, E - V , is again zero. Along this path we may write the coordinate xi of each elementary particle mi in terms of a certain parameter a. Since the integral is invariant with respect to how the parameter is chosen, we may for convenience take a to represent the distance between the centers of gravity of the nascent nuclei. T o make an accurate calculation on the basis of the liquiddrop model for the integral in (28) would be quite complicated, and we shall therefore estimate the result by assuming each elementary particle to move a distance $a in a straight line either to the right or the left according a s it is associated with the one or the other nascent nucleus. Moreover, we shall take V - E to be of the order of the fission energy Ef.Thus we obtain for the exponent in (28) approximately
(2MEj)blh.
(29)
With M=239X1.66x10-24, Ef-6 M e ~ = 1 0 - ~ erg, and the distance of separation intermediate between the diameter of the nucleus and its radius, say of the order -1.3X cm, we thus find a mean lifetime against fission in the ground state equal to 1/Xj
-
exp [( 2 x 4x
x 10-5) 41.3
X 10-12/10-27]-1030 sec. -lo2* years.
(30)
I t will be seen that the lifetime thus estimated is not only enormously large compared with the time interval of the order lO-ls sec. involved in the actual fission processes initiated by neutron impacts, but t h a t this is even large compared with the lifetime of uranium and thorium for a-ray decay. This remarkable stability of heavy nuclei against fission is as seen due to the large masses involved, a point which was already indicated in the cited article of Meitner and Frisch, where just the essential characteristics of the fission effect were stressed.
436
N. BOHR AND J. A. WHEELER
111. BREAK-UPOF THE COMPOUND SYSTEM AS A MONOMOLECULAR REACTIOX
little the critical energy, or falls below E,, specific quantum-mechanical tunnel effects will begin to become of importance. T h e fission T o determine the fission probability, we conprobability will of course fall off very rapidly sider a microcanonical ensemble of nuclei, all with decreasing excitation energy a t this point, having excitation energies between E and E+dE. the mathematical expression for the reaction rate The number of nuclei will be chosen to be exactly eventually going over into the penetration equal to the number p(E)dE of levels in this formula of Eq. ( 2 8 ) ; this, as we have seen above, energy interval, so t h a t there is one nucleus in gives a negligible fission probability for uranium. each state. T h e number of nuclei which divide T h e probability of neutron re-emission, so per unit time will then be p ( E ) d E r f / h according , important in limiting the fission yield for high to our definition of rr.This number will be equal excitation energies, has been estimated from to the number of nuclei in the transition state statistical arguments by various authors, eswhich pass outward over the fission barrier pecially Weisskopf.12T h e result can be derived in per unit In a unit distance measured a very simple form by considering the microin the direction of fission there will be (dp/h)p*(E canonical ensemble introduced above. Only a few quantum states of the micro-E,-K)dE changes are necessary with respect to the canonical ensemble for which the momentum reasoning used for the fission process. T h e transiand kinetic energy associated with the fission tion state will be a spherical shell of unit thickness distortion have values in the inter.vals d@ and just outside the nuclear surface 47rR2; the critical d K = v d p , respectively. Here p* is the density of energy is the neutron binding energy, E n ; and those levels of the compound nucleus in the the density p** of excitation levels in the transitransition state which arise from excitation of all tion state is given by the spectrum of the residual degrees of freedom other than the fission itself. nucleus. T h e number of quantum states in the At the initial time we have one nucleus in each of microcanonical ensemble which lie in the transithe quantum states in question, and consequently tion region and for which the neutron momentum the number of fissions per unit time will be lies in the range p to p + d p and in the solid angle d a will be dEJo(d@:Q) p*(E--Ef-K) = dEN*/h, ( 3 1 ) (4rR2. p2dpd0/h3)p*(E- E n- K>dE. ( 3 3 ) where N* is the number of levels in the transition state available with the given excitation. Comparing with our original expression for this number, we have
We multiply this by the normal velocity v cos 0 = (dK/dp)cos 0 and integrate, obtaining
I'f=N*/27rp(E)= (d/27)N*
for the number of neutron emission processes occurring per unit time. This is to be identified with p(E)dE(r,/h). Therefore we have for the probability of neutron emission, expressed in energy units, the result
(32)
for the fission width expressed in terms of the level density or the level spacing d of the compound nucleus. T h e derivation just given for the level width will only be valid if N* is sufficiently large compared to unity ; that is, if the fission width is comparable with or greater than the level spacing. This corresponds to the conditions under which a correspondence principle treatment of the fission distortion becomes possible. On the other hand, when the excitation exceeds by only a For a general discussion of the ideas involved in the concept of a transition state, reference is made to an article by E. Wigner, Trans. Faraday SOC.34, part 1, 29 (1938).
S
dE(4rR2.27rm/h3) p*(E-En-K)KdK
(34)
r, = ( 1 / 2 r p ) (2mR2/h2)Jp**(E-En- K ) K d K = ( d / 2 a ) ( A+ / K ' C ) Ki
(35)
i
in complete analogy to the expression
rf=(d/2r)C1 i
l2
V. Weisskopf, Phys. Rev. 52, 295 (1937).
(36)
43 7
MECHANISM
-
O F
NUCLEAR
I0 JC'
- 15ec
- I]"' IL: -
0
MV Excitation __t
I
2
4
6
1
8
10
FISSION
of J. This point is of little importance in general, as the widths will not depend much on J , and therefore in the following considerations we shall apply the above estimates of and rnas they stand. In particular, d will represent the average spacing of levels of a given angular momentum. If, however, we wish to determine the partial width Fn, giving the probability t h a t the compound nucleus will break up leaving the residual nucleus in its ground state and giving the neutron its full kinetic energy, we shall not be justified in simply selecting out the corresponding term in the sum in (35) and identifying i t with rnt. In fact, a more detailed calculation along the above lines, specifying the angular momentum of the microcanonical ensemble P E well as its energy, leads to the expression
,B
-loy'. IZ
for the partial neutron width, where the sum goes over those values of J which are realized when a nucleus of spin i is bombarded by a r7,r!, and ra refer to radiation, fission, and alpha-particle neutron of the given energy possessing spin s = 3. emission, while r,, and r, determine, respectively, the T h e smallness of the neutron mass in compariprobability of a neutron emission leaving the residual son with the reduced mass of two separating nucleus in its ground state or in a n y state. T h e latter quantities are of course zero if the excitation is less than the nascent nuclei will mean t h a t we shall have in the neutron binding, which is taken here to be about 6 MeV. former case to go to excitation energies much higher relative to the barrier than in the latter for the fission width. Just as the summation in the case before the condition is fulfilled for the latter equation goes over all those levels of the application of the transition state method. In nucleus in the transition state which are available fact, only when the kinetic energy of the emerging with the given excitation, so the sum in the particle is considerably greater than 1 Mev does former is taken over all available states of the the reduced wave-length X =X/2.rr of the neutron residual nucleus, K ; denoting the corresponding become essentially smaller than the nuclear kinetic energy E - E , - Ei which will be left for radius, allowing the use of the concepts of the neutron. K' represents, except for a factor, velocity and direction of the neutron emerging the zero point kinetic energy of an elementary from the nuclear surface. particle in the nucleus ; it is given by A%2/2mRR2 T h e absolute yield of the various processes and will be 9.3 Mev if the nuclear radius is initiated by neutron bombardment will depend A*1.48 X cm. upon the probability of absorption of the neutron No specification was made as to the angular to form a compound nucleus; this will be promomentum of the nucleus in the derivation of portional to the converse probability r,)/tt of a (35) and (36). Thus the expressions in question neutron emission process which leaves the give us averages of the level widths over states residual neutron emission process which leaves of the compound system corresponding to many the residual nucleus in its ground state. rnlwill different values of the rotational quantum num- vary as the neutron velocity itself for low neutron ber J , while actually capture of a neutron of energies ; according to the available information one- or two-Mev energy by a normal nucleus about nuclei of medium atomic weight, the will give rise only to a restricted range of values width in volts is approximately 10-3 times the
FIG. 5. Schematic diagram of the partial transition probabilities (multiplied by h and expressed in energy units) and their reciprocals (dimensions of a mean lifetime) for various excitation energies of a typical heavy nucleus.
N.
BOHR
AND
square root of the neutron energy in v01ts.l~As the neutron energy increases from thermal values to 100 kev, we have to expect then an increase of F n J from something of the order of ev to 0.1 or 1 ev. For high neutron energies we can use Eq. (37), according to which rntwill increase as the neutron energy itself, except as compensated by the decrease in level spacing as higher excitations are attained. As an order of magnitude estimate, we can take the level spacing in U to decrease from 100 kev for the lowest levels to 20 ev a t 6 Mev (capture of thermal neutrons) to $ ev for 23-Mev neutrons. With d = & ev we obtain rn,= (1/2rX5)(239$/10)2&=3 ev for neutrons from the D + D reaction. T h e partial neutron width will not exceed for any energy a value of this order of magnitude, since the decrease in level spacing will be the dominating factor a t higher energies. The compound nucleus once formed, the outcome of the competition between the possibilities of fission, neutron emission, and radiation, will be determined by the relative magnitudes of I'j, rnr and the corresponding radiation width r,. From our knowledge of nuclei comparable with thorium and uranium we can conclude that the radiation width I?, will not exceed something of the order of 1 ev, and moreover that i t will be nearly constant for the range of excitation energies which results from neutron absorption (see Fig. 5). T h e fission width will be extremely small for excitation energies below the critical energy E f . but above this point I'f will become appreciable, soon exceeding the radiation width and rising almost exponentially for higher energies. Therefore, if the critical energy E f required for fission is comparable with or greater than the excitation consequent on neutron capture, we have to expect that radiation will be more likely than fission; but if the barrier height is somewhat lower than the value of the neutron binding, and in any case if we irradiate with sufficiently energetic neutrons, radiative capture will always be less probable than division. As the speed of the bombarding neutrons is increased, we shall not expect an indefinite rise in the fission yield, however, for the output will be governed by the competition in the compound system between the 13
H. A. Bethe, Rev. Mod. Phys. 9, 150 (1937).
438
J. A. \VHEELER
possibilities of fission and of neutron emission. T h e width T', which gives the probability of the latter process will for energies less than something of the order of 100 kev be equal to r,,,,the partial width for emissions leaving the residual nucleus in the ground state, since excitation of the product nucleus will be energetically impossible. For higher neutron energies, however, the number of available levels in the residual nucleus will rise rapidly, and r n will be much larger than rn,, increasing almost exponentially n.ith energy. In the energy region where the levels of the compound nucleus are well separated, the cross sections governing the yield of the various processes considered above can be obtained by direct application of the dispersion theory of Breit and \\'igner.14 In the case of resonance, where the energy E of the incident neutron is close to a special value Eo characterizing an isolated level of the compound system, we shall have
and cr= Tk2-
2J+1
rnfrr
-.
( 2 ~ +1) (2i+ 1) ( E - E ~ ) ~( r+/ 2 ) 2
(39)
for the fission and radiation cross sections. Here k = h / p = h / ( 2 m E ) i is the neutron wave-length divided by 2 ~i and , J are the rotational quantum numbers of the original and the compound nucleus, s = + , and r=r,+r,+I'f is the total width of the resonance level a t half-maximum. In the energy region where the compound nucleus has many levels whose spacing, d , is comparable with or smaller than the total width, the dispersion theory cannot be directly applied due to the phase relations between the contributions of the different levels. A closer discussionr5 shows, however, t h a t in cases like fission and radiative capture, the cross section will be obtained by summing many terms of the form (38) or (39). If the neutron wave-length is large compared with nuclear dimensions, only those states of the compound nucleus will contribute to the l4 G. Breit and E. Wigner, Phys. Rev. 49, 519 (1936). Cf. also H. Bethe and G. Placzek, Phys. Rev. 51, 450 (1937; l5 N. Bohr, R. Peierls and G. Placzek, Nature (in press).
P771
439
MECHANISM
OF NUCLEAR
sum which can be realized by capture of a neutron of zero angular momentum, and we shall obtain
On the other hand, if X becomes essentially smaller than R , the nuclear radius (case of neutron energy over a million volts), the summation will give
The simple form of the result, which follows by use of the equation (37) derived above for rnl,is of course an immediate consequence of the fact that the cross section for any given process for fast neutrons is given by the projected area of the nucleus times the ratio of the probability per unit time that the compound system react in the given way to the total probability of all reactions. Of course for extremely high bombarding energies it will no longer be possible to draw any simple distinction between neutron emission and fission ; evaporation will go on simultaneously with the division process itself; and in general we shall have to expect then the production of numerous fragments of widely assorted sizes as the final result of the reaction.
IV. DISCUSSION OF
THE
OBSERVATIONS
A. The resonance capture process Meitner, Hahn, and Strassmann16 observed that neutrons of some volts energy produced in uranium a beta-ray activity of 23 min. half-life whose chemistry is that of uranium itself. Moreover, neutrons of such energy gave no noticeable yield of the complex of periods which is produced in uranium by irradiation with either thermal or 16L. Meitner, 0. Hahn and F. Strassmann, Zeits. f. Physik 106, 249 (1937).
P781
FISSION
fast neutrons, and which is now known to arise from the beta-instability of the fragments arising from fission processes. T h e origin of the activity in question therefore had to be attributed to the ordinary type of radiative capture observed in other nuclei; like such processes i t has a resonance character. T h e effective energy Eo of the resonance level or levels was determined by comparing the absorption in boron of the neutrons producing the activity and of neutrons of thermal energy :
Eo = (akT/4) [ ~ * t h , r m , 1 ( B ) / ~ * , , ( B ) 1 ~ = 2 5 k 10 ev.
(44)
T h e absorption coefficient in uranium itself for the activating neutrons was found to be 3 cm2/g, corresponding to an effective cross section of 3 cm2/gX238X1.66X10-24 g=1.2X10-21 cm2. If we attribute the absorption to a single resonance level with no appreciable Doppler broadening, the cross section a t exact resonance will be twice this amount, or 2.4XlO-*l cm2; if on the other hand the true width r should be small compared with the Doppler broadening A = 2(EokT/238)+=0.12 ev,
we should have for the true cross section a t exact resonance 2.7 X 10-21A/I', which would be even greater." If the activity is actually due to several comparable resonance levels, we will clearly obtain the same result for the cross section of each a t exact,resonance. According to Nier18 the abundances of U286 and U234relative to U23* are 1/139 and 1/17,000; therefore, if the resonance absorption is due to either of the latter, the cross section a t resonance will have to be a t least 139X2.4X10-21 cm2 or 3.3 X cm2. However, as Meitner, Hahn and Strassmann pointed out, this is excluded (cf. Eq. (39)) because it would be greater in order of magnitude than the square of the neutron wavelength. In fact, .rrX2 is only 25 X cm2 for 25volt neutrons. Therefore we have to attribute the capture to U23s+U239, a process in which the spin changes from i = O t o J = $ . We apply the l7 We are using the treatment of Doppler broadening given by H. Bethe and G. Placzek, Phys. Rev. 51, 450 (1937). l * A . 0. Nier, Phys. Rev. 55, 150 (1939).
N.
BOHR
AND J. A. WHEELER
resonance formula (39) and obtain 25x 1 0 - ~ ~ ~ 4 r , ~ r , / r ~ = 2.7 X 10-21(A/r) or 2.4X
(45)
according as the level width F=r,,~+rT is or is not small compared with the Doppler broadening. I n any case, we knowI3 from experience with other nuclei for comparable neutron energies t h a t rn8<
440
Fermi have been able to show that the radiative capture of slow neutrons cannot be due to the tail a t low energies of only a single level.19 I n fact, if it were, we should have for the cross section from (39) g,(thermal) = XXth2r,~(thermal)r,/E~2; (46) since rnt is proportional to neutron velocity, we should obtain a t the effective thermal energy 7rkT/4 = 0.028 ev. o,(thermal) -23 X 10-l8 X 0.003 (0.028/25) 40.1/(25)2 (47) -0.4X10-24 cm2. Anderson and Fermi however obtain for this cross section by direct measurement 1.2 X cm2. T h e conclusion t h a t the resonance absorption a t the effective energy of 25 ev is actually due to more than one level gives the possibility of an order of magnitude estimate of the spacing between energy levels in U239if for simplicity we assume random phase relations between their individual contributions. Taking into consideration the factor between the observations and the result (47) of the one level formula, and recalling t h a t levels below thermal energies as well as above contribute to the absorption, we arrive a t a level spacing of the order of d = 20 ev as a reasonable figure a t the excitation in question.
B. Fission produced by thermal neutrons According to Meitner, Hahn and StrassmannZ0 and other observers, irradiation of uranium by thermal neutrons actually gives a large number of radioactive periods which arise from fission fragments. By direct measurement the fission cross section for thermal neutrons is found to be between 2 and 3X10-24 cm2 (averaged over the actual mixture of isotopes), t h a t is, about twice the cross section for radiative capture. No appreciable part of this effect can come from the isotope W9, however, because the observations on the -25-volt resonance capture of neutrons by this nucleus gave only the 23-minute activity; the inability of Meitner, Hahn, and Strassmann to find for neutrons of this energy any appreciable yield of the complex of periods
--
19H. L. Anderson and E. Fermi, Phys. Rev. 5 5 , 1106 (1939). L. Meitner, 0. Hahn and F. Strassmann, Zeits. f. Physik 106, 249 (1937).
44 1
MECHANISM OF NUCLEAR
now known to follow fission indicates t h a t for slow neutrons in general the fission probability for this nucleus is certainly no greater than 1/10 of the radiation probability. Consequently, from comparison of (38) and (39), the fission cross section for this isotope cannot exceed something of the order uf(therma1)= (l/lO)u,(thermal) = 0.1 X cm2. From reasoning of this nature, as was pointed out in an earlier paper by Bohr, ~ v ehave to attribute practically all of the fission observed ivith thermal neutrons to one of the rarer isotopes of uraniurn.*l If we assign i t to the compound nucleus UZ3j,we shall have 17,000 cm2 for uf(therma1) ; if or 4 X x 2.5 X u e attribute the division to u / will be cm2. between 3 and 4 X ij'e have to expect t h a t the radiation width and the neutron width for slow neutrons will differ in no essential way between the various uranium isotopes. Therefore we will assume I',t(thermal) = 0.003(0.028/25)+= lop4 ev. T h e fission width, however, depends strongly on the barrier height; this is in turn a sensitive function of nuclear charge and mass numbers, as indicated in Fig. 4, and decreases strongly with decreasing isotopic weight. Thus it is reasonable that one of the lighter isotopes should be responsible for the fission. Let us investigate first the possibility that the division produced by thermal neutrons is due to the compound nucleus U235.If the level spacing d for this nucleus is essentially greater than the level width, the cross section will be due principally to one level ( J = 4 arising from i = 0), and we shall have from
the equation
r
f/
+
CEO2 r2/4]
x 10-20/23 X10-18X10-4= 17(ev)-'.
=4
(48)
Since r > r , , this condition can be put as an inequality, ~~2
< (r/4)(4,971 - r)
(49)
from which it follows first, that r 5 4 / 1 7 ev, and second, that IEol <2/17 ev. Thus the level
*'N . Bohr, Phys. Rev. 55, 418 (1939). ~3801
FISSION
would have to be very narrow and very close to thermal energies. But in this case the fission cross section would have to fall off very rapidly with increasing neutron energy; since X 0: l / v , E0:v2,rn.=v,we should have according to (38) u j 0: 1/05 for neutron energies greater than about half a volt. This behavior is quite inconsistent with the finding of the Columbia group that the fission cross section for cadmium resonance neutrons (-0.15 ev) and for the neutrons absorbed in boron (mean energy of several volts) stand to each other inversely in the ratio of the corresponding neutron velocities (1/a) .22 Therefore, if the fission is to be attributed to U235,we must assume t h a t the level width is greater than the level spacing (many levels effective) ; but as the level spacing itself will certainly exceed the radiative width, we will then have a situation in which the total width will be essentially equal to r/. Consequently we can write the cross section (40) for overlapping levels in the form ui= nX2rnc2a/d.
(50)
From this we find a level spacing d = 23
x 10-'8x
10-4x 2 ~ / x4 10-20 = 0.4 ev
which is unreasonably small : According to the estimates of Table 111, the nuclear excitations consequent on the capture of slow neutrons to form UZ3jand are approximately 5.4 Mev and 5.2 MeV, respectively ; moreover, the two nuclei have the same odd-even properties and should therefore possess similar level distributions. From the difference AE between the excitation energies in the two cases we can therefore obtain the ratio of the corresponding level spacings from the expression exp ( A E / T ) .Here T is the nuclear temperature, a low estimate for which is 0.5 MeV, giving a factor of exp 0.6=2. From our conclusion in IV-A t h a t the order of magnitude of the level spacing in U239is 20 ev, we would expect then in lJ235 a spacing of the order of 10 ev. Therefore the result of Eq. (51) makes it seem quite unlikely that the fission observed for the thermal neutrons can be due to the rarest uranium isotope; we consequently attribute it almost entirely to the reaction U235+nll,~U236-tfission. 22 Anderson, Booth, Dunning, Ferrni, Glasoe and Slack, reference 4.
N.
BOHR A N D J. A.
442
WHEELER
us to obtain from (52) a lower limit also to
I'r=R[EEz++z/4]>10 to 400 ev.
___--a; = n R * ( , = =
FIG.6. r,/d and rf/d are the ratios of the neutron emission and fission probabilities (taken per unit of time and multiplied by h ) to the average level spacing in the compound nucleus a t the given excitation. These ratios will vary with energy in nearly the same way for all heavy nuclei, except that the entire fission curve must be shifted to the left or right according as the critical fission energy E f is less than or greater than the neutron binding En. The cross section for fission produced by fast neutrons depends on the ratio of the values in the two curves, and is givcn on the left for E/-E,= Mev and on the right for E j - En= 1 MeV, corresponding closely to the cases of U239 and Th233, respectively.
(a)
\Ye have two possibilities to account for the cross section uf(therma1)- 3 . 5 x presented by the isotope P5 for formation of the compound nucleus W6,according as the level width is smaller than or comparable with the level spacing. In the first case we shall have to attribute most of the fission to an isolated level, and by the reasoning which was employed previously, we conclude that for this level rr/~~02++z/4~ = [(2s+ 1)(2i+1)/(2J+ 1)]0.15(ev)-l= R. (52)
If the spin of U235is 3 or greater, the right-hand side of (52) will be approximately 0.30 (ev)-'; but if i is as low as 3, the right side will be either 0.6 or 0.2 (ev)-'. T h e resulting upper limits on the resonance energy and level width may be summarized as follows :
i 2 3 ;=+,
r < 4 / ~ =13 ~ E o / < l / R =3
J=O
7 1.7
21
J=l
20 ev 5 ev.
(53)
On the other hand, the indicationsz2 for low neutron energies of a l / v variation of fission cross section with velocity lead us as in the discussion of the rarer uranium isotope to the conclusion that either Eo or r/2 or both are greater than several electron volts. This allows
r,: (54)
In the present case, the various conditions are not inconsistent with each other, and it is therefore possible to attribute the fission to the effect of a single resonance level. IYe can go further, however, by estimating the level spacing for the compound nucleus P 6 . According to the values of Table 111, the excitation following the neutron capture is considerably greater than in the case P9, and we should therefore expect a rather smaller level spacing than the value -20 ev estimated in the latter case. On the other hand, it is known t h a t for similar energies the level density is lower in even even than odd even nuclei. Thus the level spacing in U236may still be as great as 20 ev, but it is undoubtedly no greater. From (54) we conclude then t h a t we have probably to d o with a case of overlapping resonance levels rather than a single absorption line, although the latter possibility is not entirely excluded by the observations available. In the case of overlapping levels we shall have from Eq. (40) =
(Tv/2)rnt (2T/d)
(55)
or consequently a level spacing d = (23 X 10-18/2) X X 2 ~ / 3 . 5X
= 20
ev ; (56)
and as we are attributing to the levels an unresolved structure, the fission width must be a t least 10 ev. These values for level spacing and fission width give a reasonable account of the fission produced by slow neutrons.
C. Fission by fast neutrons T h e discussion on the basis of theory of the fission produced by fast neutrons is simplified first by the fact t h a t the probability of radiation can be neglected in comparison with the probabilities of fission and neutron escape and second b y the circumstance t h a t the neutron wavelength /27r is small in comparison with the nuclear radius (R-9X10-13 cm) and we are in the region of continuous level distribution. Thus the fission cross section will be given by uf= T~2r,/r2.4 x 10-24rr/
(rr+r,) ,
(57)
443
MECHANISM OF
NUCLEAR
or, in terms of the ratio of widths to level spacing, ar-2.4X 1 0 - 2 4 ( r , / d ) / [ ( r , / d ) + ( r , / d ) ] .
(58)
According to the results of Section 111,
r,/d=(1/2a)(A3/10
Mev)CKi
(59)
i
and
r , / d = (1/2a)N*.
(60)
In using Eq. (58) it is therefore seen that we do not have to know the level spacing d of the compound nucleus, b u t only t h a t of the residual nucleus (Eq. (59)) and the number N* of available levels of the dividing nucleus in the transition state (Eq. 60). Considered as a function of energy, the ratio of fission width to level spacing will be extremely small for excitations less than the critical fission energy ; with increase of the excitation above this value Eq. (60) will quickly become valid, and we shall have to anticipate a rapid rise in the ratio in question. If the spacing of levels in the transition state can be compared with that of the lower states of an ordinary heavy nucleus (-50 to 100 kev) we shall expect a value of N*=10 to 20 for an energy 1 Mev above the fission barrier; but in any case the value of F,/d will rise almost linearly with the available energy over a range of the order of a million volts, when the rise will become noticeably more rapid owing to the decrease to be expected a t such excitations in the level spacing of the nucleus in the transition state. The associated behavior of r,/d is illustrated in curves in Fig. 6. I t should be remarked that the specific quantum-mechanical effects which set in a t and below the critical fission energy may even show their influence to a certain extent above this energy and produce slight oscillations in the beginning of the F r / d curve, allowing possibly a direct determination of N*. How the ratio r,/d will vary with energy is more accurately predictable than the ratio just considered. Denoting by K the neutron energy, we have for the number of levels which can be excited in the residual (=original) nucleus a figure of from K/0.05 Mev to K/0.1 MeV, and for the average kinetic energy of the inelastically scattered neutron -K/2, so that the sum K : in (59) is
~3821
FISSION
easily evaluated, giving us, if we express K in MeV, r,/d-3 to 6 times K 2 . (61) This formula provides as a matter of fact however only a rough first orientation, since for energies below K = 1 Mev it is not justified t o apply the evaporation formula (a transition occurring until for slow neutrons r,/d is proportional to velocity) and for energies above 1 Mev we have to take into account the gradual decrease which occurs in level spacing in the residual nucleus, and which has the effect of increasing the right-hand side of (61). An attempt has been made to estimate this increase in drawing Fig. 6. T h e two ratios involved in the fast neutron fission cross section (58) will vary with energy in the same way for all the heaviest nuclei ; the only difference from nucleus to nucleus will occur in the critical fission energy, which will have the effect of shifting one curve with respect t o another as shown in the two portions of Fig. 6. T h u s we can deduce the characteristic differences between nuclei t o be expected in the variation with energy of the fast neutron cross section. Meitner, Hahn, and Strassmann observed t h a t fast neutrons as well as thermal ones produce in uranium the complex of activities which arise as a result of nuclear fission, and Ladenburg, Kanner, Barschall, and van Yoorhis have made a direct measurement of the fission cross section for 2.5 Mev neutrons, obtaining 0.5 X cm2 (+25 percent).23Since the contribution to this cross section due to the U235isotope cannot exceed aR2/139-0.02 X lopz4cm2,the effect must be attributed to the compound nucleus P9. For this nucleus however as we have seen from the slow neutron observations the fission probability is negligible a t low energies. Therefore we have to conclude t h a t the variation with energy of the corresponding cross section resembles in its general features Fig. 6a. In this connection we have the further observation of Ladenburg et al. t h a t the cross section changes little between 2 Mev and 3 M ~ v This . ~ points ~ to a value of the critical fission energy for U239definitely less 2sR. Ladenburg, M. H. Kanner, H. H. Barschall and C. C. van Voorhis, Phys. Rev. 56, 168 (1939).
N.
BOHR A N D J. A. W H E E L E R
than 2 Mev in excess of the neutron binding. Unpublished results of the Washington give a,=0.003 x 10-24at0.6 Mevand 0.012 X cm2 a t 1 MeV. With the Princeton observation^^^ we have enough information t o say t h a t the critical energy for U239is not far from $ Mev in excess of the neutron binding (-5.2 Mev from Table 111) : Ef(U239)-6 MeV. (62)
A second conclusion we can draw from the absolute cross section of Ladenburg et al. is t h a t the ratio of ( r f / d ) t o (Fn/d) as indicated in the figure is substantially correct; this confirms our presumption that the energy level spacing in the transition state of the dividing nucleus is not different in order of magnitude from that of the low levels in the normal nucleus. The fission cross section of Th232for neutrons of 2 to 3 hIev energy has also been measured by the Princeton group ; they find u f = 0.1 X lo-** cm2 in this energy range. On the basis of the considerations illustrated in Fig. 6 we are led in this case to a fission barrier 1: Mev greater than the neutron binding; hence, using Table 111, Ef(Th23g) -7 MeV.
(63)
A check on the consistency of the values obtained for the fission barriers is furnished by the possibility pointed out in Section I1 and Fig. 4 of obtaining the critical energy for all nuclei once we know it for one nucleus. Taking E/(U239) = 6 Mev as standard, we obtain E/(Th232) =7 Mev, in good accord with (63). As in the preceding paragraph we deduce from Fig. 4 E f ( W 6 = ) 5: MeV, Ef(U235) = 5 MeV. Both values are less than the corresponding neutron binding energies estimated in Table 111, E,(U236)= 6.4 MeV, E,(U235) = 5.4 Mev. From the values of En- Ed we conclude along the lines of Fig. 6 that for thermal neutrons r f / d is, respectively, -5 and -1 for the two isotopes. Thus it appears that in both cases the level distribution will be continuous. We can estimate the as yet entirely unmeasured fission cross section of the lightest uranium isotope for the thermal neutrons from u f= aX2rn~2a/d. (64) Reported by M. Tuve a t the Princeton meeting of the American Physical Society, June 23, 1939. 24
444
d will not be much different from what it is for say of the the similar compound nucleus order of 20 ev. Thus uf(therma1, U235)-23X10-18X 10-4X2a/20 -500 to 1OOOx cm2, (65) which is of course practically the same figure which holds for the next heaviest compound nucleus. T h e various values estimated for fission barriers and fission and neutron widths are summarized in Fig. 7. T h e level spacingffor past neutrons has been estimated from its value for slow neutrons and the fact that nuclear level densities appear to increase, according to Weisskopf, approximately exponentially as 2 ( E / a )b , where a is a quantity related to the spacing of the lowest nuclear levels and roughly 0.1 Mev in magnitude.25T h e relative values of rn,I', and d for fast neutrons in Fig. 7, being obtained less indirectly, will be more reliable than their absolute values.
V. NEUTRONS,DELAYED A N D OTHERWISE Roberts, Meyer and Wang26have reported the emission of neutrons following a few seconds after the end of neutron bombardment of a
:t FIG.7. Summary for comparative purposes of the estimated fission energies, neutron binding energies, level spacings, and neutron and fission widths for the three nuclei t o which the observations refer. For fast neutrons the values of r,, r,, and d are less reliable than their ratios. Th e values in the top line refer to a neutron energy of 2 Mev in each case. V. Weisskopf, Phys. Rev. 52, 295 (1937). B. Roberts, R. C. Meyer and P. Wang, Phys. Rev. 55, 510 (1939). 15
*6 R.
445
MECHANISM
I
ICO
I
I10
I
120
I
I33
O F
NUCLEAR
I
140
FIG . 8. Beta-decay of fission fragments leading to stable nuclei. Stable nuclei are represented by the small circles; thus t h e nucleus &n120 lies just under the arrow marked 4.1; the number indicates the estimated energy release in Mev (see Section I) in the beta-transformation of the preceding nucleus 481n120.Characteristic differences are noted between nuclei of odd and even mass numbers in the energy of successive transformations, a n aid in assigning activities to mass numbers. The dotted line has been drawn, as has been proposed by Gamow, in such a way as to lie within t h e indicated limits of nuclei of odd mass number; its use is described in Section I.
thorium or uranium target. Other observers have discovered the presence of additional neutrons following within an extremely short interval after the fission process.27 We shall return later to the question as to the possible connection between the latter neutrons and the mechanism of the fission process. The delayed neutrons themselves are to be attributed however to a high nuciear excitation following beta-ray emission from a fission fragment, for the following reasons : (1) The delayed neutrons are found only in association with nuclear fission, as is seen from the fact that the yields for both processes depend in the same way on the energy of the bombarding neutrons. ( 2 ) They cannot, however, arise during the fission process itself, since the time required for the division is certainly less than sec., according to the observations of Feather.27a (3) Moreover, an excitation of a fission fragment in the course of the fission process to an I
H . L. Anderson, E. Fermi and H. B. Hanstein, Phys. Rev. 55, 797 (1939); L. Szilard and W. H. Zinn, Phys. Rev. 55, 799 (1939); H. vori Halban, Jr., F. Joliot and L. Kowarski, Nature 143, 680 (1939). 27a N. Feather, Nature 143, 597 (1939). 27
FISSION
energy sufficient for the subsequent evaporation of a neutron cannot be responsible for the delayed neutrons, since even b y radiation alone such an excitation will disappear in a time of the order of 10-13 t o sec. (4) T h e possibility t h a t gamma-rays associated with the beta-ray transformations following fission might produce any appreciable number of photoneutrons in the source has been excluded by an experiment reported by Roberts, Hafstad, Meyer and Wang.28 ( 5 ) T h e energy release on beta-transformation is however in a number of cases sufficiently great to excite the product nucleus to a point where it can send out a neutron, as has been already pointed out in connection with the estimates in Table 111. Typical values for the release are shown on the arrows in Fig. 8. T h e product nucleus will moreover have of the order of lo4 t o lo5 levels to which beta-transformations can lead in this way, so t h a t it will also be overwhelmingly probable t h a t the product nucleus shall be highly excited. \Ye therefore conclude t h a t the delayed emission of neutrons indeed arises as a result of nuclear excitation following the beta-decay of the nuclear fragments. T h e actual probability of the occurrence of a nuclear excitation sufficient t o make possible neutron emission will depend upon the comparative values of the matrix elements for the betaray transformation from the ground state of the original nucleus to the various excited states of the product nucleus. T h e simplest assumption we can make is t h a t the matrix elements in question do not show any systematic variation with the energy of the final state. Then, according to the Fermi theory of beta-decay, the probability of a given beta-ray transition will be approximately proportional to the fifth power of the energy release.29 If there are p(E)dE excitation levels of the product nucleus in the range E to E+dE, it will follow from our assumptions t h a t the probability of an excitation in the same energy interval will be given by
w(E)dE= constant ( E o- E )5p ( E ) d E , (66) z 8 R . B. Roberts, L. R. Hafstad, R. C. Meyer and P. Wang, Phys. Rev. 55, 664 (1939). L. W. Nordheim and F. L. Yost, Phys. Rev. 51, 942 (193 7 ) .
N. BOHR
AND J. A. WHEELER
446
where Eo is the total available energy. According to (66) the probability w ( B ) of a transition t o the excited levels in a unit energy range a t E reaches its maximum value for the energy E = Em,, given by
typical fission fragment. I t is seen that there will be appreciable probability for neutron emission if the neutron binding is somewhat less than the total energy available for the beta-ray transformation. \Ye can of course draw only general conclusions because of the uncertainty in our E,,,=Eo-5/(d In p/dE)E,,,=Eo-5T, (67) original assumption t h a t the matrix elements for where T is the temperature (in energy units) to the various possible transitions show no sysnhich the product nucleus must be heated to tematic trend with energy. Still, it is clear that ha\-e on the average the excitation energy E,,,. the above considerations provide us with a Thus the most probable energy release on beta- reasonable qualitative account of the observation transformation may be said to be five times the of Booth, Dunning and Slack that there is a temperature of the product nucleus. According chance of the order of 1 in 60 that a nuclear to our general information about the nuclei in fission will result in the delayed emission of a question, an excitation of 4 Mev will correspond neutron.30 to a temperature of the order of 0.6 MeV. Another consequence of the high probability Therefore, on the basis of our assumptions, to of transitions to excited levels will be to give a realize an average excitation of 4 Mev by beta- beta-ray spectrum which is the superposition of a transformation we shall require a total energy very large number of elementary spectra. Acrelease of the order of 4+5 X0.6 = 7 MeV. cording to Bethe, Hoyle and Peierls, the observaThe spacing of the lowest nuclear levels is of tions on the beta-ray spectra of light elements the order of 100 kev for elements of medium point to the Fermi distribution in energy in the atomic weight, decreases to something of the elementary spectra.31Adopting this result, and order of 10 ev for excitations of the order of using the assumption of equal matrix elements 8 Mev, and can, according to considerations of discussed above, we obtain the curve of Fig 10 LVeisskopf, be represented in terms of a nuclear for the qualitative type of intensity distribution level density varying approximately exponen- to be expected for the electrons emitted in the tially as the square root of the excitation energy.23 beta-decay of a ty9ical fission fragment. As is {-sing such an expression for p(E) in Eq. (66), we seen from the curve, we have to expect t h a t the obtain the curve shown in Fig. 9 for the distribu- great majority of electrons will have energies tion function w ( E ) giving the probability that an much smaller in value than the actual transexcitation E will result from the beta-decay of a formation energy which is available. This is in accord with the failure of various observers to find any appreciable number of very high energy electrons following fission .32 T h e half-life for emission of a beta-ray of 8 Mev energy in an elementary transition will be something of the order of 1 to 1/10 sec., according to the empirical relation between lifetime and energy given by the first Sargent curve. Since we have to deal in the case of the nuclear fragments with transitions to lo4 or lo5 excited levels, we should therefore a t first sight expect an extremely short lifetime wlth respect to electron emission. However, the existence of a FIG. 9. The distribution in excitation of the product nuclei following beta-decay of fission fragments is estimated on the assumption of comparable matrix elements for the transformations to all excited levels. With sufficient available energy E O and a small enough neutron binding En it is seen that there will be a n appreciable number of delayed neutrons. The quantity plotted is probability per unit range of excitation energy.
30 E. T. Booth, J. R. Dunningand F. G. Slack, Phys. Rev. 5 5 , 876 (1939). 3l H. A. Bethe, F. Hoyle and R. Peierls, Nature 143, 200 (1939). 3? H. H. Barschall, W. T. Harris, M. H. Kanner and L. A. Turner, Phys. Rev. 55, 989 (1939).
44 7
MECHANISM
OF
sum rule for the matrix elements of the transitions i n question has as a consequence that the individual matrix elements will actually be very much smaller than those involved in beta-ray transitions from which the Sargent curve is deduced. Consequently, there seems to be no difficulty in principle in understanding lifetimes of the order of seconds such as have been reported for typical beta-decay processes of the fission fragments. In addition to the delayed neutrons discussed above there have been observed neutrons following within a very short time (within a time of the order of a t most a second) after fission.*' The corresponding yield has been reported as from two to three neutrons per fission.33 T o account for so many neutrons by the above considered mechanism of nuclear excitation following beta-ray transitions would require us to revise drastically the comparative estimates of betatransformation energies and neutron binding made in Section I . As the estimates in question were based on indirect though simple arguments, it is in fact possible that they give misleading results. If however they are reasonably correct, we shall have to conclude that the neutrons arise either from the compound nucleus a t the moment of fission or by evaporation from the fragments as a result of excitation imparted to them as they separate. In the latter case the time required for neutron emission will be sec. or less (see Fig. 5). T h e time required to bring to rest a fragment with 100 Mev kinetic energy, on the other hand, will be a t least the time required for a particle with average velocity 109 cm/sec. to traverse a distance of the order of 10-3 cm. Therefore the neutron will be evaporated before the fragment has lost much of its translational energy. T h e kinetic energy per particle in the fragment being about 1 MeV, a neutron evaporated in nearly the forward direction will thus have an energy which is certainly greater than 1 MeV, a s has been emphasized by S ~ i l a r dT. h~e~observations so f a r published neither prove nor disprove the possibility of such an evaporation following fission. 33 Anderson, Fermi and Hanstein, reference 2 7 . Szilard and Zinn, reference 27. H. von Halban, Jr., F. Joliot and L. Kowarski, Nature 143 680 (1939). 34 DiscusSions, Washington meeting of American Physical Society, April 28, 1939.
[3w
NUCLEAR
FISSION
FIG.10. The superposition of the beta-ray spectra corresponding t o all the elementary transformations indicated in Fig. 9 gives a composite spectrum of a general type similar to that shown here, which is based on the assumption of comparable matrix elements and simple Fermi distributions for all transitions. The dependent variable is number of electrons per unit energy range.
M'e consider briefly the third possibility that the neutrons in question are produced during the fission process itself. In this connection attention may be called t o observations on the manner in which a fluid mass of unstable form divides into two smaller masses of greater stability; it is found that tiny droplet5 are generally formed in the space where the original enveloping surface was torn apart. Although a detailed dynamical account of the division process will be even more complicated for a nucleus than for a fluid mass, the liquid drop model of the nucleus suggests t h a t i t is not unreasonable to expect a t the moment of fission a production of neutrons from the nucleus analogous to the creation of the droplets from the fluid. T h e statistical distribution in size of the fission fragments, like the possible production of neutrons a t the moment of division, is essentially a problem of the dynamics of the fission process, rather than of the statistical mechanics of the critical state considered in Section 11. Only after the deformation of the nucleus has exceeded the critical value, in fact, will there occur t h a t rapid conversion of potential energy of distortion into energy of internal excitation and kinetic energy of separation which leads to the actual process of division. For a classical liquid drop the course of the reaction in question will be completely determined by specifying the position and velocity in configuration space of the representative point of the system a t the instant when i t passes over the potential barrier in the direction of fission. If the energy of the original system is only
N.
BOHR A N D J . A.
infinitesimally greater than the critical energy, the representative point of the system must cross the barrier very near the saddle point and with a very small velocity. Still, the wide range of directions available for the velocity vector in this multidimensional space, as suggested schematically in Fig. 3, indicates that production of a considerable variety of fragment sizes may be expected even a t energies very close t o the threshold for the division process. When the excitation energy increases above the critical fission energy, however, i t follows from the statistical arguments in Section I11 that the representative point of the system will in general pass over the fission barrier a t some distance from the saddle point. With general displacements of the representative point along the ridge of the barrier away from the saddle point there are associated asymmetrical deformations from the critical form, and we therefore have to anticipate a somewhat larger difference in size of the fission fragments as more energy is made available to the nucleus in the transition state. Moreover, as an influence of the finer details of nuclear binding, it will also be expected t h a t the relative probability of observing fission fragments of odd mass number will be less when we have to do with the division of a compound nucleus of even charge and mass than one with even charge and odd mass.36
WHEELER
448
to expect for these nuclei that not only neutrons but also sufficiently energetic deuterons, protons, and gamma-rays will give rise to observable fission.
A. Fission produced by deuteron and proton bombardment Oppenheimer and Phillips have pointed out that nuclei of high charge react with deuterons of not too great energy by a mechanism of polarization and dissociation of the neutronproton binding in the field of the nucleus, the neutron being absorbed and the proton repulsed.36 The excitation energy E of the newly formed nucleus is given b y the kinetic energy Ed of the deuteron diminished by its dissociation energy I and the kinetic energy K of the lost proton, all increased by the binding energy En of the neutron in the product nucleus : E=Ed- I - K + E n .
(68)
T h e kinetic energy of the proton cannot exceed Ed+En-I, nor on the other hand will i t fall below the potential energy which the proton will have in the Coulomb field at the greatest possible distance from the nucleus consistent with the deuteron reaction taking place with appreciable probability. This distance and the corresponding kinetic energy Kmin have been calculated by Bethe.37 For very low values of the bombarding energy E D , he finds Kmin-l Mev ; when Ed rises to equality with the dissociaVI. FISSIONPRODUCED BY DEUTERONS AND tion energy I=2.2 Mev he obtains Kmin-Ed; PROTONS AND BY IRRADIATION and even when the bombarding potential reaches Regardless of what excitation process is used, a value corresponding t o the height of the it is clear that an appreciable yield of nuclear electrostatic barrier, Kmin still continues to be fissions will be obtained provided that the of order Ed, although beyond this point increase excitation energy is well above the critical of Ed produces no further rise in Kmin.Since the energy for fission and that the probability of barrier height for single charged particles will be division of the compound nucleus is comparable of the order of 10 Mev for the heaviest nuclei, with the probability of other processes leading to we can therefore assume Kmin-Ed for the the break up of the system. Neutron escape ordinarily employed values of the deuteron bombeing the most important process competing with barding energy. We conclude that the excitation fission, the latter condition will be satisfied if energy of the product nucleus will have only a the fission energy does not much exceed the very small probability of exceeding the value neutron binding, which is in fact the case, as we Emax-En- I . (69) have seen, for the heaviest nuclei. Thus we have Since this figure is considerably less than the
35 S. Flugge and G. v. Droste also have raised the question of the possible influence of finer details of nuclear binding on the statistical distribution in size of the fission fragments, Zeits. f. physik. Chemie B42 274 (1939).
36
R. Oppenheimer and M. Phillips, Phys. Rev. 48, 500
3’
H. A. Bethe, Phys. Rev. 53, 39 (1938).
(1935).
[3871
449
MECHANISM
OF NUCLEAR FISSION
estimated values of the fission barriers in thorium and uranium, we have to expect that Oppenheimer-Phillips processes of the type discussed nil1 be followed in general by radiation rather than fission, unless the kinetic energy of the deuteron is greater than 10 MeV. Lire must still consider, particularly when the energy of the deuteron approaches 10 MeV, the possibility of processes in which the deuteron as a whole is captured, leading to the formation of a compound nucleus with excitation of the order of Ed+2E,- I - E d + l O MeV. (70) There will then ensue a competition between the possibilities of fission and neutron emission, the outcome of which will be determined by the comparative values of r, and rn (proton emission being negligible because of the height of the electrostatic barrier). T h e increase of charge associated with the deuteron capture will of course lower the critical energy of fission and increase the probability of fission relative to neutron evaporation compared to what its value would be for the original nucleus a t the same excitation. If after the deuteron capture the evaporation of a neutron actually takes place, the fission barrier will again be decreased relative to the binding energy of a neutron. Since the kinetic energy of the evaporated neutron will be only of the order of thermal energies ( = 1 Mev), the product nucleus has still an excitation of the order of Ed+3 MeV. Thus, if we are dealing with the capture of 6-Mev deuterons by uranium, we have a good possibility of obtaining fission a t either one of two distinct stages of the ensuing nuclear reaction. The cross section for fission in the double reaction just considered can be estimated by multiplying the corresponding fission cross section (42) for neutrons by a factor allowing for the effect of the electrostatic repulsion of the nucleus in hindering the capture of a deuteron : a/
-
with x = ( E R / Z e 2 ) . T R is~ the projected area of the nucleus. E’ is the excitation of the compound nucleus, and E“ the average excitation of the residual nucleus formed by neutron emission. For deuteron bombardment of UZ38a t 6 Mev we estimate a fission cross section of the order of T ( ~ X ~ Oexp - ~ (-12.9)-10-29 ~ ) ~
cm2 (73)
if we make the reasonable assumption t h a t the probability of fission following capture is of the order of magnitude unity. Observations are not yet available for comparison with our estimate. Protons will be more efficient than deuterons for the same bombarding energy, since from (72) P will be smaller by the factor 21 for the lighter particles. T h u s for 6-Mev protons we estimate a cross section for production of fission in uranium of the order
-
4 9 X 10-13)2exp ( - 12.9/21) (rf/r)
cm2,
which should be observable.
B. Photo-fission According to the dispersion theory of nuclear reactions, the cross section presented by a nucleus for fission by a gamma-ray of wavelength ~ T and X energy E = h w will be given by
if we have to do with an isolated absorption line of natural frequency Eo/h. Here r r t / h is the probability per unit time t h a t the nucleus in the excited state will lose its entire excitation b y emission of a single gamma-ray. T h e situation of most interest, however, is t h a t in which the excitation provided by the incident radiation is sufficient t o carry the nucleus into the region of overlapping levels. On summing (74) over many levels, with average level spacing d , we obtain
7Ri2ecP { ,( E ’) /I- (E’)
+Crm’)/r(-WICrf(W/r(E”)11.
(7 1)
Here P is the new Gamow penetration exponent for a deuteron of energy E and velocity v:38
P = (4Ze2/hv)( arc cos x f - x i ( 1-x ) 4 , (7 2) -38H. A. Bethe, Rev. Mod. Phys. 9, 163 (1937).
13881
Without entering into a detailed discussion of the orders of magnitude of the various quantities involved in (75), we can form an estimate of the cross section for photo-fission by comparison with the yields of photoneutrons reported by various observers. T h e ratio of the cross sections
iY. B O H R A N D J . A . W H E E L E R in question will be just I'j/rn,so that 0
-
=
(rj / r n ) c n .
(76)
The observed values of un for 12 to 17 Mev gamma-rays are cmz for heavy elements.39 I n view of the comparative values of l?t and rn arrived a t in Section IV, i t will therefore be reasonable to expect values of the order of loFz7 cm2 for photo-fission of U238,and cm2 for division of Th233. Actually no radiative fission was found by Roberts, Meyer and Hafstad using the gamma-rays from 3 microamperes of 1-Mev protons bombarding either lithium or fluorine.40T h e former target gives the greater yield, about 7 quanta per 1O1O protons, or 8 X l o 5 quanta/min. altogether. Under the most favorable circumstances, all these gammarays would have passed through that thickness, -6 mg/cmz, of a sheet of uranium from which the fission particles are able to emerge. Even then, adopting the cross section we have estimated, we should expect an effect of 39W.
(1939). \ -
Bothe and W. Gentner, Zeits. f . Physik 112, 45
40 R. B. Roberts, R. C. Meyer and L. R. Hafstad, Phys. Rev. 5 5 , 417 (1939).
8 X 105X10-27X6X10-3X6.06 X1023/238-1 count/80 min;
450 (77)
which is too small to have been observed. Consequently, we have as yet no test of the estimated theoretical cross section.
COSCLUSIOS T h e detailed account which we can give on the basis of the liquid drop model of the nucleus, not only for the possibility of fission, but also for the dependence of fission cross section on energy and the variation of the critical energy from nucleus to nucleus, appears to be verified in its major features by the comparison carried out above between the predictions and observations. In the present stage of nuclear theory we are not able to predict accurately such detailed quantities as the nuclear level density and the ratio in the nucleus between surface energy and electrostatic energy; b u t if one is content to make approximate estimates for them on the basis of the observations, as we have done above, then the other details fit together in a reasonable way to give a satisfactory picture of the mechanism of nuclear fission.
XXXVIII. NUCLEAR REACTIONS IN THE CONTINUOUS ENERGY REGION (WITH R. PEIERLS AND G. PLACZEK)
Nature 144 (1939) 200-201
See Introduction, sect. 4, ref. 82.
NATURE
200
JULY 29, 1939, Vor. 144
LETTERS TO THE EDITORS The Editors do not hold themselves responsible for opinions expressed by their correspondents. They cannot undertake to return, or to correspond with the writers of, rejected manuscripts intended for this or any other part of NATURE. N o notice i s taken of anonymous communications. SOTES ON POINTS IN SOME OF THIS WEEK’S LETTERS APPEAR O N P. 208. CORRESPONDEKTS ARE INVITED TO ATTACH SIMILAR SUMMARIES TO THEIR COMMUNICATIONS.
Nuclear Reactions in the Continuous Energy Region IT is typical for nuclear reactions initiated b y
collisions or radiation that they may, to a large extent, be considered as taking place in two steps : the formation of a highly excited compound system and its subsequent disintegration or radiative transition . . t.o a less excited state. We denote by A , B , the possible alternative products of the reaction, specified by the nature, internal quantum state, and spin direction both of the emitted particle or photon and of the residual nucleus and the orbital momentum. . the probabilities, per Further, we call P A , PB . unit time, of transitions to A , B , . . . respectively, from the compound state. The cross-section for the reaction A -+ B is then evidently
.
.
where od is the cross-section for a collision in which, starting from the state A , a compound nucleus is produced. This formula implies, of course, that we are dealing with energies for which the compound nucleus can actually exist, that is, that we are either ill a region of continuous energy values or, if the levels are discrete, that we are a t optimum resonance. Moreover, it is assumed that all possible reactions, including scattering, proceed by way of the compound state, neglecting, in particular, the influence of the so-called ‘potential scattering’, where the particle is deflected without actually getting into close interaction with the individual constituents of the original nucleus. On these assumptions a very general conservation theorem of wave mechanics‘ yields the relation
where 1 is the wave-length of the incident particle and 1 is the angular momentum. I n the case of discrete levels, ( 1 ) and ( 2 ) give the same cross-section as the usual dispersion formula, if one applies it to the centre of a resonance level and neglects the influence of all other levels. I n this case we have for each resonance level a well-defined quantum state of the compound nucleus, and its properties, in particular the probabilities PA, PB, . . . then cannot depend on the kind of collision b y which it has been formed, that is, they would be the same . if we had started from the fragments B , or C, . instead of A . I n the case of the continuum, however, where there are many quantum states with energies that are indistinguishable within the life-time of the compound nucleus, the actual state of the system is a superposition of several quantum states and its properties depend on their phase relations, and hence on the process by which the compound nucleus has been produced.
.
This dependence is made particularly obvious if we consider the formula (3) for the mean value of the cross-section over an interval containing many levels. which follows from the well-known considerations of detailed balancing. Here p is the density per unit energy of levels (of suitable angular momentum and symmetry) of the compound nucleus. P i is the probability for process A in statistical equilibrium and thus refers to a microcanonical ensemble of compound states built up from . . respectively, with proper the fragments A , B statistical weights. I n the case of discrete levels, where formula ( 3 ) can also be derived directly from the dispersion formula, P j is simply an average over the individual levels of the probability P A , which in this case is well defined. I n the continuum, ( 3 ) must be identical with ( 2 ) , since the cross-section does not vary appreciably over an energy interval containing many levels, and hence, comparing ( 2 ) and ( 3 )
.
where the superscript A has been added t o the probabilities occurring in ( 1 ) in order to show explicitly the dependence on the mode of formation, and where F A )is the total energy width of the compound state concerned and d
=
1
- the average level distance. I n i‘
>
the continuum, where F A ) d , the probability of re-emitting the incident particle without change of state of the nucleus will thus be much larger than the probability of the same process in a compound nucleus produced in other ways. While the arguments used so far are of a very general character, more detailed considerations of the mechanism of nuclear excitation are required for a discussion of the dependence P ( i ) of the mode -4 of the compound nucleus provided A # B. One can think of cases in which such a dependence must obviously be expected ; in fact, if a large system be hit by a fast particle, the energy of excitation might be localized in the neighbourhood of the point of impact, and the escape of fast particles from this neighbourhood may be more probable than in statistical equilibrium. Further, if the system had modes of vibration very loosely coupled, the excitation of one of them, for example by radiation, would be unlikely to lead to the excitation of a state of vibration made u p of very different normal modes, even though the state may be quite strongly represented in statistical equilibrium. I n actual nuclei, however, the motion cannot be described in terms of loosely coupled vibrations, nor
* [There are four misprints in this paper, as indicated by handwritten corrections added onto all copies in Bohr’s reprint collection.]
13921
No. 3639, J U L Y
* *
*
29, 1939
NATURE
w ~ u l ~one l expect localization of the excitation energy to be of importance in nuclear reactions of moderate energy. I f we suppose that there are no other special circumstances which would lead to a dependence of on A , it is thus a reasonable idealization to assume that, even in the continuum, all P($ are equal to P i , except, of course, for A = B , where we have seen in (4) that the phases are necessarily such as to favour the re-emission of the incident particle. A typical case of a reaction in the continuum is the nuclear photo-effect in heavy elements, produced by y-rays of about 17 mv. I n the first experiments of 13othe and Gentner, there seemed to be marked differences between the cross-sections of different elements, but the continuation of their investigations2 indicated that these differences can be accounted for by the different radioactive properties of the residual nuclei, and that the cross-sections of all heavy nuclei cm.2. for photo-effect are of the order of 5 x I n previous discussions, based on f o r m u k ( 1 ) and ( 2 ) , where the distinction between P ( 2 )and P i was not clearly recognized, it was found difficult, however, t o account for photo-effect cross-sections of this magnitude. I n fact, if one estimates the probability of neutron escape P B at about 10'7 set.-', one should have for P A 10" set.-', and as long as this was ta,ken as P9 it seemed much too large, since it evidently must be much smaller than the total radiation probability, estimated a t about which included transitions to many more final levels besides the ground state. We see now, however, that P($ is here considerably larger than P9, since the level distance at the high excitations concerned is probably of the order of 1 volt, whereas the level width corresponding to the above value of P B is about 100 volts. From (4), or more directly from ( 3 ) , P i is thus seen to be only about lOI3set.-', which would appear quite reasonable. N. BOHR. R. PEIERLS. G. PLACZEK. Institute of Theoretical Physics, Copenhagen. July 4.
Pg)
The details of this and of the other arguments of this note will be puhlishrd in the Z'roceedinga o,f the Copenhagen Academy. Bothc, V . , and Gcntner, W.,Z . Phys., 106, 236 (1937) ; 112, 45 (1939).
20 1
XXXIX. CHAIN REACTIONS OF NUCLEAR FISSION UNPUBLISHED MANUSCRIPT 1939
See Introduction, sect. 5 , ref. 124.
P A R T I : PAPERS A N D MANUSCRIPTS RELATING TO N U C L E A R PHYSICS
This manuscript consists of 3 typewritten pages with a carbon copy, dated 5 August 1939. The manuscript is in English. The formulae and some symbols are entered in ink on both copies. The footnotes are missing. The manuscript is on microfilm Bohr MSS no. 16.
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
August 5 , 1939
Chain reactions of nuclear fission. The discovery that neutrons are released in considerable number by fission processes initiated by the impact of neutrons on Uranium nuclei (Joliot’) has given rise to much discussion concerning the possibility of liberating inter-nuclear energy on large scale by means of chain-reactions. It appears, however, in these discussions that certain circumstances hindering the establishing of fission chains have not always received sufficient attention. As is well-known uranium fission can be produced by fast neutrons (about 106E.V.) as well as by thermal neutrons (about lo-’ E.V.). From the preponderance of neutron capture process[es] compared with fission for neutrons of medium velocities (from lo-lO0E.V.) it would appear, however, that the effect of fast and thermal neutrons are due to essentially different processes arising from the two uranium isotopes U(238) and U(235). Now in both fission processes the secondary neutrons emitted must be expected to have fast velocities (about 106E.V. or more), but these fast neutrons will hardly be sufficient to produce chains directly since the cross-section for uranium nuclei for inelastic scattering is considerably higher than the cross-section for fission (Ladenburg’). In fact it would seem that the number of neutrons liberated per fission process is about 2 while the crosssection for fission of uranium for fast neutrons is less than d of the cross-section for inelastic scattering. By the latter process the energy is reduced to the order of magnitude of lo5 E.V. and enter therefore in the region where neutron capture is larger than fission and if such capture shall be prevented from stopping the chain it is therefore necessary that the neutron velocities are quickly reduced to the thermal region by an admixture of a light substance, like hydrogen to the Uranium. If the number of uranium and hydrogen atoms per unit volume are ,Y, and N , the probability that a neutron will enter this region without being captured is clearly W = e-n’LoLi’’HGH\ where n is the mean number of collisions with the H-atoms necessary to reduce the velocity sufficient and ouiand oHsare mean values for the uranium capture cross-sections and the hydrogen scattering cross-section. Due to the discrete distribution of resonance levels in uranium in the region
’ [ H . von Halban, J u n . , F. Joliot and L. Kowarski, Liberation of Neutrons in the Nuclear Explosion Uranium, Nature 143 (1939) 470-471.1 [ R . Ladenburg, M.H. Kanner, H. Barschall and C.C. van Voorhis, Study of Uranium and Thorium I;i.mion Produced by Fast Neutrons of Nearly Homogeneous Energy, Phys. Rev. 56 (1939) 168-170.1 u,/
MS,
2
P A R T I: P A P E R S A N D M A N U S C R I P T S R E L A T I N G T O N U C L E A R PHYSICS
of medium velocities the question of evaluation of the first mean value is a somewhat difficult question. If for the moment we assume that the ratio between the distance of the levels and their width is not larger than n , we can use a simple mean value over the energy which gives:
where D is the level distance and r, and & are the partial width for neutronescape and for radiative capture. This quantity in the energy region of lo3E.V. would seem to be of the order not less than and since oHsis of the order and at least 10 collisions would be necessary to bring neutrons of lo5 E.V. down to about an energy beneath the lowest resonance level in uranium (about 25 E.V.) it would seem that in order [that] an appreciable amount of neutrons entered the region NH/Nuhad to be of the order of 100. This, however, would at the same time prevent a sufficient probability for fission by thermal neutrons since for these velocities the cross-section for neutron capture is not much larger (Estimates of the various quantities see Bohr and Wheeler3.) The than 2 circumstances might in this respect be more favorable by using deuterium instead of hydrogen but even here chains would hardly be realisable since n would be at least twice as great (Placzek4) while the cross-section for capture in deuterium although it is not accurately measured would seem to be of the order of Of course these considerations refer only to the ordinary isotopic constitution of uranium. If separation of the isotopes would once be possible so one may deal with pure or highly concentrated U(235) the whole situation would be different and chain reactions would probably be realisable without any admixture of a lighter substance since for all velocities the cross-section for fission would presumably be much larger than the cross-section for radiative capture.
[N. Bohr and J.A. Wheeler, The Mechanism of Nuclear Fission, Phys. Rev. 56 (1939) 426-450.1 [Probably private communication.]
XL. THE FISSION OF PROTACTINIUM [ l ] (WITH J.A. WHEELER) “WHEELER’S FIRST PROPOSAL” UNPUBLISHED MANUSCRIPT 1939
See Introduction, sect. 5 , ref. 125.
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
This manuscript consists of a carbon copy of two typed pages in English. On top of the first page Bohr has written “Wheeler’s first proposal”. The figure % MeV is our attempt to decipher the typed number, which is almost illegible due to a correction. The manuscript is on microfilm Bohr MSS no. 16.
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
The Fission of Protactinium The mechanism of nuclear fission, according to the liquid drop model of nuclei, consists of two stages, first a distribution among the various degrees of freedom of the compound system of the excitation energy originally imparted to the nucleus, followed by the transformation of a sufficient portion of this energy into potential energy of deformation to lead to division'. A detailed discussion of fission on this basis2 leads to an estimate of the energy required to produce a critical deformation in its dependence on nuclear charge and mass, an adjustable constant being fixed by the condition that the fission energy for U239 shall give accord with the relevant observations. It is shown in the paper cited that values then result for the fission energies of U236and Th233which, together with reasonable estimates of nuclear level densities, combine to give a satisfactory account of the fission phenomena produced in uranium and thorium by slow and fast neutrons. The critical fission energy for Pa232was estimated at the same time to be about 5.5 Mev, from which it followed that neutrons should produce comparable fission in protactinium. The recent observation of such fission by v. Grosse, Booth, and Dunning3 provides an interesting confirmation of this qualitative conclusion and allows also a test of the value predicted for the fission energy. The energy released when a neutron is captured to form 91Pa232is, according to Eq. (6) of reference 2 , about 5.4 Mev (contrary to the last entry in Table 111, and comparable rather to the value for U239,in which the capture has also led from an isotope of even neutron number to one with one unpaired neutron). Thus neutrons of energy over 5.5-5.4 = 0.1 (iabout 0.5) Mev should be required to produce observable amounts of fission. v. Grosse, Booth, and Dunning find in fact that thermal neutrons and photoneutrons produce no detectable fission, whilst Be9 + H' neutrons (maximum energy about 2 Mev) produce about 30 times as much yield in protactinium as in thorium. They suggest on the basis of their observations that the fission yield for Pa is comparable with that produced by fast neutrons in U. Since the threshold for the latter reaction appears to lie at about 3/4 Mev 2 , it is seen that the estimates which one can form from the experimental and the theoretical sides for the fission energy of P a are in satisfactory accord, considering the respective accuracy of each. The observations on protactinium serve to emphasize the unique position of
' K , Bohr,
Nature 143, 330 (1939). Bohr a n d J . A . Wheeler, Phys. Rev. 56, 426 (1939). ' A . v. Grosse, E.T. Booth, and J . R . Dunning, Phys. Rev. 56, 382 (1939).
'N.
MS, p . 2
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
the isotope U235, in which neutron capture leads to an isotope with an even number of neutrons, and draws attention again to the which have led to the assignment to this isotope of the fission produced in uranium by slow neutrons. Niels Bohr Institute for Theoretical Physics, Copenhagen, Denmark John. A. Wheeler Palmer Physical Laboratory, Princeton, N. J .
XLI. THE FISSION OF PROTACTINIUM [2] (WITH J .A. WHEELER) Phys. Rev. 56 (1939) 1065-1066
See Introduction, sect. 5, ref. 127.
The Fission of Protactinium In connection with the recent observation by v. Grosse, Booth and Dunning,' t h at it is possible t o produce fission in protactinium by neutrons of less than 2 Mev energy but not by thermal neutrons, we should like to point out t h at this important discovery would seem to fit very well with the theoretical considerations about the fission mechanism developed by us in a recent paper.* This theory rests upon the idea t h a t fission, like other nuclear transmutations initiated by collisions or radiation, takes place in two stages. Of these the first is the formation of a compound nucleus in which the energy is temporarily stored among the different degrees of freedom in a way resembling thermal agitation ; the second stage is the transformation of a sufficient portion of this energy into potential energy of deformation of the compound nucleus to lead t o its division. The possibility of fission by impact of neutrons of given energy depends, therefore, on the difference between the critical energy E l of such a n unstable deformation and the excitation energy of the compound nucleus, which is determined by the binding energy W , of the added neutron. T h e considerations in our paper lead to the estimates for these quantities given in Table I. According t o this table, and in agreement with the observations of v. Grosse, Booth and Dunning, we shall just expect th a t fission is produced in protactinium more easily than in thorium but less easily than in the isotope Us5 which, according to the theory, is responsible for the large fission yield of thermal neutrons in uranium. While the accuracy of the estimates of E l - W , should be amply sufficient for such qualitative conclusions, it hardly permits TABLE I. Estimales of the differencesin Men belween the crilicd energy E l of unslable deformalions and lhe brnding energy W , of fhc added neutron.
COMPOUND h'lJCLEUS
El -
El 5.O 5.3 5.5 5.9 6.9 6.5
5.4 6.4 5.4* 5.2 5.2 5.3
-0.4 -1.1 +O.l +0.7
+1.7 +1.2
*
B y a n unfortunate error this quantity was given a s 6.4 Mev in Table 111 of reference 2 . I t is clear, however, that the case of slPa2Q is comparable not t o t h a t of ozU'J6 but t o t h a t of 92UD6. in which the removal of a neutron leads from a n isotope of odd neutron number t o one of even neutron number.
us to exclude the possibility of fission of protactinium by thermal neutrons; but the yield of such a process should at a n y rate be very much smaller than in uranium. An accurate determination of the threshold of neutron energy for protactinium fission would of course be very important and might perhaps be most easily obtained by a comparison between the fission yields for fast neutrons of well-defined energy in protactinium, uranium, and thorium, like t h at provided for the two latter elements by the experiments of Ladenburg, Kanner, Barschall and Van V o o r h i ~ ,as ~ discussed in Section IV, C (see especially Fig. 6 ) of our paper. Institute for Theoretical Physics, Copenhagen, Denmark.
NIELS BOHR JOHK
Palmer Physical Laboratory. Princeton University. Princeton, New Jersey, October 20. 1939.
'4. ~ V H E E L E R
1 A . v. Grosse, E. T. Booth and J . I<. Dunning, Phys. Rev. 56, 382 (1939). 2 N. Bohr and J . A . Wheeler, Phys. Rev. 56, 426 (193%. 3 R . Ladenburp. >f, H . Kanner. 14, I I . Barschall and C . C. Van Voorhis. Phys. Rev. 56. 168 (1939).
XLII. THE THEORETICAL EXPLANATION OF THE FISSION O F ATOMIC NUCLEI [ l ] Unpublished Synopsis of Address t o the Royal Danish Academy on 3 November 1939 (Document XLIII) TEXT AND TRANSLATION
See Introduction, sect. 5 , ref. 138.
PART I: PAPERS AND MANUSCRIPTS RELATIKG TO NUCLEAR PHYSICS
This manuscript consists of 1 typewritten page in Danish. T h e numbers evidently refer to slides to be shown during the lecture. The manuscript is o n microfilm Bohr MSS no. 16.
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
Foredrag i Videnskabernes Selskab 3/11 1939. Emnet for Forelzggelsen af Meddelelsen. Ny Type af Atomkernereaktioner. Nye Udsigter for Udvinding af Atomkerneenergien. Simpel Forklaring paa Grundlag af teoretiske Forestillinger. Oversigt over Atomkernefysikens Udvikling. Rutherfords Opdagelse af Atomkerneforvandling. L 1. Opdagelse af Neutronen. L 2. Opdagelse af kunstig Radioaktivitet. L 3. Atomkerneforvandlingen ved Neutron-Bombardement (Fermi). L 4-5. Neutron-Indfangning . L 6. Forklaring ved Draabemodel. L 7. To Stadier i alle Atomkerneforvandlinger. L 8. Unders~gelserover Uran af Fermi (Periodiske System). L 9. Unders~gelseraf Meitner, Strassmann, Curie og Savitch. Opdagelse af Hahn og Strassmann. Meitner og Frisch’s Betragtninger. L 10. Direkte Iagttagelse af Kerne-Fission (Frisch-Joliot). L 11. Oversigt over Indholdet af det forelagte Arbejde af Meitner og Frisch. Emnets videre Udvikling. Betegning. Sammenligning mellem Uran og Thorium. Uranisotopernes Forhold. B~lgemekaniskParadox for Indfangning af langsomme Neutroner. L 12. Vanskelighederne ved Energiudvinding af den naturlige Isotopblanding. Beregning af den kritiske Fissionsenergi. L 13. Sammenligning af Fissions-Energi og Neutronbinding af Uran- og L 14. Thorium-Isotoper. Nylige Opdagelse af Protactinium-Fission. (Dunning). Oversigt over Fissionsprodukterne. L 15. Forklaring af den forsinkede Neutronudsendelse. L 16. Udsigter for Emnets Videref~relse. Instituttets Hjzlpemidler og Redeg~relsen derfor i szrskilt L 17-18. Afhandling.
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
TRANSLATION
Lecture to the Royal Danish Academy, 3 November 1939. [Slide No.]
1. 2. 3. 4-5. 6. 7. 8. 9.
10. 11.
Notation 12. 13. 14.
15. 16.
17-18.
Topic for presentation of the communication. Novel type of nuclear reaction. New prospects for the release of the energy of atomic nuclei. Simple explanation in terms of theoretical ideas. Review of the history of nuclear physics. Rutherford’s discovery of nuclear transmutation. Discovery of the neutron. Discovery of artificial radioactivity. Nuclear transmutation under neutron bombardment (Fermi). Neutron capture. Explanation through the liquid-drop model. Two stages in every nuclear transmutation. Investigations by Fermi on uranium (Periodic system). Investigations by Meitner, Strassmann, Curie and Savitch. Discovery by Hahn and Strassmann. Considerations of Meitner and Frisch. Direct observations of fission (Frisch-Joliot). Summary of the contents of the submitted paper by Meitner and Frisch. Further development of the subject. Comparison between uranium and thorium. Behaviour of the uranium isotopes. Wave mechanical paradox in the capture of slow neutrons. Difficulties in energy release with the natural isotopic mixture. Calculation of the critical energy for fission. Comparison of fission energy and neutron binding energy for the uranium and thorium isotopes. Recent discovery of protactinium fission (Dunning). Survey of the fission products. Explanation of delayed neutron emission. Prospects of further developments. The facilities of the Institute and their description in a separate paper.
XLIII. THE THEORETICAL EXPLANATION OF THE FISSION OF ATOMIC NUCLEI [2] DEN TEORETISKE FORKLARING AF ATOMKERNERNES FISSION Overs. Dan. Vidensk. Selsk. Virks. Juni 1939 - Maj 1940, p. 28 Communication to the Royal Danish Academy on 3 November 1939 ABSTRACT TEXT AND TRANSLATION
See Introduction, sect. 5, ref. 137.
NIELS BOHR giver en Meddelelse om den teoretiske For kla ri n g a f Atom ke r n e rn e s Fission . I Meddelelsen bliver det vist, hvorledes den ved Neutronbombardement fremkaldte S ~ n d e r d e l i n gaf tunge Atomkerner simpelt kan forstaas ud fra de i d e senere Aar udviklede Forestillinger om Atomkerners Reaktioner, sanit hvorledes disse Forestillinger tillader at gsre Rede for mange ejendommelige T r z k hos Fissionsprocesserne.
TRANSLATION Niels Bohr presents a communication on the theoretical explanation of nuclear fission. The communication shows how the splitting of heavy nuclei under neutron bombardment can be understood in a simple manner from the ideas about nuclear reactions developed in recent years, and how these ideas make it possible to account for many characteristic features of the fission processes.
XLIV. RECENT INVESTIGATIONS OF THE TRANSMUTATIONS OF ATOMIC NUCLEI NYERE UNDERSQGELSER OVER ATOMKERNERNES OMDANNELSER Fys. Tidsskr. 39 (1941) 3-32 Address to the Society for the Dissemination of Natural Science in Copenhagen on 6 December 1939 and to the Norwegian Society of Engineers in Oslo on 5 April 1940 TEXT AND TRANSLATION
See Introduction, sect. 5, ref. 140.
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
This address was also published in the Norwegian journal Fra Fysikkens Verden 3 (1941/1942) 1-22 and 81-96, and, after the war, in the Swedish journal Kosmos 24 (1946) 24-57. In an editorial note to the Norwegian publication it is mentioned that the title of Bohr’s talk in Oslo was “Sperrgsmaalet om Atomenergiens Udnyttelse” (The Question of Utilisation of Atomic Energy), of which a preliminary report was given by E.K. Broch in Teknisk Ukeblad, no. 18, 1940. For the benefit of the Norwegian readers a supplement to Bohr’s paper, “Atomkjernernes sammensetning og omdannelser” (The Composition and Transmutations of Atomic Nuclei) was written by E.A. Hylleraas. Both for this supplement and for the preliminary report, Bohr placed at the disposal of the editors some of the many slides shown during the lecture.
Scertryk a/ sFysisk Tidsskrijt I
N r . 1-2,
1941.
Nyere Unders~rgelserover Atomkernernes Omdannelser"). Af N. Bohr. Skrant Rutherfords Opdagelse af Atomets Kerne ligger mindre end 30 Aar tilbage, 08 det ikke er mere end 20 Aar siden, det frarste Gang lykkedes ham a t paavise, at det er muligt at frembringe Omdannelser af Atomkerner, er Studiet af disse Omdannelser i Dag e t af Hovedemnerne for den fysiske Forskning. Nssten hvert eneste Aar har jo pan dette Omraade bragt vigtige Fremskridt, der har givet 0 s Indblik i dybtliggende fysiske Lovmsssigheder og banet nyeVeje for fortsat Udvikling. Det vil ikke vaere mig muligt i Enkeltheder at gaa ind paa den Betydning, som Atomkernefysikken allerede har faaet for mange af Naturvidenskabens mest forskellige G e n e , og paa de Perspektiver, der her aabnes. Jeg skal derimod forsrage a t vise, hvorledes mange af de ofte saa overraskende Erfaringer vedrrarende Atomkernernes Omdannelser kan sammenfattes ved Hjzelp af ganske simple Synspunkter. I s s r skal vi se, hvorledes disse Synspunkter ogsaa kan benyttes ti1 a t forklare de allertungeste Atomkerners Ssnderdeling, hvis Opdagelse i de sidste Aar har tiltrukket sig saa stor Interesse**). * ) Cversigtsartikel, udarbejdet paa Grundlag af e t Foredrag holdt i Selskabet for Naturlierens Udbredelse den 6. December 1939. **) De omhandlede Synspunkter vedrorende Atomkerneomdannelsers For10b er forst fremstillet i en Artikel i Nature, CXXXVII, 344, 1936 (se ogsaa Fysisk Tidsskrift 1936, S. 186) og niermere udviklet i en Afhandling af F. Kalckar og Forfatteren i D.Kgl. Danske Vidensk. Selsk. math.-fys. Medd. XIV, 10, 1937. Teorien for de tungeste Atomkerners Spaltning er indgaaende behandlet af J. A. Wheeler og Forfatteren i Physical Review, LVI, 426, 1939. Endvidere kan henvises til, a t Taagekammerbilleder af de ved Uranspaltningen udslyngede Kernedeles Baner, hvoraf her kun et enkelt er gengivet, for nylig er offentliggjort og udforligt diskuteret af J. K. B ~ g g i l d , K. J. Brostrnm og T. Lauritsen i D.Kg1. Danske Vidensk. Selsk. math.fys. Medd. XVIII, 4, 1940. I*
4
N. Bohr:
1. Atomkernernes Opbygning. For a t fremhsve Atomkerneproblemernes ssrlige Karakter skal jeg ti1 Sammenligning allerfprrst minde om de Hovedtrsk ved Atomernes Opbygning, hvis Erkendelse har dannet Grundlaget for den indgaaende Forklaring af Stoffernes sadvanlige fysiske og kemiske Egenskaber, som vi i Lsbet af den sidste Menneskealder er naaet til. Den store Simpelhed, der kendetegner vore Forestfinger om Atombygningen, beror jo fprrst og fremmest paa, a t Afstandene mellem de enkelte Partikler i Atomet er tilstrskkelig store til, at saavel Kernen som Elektronerne med vidtgaaende Tilnsrmelse kan betragtes som elektriske Massepunkter, mellem hvilke der virker K r s f ter af samme Art som mellem almindelige elektriserede Legemer. I denne Henseende sndres intet ved Erkendelsen af, a t de ssdvanlige mekaniske Bevsgelseslove er ganske utilstrzekkelige ti1 at gprre Rede for Elektronbindingen i Atomet, fordi vi paa Grund af dettes ringe Stsrrelse ikke som ved de almindelige mekaniske Systemer har a t gprre med Virkninger, der er store nok til, a t vi kan se bort fra det universelle Virkningskvantum. At Elektronerne kan bindes paa stabil Maade til Kernen i Afstande fra denne, der er overordentlig store i Forhold til Kernens egen Udstrskning, har det endda fsrst v s r e t muligt a t forstaa efter Kvantebegrebernes Indfprrelse i Atomfysikken. Saa snart vi gaar over til a t betragte Spsrgsmaalet om Atomkernernes egen Bygning og deres Omdannelser, ligger Forholdene imidlertid ganske anderledes. Ikke alene har vi i Atomkernerne a t gsre med en overordentlig t s t Sammenpakning af Partikler, der paavirker hinanden med Krsfter af en Art, hvortil intet Sidestykke haves fra sadvanlige fysiske Erfaringer, men det er ikke engang muligt a t tale om Kernernes Byggestene paa samme simple Maade, som vi taler om Atomernes Opbygning af Kerner og Elektroner. Det ved massespektroskopiske Undersprgelser klarlagte Forhold, at ethvert Atoms Masse kan udtrykkes ved e t helt Tal, naar man vslger en Enhed, der falder n s r sammen med Brintatomets Masse, ledte tidligt ti1 den Opfattelse, a t Brintkernen, den saakaldte Proton, maatte vsre en vssentlig Bestanddel af alle Atomkerner. Da Forholdet mellem Ladning og Masse er mindre for de tungere Atomkerner end for Protonen, gik man dog til a t begynde med ud fra, a t Kernerne ogsaa maatte indeholde et Antal Elektroner; denne
Nyere Undersegelser over Atomkernernes Omdannelser.
5
Antagelse var jo ogsaa meget nsrliggende paa Grund af den Omstsndighed, a t der fra de naturlige radioaktive Stoffers Atomkerner foruden tungere Partikler (a-Straaler) tillige kan udsendes Elektroner (p-Straaler). Efter Kvantemekanikken er det imidlertid udelukket a t antage, a t saa lette Partikler som Elektroner kan bindes paa stabil Maade indenfor Rumomraader saa smaa som Atomkernerne, og vi tvinges derfor til den Opfattelse, a t de Elektroner, der udsendes fra radioaktive Stoffer, ferrst dannes under selve Udsendelsesprocessen. Dette Forhold er issr blevet klart, efter at det har vist sig, a t der ved Atomkerneomdannelser ikke alene kan frembringes radioaktive Isotoper, der ligesom de naturlige radioaktive Stoffer udsender negative Elektroner, men ogsaa radioakt,ive Isotoper, der udsender positive Elektroner, som efter deres Art ikko kan findes sammen med negative Elektroner, uden a t de parvis forenes og forsvinder under Udsendelse af elektromagnetisk Straaling. Om der ved en radioaktiv Proces udsendes en positiv eller en negativ Elektron, har vist sig alene a t afhsnge af Forholdet mellem den paagsldende Atomkernes Masse og Ladning. For en given Masse er der nemlig i Almindelighed kun e t ringe Spillerum for den Ladning, en stabil Atomkerne kan besidde, og saa snart Ladningen bliver enten for stor eller for lille i Forhold til Massen, opstaar saa a t sige en Tilberjelighed hos Kernen til at formindske eller forerge sin Ladning ved Udsendelse af en positiv eller en negativ Elektron. E t afgsrende Fremskridt for vore Forestillinger om Atomkernernes Bygning betsd dog fmst og fremmest Opdagelsen af, a t der ved visse Atomkerneomdannelser kan frigerres en Partikel, der har omtrentlig samme Masse som Protonen, men ingen elektrisk Ladning, og som derfor har faaet Navnet Neutron. Det er jo straks klart, a t vi kan gerre Rede for alle Atomkerners Masse- og Ladningstal ved a t taenke 0 s Kernerne opbygget alene af Neutroner og Protoner. Ved en konsekvent Videreferrelse af den kvantemekaniske Formalisme har det ydermere vist sig muligt a t opfatte Neutronen og Protonen som elektrisk forskellige Tilstandsformer af en og samme Elementarpartikel, som man fornylig er begyndt a t kalde Nucleon. Efter denne Opfattelse er saaledes Elektronudsendelsen fra radioaktive Kerner netop forbundet med Nucleonernes Tilstandssndringer. Det vilde dog fme 0s altfor langt bort fra vort Emne a t gaa naermere ind paa disse dybtliggende Spsrgsmaal og de nye Udsigter,
6
N. Bohr:
der her aabnes for en videre Udbygning af Atomteoriens Grundlag. For vort Formaals Skyld skal vi ikke engang beharve i Enkeltheder a t besksftige 0 s med de store Fremskridt, som den kvantemekaniske Behandling af Vekselvirkningen mellem Kernepartiklerne i de seneste Aar har bragt. Det vil v s r e tilstrskkeligt a t minde om, a t man derved har faaet en Forklaring pae det tidligt erkendte ejendommelige Forhold, a t alle Atomkerner, bortset fra de allerletteste, har en paafaldende ensartet Tsthed af Masse og elektrisk Ladning. Ti1 Trods for, a t denne Tsthed af Kernestoffet er saa uhyre stor i Forhold ti1 de ssdvanlige Stoffers, minder Atomkernernes Tilstandsform ikke desto mindre, som vi skal se, i mange Henseender om Vsdsketilstanden hos almindelige Stoffer.
2 . A t o m k e r n e o m d a n n e l s e r n e s Forlerb. Den store Forskel mellem hele Atomets og Kernens egen Tsthed viser sig i s m ved en gennemgribende Modsstning mellem den Maade, hvorpaa Atomet som Helhed reagerer ved e t Sammenstard med en hurtig Partikel, og Forlarbet af et Sammensterd, hvori Partiklen t r s n ger ind i selve Kernen. Ved de Sammenst~dsprocesser,der har vsret Hovedkilden til Oplysninger om Atomernes Byggestene, vil Partiklen jo i Almindelighed gaa frit igennem Atomets aabne Bygning og kun hsndelsesvis komme saa n a r ti1 en af Atompartiklerne, a t den vil undergaa en vssentlig Bevaegelsessndring, og den ramte Partikel udjages af Atomet. Derimod vil de sterke Krsfter, der virker mellem . de tst sammenpakkede Partikler indenfor Atomkernen, bevirke, a t en Partikel, der rammer Kernen selv, almindeligvis ikke vil kunne trsnge igennem den. Paa Grund af Kernepartiklernes staerke Vekselvirkning saavel med hverandre som med den i Kernen indtrsngende Partikel vil, som vi skal se, Partiklen forene sig med den ramte Kerne ti1 en ny Kerne med forholdsvis lang Levetid. Det endelige Resultat af Sammenstardet vil derfor v s r e betinget af Omdannelsesprocesser, som denne nye Kerne kan undergaa, og som er uafhsngige af den Maade, hvorpaa den er dannet, men alene bestemt af dens Sammensstning og Energitilstand. Disse Forhold er issr blevet klarlagt efter Opdagelsen af Neutronen, der m a r t viste sig a t v s r e saa effektivt et Middel ti1 Frembringelse af Atomkerneomdannelser. Tidligere var man j o ved saadanne Undersergelser henvjst ti1 a t benytte elektrlsk ladede Partikler som a-Straaler
Nyere Undersngelser over Atomkernernes Omdannelser.
7
fra Radium eller kunstigt accelererede Protoner. I saadanne Tilfslde vil imidlertid den stsrke Frasterdning bevirke, a t Partiklen har Vanskelighed ved a t trsnge ind i Kernen, og Forholdene ligger derfor langt mere overskueligt ved Bombardement af Atomkerner med Neutroner, hvor ingen elektrisk Frasterdning hindrer Opnaaelse af Ber~ringved Sammenst.sd. Afgerrende for Udviklingen af vore Forestillinger om Kerneomdannelsernes Forlerb har i s m den Iagttagelse v s r e t , a t et Sammenst0d mellem en Neutron og en tungere Atomkerne har en betydelig Sandsynlighed for simpelthen a t ferre ti1 Neutronens Indfangning i Atomkernen under Dannelse af en ny Kerne, der i Almindelighed vil vsre radioaktiv. Som et typisk Eksempel herpaa skal vi betragte Indfangningen af en Neutron i en Jodkerne, en Proces, der kan fremstilles ved ferlgende Skema 127J
53
I-
--t 'i!J*,
hvor J er det ssdvanlige kemiske Symbol for Jod, medens n betegner Neutronen. De til Symbolerne foroven og forneden tilfsjede Tal er henholdsvis Partiklernes Masse- og Ladningstal. Da der kun findes een stabil Jodisotop, er for den f ~ r s t eJodkernes Vedkommende det erverste Tal Jodets kemiske Atomvsgt, medens det nederste Tal angiver Jodets Nummer i Grundstoffernes naturlige System. Den ved Processen dannede Jodisotop er, som antydet ved Tilf~jelsenaf en Stjerne, instabil, og da den er tungere end den stabile Isotop, forlerber den radioaktive Proces efter Skemaet
Her betegner det f ~ r s t eSymbol paa herjre Side en af de mange stabile Xenonisotoper, det sidste en Elektron med negativ Enhedsladning og med en Masse, der er saa lille i Forhold ti1 Neutronens og Protonens, a t den med den anvendte Tilnsrmelse kan ssttes lig Nul. Da den ved Skemaet (11)fremstillede radioaktive Proces forl ~ b e med r en Halveringstid paa omtrent en halv Time, medens Indfangningsprocessen (I)finder Sted indenfor en meget ringe Brerkdel af et Sekund, kan de to Processer naturligvis betragtes som uafhsngige af hinanden, 08 i Ssrdeleshed kan Sperrgsmaalet om Energiens Bevarelse ved hver af dem underserges for sig.
8
N. B o b :
Medens ved de tidligere undersergte Omdannelser af Atomkerner ved Sammensterd, hvor Resultatet af Vekselvirkningen altid var Dannelsen af to nye Kerner, Energioverskuddet efter Processen direkte gav sig til Kende ved den Bevaegelsesenergi, hvormed de nydannede Kerner slyngedes fia hinanden, mgder vi, netop hvad Energibalancen angaar, saerlige Forhold ved Indfangningsprocesser sorn den omhandlede, hvor der ikke er nogen anden materiel Partikel, der kan optage Energioverskuddet. For at hindre, at den indtrsngende eller en anden Neutron undslipper fra den nydannede Kerne, er det derfor nadvendigt, a t denne hurtigt skiller sig af med den overskydende Energi i Form af elektromagnetisk Straaling, saaledes som det og,saa ved forskellige Indfangningsprocesser direkte har kunnet paavises. Ud fra Kernens Dimensioner og samlede Ladning er det imidlertid let a t beregne en nedre Graense for den Tid, Udsendelsen af et Straalingskvantum fra Kernen i Middel vil kraeve, og det viser sig nu, a t denne Tid, omend den kun udgerr en yderst ringe Brerkdel af et Sekund, dog er overordentlig lang i Forhold til den Tid, som det oilde tage en Neutron med de Hastigheder, det drejer sig om, at gennemlerbe en Straekning svarende til Kernedimensionerne. Det er derfor klart, at hele den overskydende Energi meget hurtigt vil fordele sig mellem alle Partiklerne i Kernen paa en saadan Maade, at ingen enkelt af disse i den naermest ferlgende Tid har Energi nok til at lersrive sig fra de andre Partikler og forlade Kernen. Dersom i Mellemtiden intet Energitab finder Sted ved Straaling, vil der naturligvis under Overskudsenergiens tilfaeldige Fluktuationer mellem Kernepartiklerne stadigvsk vaere Mulighed for, a t en af Partiklerne paa Kernens Overflade vil kunne faa den for en Lersrivelse nerdvendige Energi. Dette vil dog i Almindelighed h a v e en forholdsvis lang Tid, og netop derved opstaar en betydelig Sandsynlighed for, a t Energien forinden kan gaa bort i Form af Straaling med det Resultat, a t alle Partiklerne maa forblive bundne til den ved Sammensterdet dannede nye Kerne. Det Indblik i Forlerbet af Atomkerneomdannelser, sorn Studiet af Neutroners Jndfangning i tunge Kerner saaledes har givet os, har vist sig meget frugtbart for Forklaringen af mange for alle Atomkerneomdannelser karakteristiske Forhold. Naar to Atomkerner st0der sammen, vil de nemlig, saasnart som en Berming er opnaaet, og den staerke Vekselvirkning mellem Kernedelene har gjort sig gael-
Nyere Undersogelser over Atomkemernes Omdannelser.
9
dende, forene sig til en ny Kerne, hvis Levetid i Almindelighed vil vsre overordentlig lang sammenlignet med de Tider, som Kernerne vilde bruge til frit a t passere igennem hinanden. Slutresultatet af Sammenstsdet vil derfor, ganske ligesom ved Neutronindfangningen, bero paa en saa at sige fri Konkurrence mellem alle de Lssrivelsesog Straalingsprocesser, som den nydannede Atomkerne kan undergaa ved den tilstedevsrende Energi. Disse Forestfinger giver ikke alene en umiddelbar Forklaring paa den overordentlige Lethed, hvormed Atomkerner reagerer med hverandre ved Semmenstsd, og paa den iagttagne store Mangfoldighed i Reaktionernes Forlsb, men har tillige aabnet Mulighed for ved Betragtninger, velkendte fra andre Omraader af Fysikken, at vinde et nsrmere Indblik i de Forhold, der er bestemmende for den relative Hyppighed af de forskellige Kernereaktioner. Fremfor alt har Analogier hentet fra Varmelsren vist sig meget frugtbare for Forklaringen af vigtige Egenskaber hos de energirige Kerner, der optrsder sorn Mellemprodukt ved Atomkerneomdannelser. 3. E n e r g i r i g e At o m k e r n e r s +Te m p e r a t u r ({. Energiens Fordeling mellem Partiklerne i en Kerne, dannet ved Sammensterd mellem to Atomkerner, leder straks Tanken hen paa Varmeenergiens Fordeling mellem et fast Legemes eller en Vsdskes Molekyler, og vi fmes derfor naturligt til at sammenligne Neutronlssrivelse og Straalingsudsendelse fra energirigeAtomkerner med s s d vanlige Legemers Fordampning og Varmestraaling. Vel er de Lssrivelsesenergier og Straalingskvanter, sorn det ved Kerneprocesserne drejer sig om, mange Gange stmre end den Energi, som krsves til Lssrivelsen af et Molekyle fra en Vsdske, eller som indeholdes i de Kvanter, hvoraf et sort Legemes Udstraaling under ssdvanlige Forhold bestaar, men til Gengsld er de Temperaturer, der er Tale om for en ved Sammenstod dannet Atomkerne, uhyre store i Forhold ti1 dem, vi under almindelige Omstsndigheder har med at gerre. Maalt i den ssdvanlige Skala vil de Temperaturer, som det ved Atomkerneprocesserne drejer sig om, b e l ~ b esig til Milliarder af Grader og er saaledes omkring tusind Gange h ~ j e r eend selv de Varmegrader vi finder i Solens Indre. Ganske vist har, som man i de sidste Aar har erkendt, Solens enorme Varmeudsendelse netop sin Kilde i Atomkerneomdannelser, hvorved Heliumkerner opbygges af
10
N. Bohr:
Protoner under Udsendelse af positivt ladede Elektroner. For disse Processer gslder imidlertid ssrlige Forhold, og for a t forstaa, hvordan de tungeste Grundstoffer er blevet til, maa vi t s n k e os, a t der engang i Verdensrummet har v s r e t Steder, hvor Temperaturen virkelig har naaet den ovennsvnte svimlende Hsjde. Ved saadanne Temperaturer kan naturligvis de ssdvanlige Stoffer slet ikke bestaa, ja, vi ved jo endda, hvordan allerede i Solen Atomerne selv er adskilt i deres Bestanddele. Kernestoffets efter ssdvanlige Maalestok uhyre store Tsthed bevirker imidlertid, som vi straks skal se, at Atomkernerne under deres Omdannelser, betragtet i rette Perspektiv, slet ikke skal sammenlignes med s t s r k t opvarmede Legemer, men snarere med Legemer ved de laveste Temperaturer, vi i Laboratorierne kan frembringe. For a t bedsmme disse Forhold maa vi se lidt nsrmere paa Stsrrelsen af den Energi hos Atomkernerne, der skal sammenlignes med Varmeenergien, og paa Arten af de indre Kernebevsgelser, hvorpaa den er fordelt. Den Energi, vi her har med a t gsre, hidrarer dols fra de sammenstsdende Kerners Bevsgelsesenergi, dels fra den Bindingsenergi, der bliver fri ved Kernernes Forening. Denne sidste Energi kan v s r e meget forskellig for forskellige Kerner, men som Fslge af den under Omtalen af Kernernes ,%3male-Radioaktivitet allerede nsvnte Balance mellem stabile Atomkerners Ladning og Masse vil for enhver Kerne Bindingsenergien v s r e omtrent ens for e n Neutron og for en Proton. Denne Bindingsenergi, der i det hele og store aftager j s v n t med voksende Nucleontal, ligger for lettere Kerner omkring 8 Millioner og for de tungeste Kerner omkring 6 Millioner Elektronvolt ; som Betegnelsen antyder, forstaar man ved en Elektronvolt (EV) den Energi, der modtages eller afgives af en Elektron, naar den gennemlsber et SpEndingsfald paa 1 Volt. Ti1 Sammenligning kan nsvnes, a t den Energi, der krsves ti1 a t fjerne en af de lssest bundne Elektroner fra et Atom, er ca. 10 EV, samt a t Fjernelsen af de fastest bundne Elektroner i de tungeste Atomer krsver ca. 100.000 EV. Medens Elektronerne i fsrste Tilnsrmelse bevsger sig uafhsngigt af hverandre i det Atomkernen omgivende Kraftfelt, og man derfor for hver enkelt Elektron i Atomet kan tale om en ved bestemte Kvantetal karakteriseret Bindingstilstand, ligger Forholdene ganske anderledes for Kernen, hvor Partiklernes s t s r k e Vekselvirkning udelukker enhver Mulighed for a t skelne mel-
Nyere Unders0gelser over Atomkernernes Omdannelser.
11
lem de enkelte Nucleoners Bindingsmaade. I Modsstning til et Atom, hvor enhver mulig Energiforugelse svarer til en Bndring af Bindingstilstanden for en eller eventuelt flere Elektroners Vedkommende, vil en Kernes Energiindhold v s r e fordelt paa oscillerende Bevaegelser, hvori samtlige Nucleoner tager Del. En energirig Atomkernes indre Bevsgelser beherskes af Kernestoffets Sammenhaengskrsfter, og ti1 Trods for disse Kraefters overordentlige Sterrrelse i Sammenligning med Sammenhaengskrsfterne for ssdvanlige Legemer kan vi paa ganske lignende Maade som for en Vsdskedraabe tale om en Overfladespsnding, der bestemmer Atomkernernes Form og Bevsgelsesmuligheder. Atomkernens oscillerende Bevsgelser svarer saaledes noje ti1 en Vsdskedraabes Svingninger om Kugleformen under Overfladespsndingens Indflydelse, blot vil Svingningstiderne for Kerneoscillationerne paa Grund af den store Sammenhsngskraft og Kernernes ringe Storrelse v s r e meget smaa, selv i Forhold ti1 Omlerbstiderne for Atomelektronerne. De ti1 Oscillationerne svarende, med Svingningstiden omvendt proportionale Energikvanter vil derfor vaere meget store, og for middeltunge Kerner vil selv de mindste Kvanter ligge omkring 1 Million Elektronvolt (MEV). E n Atomkerne med et Energiindhold paa noglo faa Millioner Elektronvolt vil folgelig have skarpt adskilte stationaere Tilstande, ligesom et Atom med tilsvarende lavere Energi. Med stigende Energiindhold vil Afstanden imellem Energiniveauerne imidlertid for Kernerne aftage langt hurtigere end for Atomerne. Svarende ti1 det hastigt voksende Antal mulige Kombinationer af de stark sammenkoblede Kerneoscillationer, vil Energiniveauerne nemlig hurtig rykke tst sammen, og ved Energier af samme Storrelsesorden som Bindingsenergien for en Neutron vil Energiniveauernes Afstand for tungere Kerner kun belobe sig ti1 nogle faa Elektronvolt. Saasnart Energien overskrider Neutronbindingsenergien, begynder endvidere Niveauernes Bredde a t tiltage med det Resultat, a t de flyder fuldstsndigt sammen, naar Varmeenergien blot overstiger Bindingsenergien med ca. 1 MEV. Tilstedevaerelsen af et kontinuert Energiomraade over denne Grsnse er netop ogsaa Betingelsen for, a t t o Kerner ved Sammenstud altid vil kunne forenes, naar blot Varmeenergien af den nydannede Kerne bliver tilstrskkelig stor. Naar vi nu vender tilbage ti1 Sperrgsmaalet om den Temperatur, der maa tilskrives de ved Sammenstud mellem Atomkerner dannede
12
N. Bohr:
energirige nye Kerner, faar vi Brug for Betragtninger af ganske samme Art som de, der i de ferrste Aar efter Virkningskvantets Opdagelse ledte til Opklaring af den indtil da uforstaaelige Maade, hvorpaa de ssdvanlige Legemers Varmefylde varierer med Temperaturen. Det, vi her lsrte, var jo, a t Varmeenergien kun vil v s r e ligelig fordelt paa de enkelte Svingninger, hvori et Legemes indre Bevsgelse kan oplerses, saalsnge de selv ti1 de hurtigste Svingninger svarende Energikvanter er smaa i Forhold ti1 den med Temperaturen proportionale Energivsrdi, som efter den simple mekaniske Varmeteori i Middel skulde falde paa hver enkelt Svingning. Saa m a r t dette ikke er Tilfsldet, vil alle de Svingninger, hvis Kvanter er sterrre end denne Vsrdi, i Middel faa en langt mindre Energi, og under en vis, for hvert Stof karakteristisk Temperatur vil derfor Legemets Varmefylde, i Stedet for a t v s r e konstant, aftage med faldende Temperatur og forsvinde helt ved det absolute Nulpunkt. For en middeltung Atomkerne indeholdende ca. 100 Nucleoner vilde efter de ssdvanlige mekaniske Forestillinger Energien v s r e ligeligt fordelt paa ca. 300 Svingninger, og for et samlet Energiindhold paa omkring 10 MEV vilde derfor enhver af disse i Middel kun faa en Energi paa kun ca. 30.000 EV. Da alle de til Kerneoscillationerne svarende Kvanter er vssentlig sterrre, kan der imidlertid slet ikke blive Tale om en saadan ligelig Energifordeling, men i Lighed med de Forhold, der g0r sig gddende i ssdvanlige Legemer ved meget lave Temperaturer, vil Kernens Varmeenergi nssten udelukkende optages af et Faatal af de langsomste Svingninger. Efter den ssdvanlige Definition paa et Legemes Temperatur bestemmes dennes absolute Stmrelse ved den gennemsnitlige Bevsgelsesenergi for Molekylerne i en Luftart, der befinder sig i Varmeligev s g t med Legemet. Denne Energi, der for en Temperatur paa 10.000 Grader belaber sig ti1 ca. 1 EV, vil vi i det ferlgende kort betegne som ))Temperaturenergienc. Beregnet i nerje Tilslutning til de velkendte Teorier for Varmefyldens Bndring ved lave Temperaturer vil, for en middeltung Atomkerne med en Varmeenergi paa, 10 MEV, Temperaturenergien blive omtrent 1 MEV. Med voksende Energiindhold vil Kernens Temperatur kun stige forholdsvis langsomt, fordi Energien fordeles paa et stadig starre Antal Svingninger, og selv for et Energiindhold paa 100 MEV vil Kernens Temperaturenergi kun v s r e nogle faa Millioner Elektronvolt. Til Trods for de enorme
Nyere Undersc5gelser over Atomkernernes Omdannelser.
13
Tal, hvormed Kernetemperaturerne udtrykkes i den ssdvanlige Skala, svarer derfor, som ovenfor bemzerket, Kernernes termiske Egenskaber til de szedvanlige Legemers ved meget lave Temperaturer, ja endda saa lave, a t ma godt som alle Stoffer for lsngst vilde have antaget den faste Tilstandsform. I de seneste Am har vi imidlertid hos fortaettet Helium, der selv ved de lavest opnaaelige Temperaturer bevarer Vaedsketilstandens Egenskaber, fundet en i mange Henseen,der vidtgaaende Analogi ti1 Kernestoffet.
4. A t o m ke r n e r s ))Ford a m p n i n g (( o g 1) V a r m e s t r a a 1i n g G. Vaerdien af a t indferre Begreber hentet fra Varmelaeren til a t beskrive energirige Atomkerners Egenskaber trzeder szerlig klart frem, naar vi gaar over til i Enkeltheder a t betragte den allerede antydede Lighed mellem Kernernes Udsendelse af Partikler og elektromagnetisk Straaling og szedvanlige Legemers Fordampning og Varmestraaling. Baggrunden for denne Sammenligning er for Partikeludsendelsens Vedkommende givet ved, a t der til Overvindelsen af Nabopartiklernes Tiltraekning krzeves et Lersrivelsesarbejde, der er langt stmre end Partiklernes gennemsnitlige Bevsgelsesenergi, og derfor ganske ligesom Fordampning fra en Vzedske forlanger en tilfaeldig Koncentration af Energien paa en Partikel ved Overfladen. Hvad Kernernes Straaling angaar, beror Ligheden med Varmestraalingen fra almindelige Legemer simpelthen derpaa, a t det i begge Tilfdde drejer sig om en Udstraaling i Form af Kvanter, der hver i s m er smaa i Forhold til hele Energiindholdet. E n meget lsrerig Analogi til Neutronlersrivelse fra en energirig Atomkerne finder vi i de smukke Forserg over Kvikserlvdraabers Fordampning, som Professor Martin Knudsen udferrte for 25 Aar siden i Forbindelse med sine grundlsggende Undersragelser over Luftarters Egenskaber ved lave Tryk. Som bekendt, viste Prof. Knudsen ved disse Forsag, a t det Antal Molekyler, der i given Tid forlader et Fladeelement af en ren Kvikserlvoverflade, netop er lige saa stort som det Antal Molekyler, der i den betragtede Tid fra en Beholder med m s t t e t Kvikserlvdamp ved samme Temperatur vil strermme ud i et lufttomt Rum gennem en Aabning paa Strarrelse med Fladeelementet , naar blot dettes Dimensioner er smaa i Forhold til den frie Middelvejhngde for Molekylerne i Damprummet. Da en Vedske, der befinder sig i Ligevaegt med sin mettede Damp,
14
S . Bohr:
indenfor ethvert givet Tidsrum i Middel maa afgive det samme Antal Molekyler gennem Fordampning, som den igen indfanger fra Dampen, kunde Prof. Knudsen derfor af sin Iagttagelse drage den vigtige Slutning, a t der ved en ren Kviksalvoverflade ingen Refleksion af Dampmolekyler finder Sted, men a t derimod ethvert Molekyle, der rammer Overfladen, straks optages i Vsdsketilstanden og forst kan undslippe fra dette ved en senere, af Sammenstadet uafhaengig, elementsr Fordampningsproces. Ted Sammenstad mellem Neutroner og tungere Atomkerner mader vi netop, som vi har set, ganske lignende Forhold, og ved Hjaelp af den for Kviksalvdraaber gsldende simple Forbindelsc mellem maksimal Fordanipningshastighed og Damptaethed er det derfar muligt a t beregne Sandsynligheden for, a t der indenfor et givet Tidsrum vil lasrives en Neutron fra en energirig Kerne. Indenfor vore eksperimentelle Muligheder kan der naturligvis ikke v a r e Tale om a t virkeliggare en Ligevsgtstilstand mellem energirige Btomkerner og en Neutronatmosfaere, men ikke desto mindre kan man efter velkendte Principper, udfra vort Kendskab ti1 Kernestoffets T s t h e d og Starrelsen af Losrivelsesarbejdet, beregne den Taethed, soni en saadan Neutronatniosfsre niaatte have for enhver given Kernetemperatur. Selv om Sammenligningen mellem Neutronlasrivelse og Fordampning kan forfalges meget vidt, er der dog en Grsnse for Gyldigheden af saa simple Betragtninger som de antydede. Trods det relativt store Energiindhold af de ved Atomkernesammenstad dannede nye Kerner vil nemlig ved mange Atomkerneomdannelser Lasrivelsesarbejdet for en enkelt Neutron vaere af samnie Starrelsesorden som Kernens Varmeenergi, og i saadanne Tilfslde vil derfor Ternperaturen af den efter Lmrivelsen tiloversblevne Kerne vaere vssentlig mindre end den oprindelige Kernes. Derimod er der, selv for en lille Vaedskedraabe, selvfalgelig ikke Tale om nogen Temperaturaendring ved en elementsr Fordampningsproces, fordi Draabens hele Varmeenergi praktisk talt er uendelig stor i Forhold ti1 Lasrivelsesarbejdet for e t Molekyle. For Kerner dannede ved Sammenstod med Neutroner med Bevaegelsesenergier paa nogle faa Millioner Elektronvolt komnier den Omstaendighed til, a t den tiloversblevne Kernes Energi falder indenfor det Omraade, hvor Energiniveauerne endnu er skarpt adskilte. I saadanne Tilfaelde maa vi derfor ved najagtig Beskrivelse benytte mere eksakte statistiske Betragtninger ; ja, som vi skal se, maa ved Sammensterd med de allerlangsomste Neutroner endda typiske kvantemekaniske Metoder bringes i Anvendelse.
Nyere Gnders0gelser over Atomkernernes Omdannelser.
15
J o stsrre Kernernes Energiindhold er, desto nujere gslder imidlertid simple termodynamiske Analogier, og for Energier, der er tilstrskkelig store ti1 a t tillade Losrivelsen af flere Kernepartikler, t r s der Ligheden med en Vsdskedraabes Fordampning ssrlig tydeligt frem. Saaledes har det vist sig, a t et Sammenstod mellem en tungere Atomkerne og en Neutron med en Bevsgelsesenergi paa over 10 MEV i Stedet for a t fure til en Neutronindfangning ofte kan bevirke, a t ikke blot een, men flere Neutroner forlader Kernen. Da dette niaa antages a t finde Sted ved en Rskke paa hinanden fulgende uaf-
Pig. 1 .
hsngige Losrivelsesprocesser, vil i Lighed med Molekyler, der fordamper fra en Vsdskedraabe, enhver af de ved disse Processer efterhaanden undslippende Neutroner i Middel have en Bevsgelsesenergi, der svarer ti1 et Luftmolekyles ved den paagsldende Kernetemperatur. Selv efter et Sammenstsd mellem en Atomkerne og en Neutron med en Bevsgelsesenergi paa 100 MEV vil Energien sf hver af de undslippende Neutroner derfor kun belobe sig til nogle faa Millioner Elektronvolt, og i et saadant Tilfslde maa vi derfor vente, a t et stort Antal Partikler efter hinanden vil forlade Kernen. Overmaade interessante Eksempler paa en saadan fremskreden Fordampning af Atomkerner har man i de sidste Aar fundet ved paa hrajtliggende Steder a t udsstte Fotografiplader med ssrlig tykke Emulsionslag for den kosmiske Straaling. Som det ses paa det i Fig. 1 reproducerede, s t s r k t forstorrede Fotografi, der er optaget af Blau og Wambacher, iagttages under saadanne Omstsndigheder Kernessnderdelinger, der viser sig ved et Antal retlinede Baner udstraalende stjerneformet fra samme Punkt. Banesporene maa antages a t hidrore fra Protoner, og en Optdling af de i Emulsionen langs Sporene fremkaldte Korn viser, a t Protonernes Bevaegelsesenergier gennemsnitlig belober sig ti1 nogle faa Millioiier Elektronvolt. Derimod
16
N. Bohr:
vil de Neutroner, der ogsaa maa antages at v s r e udsendt i stort Antal fra den fordampende Kerne, naturligvis ikke efterlade sig noget Spor paa Fotografipladen. Sammenligningen med en Vsdskedraabes Fordampning har ogsaa vist sig meget frugtbar ved Forstaaelsen af mange Forhold vedrsrende bsrivelsen af elektrisk ladede Partikler fra energirige Atomkerner. Der er imidlertid forskellige Omstsndigheder, som ssrlig maa tages i Betragtning for ladede Paxtiklers Vedkommende. Farrst og fremmest vil der efter Kvantemekanikken bestaa en vis Sandsynlighed for, at en saadan Partikel kan undslippe fra en Atomkerne, selv om den Energi, hvormed den udsendes, er mindre end den, der efter ssdvanlige mekaniske Forestillinger vilde krsves for at bringe den tilbage til Kernen under Overvindelse af dennes Frastsdning. Det er jo netop paa denne Omstsndighed, at Muligheden for a-Straalers Udsendelse fra naturlige radioaktive Stoffer beror. Middellevetiden for radioaktive Atomkerner i Normaltilstanden er imidlertid uhyre lang i Forhold til de Tidsrum, indenfor hvilke de konkwrerende Lrasrivelses- og Straalingsprocesser, som bestemmer Forlsbet af Omdannelserne af de ved Sammenstrad frembragte energirige Atomkerner, finder Sted. For a t en Udsendelse af ladede Partikler som a-Straaler eller Protoner skal grare sig gsldende i Konkurrencen, krsves ligesom til Udsendelsen af Neutroner en til Fordampning svarende Lmrivelse af Partiklerne fra Kernens Overflade. For ladede Partikler er der blot den Forskel, at de, efter a t v s r e kommet 10s fra’Kernen ved Varmeenergiens Hjslp, yderligere vil accelereres paa Grund af den elektriske Frastgdning og sluttelig opnaa en Bevsgelsesenergi, der ofte kan v s r e langt strarre end den til Kernetemperaturen svarende Molekylenergi. Da den Energi, der krsves for at fjerne en Proton til store Afstande fra Kernen, som allerede nsvnt, er omtrent den samme som Neutronbindingsenergien, vil derfor under saadanne Omstsndigheder det til Fordampningsvarmen svarende b s rivelsesarbejde vsre langt stmre for ladede Partikler end for Neutroner. Dette forklarer, at Proton- og a-Straaleudsendelsen, der ved Omdannelse af lettere Atomkerner ofte kan v s r e overvejende, gradvis forsvinder i Forhold til Neutronudsendelsen, naar vi gaar over til tungere Kerner. Under forngden Iagttagelse af alle ssrlige Omstsndigheder kan termodynamiske Analogier paa lsrerig Maade ogsaa anvendes til
17
Nyere Undersegelser over Atomkememes Omdannelser.
Klarlsggelsen af de Forhold, der betinger Udsendelsen af elektromagnetisk Straaling fra energirige Atomkerner. Som allerede antydet, drejer det sig her om en vidtgaaende Lighed med Varmestraalingen fra ssdvanlige Legemer, der beror paa, a t Energien af de ved Samniensterd mellem Atomkerner dannede n3-e Kerner er fordelt paa svingende Bevsgelser af Kernestoffet, hvis tilsvarende Energikvanter er smaa i Forhold ti1 hele Kernens Energiindhold. Straalingen fra, saadanne Kerner vil derfor bestaa a€ e t Antal Straalingskvanter, hvis Energi i Middel vil v s r e omtrent den samme som for de Kvanter, hvoraf Varmestraalingen efter Plancks Teori vilde bestaa ved de paagsldende Temperaturer. Da Kernetemperaturen jo, som omtalt, kun vil sndre sig forholdsvis lidt, selv om Kernens Energiindhold stiger s t s r k t , vil Middelenergien af de udsendte Straalingskvanter i et stort Energiomraade derfor stadig v s r e af samme Sterrrelsesorden og ligge omkring 1 MEV. Svarende til den Maade, hvorpaa Intensiteten af et Legemes Varmestraaling afhsnger af Temperaturen, vil ligeledes det Antal Straalingskvanter, der i en given Tid udsendes fra en energirig Atomkerne, kun zendre sig forholdsvis lidt, selv om Energiindholdet stiger betydeligt . Disse Forhold er af stmste Betydning for Bedermmelsen af den Konkurrence mellem Lersrivelse af P a r t i l e r og Udsendelse af elektromagnetisk Straaling, hvorpaa Forlerbet af Sammenstgd mellem Atomkerner beror. I s m forstaar vi umiddelbart, a t Sandsynligheden for Indfangning af en Neutron ved Sammensterd med en tungere Atonikerne aftager meget s t s r k t med voksende Neutronenergi. Sandsynligheden for, at der i en given Tid undslipper en Neutron fra den nydannede Kerne, vil nemlig vokse meget hurtigt med Kernetemperaturen, svarende ti1 Fordampningshsstighedens velkendte raske Stigning med Temperaturen for szedvanlige Vsdsker. Derimod vil Sandsynligheden for Udsendelse af Straalingskvanter fra Kernen indenfor den samme Tid tiltage langt mindre, i Lighed med Varmestraalingens mindre stsrke Af hsngighed af Temperaturen. Dette forklarer, a t Sandsynligheden for Neutronindfangning i tungere Atomkerner ban vsre stor for Neutronenergier under 1 MEV, medens den kun er ringe, saa snart Neutronenergien blot kommer op paa nogle faa Millioner Elektronvolt. Den Omstsndighed, a t Kernetemperatiiren for samme Energiindhold aftager med voksende Nucleontal , forklarer endvidere, a t Sandsynligheden for Indfangning af Neutroner med 2
18
N. Bohr:
samme Euergi er h n g t sterrre ved Sammensterd med tnngere end med lettere Atomkerner.
5. S e l e k t i v e A t o m k e r n e r e a k t i o n e r . Den forholdsvis jsvne Maade, hvorpaa Atomkernernes Reaktioner i det store og hele forandrer sig med Nucleontallet, beror paa, a t den ved Sammensterdet dannede Kernes Varmeenergi som oftest, falder indenfor det kontinuerte Energiomraade. Saasnart dette ikke er Tilfseldet, merder vi typbk selektive Fsnomener, idet den ti1 Reaktion krsvede midlertidige Forening af Kerne og Partikel kun kan finde Sted, naar den sterdende Partikel har en Energi, der netop svarer til en af dette Mellemprodukts odskilte Energiniveauer. For varierende Partikelenergi vil derfor Udbyttet vise en Rskke skarpe Maksima, hvis Beliggenhed kan v s r e ganske forskellig selv for Kerner med omtrent samme Masse- og Ladningstal. Saadanne selektive Kernereaktioner er saerlig hyppige for lettere Atomkerner, hvor Grsnsen for det kontinuerte Omraade ofte kan ligge adskiUige Millioner Elektronvolt over den Bindingsenergi, der frigerres ved den sterdende Partikels Forening med Kernen. Tidligere tsnkte man sig, a t Kernepartiklerne bevzegede sig tilnsrmelsesvis uafhsngigt af hverandre ligesom Elektronerne i et Atom, og antog derfor, a t disse Reaktionsmaksima svarede til forskellige Maader, hvorpaa den sterdende Partikel kunde bindes i Kernens indre Kraftfelt. Nyere Undersergelser over de selektive Kernereaktioner har imidlertid netop vist, at disse er ganske uafhsngige af den Sammensterdsproces, hvorved Mellemtilstanden dannes. Saaledes har man fundet, a t Reaktioner, der indledes ved Sammenstsd med forskelligartede Partikler og forskellige Kerner, har ganske samme Reaktionsmaksima, naar blot Mellemprodukterne har samme Ladning og samme Massetal. Medens vi i Almindelighed ved Sammenstad mellem Neutroner og tungere Kerner har at glare med Reaktioner, hvis Udbytte sndrer sig j s v n t med Neutronens Energi, msder vi imidlertid typiske selektive Fsnomener , naar Neutronernes Bevsegelsesenergi kun udgerr nogle faa Elektronvolt De i mange Henseender laererige Oplysninger om olangsommecc Neutroners Reaktioner med Atomkerner skyldes i s m Fermi, der ferrst paaviste, hvorledes de ))hurtiger, fra Atomkerneomdannelser stammende Neutroner ved at gaa igennem brintholdige Stoffer som Vand eller Paraffin under Sammenstgdene med Proto-
.
19
Nyere Undersngelser over Atomkernernes Omdsnnelser.
nerne efterhaanden taber Energi, indtil deres Hastigheder slutteligt synker helt ned til Brintatomers Hastighed ved saedvanlige Temperaturer. Isaer viser det sig, at Neutroner med saadanne atermiskect Hastigheder har en overordentlig stor Sandsynlighed for a t blive indfanget i visse tungere Atomkerner under Dannelse af nye radioaktive Isotoper, medens andre Atomkerner med naesten samme Nucleontal ikke viser nogen ssrlig Indfangningseffokt. Betingelsen for en saadan Effekt, er jo, at der netop ligger et Energiniveau af den nydannede Kerne indenfor et meget snsvert Energiomraade paa ca. EV’s Bredde umiddelbart over Neutronbindingsenergien; at dette indtrsffer for et ikke helt ringe Antal tunge At,omkerner skyldes overhovedet kun, a t Middelafstanden mellem Energiniveauerne for saadanne Atomkerner i det betragtede Energiomraade blot er nogle faa Elektronvolt. Har vi a t gme med et saadant Sammentrsf, mgder vi ti1 Gengald ganske saerlig gunstige Forhold for Neutroners Indfangning. F o r s ~ gover langsomme Neutroners Absorption i forskellige Grundstoffer viser saaledes, at det Antal Neutroner, der indfanges af Atomkernerne i visse Stoffer, endog kan blive mange Tusinde Gange sterrre end Antallet af de Sammenst~d,man efter simple mekaniske Forestillinger maatte vente vilde finde Sted mellem Kerner og Neutroner. Dette i fmste Wjeblik saa overraskende Fsnomen beror paa, a t ssdvanlige mekaniske Billeder bun kan anvendes til Beskrivelse af Sammenst0dene, saalsnge den til Neutronens Bevsgelse svarende de Broglie B~lgelsngdeer lille i Forhold til Kernens Dimensioner eller hgjst af samme Stmrelsesorden. Medens dette endnu er Tilfsldet for Neutroner med en Bevsgelsesenergi paa omkring 1 MEV, er Bralgelsngden for termiske Neutroner med Energier paa en Brgkdel af en Elektronvolt over 1000 Xange s t ~ r r end e Kernens Diameter. Under saadanne Omstsndigheder er det derfor ganske udelukket a t anvende nogen Forestilling om en Bane i ssdvanlig mekanisk Forstand for en Neutron i Narheden af Kernen. Sandsynligheden for Neutronens Optagelse i Kernen vil derimod vsre et typisk kvanteniekanisk Resonansproblem, der minder om akustisk Resonans, ved hvilken, som bekendt, ikke Resonatorens ydre Dimensioner, men alene Frekvensen og Dsmpningen af dens Egensvingninger er afgarrende. Helt bortset fra de saerlige kvantemekaniske Probiemer, som vi her merder, har vi ved langsomme Neutroners Indfangning i tunge 2.
20
N. Bohr:
Atomkerner a t gerre med e t ekstremt Tilfslde, hvor Straaling fra Mellemtilstanden er langt mere sandsynlig end Partikellersrivelse. Med voksende Energi forskydes imidlertid Balancen mellem de konkurrerende Processer hurtigt, og naar Mellemtilstandens Energi blot er 1 MEV strarre end Neutronbindingsenergien, er selv for tungere Kerner Straalingssandsynligheden betydelig mindre end Sandsynligheden for Neutronlersrivelse. Ved Omdannelsen af lettere Atomkerner er Straalingens Betydning n m t e n altid forsvindende, saaledes at der kun bliver Tale om en Konkurrence mellem Udsendelse af forskellige Slags Partikler fra Mellemproduktet. E t interessant Undtagelsestilfalde, hvor Straalingen spiller en vaesentlig Rolle, mrader vi imidlertid ved Bombardement af visse lette Atomkerner nied kunstigt accelererede Protoner. Den Omstandighed, a t det har v m e t muligt a t opnaa Kerneomda nnelser ved Protonenergier paa betydelig mindre end 1 MEV, beror j o paa, at der efter Kvantemekanikken, som allerede berrart, er en vis, omend oftest ringe Sandsynlighed for, at en ladet Partikel kan optages i en Kerne, selv om Frastradningen efter de ssdvanlige mekaniske Forestillinger vilde hindre Partiklen i at naa ind ti1 Kernens Overflade. Da samtidig ogsaa Sandsynligheden for, a t en Proton igen kan undslippe fra den nydannede Kerne, er ringe, kan derfor i swlige Tilfslde, hvor ingen anden ladet eller uladet Partikel har stc3rre Mulighed for a t undslippe fra Mellemproduktet, Straaling gore sig galdende, med det Resultat, at Protonen indfanges ved Sammenstradet. Da endvidere her Afstanden mellem Mellemtilstandens Energiniveauer er langt strarre end ved Neutronbombardement af tunge Kerner, har man hos et Antal lettere Kerner iagttaget udpraeget, selektive Indfangningsprocesser, svarende ti1 Protonenergier paa nogle Hundrede Tusinde Elektronvolt.
6. D e t u n g e s t e A t o m k e r n e r s S p a l t n i n g . I de senere Aar er der udfrart et stort Antal ITndersragelser over Atomkerneomdannelser ved Neutronbombardement, hvorved vi har l s r t mange nye radioaktive Isotoper sf nssten alle Grundstoffer a t kende. I Overensstemmelse med de i det foregaaende udviklede Betregtninger har det for de tungere dtomkerners Vedkommende ved disse Omdannelser altid drejet sig enten om Indfangning eller om Udjagning af en Neutron fra Kernen, alt eftersom langsomme eller hurtige Neutroner blev benyttet ti1 Bonibardementet. Ved de aller-
Nyere Vndersegelser over Atomkernernes Omdannelser.
21
tungeste Grundstoffer, Uran og Thorium, gav Undersegelserne dog mere indviklede Resultater, hvis Tydning forvoldte de sterste Vanskeligheder, indtil Hahn og Strassmann i Begyndelsen af 1939 paaviste, at vi her har a.t gere med en helt ny Type af Kerneomdannelser, hvorved den tunge Atomkerne spaltes i t o omtrent lige store Dele med tilsvarende lavere Masse- og Ladningstal. Da for stabile Atomkerner Forholdet mellem Masse og Ladning er vssentlig sterre for tungere end for lettere Kerner, vil de ved Spaltningen opstaaede nye Kerner v s r e i hej Grad instabile og i den efterfelgende Tid
Fig. 2.
hver issr undergaa en Rskke radioaktive Omdannelser under Elektronudsendelse. Det er netop paa denne Omstandighed, a t Fsnomenets i den ferste Tid saa forvirrende Righoldighed beror. Ved Spaltningen af de tungeste Atomkerner frigeres der en Energi, der er langt sterre end den, som var kendt fra tidligere undersegte Atomkerneomdannelser. Som det snart blev paavist ved direkte Maalinger af de udslyngede Kerners Ioniserings- og Gennemtrsngningsevne, beleber Bevsgelsesenergien for hver af Delene sig ti1 omkring 100 MEV. Saadanne Maalinger optoges omtrent samtidig i mange forskellige Laboratorier, hvor de nye Opdagelser overalt tiltrak sig den sterste Opmsrksomhed. De ferste Forseg blev udfert af Frisch, der paa dette Tidspunkt arbejdede i Kebenhavn paa Universitetets Institut for teoretisk Fysik. Her, som andre Steder, lykkedes det ogsaa efterhaanden ved Hj a l p af den Wilsonske Taagekammermetode at optage Billeder af Banerne af de ved Uranspaltningen udslyngede Atomkerner. E t fornylig pa.a Instituttet optaget Fotografi er reproduceret i Fig. 2. Uranet, der udsattes for Neutronbombardementet, var anbragt som et tyndt Lag paa et Aluminiumfolie, udspsndt i det med Helium fyldte Taagekammer paa en Ramme, der ses midt paa Billedet. Medens de overalt pea Billedet forekommende
22
N. Bohr:
korte retlinede Banespor hidrsrer fra Sammenstsd mellem Heliumkerner og Neutroner, stammer de to intensivt ioniserede Banespor fra en Uranspaltning, ved hvilken de to Kernedele udslynges med store Energier i modsatte Retninger. Banerne viser tydeligt et Antal Forgreninger, der hidrsrer fra Sammenstsd med Heliumkerner, og hvis Hyppighed netop er betinget af Kernedelenes store elektriske Ladning. Vi skal dog ikke her gaa nsrmere ind paa saadanne Enkeltheder, hvis Studium har givet interessante nye Oplysninger om tunge, staerkt ladede Partiklers Bremsning og Spredning i Stoffer, men skal straks gaa over til at omtale, hvorledes selve Spaltningsprocessen simpelt kan forklares udfra de i det foregaaende udviklede almindelige Synspunkter. Ganske ligesom for de saedvanlige Atomkerneomdannelser, frembra@ ved Bombardement med Neutroner, maa vi antage, a t de omhandlede Processer forlsber paa den Maade, a t Neutronen fsrst optages i den ramte Kerne, og a t det endelige Resultat af Sammenstsdet derefter bestemmes ved en Konkurrence mellem de forskellige uaf haengige Straalings- og Ssnderdelingsprocesser, som den saaledes dannede energirige Kerne kan undergaa. Forskellen er blot, at vi her ved Ssnderdelingsprocesserne foruden med en Neutronlmrivelse ogsaa maa regne med en Spaltning af hele Kernen i to nasten lige store Dele. For Neutronlmrivelsen krsves, som omtalt, ligesom ved en Vsdskedraabes Fordampning, en Koncentration af Varmeenergien paa en Partikel ved Overfladen. Derimod krsver Spaltningen en Deformation af hele Kernen, der er tilstrskkelig stor til, at Overfladespandingen ikke lsngere kan tvinge den tilbage til Kugleformen, og Kernen derfor opdeles i to mindre Kerner, svaxende til en Vaedskedraabes Adskillelse i to Smaadraaber. Ved lettere Kerner d den Energi, der er nsdvendig for en saadan Deformation, vaere langt stsrre end Neutronbindingsenergien, men netop for de tungeste Kerner v i l de to Energier vare af samme Stsrrelsesorden. Her v i l nemlig, som fmst fremhaevet af Frisch og Meitner, de af Kernens store Ladning betingede stsrke elektriske Frastsdningskrsfter i vasentlig Grad modvirke Overfladespsndingens Indflydelse og derved betydeligt formindske det ti1 en kritisk Deformation k r a vede Energiforbrug. I fsrste Ojeblik kunde det maaske synes svaert a t forstaa, hvorledes den ved Sammenstsdet dannede Kernes Energi vil kunne om-
N y e r e Undersegelser over Atomkernernes Omdannelser.
23
formes paa en saa specie1 Maade, som en til Instabilitet af Kernen fsrende Deformation kraever. Vi maa imidlertid betaenke, a t det saavel ved Neutronlssrivelsen som ved Kernespaltningen drejer sig om rent tilfaldige Fluktuationer i Fordelingen af Kernens Varmeenergi paa mulige Bevaegelsesformer, der hver for sig er overordentlig lidt sandsynlige, og derfor kun kan gsre sig gsldende i Konkurrencen, naar der ingen lettere Adgang findes for Forbruget af Kernens Energi. Ligesom for de lettere Kerner viser det sig, som vi skal se, ogsaa for flere af de allertungeste Atomkerner, at Sammenstsd med langsomme Neutroner kun fsrer ti1 Neutronindfangning, for& Sandsynligheden for Straaling langt overstiger Sandsynligheden for enhver Form af Ssnderdeling. Med tiltagende Energiindhold af Kernen vil imidlertid Sandsynligheden for Ssnderdelingsprocesserne vokse meget staerkere end for Straalingsprocesserne og vil allerede vaere langt overvejende for Sammenstsd med Neutroner med en Bevaegelsesenergi paa omkring 1 MEV. I nsje Tilknytning til de Betragtninger, som vi har anstiUet for Neutronlssrivelsens Vedkommende, kan ogsaa Sandsynhgheden for, a t Spaltningen af en energirig Atomkerne finder Sted i en given Tid, bestemmes ved Hjslp af velkendte termodynamiske og statistiske Lovmassigheder. I Stedet for en Sammenligning med en Vaedskedraabes Fordampning drejer det sig blot her om en Analogi med kemiske Forbindelsers Dissociation. Som bekendt, maa man ved en saadan Dissociation i Almindelighed strengt skelne mellem den totale ved Molekylernes Smderdeling forbrugte eller vundne Energi, den saakaldte Dissociationsenergi, og den Energi, som maa v s r e til Stede i Molekylet for at indlede Ssnderdelingen, den saakaldte Aktiveringsenergi. Medens Dissociationsenergien er afgsrende for den kemiske Ligevagt, er det jo netop Aktiveringsenergien, der bestemmer Reaktionshastigheden. For Kernespaltningens Vedkommende har Dissociationsenergien for de tungeste Atomkerner en uhyre stor negativ Vsrdi paa nresten 200 MEV, medens Aktiveringsenergien, der svarer til den for den kritiske Deformation af Kernen kraevede minimale Energi, er positiv og for Uran og Thorium betydelig mindre end 10 MEV. Strengt taget vil der ogsaa for e t lavere Energiindhold, ja endda for Kernens Normaltilstand, efter Kvantemekanikken bestaa en vis Sandsynlighed for, a t en Spaltning af en Atomkerne kan finde Sted. Ligesom ved saedvanlige eksplosive kemiske Forbindelser vil
24
N. Bohr:
imidlertid Sandsynligheden for saadanne spontane Processer i Almindelighed v m e yderst ringe i Forhold ti1 de Sandsynligheder, som opnaas ved en til Antsndelse svarende kritisk Deformation af Atomkernen. Saasnart Kernens Energiindhold overstiger den til en saadan Deformation nerdvendige Energi, vil Sandsynligheden for, a t en Spaltning finder Sted indenfor en given Tid, vokse meget hurtigt med Energiindholdet og afhsiige af Kernetemperaturen paa en Maade, der nerje svarer ti1 monomolekulaxe kemiske Reaktioners Temperaturaf hsngighed. 7 . Atomkernespaltningernes n s r m e r e Forleb. Efter de foregaaende Betragtninger maa vi vente, a t den for Forlerbet af e t Sammensterd mellem en Neutron og en tung Atomkerne afgerrende Konkurrence mellem Straalings- og Sernderdelingsprocesserne paa simpel Maade vil v s r e bestemt af Forskellen mellem Neutronbindingsenergien og den kritiske Spaltningsenergi. Den ensartede Maade, hvorpaa Fordampnings- og Reaktionshastigheder varierer med Temperaturen, forklarer saaledes den Iagttagelse, a t Forholdet mellem Sandsynlighederne for Neutronlersrivelse og Kernespaltning for Kerneenergier, der ligger betydelig herjere end saavel Neutronbindingsenergien som den kritiske Spaltningsenergi, nsrmer sig en konstant, af Differensen mellem disse Vsrdier afhsngig Starrelse. For mindre Kerneenergier msder vi imidlertid, som vi skal se, Forhold, der er vssentlig forskellige, alt eftersom Neutronbindingsenergien er sterrre eller mindre end den kritiske Spaltningsenergi. For bedre a t kunne overse disse Forhold, skal vi dog farst lidt nsrmere betragte de forskellige med hinanden konkurrerende Maader, hvorpaa et Sammensterd mellem en Neutron og en tung Kerne kan forlabe. For dette Formaal er der paa Fig. 3 givet en skematisk Fremstilling af Processernes forskellige Stadier. Wverst paa Billedet er som Stadium A fremstillet Tilstanden umiddelbart far Sammenstadet. Medens den lille Cirkel med v e d f ~ j e tPi1 skal betegne den med mindre eller sterrre Hastighed ankommende Neutron, betegner den store Cirkel den tunge Kerne, der ferr Stadet jo vil v s r e i Normaltilstanden, hvad der er antydet ved, at denne Cirkel er tom. Som Stadium B er fremstillet den Mellemtilstand med forholdsvis lang Levetid, hvor Neutronen er optaget i Kernen, og den nydannede Kerne endnu ikke har afgivet noget af sin Energi. Kernens hGje
Nyere Undersmgelser over Atomkernernes Omdannelser.
25
Energitilstand er her antydet saavel ved Konturens uregelmsssige Form som ved Indholdets Skravering. Skraveringens vekslende T s t hed skal tillige erindre om, a t Varmeenergien ikke er ligelig fordelt, men undergaar stadige Fluktuationer paa de forskellige Steder a€ Kernen. Endelig er under C fremstillet, hvorledes Processens sidste
Fig. 3.
Stadium kan f o r l ~ b epaa tre forskellige Maader, hvis relative Sandsynligheder vil afhsnge af Mellemproduktets s t ~ r r eeller mindre Energiindhold, der igen er bestemt ved den s t ~ d e n d eNeutrons Bevsgelsesenergi. Lsngst ti1 venstre er ved Rskke I fremstillet et F o r l ~ b svarende , ti1 Neutronens endelige Indfangning. F r a oven og nedefter er antydet, hvordan Kernens Energi i et saadant Tilfslde gradvis bortgaar gennem Udsendelse af et Antal Straalingskvanter, indtil sluttelig den nye Kerne efterlades i Normaltilstanden. Den lille Stjerne midt i den tomme Cirkel skal niinde om, a t denne Kerne i Almindelighed vil v s r e radioaktiv og udsende en Elektron efter en vis Middellevetid, der er uhyre lang i Forhold ti1 de Tidsrum, der kommer i Betragtning ved Kernereaktionerne. Ved Rzkke I1 er fremstillet et For-
26
N. B o b :
lab, hvorunder en Neutron undslipper fra Kernen, og denne derefter, under Udsendelse af et eller flere Straalingskvanter, antager ganske den samme Tilstand som den Kerne, der i Stadium A oprindelig ramtes af Neutronen. Som vist paa det averste Billede i Rskken, skyldes Neutronudsendelsen en Koncentration af en betydelig Del af den hele Varmeenergi paa en enkelt Partikel ved Kernens Overflade. Dette er angivet saavel ved den t s t t e Skravering i et vilkaarlig valgt Kerneomraade til hajre som ved, a t den ovrige Del af Kernen er svagere skraveret end Tilstanden B. Som antydet ved Lsngden af den Pil, der er anbragt ved den lille Cirkel paa det nsste Billede, vil den udsendte Neutrons Hastighed i Almindelighed v s r e langt mindre end Hastigheden af den Neutron, der i Stadium A ramte Kernen. I det nederste Billede i Rskken er antydet, hvorledes den tiloversblevne Energi senere udsendes i Form af Straaling. Lsngst til hajre er endelig i Rskke I11 fremstillet et til en Kernespaltning svmende Forlab af Processens sidste Stadium. Det overste Billede i Rskken skal vise, hvorledes en saadan Spaltning indledes ved en Deforma.tion af Kernen, der er tilstrskkelig stor til, a t den elektriske Frast~dningmellem de lsngst bortliggende Dele kan holde Overfladespsndingens sammentrskkende Virkninger i Ligevsgt. Som antydet ved den forholdsvis svage Skravering, vil der til en saadan Deformation, ganske ligesom til den Energikoncentration, der er nadvendig for en Neutronudsendelse, medgaa en betydelig Del af Kernens hele Energiindhold. I det nsste Billede i Rskken er fremstillet en Tilstand, hvor Kernen allerede er spaltet, og hvor de 10srevne Dele pea Grund af Frastadningen har opnaaet store Hastigheder bort fra hinanden. I dette Billede er Skraveringen atter tsttere, fordi den betydelige Deformation, som hver af Delene i Lasrivelsesajeblikket vil have, under Overfladespsndingens Indflydelse hurtigt atter vil omdannes til indre Bevsgelsesenergi. De to fdgende Billeder i Rskke I11 illustrerer den meget interessante Iagttagelse, at der ved Kernespaltning udsendes et Antal Neutroner, gennemsnitlig to pr. Spaltning. 8om antydet i Billederne, maa dette Fsnomen - ganske ligesom Neutronlasrivelsen fremstillet paa de to f ~ r s t eBilleder i Rskke I1 - antages at hidrare fia tiLfsldige Energikoncentrationer ved de nye s t s r k t opvarmede Kerners Overflader. F0r vi gaar ind paa de vigtige Spargsmaal, som Iagttagelsen af denne Neutronl~srivelseved Kernespaltninger har rejst, skal vi
Nyere Undersegelser over Atomkernernes Omdannelser.
27
dog, for a t gwre 0 s fsrdige med Omtalen af den skematiske Fremstilling paa Fig. 3, endnu blot nsvne, a t det sidste Billede i Raekke I11 fremstiller, hvorledes den Energi, som Kernerne endnu her tilbage efter Neutronlr?srivelsen, bortgaar sorn Straalingskvanter. De nye Kerner vil, som allerede nsvnt, vere s t s r k t radioaktive og vil, som angivet ved et Antal Stjerner indenfor de tomme Cirkler, i Lwbet af den efterfwlgende Tid hver i s m undergaa en Rskke Omdannelser under Elektronudsendelse, indtil det for stabile Kerner kraevede Forhold mellem Masse og Ladning er opnaaet. 8. Spwrgsmaalet om A t o m e n e r g i e n s U d v i n d i n g . Den store Interesse, der knytter sig ti1 Udsendelsen af Neutroner ved Kernespaltninger, beror paa, a t der derved aabner sig helt nye Udsigter for en mulig Udvinding af den store Energi, der findes i de tunge Atomkerner og hvis Tilstedevsrelse har vsret erkendt lige siden Opdagelsen af de naturlige radioaktive Stoffer. Det er jo Hart, at der bestaar den Mulighed, at de ved en Spaltningsproces udsendte Neutroner ved Sammensterd med andre tunge Kerner kan indlede nye Spaltninger. Da der endvidere ved hver Spaltning i Middel udsendes mere end een Neutron, kunde man derfor vente, at der under egnede Omstsndigheder, ved en lavineagtig Forragelse af Spaltningsprocesserne, vil kunne finde en eksplosionslignende Energifrigivelse Sted. Naar man tsnker paa, at det ved de kraftigste kemiske Reaktioner, som man har a t gme med hos de ssdvanlige eksplosive Stoffer, kun drejer sig om en Energifrigivelse af hr?jst nogle faa Elektronvolt pr. Molekyle, medens der ved Spaltningen af en tung Atomkerne frigives naesten 200 Millioner Elektronvolt, forstaar man, hvilke forfaerdende Perspektiver vi var stillet overfor, hvis betydelige Uraneller Thoriummsngder virkelig skulde kunne bringes ti1 at eksplodere. Som vi skal se, ligger dog Forholdene ved naermere Betragtning saaledes, at der ikke er Anledning til nogen Bngstelse i denne Henseende, omend man nsppe med Sikkerhed kan sige, a t enhver Udvinding af Atomenergien i sterrre Maalestok er ganske udelukket. For at kunne bedwmme Muligheden for Energiudvinding ved Atomkernespaltning ved Neutronstwd, maa vi se nojere paa den Maade, hvorpaa Spaltningssandsynligheden afhsnger af Neutronenergien. Netop for Urans Vedkommende mwder vi her den i ferrste 0jeblik overraskende Omstsndighed, a t Atomkernespaltninger kan frem-
28
N. Bohr:
bringes saavel med termiske Neutroner med Energier paa en B r ~ k del af en Elektronvolt som med hurtige Neutroner nied Energier over 1 MEV. -4llerede nogle Aar fOr man blev klar over, a t vi ved disse Processer har a t gme med en virkelig Kernespaltning, havde imidlertid Hahn og Meitner fundet, a t der ved St0d mellem Urankerner og Neutroner med niellemliggende Bevsgelsesenergier dannedes radioaktive Kerner med helt andre Levetider end de, der frembringes ved langsommere og hurtigere Neutroner. Navnlig fandt man, a t der omkring 20 EV eksisterer ganske snsvre Energiomraader, hvor Virkningen af Xeutronbombardementet paa Uran var stwlig fremtredende. Det var derfor indlysende, a t Processen bestod i en selektiv Indfangning af Neutroner, svarende ti1 diskrete Energivaerdier for den ved Sammenst~detdannede nye Kerne, og paa Grund af Udbyttets Stmrelse kunde man slutte, a t Penomenet maatte tilskrives den hyppigst forekommende Uranisotop med Massetal 238. Vel indeholder sedvanligt Uran ogsaa lettere Isotoper med Massetal 235 og 234, men kun i saa smaa Maengder, a t de selv for fuldkommen Resonans ikke kunde give Anledning ti1 Virkninger af den iagttagne Stmrelse. Efter vore almindelige Forestillinger om Atomkerneomdannelsernes F o r l ~ bmaa vi, for a t faa en Oversigt over Forholdene, undersarge, hvorledes Sandsynlighederne for de forskellige paa Fig. 3 fremstillede konkurrerende Processer rnaa ventes at variere med Energien af den Neutron, der ved sit Sammenst~dmed det tunge Atom indleder Spaltningen. Det typiske F o r l ~ baf denne Afhengighed er paa Fig. 4 fremstillet ved Kurverne I , I1 og 111, der i relativt Maal angiver Sandsynlighederne for henholdsvis Straalingsudsendelse, Neutronbsrivelse og Kernespaltning. Medens Kurverne I og I1 maa forudszttes at forbbe meget naer paa samme Maade for alle tunge Kerner, af haenger Spaltningssandsynligheden derimod vaesentlig af den for de enkelte Kernetyper karakteristiske Differens mellem Neutronbindingsenergien og den kritiske Spaltningsenergi. For Kurve 111, er det saaledes antaget, a t Spaltningsenergien er ca. 1 METT sterre end Bindingsenergien for Neutronen, og for Kurve 111, er denne Differens antaget a t belnbe sig ti1 omtrent 2 MET’. Derimod svarer Kurve 111, til det Tilfelde, a t den kritiske Spaltningsenergi ligger ca. 1 MEV under Neutronbindingsenergien. Dersom vi et Ojeblik ser ganske bort fra Forholdene for lang-
Nyere Unders0gelser over Atomkernernes Omdannelser.
29
somme Neutroner og ferrst betragter Energiomraadet fra omkring 1 MEV og opefter, finder vi, a t Iagttagelserne saavel for Uran som for Thorium gengives paa, tilfredsstillende Maade ved Kurvernes Forlerb, naar vi i det ferrste Tilfaelde for Spaltningssandsynlighedeiis Vedkommende vslger Kurve 111, og i det sidste Tilfaelde Kurve 111,. Med voksende Neutronenergi begynder Spaltningen for Uranets Vedkomniende nemlig fmst igen a t gerre sig galdende ved omkring 1 MEV, medens naesten 2 MEV er nerdvendige for a t frembringe en Spaltning
Fig. 4.
af den noget mindre staerkt ladede Thoriumkerne. Ogsaa i kvantitativt Henseende stemmer Forlerbet af Kurverne 111, og 111, overens med de for Uran og Thorium ved Bombardement med hurtige Neutroner iagttagne Virkninger. Sealedes vil, som allerede n s v n t , det relative Forlerb af Kurverne I11 i Forhold ti1 Kurve I1 netop betyde, a t Sandsynligheden for, a t Neutronsammensterdet frembringer en Kernespaltning, efter Overskridelsen af den kritiske Spaltningsenergi hurtigt vil nsrme sig en konstant Vsrdi; for Uran er denne Vsordi omtrent medens Spaltningsudbyttet for Neutronsammensterd for Thorium kun belerber sig ti1 ca. 1/25. Ved Sammensterd med Neutroner med mindre Energi end 1 MEV for Uran og 2 MEV for Thorium skulde efter Kurvernes Forlerb vssentlig kun de ved Rskkerne I og I1 paa Fig. 3 fremstillede Kernereaktioner komme i Betragtning. Hvilken af disse to Processer, der er den mest sandsynlige, afhsnger naturligvis af, hvilken af de t o tilsvarende Kurver paa Fig. 4, der ligger herjest for den betragtede Neutronenergi. For de mindste Neutronenergier, hvor Kurve I endnu ligger over Kurve 11, niaa saaledes Neutronindfangningen ventes a t
30
N. Rohr:
vaere overvejende, og det er ogsaa netop indenfor dette Omraade, a t der saavel for Uran som for Thorium er iagttaget udpraeget selektive Indfangningsvirkninger. Paa denne Maade faar vi imidlertid ingen Forklaring paa, a t der, som omtalt, er fundet en stor Sandsynlighed for Spaltning af Uran ved Bombardement nied termiske Neutroner. Vi tvinges derfor ti1 a t antage, a t disse Virkninger ikke son1 de fOr omtalte stammer fra den ssdvanlige Uranisotop, men fra en af de lettere Isotoper, en Antagelse, der ogsaa er meget nsrliggende, d a der hos Thorium, der kun bestaar af een enkelt Isotop med Massetal 232, ingen Spaltningsvirkninger er iagttaget for smaa Neutronenergier. I ferrste Ojeblik kunde det maaske synes overraskende, a t saa store Virkninger som de fundne kan hidrme fra en Isotop, der kun er ti1 Stede i saa ringe Msngde som de lettere Uranisotoper. Faktisk indeholder det i Naturen forekommende Uran over 99% af den tungere Isotop ";U, medens Resten hovedsagelig best a x af Isotopen '~~U Vi. har imidlertid her a t g0re med kvantemekaniske Resonansfaenomener, ved hvilke - som allerede omtalt i Forbindelse med Indfangningen af langsomme Neutroner - Reaktionssandsynligheden kan blive meget st0rre end Sandsynligheden for et Sammenst~d, beregnet ud fra saedvanlige mekaniske Forestillinger. Betingelsen for, a t Bombardementet med langsomme Xeutroner kan fme ti1 Spaltningsprocesser af den iagttagne Hyppighed, e r imidlertid, a t Sandsynligheden for Spaltningen af den paagsldende Kerne allerede for smaa Energivaerdier er stmre end Sandsynligheden for Straaling, og a t derfor den ferrste Sandsynlighed maa vaere givet ved en Kurve af samme Type som 1113 paa Fig. 4. Netop et. saadant Forlprb af Kurven maa, vi ogsaa forvente for Sammenst0d mellem en Neutron og en Atomkerne 'i;U, idet den kritiske Spaltningsenergi for den ved Sammenst~detdannede Kerne, i Modsstning ti1 hvad der er Tilfsldet, ved et Sammenstgd mellem en Neutron og en Kerne af den hyppige Uranisotop ":U, niaa antages a t vaere mindre end Neutronbindingsenergien. Dette beror dels paa, a t Spaltningsenergien for Kernen 'i;U er noget mindre end for Kernen :U ' som F d g e af det noget stmre Forhold mellem Lsdning og Masse, dels pea, a t Neutronbindingsenergien er betydelig storre for den fmste Keriie end for den anden. Som F d g e af Kernekraefternes saerlige Art vil nemlig Atomkerner, for hvilke saavel Ladnings- som Massetal er hge, vaere mere stabile end Kerner med omtrent samme
Nyere Undersmgelser over Atomkernernes Omdannelser.
31
Masse, men hvor et af disse Tal eller begge to er ulige. Denne Regel, hvorpaa vi har et velkendt Eksempel i a-Partiklens saerlige Stabilitet i Forhold ti1 andre lette Atomkerner, er navnlig i de seriere Aar blevet bekraeftet gennem Studiet af de talrige ved Btomkerneomdannelser frembragte radioaktive Isotoper. Drt netop Spargsmaalet om Oprindelsen af de ved langsomme Neutroner frembragte Kernespaltninger, som vi skal se, er afgerrende for Bedamnielsen af Mulighederne for en Energiudvinding ved Uransmderdelingen, har det vaeret meget paakrsvet a t prme de omtalte Slutninger ved direkte Forsag med adskilte Uranisotoper. Vanskeligheden ved a t adskille Isotoper, selv i mindre Maengder, er imidlertid, som bekendt, meget store, og saadanne Forsag er derfor farst i den allersidste Tid lykkedes. Dette Arbejde, der er udfmt af Nier, Booth, Dunning og Grosse, er et i flere Henseender yderst bemaerkelsesvardigt, T'idnesbyrd om Eksperimentalteknikkens vidunderlige Udvikling paa dette Omraade. Ti1 Trods for, at den sjaeldne Uranisotop zEiU kun blev renfremstillet i Maengder, der belab sig ti1 mindre end en Milliontedel af et Milligram og derfor ikke engang var tilstraekkelige ti1 a t dakke en Kvadratmillimeter med e t enkelt sammenhangende Lag af Atomer, lykkedes det ikke desto mindre a t vise, a t hele Udbyttet ved Spaltning af Uran nied termiske Neutroner skyldtes denne Isotop. For a t vende tilbage ti1 Spargsmaalet om Udvindingen af Atomkerneenergien skal vi nu undersage, hvor stor Sandsynligheden er for, a t de ved Spaltning af en Uran- eller Thoriumkerne frembragte Neutroner kan foraarsage videre Omdannelser. Allerfarst kan vi let indse, a t Mulighederne for a t frembringe Ksdeprocesser i Thorium er altfor begraensede, fordi en Spaltning af Thoriumkerneri krEver en Neutronenergi paa nssten 2 MEV, medens de i Forbindelse med Kernespaltningen udsendte Keutroner i Middel kun vil have en Energi paa omkring 1MEV, svarende ti1 de lssrevne Kernedeles Temperaturenergi. For Urans Vedkommende er denne Energi ganske vist af en saadan Stmrelsesorden, a t Neutronerne netop vil kunne frembringe en Spaltning af den hyppige Uranisotop, men vi maa betaenke, a t selv hurtige Neutroners Sammenstad med en saadan Atomkerne kun i hvert femte Tilfaelde vil fare til Spaltning. Resultatet af de ovrige Sammenstad vil blive, a t en Neutron undslipper fra den ved Sanimenstadet dannede Kerne med en Energi,
32
N. Bohr : Nyere Undersogelser over Atomkernernes Omdannelser.
der i Middel er betydelig mindre end Energien af den indtrengende Neutron, og derfor vil v s r e ude af Stand ti1 a t frembringe nye Spaltninger af Kernen ":U. Selv om der derfor kan opnaas K s der af Spaltningsprocesser i denne Uranisotop, vil de dog blive altfor korte og sjsldne til, a t der kan blive Tale om nogen Eksplosion. Forholdene vilde imidlertid ligge ganske anderledes, hvis vi havde en tilstrzkkelig stor Msngde af den lettere Uranisotop "!JJ ti1 Raadighed ; her vilde nemlig enhver ved en Kernespaltning frembragt Neutron have en langt overvejende Sandsynlighed for a t frembringe e n ny Spaltning ved Sammenst~jdmed andre Urankerner, og da der ved hver Spaltning i Middel udsendes to Neutroner, vil en Eksplosion v s r e den uundgaaelige Fdge. Med de nuvmende tekniske H j s l pemidler er det dog udelukket a t renfremstille den sjsldne Uranisotop i saa store Msngder, a t de omhandlede Kzdeprocesser kan realiseres. Det afgcarende Spmgsmaal er derfor, hvorvidt den i Naturen forekommende Rlanding af Uranisotoper kan benyttes ti1 Energiudvinding i stcarre Maalestok. Den nsrliggende Fremgangsmaade vilde bestaa i a t blande Uran med brintholdige Stoffer for derved a t opnaa, at de ved Spaltningen frigjorte Neutroner ved Protonsammensterd efterhaanden bliver langsomme nok ti1 med tilstrskkelig Sandsynlighed a t kunne reagere med den sjsldne Uranisotop. I Forsag med saadanne Blandinger har man virkelig opnaaet Ksdeprocesser af Here paa hinanden fdgende Spaltninger, men det er paa Forhaand klart, at der ved denne Fremgangsmaade aldrig kan blive Tale om Eksplosioner, hvor en vssentlig Del af Atomenergien pludseligt frigives. Fsr saadanne Eksplosioner vilde indtrsde, maa nemlig Blandingens Temperatur stige ti1 Milliarder af Grader, men saasnart Temperaturen blot kommer op paa nogle faa Tusinde Grader, vil hele Processen standse, fordi Protonerne i Blandingen vil have for store Bevsgelsesenergier ti1 a t kunne bremse de ved Spaltningerne udsendte Neutroner tilstrskkeligt. Sandsynligheden for Neutroners Reaktion med den sjsldne Uranisotop vil nemlig aftage meget hurtigt med voksende Neutronenergi 08 allerede ved Energier paa faa Elektronvolt v s r e mindre end Sandsynligheden for Neutronindfangning i den hyppige Isotop. Om de sidste Indfangningsprocesser i alle Tilfslde vil hindre, a t Ksdeprocesserne bliver tilstrskkelig lange til, at en praktisk Energiudvinding kan opnaas, er imidlertid et Spargsmaal, hvis Resvarelse vil af hsnge af yderligere Unders~gelser.
PART I : PAPERS AND MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
TRANSLATION
Recent Investigations of the Transmutations of Atomic Nuclei’
N . Bohr Although Rutherford’s discovery of the atomic nucleus took place less than 30 years ago, and it is not more than 20 years since his first demonstration of the possibility of the artificial transmutation of nuclei, the study of these transmutations is today one of the main research topics in physics. Nearly every single year has brought important advances in this field, which have given us insight into deep-lying physical regularities, and paved the way for further progress. I shall not be able to enter in detail into the significance which nuclear physics has had already for the most diverse branches of natural science, and into the perspectives which it opens. However, I shall try to show how many of the often so surprising results concerning nuclear transmutations can be accounted for with the help of quite simple points of view. We shall see in particular how these points of view can be used to explain the fission of the heaviest nuclei, whose discovery has in recent years attracted so much interest.2 1. Structure of the atomic nucleus.
To bring out the peculiar character of the problems of the atomic nucleus, I shall first of all recall for comparison the main features of the structure of the atom, the understanding of which has laid the foundations for the full explanation of the normal physical and chemical properties of substances which we have achieved during the past generation. The great simplicity which characterised our ideas about atomic structure comes above all from the fact that the distances between the individual particles in the atom are large enough to enable both the
’
Review article, based on a lecture given to the Society for the Dissemination of Natural Science on 6 December 1939. The points of view concerning the mechanism of nuclear reactions which are dealt with here were first put forward in an article in Nature 137 (1936) 344 (see also Fys. Tidsskr. 1936, p. 186) and further developed in an article by F. Kalckar and the author in Mat.-Fys. Medd. Dan. Vidensk. Selsk. 14, no. 10 (1937). The theory of the fission of the heaviest nuclei is dealt with fully by J.A. Wheeler and the author in Phys. Rev. 56 (1939) 426. We may also point out that the cloud chamber pictures of the tracks of the fragments emitted in the fission of uranium, of which only a single one is reproduced here, have recently been published and fully discussed by J . K . Bsggild, K.J. Brostrsm and T. Lauritsen in Mat.-Fys. Medd. Dan. Vidensk. Selsk. 18, no. 4 (1940).
P A R T 1: P A P E R S A N D M A N U S C R I P T S R E L A T I N G T O N U C L E A R P H Y S I C S
nucleus and the electrons to be considered to a very good approximation as electric point charges with interaction forces of the same kind as between ordinary charged bodies. In this respect it makes no difference that the usual mechanical laws of motion are completely inadequate to account for the binding of electrons in the atom, because its small size means that we are not dealing, as in the usual mechanical systems, with actions large enough to neglect the universal quantum of action. The fact that the electrons can be bound in a stable manner at distances from the nucleus extremely large compared to the size of the nucleus itself, could be understood only after the introduction of the quantum concept into atomic physics. However, when we consider the question of the structure of the nucleus itself, and of its reactions, conditions are quite different. In the nucleus we are not only dealing with an extraordinarily tight packing of particles, interacting with forces which have no counterpart in our ordinary physical experience, but it is not even possible to speak of the nuclear constituents in the same simple manner in which we talk about the composition of the atoms in terms of nuclei and electrons. The conclusion from mass spectrograph experiments that the mass of every atom can be expressed as an integer if one uses a unit which is very close to the mass of the hydrogen atom, led very early to the view that the hydrogen nucleus, the so-called proton, must be an essential constituent of all nuclei. Since the ratio of charge to mass is less for heavier nuclei than for the proton, it was at first assumed that the nuclei contained also a number of electrons; indeed this assumption was also made very plausible by the fact that the nuclei of natural radioactive substances can emit electrons (P-rays) as well as heavier particles (arays). However, according to quantum mechanics it is impossible to assume that particles as light as electrons can be stably bound in a region of space as small as a nucleus, and we are therefore forced to conclude that electrons emitted by radioactive substances are created only in the emission process itself. This situation was made particularly clear when it turned out that nuclear reactions can lead not only to radioactive isotopes which emit negative electrons like the natural radioactive substances, but also to radioactive isotopes which emit positive electrons, which by their nature can never be found together with negative electrons without combining and disintegrating with the emission of electromagnetic radiation. Whether in a radioactive transition a positive or negative electron is emitted depends only on the mass-to-charge ratio of the relevant nucleus. For any given mass there is usually only a small range of possible charges for a stable nucleus, and as soon as the charge becomes either too large or too small in relation to the mass, the nucleus shows a tendency to reduce or increase its charge by the emission of a positive or negative electron. A decisive step in our ideas about the structure of the nucleus, however, came
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
above all from the discovery that certain nuclear reactions can liberate a particle which has about the same mass as the proton, but no electric charge, and which was therefore given the name neutron. It is immediately clear that we can account for the mass and charge numbers of all nuclei by regarding them as being built only of neutrons and protons. In a consistent extension of the quantum mechanical formalism it has moreover proved possible to consider neutrons and protons as electrically different states of one and the same elementary particle, which one has recently started calling the nucleon. According to this view the electron emission from radioactive nuclei is thus connected with the change of state of a nucleon. It would, however, lead us much too far from our subject to consider further these fundamental questions and the new prospects which open up here for a wider extension of the foundations of atomic theory. For our purpose we shall not even need to go into details of the great progress made in recent years in the quantum mechanical treatment of the interaction between nuclear particles. It will be sufficient to recall that this has provided an explanation of the long-known peculiar fact that all nuclei, except for the very lightest, have very strikingly similar densities of mass and charge. In spite of the fact that this density of nuclear matter is so enormously high compared to ordinary matter, the state of aggregation of the nucleus is nevertheless in many respects reminiscent of the liquid state of ordinary matter, as we shall see. 2 . The course of nuclear reactions. The great difference between the intrinsic densities of the whole atom and the nucleus shows up particularly in a radical contrast between the way in which the whole atom reacts to a collision with a fast particle, and the course of a collision in which the particle penetrates into the nucleus itself. Indeed, in the collisions which formed the main source of information about atomic structure, the particle will in general move freely through the open structure of the atom, and only occasionally conie so close to one of the atomic particles as to undergo a substantial change in its motion, with the struck particle being ejected from the atom. In contrast the strong forces acting between the tightly packed particles inside the nucleus will have the effect that a particle which collides with the nucleus itself will in general not be able to penetrate it. Because of the strong interaction of the nuclear particles with each other as well as with the incoming particle, that particle will, as we shall,see, combine with the target nucleus into a new nucleus of a relatively long life. The final result of the collision will therefore be determined by the reactions which this new nucleus can undergo, and which are independent of the manner in which it was formed, but depend only on its composition and energy level. This situation was demonstrated particularly after the discovery of the neutron, which soon proved itself to be such an effective tool
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
for producing nuclear reactions. Previously one had to use in such investigations charged particles, such as a-particles from radium, or artificially accelerated protons. However, in that case the strong repulsion causes the particle difficulties in reaching the nucleus, and the situation is therefore much more transparent in the case of the bombardment of nuclei with neutrons, where there is no electric repulsion to impede the occurrence of contact in a collision. For the development of our ideas about the course of nuclear reactions the observation was particularly decisive that a collision of a neutron with a heavier nucleus has a substantial probability of leading simply to capture of the neutron by the nucleus, with the formation of a new nucleus, which in general will be radioactive. As a typical example of this we shall consider the capture of a neutron by an iodine nucleus, a process which can be represented by the following formula 127 128 531 + An * d*, (1) where I is the usual chemical symbol for iodine, while n denotes the neutron. The upper and lower indices attached to each symbol are the mass and charge numbers of the respective particles. Since there exists only one stable iodine isotope, the upper index for the first iodine nucleus which occurs here is also the chemical atomic weight of iodine, whereas the lower index gives the number of iodine in the natural system of elements. The iodine isotope created in the process is unstable, as indicated by the addition of an asterisk, and since it is heavier than the stable isotope, its decay process proceeds according to the scheme 0
le.
Here the first symbol on the right-hand side indicates one of the many stable isotopes of xenon, the second an electron with a negative unit of charge and with a mass so small in relation to that of the neutron or proton that to the approximation used here it can be taken as zero. Since the radioactive decay represented by formula (11) proceeds with a half-life of about half an hour, whereas the capture process (I) takes place in a very small fraction of a second, the two processes can of course be considered as independent of each other, and in particular the question of the conservation of energy can be studied for each of them on its own. Whereas in the collision reactions studied previously, where the result of the interaction was always the production of two new nuclei, the excess energy in the reaction showed itself directly in terms of the kinetic energy with which the new nuclei flew apart, we find in a capture process like the one discussed a special situation concerning the energy balance, since there is no other material particle
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
to take up the excess energy. To prevent the incoming neutron, or another one, from escaping from the newly formed nucleus, it is therefore necessary that this should quickly get rid of the excess energy in the form of electromagnetic radiation, and this could also be observed directly in various capture processes. From the dimensions of the nucleus and the total charge it is however easy to calculate a lower limit for the average time required for the emission of a radiation quantum from the nucleus, and it then turns out that this time, while amounting to only an extremely small fraction of a second, is yet extraordinarily long compared to the time taken by a neutron with the appropriate velocity to cross a distance of the order of the nuclear dimensions. It is therefore clear that the whole excess energy must distribute itself rapidly amongst all particles in the nucleus in such a way that none of these has in the immediately following period enough energy to break away from the other particles and to leave the nucleus. If then no radiative energy loss occurs in the meantime, accidental fluctuations in the distribution of the excess energy over the particles may give still the possibility of one of the particles in the nuclear surface acquiring the energy necessary for separation. This will in general require a relatively long time, and just for that reason there arises a significant probability of the energy getting away in the form of radiation, with the result that all particles remain bound to the new nucleus formed in the collision. The insight into the mechanism of nuclear reactions which the study of neurron capture by heavy nuclei has thus given us, has proved very fruitful in explaining many of the features characteristic of all nuclear reactions. On this view, when two nuclei collide, they will, as soon as contact has taken place and the strong interaction between the particles has come into play, combine into a new nucleus, with a lifetime in general extremely long compared to the time the nuclei would take t o pass each other freely. The end result of the collision will therefore depend, just as in the case of negtron capture, on a so-to-say free competition between all disintegration and radiative processes which the newly formed nucleus can undergo with the available energy. These ideas not only provide an immediate explanation for the extraordinary facility with which nuclei react with each other in collisions, and for the great variety observed in the mechanism of reactions, but also open the possibility of using familiar considerations from other fields of physics to find a deeper insight into the conditions which determine the relative frequency of the different nuclear reactions. Above all, the analogy with thermodynamics has proved fruitful for the explanation of important properties of highly excited nuclei occurring as intermediate products in nuclear reactions.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
3. The ‘‘temperature” of excited nuclei. The distribution of energy over the particles in a nucleus formed in a collision between two nuclei immediately brings to mind the distribution of thermal energy over the molecules of a solid body or a liquid, and this leads us naturally to an analogy between the emission of neutrons or radiation from an excited nucleus and the evaporation or thermal radiation from an ordinary substance. Admittedly the binding energies and the radiation quanta relevant to the nuclear processes are many times greater than the energy needed to detach a molecule from a liquid, or that contained in the quanta of radiation emitted by a black body under normal conditions, but on the other hand the temperature involved in the creation of a nucleus in a collision is enormous compared to those we encounter in ordinary circumstances. In the usual units the temperatures arising in nuclear reactions amount to milliards of degrees, and are therefore about a thousand times higher than even the temperatures found in the interior of the sun. True enough, as has been recognised in recent years, the enormous heat emission of the sun has its source in nuclear reactions in which protons are converted into helium nuclei with the emission of positive electrons. However, for these processes there apply special circumstances, and to understand the origin of the heaviest elements we have to imagine that at some time there were in space places where the temperature really reached the dizzy heights mentioned above. At such temperatures ordinary matter cannot of course exist, and indeed we know how already in the sun the atoms themselves are split into their constituent parts. However, the enormous density of nuclear matter on an ordinary scale has, as we shall presently see, the result that, in proper perspective, nuclei involved in reactions are not comparable with very hot bodies, but rather with bodies at the lowest temperatures we can produce in the laboratory. To appreciate this relation we must look a little more closely at the magnitude of nuclear energy, which is to be compared with thermal energy, and at the nature of the internal movements of the nucleus over which it is distributed. The energy with which we are concerned comes in part from the kinetic energy of the colliding nuclei, and in part from the binding energy liberated in the combination of the nuclei. This latter energy can vary much for different nuclei, but because of the balance between charge and mass of stable nuclei, already mentioned in the discussion of nuclear 6-radioactivity, the binding energy of every nucleus is about the same for a neutron as for a proton. This binding energy, which, by and large, decreases steadily with increasing nucleon number, is for the lighter nuclei about 8, and for the heaviest nuclei about 6 million electron volt; as the notation suggests one means by an electron volt (eV) the energy which an electron receives or loses in passing through a potential difference of 1 volt. For comparison one can mention that the energy needed to remove one of the most loose-
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ly bound electrons from an atom is about 10 eV, while the removal of the most tightly bound electrons from the heaviest atoms requires about 100 000 eV. Whereas the electrons move in first approximation independently of each other in the field of force surrounding the nucleus, and one can therefore speak for each electron in the atom of a bound state with well-defined quantum numbers, conditions are quite different in the nucleus, where the strong interaction between the particles excludes any possibility of distinguishing the states of individual nucleons. In contrast to the atom, where any possible energy increase corresponds to a change of state of one or perhaps a few electrons, the energy content of a nucleus will be distributed over oscillatory motions in which all nucleons take part. The internal motion of an energetic nucleus is dominated by the cohesive forces of nuclear matter, and in spite of the extraordinary strength of these forces in comparison with the cohesive forces of ordinary substances we can talk, just as in the case of a liquid drop, of a surface tension which determines the form and possible motion of the nuclei. The oscillatory motion of the nucleus thus corresponds exactly to the vibrations of a liquid drop about the spherical shape under the influence of the surface tension, except that the period of oscillation of the nuclear vibrations will be very short, even in comparison with the orbital periods of the atomic electrons, because of the strong cohesive force and the small size of the nucleus. The energy quanta corresponding to the oscillations, which are inversely proportional to the period of oscillation, will therefore be very large, and for medium heavy nuclei even the smallest quanta will amount to about 1 million electron volt (MeV). A nucleus with an energy content of a few million electron volt will therefore have sharply distinct stationary states, like an atom at correspondingly lower energy. However, with increasing energy content the distance between energy levels decreases for nuclei far more rapidly than for atoms. Because of the rapidly risingnumber of combinations of the strongly coupled nuclear oscillations, the energy levels will rapidly become more closely spaced, and, for energies of the order of magnitude of the binding energy of a neutron, the spacing of the energy levels of heavier nuclei will amount to only a few electron volt. As soon as the energy exceeds the neutron binding energy, the width of the levels furthermore begins to increase, with the result that they merge completely when the thermal energy exceeds the binding energy by only about 1 MeV. The presence of a continuous energy region above this limit is also just the condition that two colliding nuclei are always able to merge, if only the thermal energy of the newly formed nucleus becomes sufficiently large. If we now return to the question of the temperature to be ascribed to an excited new nucleus formed in a nuclear collision, we make use of arguments of exactly the same kind as those which led in the first years after the discovery of the quan-
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
tum of action to the explanation of the way in which the heat content of ordinary substances varies with temperature, which had previously been unintelligible. As we then learned, the thermal energy can be distributed equally over only those individual oscillations, of which the internal motion of the body can be made up, as long as the energy quanta of even the fastest oscillations are small compared to the temperature-proportional energy which, according to the simple kinetic theory of heat, on the average should belong to every oscillation. As soon as this is not the case, all the oscillations whose quanta are larger than this energy will on the average receive a far smaller energy, and below a certain temperature, which is characteristic for each substance, the specific heat of the body, instead of being constant, will decrease with falling temperature, and vanish completely at absolute zero. For a medium-heavy nucleus containing about 100 nucleons, the energy would, according to classical mechanical ideas, be uniformly distributed over about 300 oscillations, and for a total energy content of about 10 MeV each of these would on the average contain only about 30 000 eV. Since all the quanta corresponding to nuclear oscillations are substantially greater, there can however be no question of such a uniform distribution of energy, but in analogy with the situation which applies to ordinary bodies at very low temperatures, the thermal energy of the nucleus will be carried almost exclusively by a small number of the slowest oscillations. By the usual definition of the temperature of a body, its magnitude is determined by the average kinetic energy of the molecules in a gas which is in equilibrium with the body. This energy which, for a temperature of 10 000 degrees, amounts to about 1 eV, will from now on be called briefly the “temperature energy”. By a calculation following closely the well-known theory of the temperature variation of the specific heat at low temperatures, one finds for a medium-heavy nucleus with a thermal energy of 10 MeV a temperature energy of about 1 MeV. With increasing energy content the nuclear temperature rises only relatively slowly, since the energy is distributed over a steadily increasing number of vibrations, and even for an energy content of 100 MeV the temperature of the nucleus will be only a few million electron volt. In spite of the enormous magnitude of the nuclear temperature in the usual units, the thermal properties of the nucleus therefore correspond, as already mentioned, to those of ordinary bodies at very low temperatures, so low indeed that practically all substances would long ago have solidified. In recent years we have however found in condensed helium, which even at the lowest attainable temperatures retains the properties of the liquid state, an analogy with nuclear matter which in many respects is very far-reaching.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
4 . The “evaporation” and “heat radiation ’’ of nuclei. The value of introducing into the description of the properties of energetic nuclei concepts taken from thermodynamics becomes particularly clear when we come to consider in detail the analogy, already mentioned, between the emission of particles and electromagnetic radiation by nuclei and the evaporation and thermal radiation of ordinary bodies. The background for this analogy is, in the case of the emission of particles, provided by the fact that surmounting the attraction of the neighbouring particles requires a separation energy much larger than the average kinetic energy of the particles and therefore, just like the evaporation from a liquid, requires an accidental concentration of energy on a surface particle. As regards the radiation from nuclei, the similarity with the heat radiation from ordinary bodies lies simply in the fact that both cases involve radiation in the form of quanta of which each is small compared to the whole energy content. A very instructive analogy with the neutron emission from an energetic nucleus is found in the beautiful experiment on the evaporation of mercury droplets, which Professor Martin Knudsen did 25 years ago in connection with his fundamental investigations on the properties of gases at low pressures. As is well known, Professor Knudsen showed in this experiment that the number of molecules which in a given time leave an element of area of a clean mercury surface is just equal to the number of molecules which, in the given time, will stream from a container with saturated mercury vapour at the same temperature into an evacuated space through an opening of the size of the element of area, as long as the dimensions of this are small compared to the mean free path of the molecules in the vapour space. Since a liquid in equilibrium with its saturated vapour must emit through evaporation during any given time interval on the average the same number of molecules as it captures from the vapour, Professor Knudsen could therefore draw from his observation the important conclusion that there is no reflection of vapour molecules from a clean mercury surface, but that, on the contrary, every molecule which hits the surface is immediately taken up in the liquid state and can escape from this only in a later elementary evaporation process, which is independent of the initial collision. In collisions between neutrons and heavier nuclei we find a quite similar situation, as we have seen, and with the help of the simple connection between the maximum speed of evaporation and the vapour density, which is valid for the mercury drops, one can therefore calculate the probability of a neutron escaping from an energetic nucleus in a given time. Within our experimental possibilities there can of course be no question of realising an equilibrium state between energetic nuclei and an atmosphere of neutrons, but one can nevertheless calculate, using well-known principles, the density which such a neutron atmosphere would have for any
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given nuclear temperature in terms of the density of nuclear matter and the separation energy. Even though the analogy between neutron escape and evaporation can be pursued very far, there is still a limit to the validity of such simple arguments as those indicated. In spite of the relatively large energy content of the new nuclei created in the nuclear collision, the neutron binding energy will in many nuclear reactions be of the same order of magnitude as the thermal energy of the nucleus, and in that case the temperature of the residual nucleus after the neutron escape will be substantially lower than that of the original nucleus. For even a small liquid drop, on the other hand, there can of course be no question of a change of temperature in an elementary act of evaporation, since the total heat energy of the drop is practically infinite compared to the binding energy of one molecule. For the nuclei produced in collisions with neutrons df a kinetic energy of a few million electron volt there is the additional fact that the energy of the residual nucleus falls within the region of sharply separated energy levels. In such cases one must therefore use more rigorous statistical arguments for an exact description; indeed, as we shall see, collisions with the very slowest neutrons even require the use of typical quantum mechanical methods. However, the simple thermodynamic analogies are more accurately valid the higher the energy of the nucleus, and for energies high enough to allow the emission of several nuclear particles, the similarity with the evaporation of a liquid drop becomes particularly pronounced. Thus it has been found that a collision between a heavy nucleus and a neutron with a kinetic energy of over 10 MeV can often lead, instead of to neutron capture, to the departure of not only one but several neutrons from the nucleus. Since these departures can presumably be regarded as a series of successive independent emission processes, each of the neutrons gradually escaping in these processes will, like the molecules evaporating from a liquid drop, have a kinetic energy corresponding on the average to that of a gas molecule at the temperature applying to the nucleus. Even after a collision with a nucleus of a neutron of 100 MeV kinetic energy, the
Fig. 1
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
energy of each of the emitted neutrons will therefore amount to only a few million electron volt, and in this case one must therefore expect a large number of particles to leave the nucleus in succession. Exceedingly interesting examples of such progressive evaporation of nuclei have been found in recent years in photographic plates with special thick emulsions exposed at high altitude to the cosmic radiation. As shown in fig. 1 which reproduces at great magnification, a photograph taken by Blau and Wambacher, one observes under these conditions nuclear reactions in which a number of straight tracks radiate in star fashion froin a point. The tracks can be taken to be due to protons, and by counting the developed grains in the emulsion along the track one finds that the kinetic energy of the protons amounts on the average to a few million electron volt. However the neutrons, which must also be assumed to be emitted in great numbers from the evaporating nucleus, will of course leave no tracks in the photographic plate. The comparison with the evaporation of a liquid drop has also proved very fruitful for the understanding of many features of the emission of charged particles from excited nuclei. There are however several circumstances which have to be taken into account in the case of charged particles. First of all, there is, according to quantum mechanics, a certain probability for such a particle escaping from a nucleus even when the energy with which it is emitted is less than that required according to ordinary mechanical ideas to bring it back to the nucleus against its repulsion. It is just this fact which is responsible for the possibility of the emission of a-rays from natural radioactive substances. However the mean life for the radioactive nuclei in their normal state is enormously long compared to the time scale of the competing emission and radiation processes, which determine the course of the reaction of the highly excited nucleus produced in the collision. If the emission of charged particles such as a-particles or protons is to have a share in the competition, there must be, just as in the case of neutrons, an emission of particles from the nuclear surface corresponding to evaporation. Only for charged particles there is the difference that, after leaving the nucleus with the help of thermal energy, they will subsequently be accelerated by the electric repulsion, and ultimately acquire a kinetic energy which can often be far greater than the molecular energy corresponding to the nuclear temperature. Since the energy required to remove a proton t o a great distance from the nucleus is about the same as the binding energy of a neutron, as was mentioned above, the separation energy corresponding to the heat of evaporation will in such circumstances be much greater for charged particles than for neutrons. This explains why the emission of protons and a-rays, which for the lighter nuclei can often be dominant, gradually decreases by comparison with neutron emission when one goes towards heavier nuclei.
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With the necessary attention to all special circumstances the thermodynamic analogies can also be instructively applied to the clarification of the conditions which determine the emission of electromagnetic radiation from highly excited nuclei. As already indicated, we are here concerned with a far-reaching analogy with the heat radiation from ordinary bodies, based on the fact that the energy of the new nucleus produced in the collision between nuclei is distributed over oscillatory motions of the nuclear matter, with the corresponding quanta being small compared to the energy content of the whole nucleus. The radiation from such nuclei will therefore consist of a number of quanta whose energy will on the average be about the same as for the quanta which thermal radiation should contain at the temperatures in question according to Planck’s theory. Since the temperature of the nucleus, as mentioned above, will change relatively little even if the energy content of the nucleus increases sharply, the average energy of the emitted quanta of radiation in a large energy region will therefore still be of the same order of magnitude, about 1 MeV. Corresponding to the way in which the intensity of the heat radiation of a body depends on the temperature, the number of quanta of radiation emitted from a highly excited nucleus in a given time will similarly change only relatively little, even if the energy content increases considerably. These circumstances are of the greatest importance for deciding the outcome of the competition between particle escape and the emission of electromagnetic radiation on which the outcome of the nuclear collision depends. In particular we can immediately understand that the probability of neutron capture in a collision with a heavy nucleus decreases rapidly with increasing neutron energy. The probability of a neutron escaping from the newly formed nucleus in a given time will indeed increase rapidly with the nuclear temperature, corresponding to the well-known rapid rise of the evaporation rate of ordinary liquids with temperature. On the other hand, the probability of the emission of quanta of radiation from the nucleus during the same time interval increases much less, similarly to the weaker temperature dependence of the heat radiation. This explains why the probability of neutron capture in heavier nuclei can be large for neutron energies below 1 MeV, whereas it is only small as soon as the neutron energy reaches a few million electron volt. The fact that the nuclear temperature at constant excitation energy decreases with increasing nucleon number explains further that the probability of neutron capture is, at the same energy, much greater in a collision with heavier nuclei than with lighter ones.
5. Selective nuclear reactions.
The relatively smooth way in which the behaviour of nuclei changes by and
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large with the nucleon number is due to the fact that the thermal energy produced in the collision most often falls in the continuous energy region. As soon as this is not the case, we meet typical selective behaviour since the intermediate merging of nucleus and particle, which is necessary for the reaction, can occur only when the incident particle has an energy which just corresponds to one of the distinct energy levels of the intermediate product. For varying particle energy the yield will therefore show a series of sharp maxima, whose positions can be quite different even for nuclei with nearly the same mass and charge number. Such selective reactions are particularly common for the lighter nuclei, where the beginning of the continuous spectrum can often lie several million electron volt above the binding energy which is liberated when the incident particle merges with the nucleus. It was previously believed that the nuclear particles move approximately independently of each other, like the electrons in the atom, and one assumed therefore that these maxima in the reaction corresponded to different ways in which the colliding particle could be bound in the internal field of force of the nucleus. However, more recent studies of the selective nuclear reactions have shown indeed that these are quite independent of the collision process by which the intermediate state has been formed. Thus it has been found that reactions initiated by the collision of different particles with different nuclei have identical maxima, if only the intermediate nucleus has the same charge and the same mass number. Whereas in the collision of neutrons and heavier nuclei we generally find yields varying smoothly with neutron energy, we meet, however, typical selective phenomena when the neutron energy amounts to only a few electron volt. The information about the reactions of “slow” neutrons with nuclei, which are instructive in many ways, is due especially to Fermi, who first demonstrated how the “fast” neutrons resulting from nuclear reactions, on passing through hydrogenous substances such as water or paraffin, gradually lose energy by collisions with protons, until finally their speed has dropped to the speed of hydrogen atoms at ordinary temperatures. It turns out in particular that neutrons with such “thermal” velocities have an exceedingly large probability of being captured by certain heavier nuclei, with the creation of new radioactive isotopes, whereas other nuclei with nearly the same nucleon number show no particular tendency to capture. The condition for such capture is that an energy level of the newly produced nucleus should lie just within the very narrow energy region, only about eV wide, immediately above the neutron binding energy; that this can happen for a not negligible number of heavy nuclei is indeed due only to the fact that the average distance between energy levels for such nuclei in the region considered is only a few electron volt. Once we encounter such a coincidence, on the other hand, this provides for us a quite specially favourable situation for
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
neutron capture. Experiments with the absorption of slow neutrons in various elements have thus shown that the number of neutrons captured by the nuclei in certain substances can be even many thousand times larger than the number of collisions between neutrons and nuclei which one would expect to occur according to simple mechanical ideas. This phenomenon, which at first sight appears so surprising, arises because the ordinary mechanical picture can be used for the description of the collision only when the de Broglie wavelength for the motion of the neutron is small compared to the dimensions of the nucleus, or at most of the same order of magnitude. While this is still the case for neutrons with a kinetic energy of about 1 MeV, the wavelength for thermal neutrons with energies of a fraction of an electron volt is over 1000 times greater than the diameter of a nucleus. In such a situation it is therefore quite impossible to apply the idea of an orbit in the usual mechanical sense to a neutron in the neighbourhood of the nucleus. The probability of the neutron entering the nucleus will, on the contrary, be a typical quantum mechanical resonance, for which it is well known that only the frequency and the damping of the characteristic vibrations, and not the external dimensions of the resonator are decisive. Quite apart from the special quantum mechanical problems that we meet here, the capture of slow neutrons in heavy nuclei presents us with an extreme case in which the emission of radiation from the intermediate state is far more probable than the escape of a particle. With increasing energy the balance between the competing processes shifts rapidly, and when the energy of the intermediate state has risen to only 1 MeV above the neutron binding energy, the probability of radiation is, even for heavy nuclei, substantially less than the probability of neutron emission. In the reactions of lighter nuclei the significance of radiation is nearly always negligible, so that the only question which remains is the competition between the emission of various particles from the intermediate nucleus. An interesting exception, where radiation plays an important part, is however the bombardment of certain light nuclei with artificially accelerated protons. The fact that it has been possible to obtain nuclear reactions with proton energies well below 1 MeV is due to the fact, already mentioned, that, according to quantum mechanics, there is a certain, though often very small, probability of a charged particle entering the nucleus even when the repulsion would, according to the ordinary ideas of mechanics, prevent the particle reaching the surface of the nucleus. Since at the same time the probability of the proton escaping again from the newly formed nucleus is also very small, the radiation therefore makes itself felt in special cases, in which no other particle, charged or uncharged, has an appreciable possibility of escaping from the intermediate nucleus, with the result that the proton is captured in the collision. Moreover, since the spacing of
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the energy levels in the intermediate state is here much greater than in the case of the neutron bombardment of heavy nuclei, one finds for a number of light nuclei pronounced selective capture processes at proton energies of a few hundred thousand electron volt. 6. The fission of heavy nuclei. In recent years a large number of investigations on nuclear reactions under neutron bombardment have been carried out, and from these we have become acquainted with many new radioactive isotopes of nearly all elements. In agreement with the preceding considerations these reactions consisted for the heavier nuclei either of the capture or of the ejection of a neutron from the nucleus, depending on whether slow or fast neutrons were used in the bombardment. However for the heaviest elements, uranium and thorium, the experiments gave more complex results, and their interpretation brought the greatest difficulties, until Hahn and Strassmann showed in the beginning of 1939 that we are here concerned with a completely new type of nuclear reaction, 'in which the heavy nucleus splits into two fragments of about equal size, with accordingly lower mass and charge number. Since for stable nuclei the ratio between mass and charge is substantially greater for heavier than for lighter nuclei, the new nuclei resulting from the splitting will be highly unstable, and each will undergo subsequently a series of radioactive transformations with the emission of electrons. This is just the reason for the richness of the phenomenon, which was initially so confusing.
Fig. 2.
The splitting of the heavy nuclei releases an energy which is much greater than that from nuclear reactions studied earlier. It was soon shown by direct measurements of the ionising and penetrating power of the ejected nuclei that the kinetic energy for each of the fragments amounted to about 100 MeV. Such measurements were carried out almost simultaneously in many different laboratories, where the new discoveries everywhere attracted the greatest attention. The first experiment was carried out by Frisch, who at the time was working in Copenhagen in the University Institute for Theoretical Physics. Here, as well
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as at other places, it eventually proved possible to take Wilson cloud chamber pictures of the tracks of the atoms expelled in the fission of uranium. A photograph taken recently in the Institute is reproduced in fig. 2 . The uranium exposed to neutron bombardment was placed in the form of a thin layer on an aluminium foil, which was stretched inside the helium-filled cloud chamber in a frame visible in the middle of the picture. While the short straight tracks occurring throughout the picture represent collisions between neutrons and helium nuclei, the two intensely ionising tracks come from the uranium fission, in which the two nuclei are emitted with great energy in opposite directions. The tracks show clearly a number of branchings, which are due to collisions with helium nuclei, and whose high frequency results just from the high electric charge of the fragments. However, we shall here not go any further into such details, whose study has given interesting new information about the stopping and scattering of heavy and highly charged particles in matter, but shall at once turn to discuss how the fission process itself can be simply explained from the general points of view developed above. Exactly as for the usual nuclear reactions caused by neutron bombardment, we must assume that the process under discussion proceeds in the way that the neutron is first attached to the struck nucleus, and that the final result of the collision is then determined by the competition between the various independent radiative and disintegration processes which can happen in the nucleus so formed. The only difference is that here we must include in the disintegration processes not only the emission of a neutron, but also the splitting of the whole nucleus into two parts of about equal size. The neutron emission requires, as we discussed, a concentration of heat energy on a surface particle, as in the case of evaporation from a liquid drop. The fission, on the other hand, requires a deformation of the whole nucleus of sufficient magnitude that the surface tension can no longer force it back into spherical shape, and the nucleus therefore divides int o two smaller nuclei, corresponding to the separation of a liquid drop into two small drops. For lighter nuclei the energy necessary for such a deformation will be much larger than the neutron binding energy, but just for the heaviest nuclei the two energies will be of the same order of magnitude. Indeed in this case the strong electric repulsion caused by the high charge of the nucleus will, as was first emphasised by Frisch and Meitner, substantially counteract the influence of the surface tension, and thereby reduce substantially the energy required for the critical deformation. At first sight it could perhaps appear difficult to understand how the energy of the nucleus formed by the collision could be transformed in such a special manner as is required for the deformation leading to an unstable shape of the nucleus. However, we have to consider that both for the neutron emission and
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for fission we are dealing with purely accidental fluctuations in the distribution of the heat energy over the possible modes of motion, which in themselves are both extremely unlikely, and can therefore make themselves felt in the competition only if there is no easier outlet for the energy of the nucleus. Similarly to the case of the lighter nuclei, it turns out, as we shall see, that also for many of the very heaviest nuclei collisions with slow neutrons can lead to capture only because the probability of radiation greatly exceeds the probability of any form of disintegration. With increasing excitation energy of the nucleus, however, the probability of disintegration will rise more rapidly than that of radiative processes, and will already have become far greater in a collision with neutrons with a kinetic energy of about 1 MeV. In close connection with the arguments we have used concerning the neutron emission, the probability of fission of an excited nucleus taking place in a given time can also be determined with the help of well-known thermodynamic and statistical laws. Instead of the analogy with the evaporation of a liquid drop we are here concerned with an analogy with the dissociation of a chemical compound. It is well known that for such a dissociation one must in general distinguish clearly between the total energy lost or gained in the disintegration of the molecule, the so-called dissociation energy, and the energy which the molecule must possess to initiate the dissociation, the so-called activation energy. While the dissociation energy determines the chemical equilibrium, it is just the activation energy which governs the reaction rate. In the case of nuclear fission the dissociation energy has the enormous negative value of about 200 MeV for the heaviest nuclei, whereas the activation energy, corresponding to the minimum energy required for the critical deformation of the nucleus, is positive and, for uranium and thorium, is substantially less than 10 MeV. Strictly speaking there will be, according to quantum mechanics, a certain probability that fission of a nucleus can take place also at lower energy, and even for a nucleus in its normal state. As in the case of ordinary chemical explosives, the probability of such spontaneous processes is in general extremely small compared to the probability which arises from a critical deformation of the nucleus, analogous to ignition. As soon as the excitation energy of the nucleus exceeds the value required for such a deformation, the probability of fission per unit time will rise very quickly with energy content, and will depend on the temperature of the nucleus in a manner strictly corresponding to the temperature dependence of monomolecular chemical reactions. 7. The detailed mechanism of nuclear fission. From the foregoing considerations we must expect that the competition between radiative and disintegration processes, which determines the course of the
PART I: PAPERS AND MAKUSCRIPTS RELATING TO KUCLEAR PHYSICS
collision of a neutron with a heavy nucleus, should depend in a simple manner on the difference between neutron binding energy and the critical energy for fission. The identical temperature variation of evaporation and reaction rates explains therefore the observation that the ratio between the probabilities for neutron emission and fission remains constant for energies higher than both the neutron binding energy and the critical energy for fission, and depends on the difference between these values. However, for lower excitation energies we find, as we shall see, an essentially different behaviour, depending on whether the neutron binding energy is greater or less than the critical energy for fission. To obtain a clearer view of this situation we shall first consider in a little more detail the various competing modes in which the collision between a neutron and a heavy nucleus can develop. For this purpose fig. 3 gives a schematic representation of the various stages of the process. The top of the figure shows as stage A the situation immediately before the collision. The small circle with an attached arrow denotes the incoming slow or fast neutron, while the large circle indicates the heavy nucleus, which before the collision is of course in its ground state, indicated by the circle being empty. Stage B shows the intermediate state of relatively long life, in which the nucleus has absorbed the neutron, and the newly formed nucleus has not yet given up any of its energy. The high state of
Fig. 3.
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excitation of the nucleus is indicated both by the irregular form of the contour and by the shading inside. The varying density of shading is intended to remind us that the heat energy is not uniformly distributed, but undergoes continuous fluctuations in the different parts of the nucleus. Finally stage C shows how the final stage of the process can proceed in three different ways, whose relative probabilities will depend on the magnitude of the excitation energy of the intermediate nucleus, which in turn depends on the kinetic energy of the incident neutron. Column I, on the extreme left, represents the process in which the neutron is finally captured. Reading from the top down we are shown how the energy of the nucleus decreases gradually, in this case by the emission of a number of quanta of radiation, until the new nucleus is finally left in its ground state. The small asterisk in the empty circle recalls that this nucleus is in general radioactive and will emit an electron after a certain mean life, which is extremely long compared to the time involved in the nuclear reaction. Column I1 represents the process in which a neutron escapes from the nucleus, which subsequently, by the emission of one or more quanta of radiation assumes the same state as the nucleus which originally in stage A was hit by the neutron. As indicated in the top picture of the column, the neutron emission is due to the concentration of a substantial part of the total thermal energy on a single particle in the nuclear surface. This is indicated both by the dense shading in an arbitrarily chosen region on the right, and by the rest of the nucleus being more lightly shaded than in stage B. As indicated by the length of the arrow attached to the small circle in the next figure down the velocity of the emitted neutron is in general much less than that of the neutron which hit the nucleus in stage A. The last figure of the column indicates how the remaining energy is emitted in the form of radiation. Finally in column 111, at the extreme right, the final stage of the development of the process leading to fission is shown. The first picture of the column shows how such a fission starts with a deformation of the nucleus which is sufficiently large so that the electric repulsion between the most distant parts can balance the contracting effect of the surface tension. As indicated by the relatively light shading, such a deformation requires a substantial part of the whole energy content of the nucleus, quite similar to the energy concentration required for neutron escape. The next picture of the column represents a state in which the nucleus is already split, and the separate parts have acquired a high velocity away from each other, because of their mutual repulsion. In this picture the shading is again denser, because the substantial deformation which each fragment will have at the instant of separation will again be quickly transformed into internal kinetic energy under the influence of the surface tension. The two following pictures in column I11 illustrate the very interesting observa-
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tion that in fission a number of neutrons are emitted, on the average two per fission. As indicated in the pictures this process - exactly like the neutron emission shown in the first two pictures of column I1 - must be assumed to result from accidental energy concentrations in the surface of the new strongly heated nuclei. Before we enter into a discussion of the important questions to which the discovery of this neutron emission in fission has led, we shall complete our review of the schematic representation in fig. 3 by mentioning only that the last picture of column I11 shows how the energy, left over in the nucleus after the neutron emission, is lost as quanta of radiation. The new nuclei will be strongly radioactive as mentioned already, and a number of asterisks in the empty circles indicates that subsequently each fragment will undergo a series of transmutations with electron emission, until the ratio between mass and charge has reached the value appropriate to stable nuclei. 8. The question of release of atomic energy. The great interest attached to the emission of neutrons in fission is due to the fact that this opens up entirely new prospects of a possible release of the great energy contained in the heavy nuclei, whose existence has been known since the discovery of natural radioactive substances. It is quite evident that there exists the possibility that the neutrons emitted in the fission process can, by colliding with other heavy nuclei, cause further fission. Since, furthermore, on the average more than one neutron is emitted per fission, one could therefore expect that in suitable conditions there might develop an avalanche of fission processes, so that we would face an explosive release of energy. If one remembers that, even for the strongest chemical reactions which occur in the ordinary explosive substances, we are dealing with an energy release of at most a few electron volt per molecule, whereas the fission of heavy nuclei releases nearly 200 million electron volt, one can understand what terrifying perspectives we would face if substantial amounts of uranium or thorium could really be made to explode. As we shall see, a closer consideration shows the situation to be such that there is no cause for alarm in this respect, although one can hardly say with certainty that any large-scale release of atomic energy is entirely ruled out. To be able to judge the possibility of energy release by nuclear fission under neutron bombardment, we must look more closely at the way in which the fission probability depends on the neutron energy. In the particular case of uranium we meet here the situation, surprising at first sight, that fission can be caused both by thermal neutrons with energies of a fraction of an electron volt, and by fast neutrons with energies of over 1 MeV. However, already some years before it became clear that in these processes one had to d o with a real fission of the nuclei, Hahn and Meitner found that the radioactive nuclei formed by the colli-
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sion between uranium nuclei and neutrons of intermediate energy had quite different mean lives from those produced with slower or faster neutrons. It was found in particular that around 20 eV there exist quite narrow energy regions in which the effect of neutron bombardment of uranium was particularly pronounced. This suggested therefore, that the process consisted of a selective neutron capture, indicating discrete energy levels for the new nucleus formed in the collision, and from the magnitude of the yield one could conclude that this process must be ascribed to the most abundant uranium isotope of mass number 238. Uranium contains also lighter isotopes of mass numbers 235 and 234, but only in such small quantities that they could not even at full resonance give rise to effects of this magnitude. From our general ideas about nuclear reactions we must, for a review of the situation, investigate how the probability of the several competing processes represented in fig. 3 should be expected to vary with the energy of the neutron whose collision with the heavy nucleus initiates the fission. The typical behaviour of this dependence is shown in fig. 4, curves I, I1 and 111, which on a relative scale give the probabilities for radiation, neutron emission and fission, respectively. Whereas curves I and I1 can be assumed to have nearly the same shape for all heavy nuclei, the fission probability, on the other hand, depends essentially on the difference between neutron binding energy and critical energy for fission, which is characteristic of each type of nucleus. For curve 1111 it is thus assumed that the fission threshold is about 1 MeV above the neutron binding energy and for curve I112 this difference is assumed to amount to about 2 MeV. Curve 1113, on the other hand, corresponds to the case in which the critical energy for fission is about 1 MeV below the neutron binding energy.
Fig. 4.
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If we disregard for a moment the situation with slow neutrons, and first consider the energy region around 1 MeV and above, we find that the observations both for uranium and for thorium are reproduced satisfactorily by the curves if we choose for the fission probability in the former case curve 1111and in the latter case curve 1112. With rising neutron energy the fission begins to make itself felt again, in the case of uranium first at about 1 MeV, whereas nearly 2 MeV is required to cause fission in the somewhat less strongly charged thorium nucleus. Also quantitatively the course of the curves 1111 and I112 agrees with the effects observed in the bombardment of uranium and thorium with fast neutrons. Thus, as already mentioned, the position of curves I11 in relation to curve I1 means just that the probability of the neutron impact causing fission rapidly approaches a constant value, once the critical energy for fission has been exceeded; for uranium this value is about f , whereas the fission yield for a neutron collision in thorium amounts to only about &. In a collision with neutrons of an energy below 1 MeV for uranium and 2 MeV for thorium the curves would predict that essentially only the reactions represented in columns I and I1 of fig. 3 need be considered. Which of these two processes is the more probable depends of course on which of the relevant curves of fig. 4 lies higher at the neutron energy under consideration. For the lowest neutron energies, for which curve I still lies above curve 11, neutron capture must thus be expected to dominate, and it is also just in that region that pronounced selective capture effects have been found both for uranium and for thorium. However, in this way we do not obtain any explanation of the high probability of fission in the bombardment of uranium with thermal neutrons, which has been observed, as already mentioned. We are therefore forced to assume that these effects are not due to the common uranium isotope, like those discussed, but to one of the lighter isotopes, an assumption which is also very plausible because in thorium, which consists of only a single isotope of mass number 232, no fission has been observed at low neutron energy. At first sight it could appear surprising that such strong effects could be due to an isotope which is present only in such small amounts as the lighter uranium isotopes. In fact natural uranium contains over 99% of the heavier isotope '&J, while the rest consists mainly of the isotope '?&.J. However, we are here concerned with quantum mechanical resonance phenomena for which - as we mentioned already in connection with the capture of slow neutrons - the reaction probability can be much larger than the probability of a collision calculated from ordinary mechanical ideas. The condition that the bombardment with slow neutrons can lead to fission processes of the observed frequency, is however that the fission probability of the relevant nuclei should already at low energy exceed the probability of radia-
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tion, and that therefore the former probability should be given by a curve of the type of curve I113 in fig. 4. This is just the kind of curve we must expect for the collision between a neutron and a nucleus '?d:U, since the critical energy for fission for the nucleus produced in this collision must be assumed to be less than the neutron binding energy, contrary to the situation in the case of a neutron collision with a nucleus of the abundant isotope '%U. This is partly due to the fact that the critical energy for fission in the nucleus 'i?%J is somewhat lower than for '$zU because of the larger ratio of charge to mass, and partly to the neutron binding energy being considerably larger for the former nucleus than for the latter. Indeed it is a consequence of the peculiar nature of the nuclear forces that nuclei for which both charge and mass numbers are even, are more stable than nuclei of about the same mass, but for which either or both of these numbers are odd. This rule, of which a familiar example is the particular stability of the a-particle in comparison with other light nuclei, has in recent years been confirmed by studies of the numerous radioactive isotopes created by nuclear reactions. Since just this question of the origin of the fission produced by slow neutrons is critical for estimating the possibility of energy release by uranium fission, as we shall see, it became very desirable to prove the above conclusions by direct experiment with separated uranium isotopes. The difficulty in separating isotopes even in small quantities is however well known to be very great, and such an experiment has succeeded only very recently. This work, carried out by Nier, Booth, Dunning and Grosse, is in many respects the most remarkable evidence of the wonderful development of experimental technique in this field. Although the rare isotope '?d:U could be purified only in quantities amounting to onemillionth of a milligram and therefore was not even sufficient to cover a square millimetre with a single continuous layer of atoms, it was nevertheless proved successfully that the whole yield of fission of uranium with thermal neutrons was due to this isotope. To return to the question of the release of atomic energy, we shall now investigate what is the probability that the neutrons generated in the fission of uranium or thorium nuclei can cause further reactions. First of all it is easy to see that the possibility of producing a chain reaction in thorium is altogether limited, since the fission of a thorium nucleus requires an energy of nearly 2 MeV, whereas the neutrons emitted in connection with the fission have an energy of only 1 MeV on the average, corresponding to the temperature energy of the fission fragments. As regards uranium this energy is certainly of such an order of magnitude that the neutrons can just produce splitting of the abundant uranium isotope, but we must remember that the impact of even a fast neutron on such a nucleus can lead to fission only in one case out of five. The result of the remaining collisions will be that a neutron will escape from the nucleus form-
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ed in the collision with an energy which on the average will be much less than the energy of the incoming neutron, and therefore will be unable to cause fission in :';U nuclei. Therefore, even if reaction chains can occur in this uranium isotope, these will remain too short and rare for there to be any question of an explosion. The situation would however be quite different if we had a sufficiently large quantity of the lighter isotope %U available; for here every neutron produced in the fission process would have a very considerable probability of causing further fission in a collision with other uranium nuclei, and since for each fission two neutrons are emitted on the average, an explosion would be the unavoidable consequence. With present technical means it is however impossible to purify the rare uranium isotope in sufficient quantities to realise the chain reaction discussed above. The decisive question is therefore how far the natural mixture of uranium isotopes can be used to release energy on a large scale. The obvious approach would be to mix uranium with materials containing hydrogen so as to ensure that the neutrons produced in the fission will subsequently be slowed down, by collisions with the protons, sufficiently to react with the rare isotope with sufficient probability. In experiments with such mixtures one has indeed obtained chains of several successive fissions, but it is clear beforehand that with this approach there can never be a question of explosions which would suddenly release a substantial part of the atomic energy. For such explosions to occur the temperature of the mixture would have to rise to milliards of degrees, but as soon as the temperature reaches just a few thousand degrees the process will stop because the protons in the mixture will have too high a kinetic energy to slow down the fission neutrons sufficiently. Indeed, the probability of a neutron reacting with the rare uranium isotope decreases rapidly with rising neutron energy, and already at energies of a few electron volt it is less than the probability of neutron capture in the abundant isotope. Whether the latter capture process will in all cases prevent the development of sufficiently long chain reactions to allow a practical energy release to develop is, however, a question which can only be answered after further research.
XLV. ON THE STATISTICAL DISTRIBUTION OF FISSION FRAGMENTS UNPUBLISHED MANUSCRIPT [ 1939?]
See Introduction, sect. 5 , ref. 128.
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
This manuscript, catalogued as of [1939-19401, consists of a carbon copy of 6 pages in English with a few amendments in pencil in Rosenfeld’s handwriting. On top of the first page there is in red pencil an unintelligible word and the word “gammel” (“old”). There are photostats, in duplicate, of 3 diagrams and a sheet with captions for the diagrams. This version is reproduced here. There are further 3 typewritten pages, numbered 2 to 4, of a different version. The manuscript is on microfilm Bohr MSS no. 16.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
On the statistical distribution of the fission fragments. In a recent paper’, we have given a theoretical treatment of the fission of heavy nuclei initiated by neutron impact. In particular, it was found possible by simple considerations to account for the relative fission yields by neutron bombardment or uranium, thorium, and protactinium and the dependence of these yields on neutron velocity. In these considerations, however, it was not attempted to discriminate between the various modes of division of the nuclei concerned, and it was for simplicity assumed that this division takes place in an approximately symmetrical way. Several experimental investigations, however, and especially the experiments of Booth, Dunning and Slack2, have shown that the statistical distribution of the kinetic energies of the fragments resulting from uranium fission presents two sharp maxima, disclosing a pronounced selectivity for an asymmetrical mode of division of the uranium nucleus in two parts with a mass ratio of about 3:4. Such a selectivity in the course of the fission process is also revealed by the study of the chemical properties of the radioactive fission products of thorium and uranium fission3. It might therefore be of interest to point out how the preponderance of a certain degree of asymmetry in the mode of division may be simply interpreted on the basis of the general considerations on the fission mechanism developed in our paper. These considerations are based on the assumption that in the fission phenomenon, just as in the other reactions of heavy nuclei, we have to do with a process which takes place in two well separated stages4. Of these the first is the formation of a highly excited compound system of comparatively long life-time and the second is the subsequent disintegration of this system or a radiative transition to a still more stable state. The ultimate course of the reaction is therefore determined by the relative probabilities of the different possible disintegrative or radiative transition processes of the compound system. Now, for the heavy nuclei concerned, essentially only two kinds of disintegrative processes compete: the escape of a neutron from the compound system and its division into two nuclei of comparable charges and masses.* The first process involves the fortuitous concentration of a considerable part of the excitation energy, statistically distributed over all degrees of freedom of the compound system, on some parti-
’ N.
Bohr and J.A. Wheeler, Phys. Rev. 56, 426 (1939). See also Phys. Rev. 56, 1065 (1939).
’ E.T. Booth, J . R . Dunning and F.G. Slack, Phys. Rev. 55, 981 (1939).
Cf.0. Hahn [and F . Strassmann], Phys. ZS. [40 (1939) 673-6801 and especially L. Meitner and R . Frisch, Math.-phys. Cornrn. Copenhagen Academy [17, no. 51 (1939). Cf. N. Bohr, Nature 144, 200 (1939) and Phys. Rev. 55, 418 (1939).
* [An insertion in pencil is illegible and has been omitted.]
CIS,
2
PART I: PAPERS AND MANUSCRIPTS RELATIKG TO NUCLEAR PHYSICS
hlS. p . 4
cle at the nuclear surface, in order to overcome the short-range attractions from the neighbouring particles. The second process demands a concentration of excitation energy into a deformation of the shape of the nuclear surface sufficient to lead to a rupture of the compound nucleus. While all the nuclei concerned are stable against small deformations from spherical shape, there will for each nucleus exist a multitude of more or less unsymmetrical dumbbell shapes, corresponding to unstable equilibrium. It is just these unstable configurations which must be regarded as transition states in the course of the fission process, and the facility of fission of the heaviest nuclei depends on the circumstance that the potential energy of critical deformation, which for lighter nuclei is much larger than the binding energy of a neutron, only for such nuclei is of the same order of magnitude as the latter energy. As shown in our paper, this can be understood from a simple estimate of the variation of the potential energy for increasing deformations of symmetrical character. It is also clear that the critical energies of deformation demanded for very unsymmetrical modes of fission are much larger than for symmetrical division but, as we shall see, it is actually to be expected that for the nuclei concerned the critical energy will exhibit a minimum not for exactly symmetrical division but for a division of a degree of asymmetry of the order indicated by the observed selectivity of the fission phenomenon. In the first place, we observe that due to the almost linear variation of the mass defect curve just in the region of atomic weights corresponding to about half the mass of the uranium nucleus, the total energy released by division of the compound nucleus will be very nearly the same for a wide range of modes of division, including that with a mass ratio 3:4 of the fragments, and will first begin rapidly to decrease for still higher asymmetry of division. In fact, a closer estimate based on the considerations developed in Section I of our paper, and assuming that the charges of the fragments are divided approximately in the same ratio as the masses, shows that the energy released in a division of asymmetry ratio 3:4 will not differ from that released in symmetrical division by more than one or two million volts. Already for an asymmetry ratio 1:2, however, this energy will be about 40 MeV smaller than for symmetrical division. On the other hand, the potential energy of the two separated fragments due to their charge will for the same distance decrease much more smoothly with increasing asymmetry. Thus, for fragments at contact, the difference in this energy for symmetrical division and for divisions of charge ratios 3:4 and 1:2 will be about 4 and 20 MeV, respectively. Due to the high excitations of the separating fragments shown by the neutron emission accompanying fission it is of course not possible to deduce the critical energy of division from a simple comparison between the total energy released
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and the potential energy of the fragments at contact. From the way in which these energies vary with the degree of asymmetry we may nevertheless expect that, although the critical fission energy is much smaller for symmetrical division than for a division of asymmetry ratio of about 1:2, it will actually be a few million volts lower for a division of mass and charge ratios of about 3:4 than for a symmetrical division.
Fig. I . Potential energy variation in the course of fission. The abscissa represents roughly the increasing degree of deformation of the compound system and distance between the separated fragments, while the ordinates represent the energies in a suitable scale, with the notations explained in the text.
Fig. 2 . Probable courses of potential energy curves for fission processes of different asymmetry ratios.
This argument is illustrated in Fig. 1 and 2. The first figure represents in a general way the variation of the potential energy at different stages of the deformation of the compound system NOand its rupture into two separated nuclei N 1 and Nz.The two parts of the curve drawn in full correspond to the energy of stable deformations of the compound nucleus and to the Coulomb energy of the two separated nuclei respectively, and the broken line joining them corresponds to the instability region. While the energies of the three nuclei in their normal state are denoted by Eo,E l , Ez,the energies in the excited states involved in the initial and final stages of the process are denoted by Eg, ET, and E;. The difference between the maximum of the curve and the energy EO represents the critical fission energy Ef.In the second figure, the probable runs of the upper parts of the potential curves are sketched in a somewhat larger scale for symmetrical division (1:l) and for divisions with asymmetry ratios 3:4 and 1:2. For
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
MS,p 5
convenience of comparison, the zero-point for the ordinates is in all three cases chosen as the energy of the separated excited fragments at large distance apart, so that the potential curves will all have as an asymptote the axis of abscissae not shown in the figure. The joining of the two parts of the curve evidently implies a much greater value of Ef for 1:2 division than for the two others. Moreover, it is seen that in the two latter cases the separation of the right parts of the curves is considerably larger than that of the beginning of the left parts and that, therefore, we shall expect a value of Ef some million volts lower for 3:4 division than for symmetrical division. The expected variation of Efwith increasing asymmetry of division, exhibiting a sharp minimum in the neighbourhood of the division ratio 3:4, is roughly indicated in Fig. 3.
Fig. 3 . Probable variation of critical fission energy with division ratio for uranium. The abscissa represents the division ratio, and the ordinate energies in MeV.
While these remarks may be regarded as supplementing the arguments in Section I1 of our paper, the considerations given in Section I11 concerning the probability of a given mode of fission may be applied without any alteration. Strictly speaking, it has in our formula (32) for rfbeen assumed that fission takes place only according to one mode of division and the approximate agreement between the formula and the value of rf deduced from experiment may therefore be regarded as being in conformity with the observation of a pronounced selectivity in the fission phenomena. In fact, if the division could take place in a large number of ways with comparable probabilities, a fission yield much larger than
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that actually found should be expected. Actually, however, the formula (32) will for a given excitation of the compound system, if we take account of a dependence of E'f on the mode of division as that indicated in Fig. 3, lead to fission yields exhibiting a pronounced maximum for an asymmetry ratio coinciding with that of minimum critical energy, and this maximum will be the sharper the less the excitation of the compound nucleus exceeds the minimum fission energy. As regards the question of the dependence of the distribution of the fragments on the energy of the neutrons producing fission, we must in uranium of course distinguish between the contribution from the abundant isotope 238 and the rare isotope 235 responsible for the effects produced by high speed neutrons and slow neutrons respectively. According to the discussion in Section IV of our paper (cf. Fig. 7 ) , the excitation should in the latter case lie less than a million volts above the critical fission energy, and since the difference between the minimum fission energy and that for symmetrical division is, as estimated above, of the same order or still larger, we should in this case expect a very small yield indeed for symmetrical division. For high neutron energies, for which only the abundant uranium isotope comes into consideration, we should expect similar conditions up till at least 2 MeV neutron energies. For still higher energies, symmetrical division should never exceed a small fraction of the yield for unsymmetrical division with mass ratio of about 3:4. The variation of the ratio between the yields of unsymmetrical and symmetrical division with neutron energy in uranium should in fact closely resemble the variation of the ratio between the total yields of fission in uranium and thorium, in which case the difference in critical fission energy is estimated, in Section IV of our paper (cf. Fig. 6), to about a million volt. Also in thorium or protactinium, we shall of course expect similar circumstances as regards the distribution of the fission fragments. Apart from a relatively small displacement of the maxima towards smaller atomic weights we must, however, due to the delicacy of the energy balance concerned, be prepared for other minor changes in the shape of the distribution curve. Such differences between the distribution curves for uranium and thorium seem in fact, as pointed out by Meitner and Frisch (loc. cit.), indicated by the chemical analysis of the fission products in the two cases. Continued experiments on such lines and especially on the dependence of the statistical distribution of fission products on neutron energy for the various heavy elements should certainly offer most valuable material for further development of the theory of the fission mechanism.
MS, P 6
XLVI. SUCCESSIVE TRANSFORMATIONS IN NUCLEAR FISSION Phys. Rev. 58 (1940) 864-866
See Introduction, sect. 5 , ref. 135.
Reprinted from THE PHYSICAL RCVIELV, Vol. 58, KO.10, 864-866, h’ovember 15, 1940 Printed i n U. S. A.
Successive Transformations in Nuclear Fission N . BOHR Institute of Theoretical Physics, University of Copenhagen, Copenhagen, Denmark (Received August 17, 1940)
If it be assumed that fission of heavy nuclei takes place in competition with the escape of a neutron from the highly excited compound system, we should expect t h at , for sufficiently high excitation of the system, fission of the residual nucleus left after neutron escape may still occur. Since, in this second stage of the process, the conditions for the competition with neutron escape are in several cases more favorable than in the first stage, such effects may give rise to much increased cross sections for the fission process.
AS
has been shown in earlier papers,’ it is possible to explain the principal features of the fission of heavy nuclei on the basis of the assumption that the process involves a comparatively long-lived intermediate state of the compound system in which the excitation energy is distributed over all degrees of freedom, as in temperature equilibrium. In fact, the excessive deformations of the compound nucleus leading to rupture are to be attributed to fluctuations in this energy distribution occasionally resulting in the concentration of a considerable part of the excitation energy in particular modes of oscillation of the closely coupled system of nuclear particles. T h e probability t h a t a fission of the compound system takes place is therefore determined by a competition with other disintegrative or radiative processes leading to a N. Bohr, Nature 143, 330 (1939); Phys. Rev. 5 5 , 418 (1939), and especially N. Bohr and J. A. Wheeler, Phys. Rev. 5 6 , 426, 1065 (1939), (referred to in the following a s Bn‘).
decrease in the excitation energy of the residual system to such an extent t h a t fission is no longer possible. In the ordinary cases, where the compound system has an energy not greatly exceeding that required for fission, the occurrence of one or the other competing process will reduce the energy available below the critical value. If, however, the excitation of the compound system is very high, the residual system may have a sufficient excitation to permit fission. In the second stage, the probability of fission will, of course, again depend on a competition with other disintegrative or radiative processes. Such progressive transformations have already been briefly discussed (BW, p. 449) especially in connection with deuteron incited fission, b u t a t t h a t time no experimental evidence for their occurrence was available. Recent experiments on fission with high speed neutrons as well as with deuterons seem, however, to afford definite evidence of successive transformation and, as they a t the
865
T R A K S F O R hl A T I 0 N S
I N
Ii L C I. E A R F I S S I 0 N
same time elucidate the competitive character mass and charge number A and 2.The difference of the fission process, it may be of interest here i n the two constants represents just the difference to consider them in some detail. of about 1 )lev between the binding energy of a I n the first place, it has been found by Ageno, neutron in a heavy nucleus for even and odd Amaldi, Bocciarelli and Trabacch? that the numbers ( A -2)of nuclear neutrons. cross section for fission in uranium by neutron For 92L239 and 9 2 U 2 1 8 , formula (1) gives impact remains practically constant for neutron AE= +0.7 hlev, and AE= -0.6 MeV, from energies from about one million volts to about which one deduces that, for sufficiently high ten million volts, but t h a t it increases consider- excitation the ratio p betLveen the probabilities ably for neutrons with still higher energies, for neutron escape and fission, which for g2L21q obtained by the bombardment of lithium with is about 4 : 1, will for 92U’38be less than 1 : 3. deuterons. This result can easily be understood For the average cross sections u,’ and u,” for by considering that, for the lower energies, we uranium fission n.ith fast neutrons in one and have simply to do with a competitisn between two stages, respectively, we get neutron escape from the compound nucleus 92U*39 1 1 4 3 and its fission, the ratio between the probability of these competing processes being nearly constant for neutron energies above 1 MeV. If, however, the neutron energy is above 10 hlev, where uo is the cross section for formation of and the factor a there is a considerable probability t h a t the the compound system 92U23q roughly represents the fraction of the residual residual nucleus 92U238 left after neutron escape nuclei 9 2 P 8 having excitation greater than the will have a sufficient excitation itself to undergo critical fission energy. Since the esperimen ts fission. Jloreover, the condition for fission is, in show that the average cross section for D + L i this case, especially favorable since in 92U238 we neutrons is 40 percent higher than that for have to do with a nucleus of even charge and mass number for which, just as in the compound D + B e and D f B neutrons, a should in this nucleus 92U236 formed by neutron impact on the case have an average value somewhat larger rare uranium isotope 92U2355, the critical energy than &, which appears reasonable from the for fission is somewhat lower than the binding knmvn spectrum of the D f L i neutron^.^ A comparatively larger effect from successive energy of a neutron. Thus, for excitation energies transformations should be expected in the case of the nucleus ,2U238 just above the critical energy of the fission of thorium with fast neutrons. I n for fission, no neutron escape can take place; fact, from formula (1) ive get for 90Th233 and and, even a t higher excitation, the probability 90Th232 approximately AE = 1.7 and +0.4, correfor fission in this process is much greater than sponding to values for p of about 24 : 1 and for neutron escape. An estimate of the difference between the 2 : 1. In this case, we therefore get critical fission energy E f and the neutron binding u,‘= uo/25, u,”= 8 a . ao/25. energy E n can, for all the nuclei concerned, be arrived a t by simple considerations (BW, pp. 43C, \I‘ith the same value of a as above, Ive shall 433), the result of which may be summarized in thus expect t h a t the average cross section for D+Li neutrons will be almost twice that for the following approximate formula : D + B e neutrons. Still more conspicuous effects .If? El -En = 0.27 ( A - 238) - 1.32(Z - 92) should, of course, be expected in the case of neutrons with well-defined high velocities for (1) which a can be almost 1, giving a total fission cross section nearly 10 times greater than that giving AE in Mev for a compound nucleus with obtained for neutrons with only a few million volts energy, for which a! is still zero. 1
M. Ageno, E. Amaldi, D. Bocciarelli and G. C. Trabacchi, Atti Acc. d’ltalia, in press; kindly communicated to the author by Professor Amaldi.
3T.W. Bonner and W. Brubaker, Phys. Rev.
(1935).
48, 748
866
N. B O H R I n this connection it inay be of interest to point out that similar effects can also be expected in the fission of protoactinium with fast neutrons. Here, for the compound nuclei g1Pa232and glPa23*, we get from formula ( I ) ,
AE=+0.1
and
AE=-1.2
giving values for p of about 1 : 1 and 1 : 10, leading to uf’= & n o , nf” = 5 , . u o j l 1.
for the successive uranium transforniatiotis, and
AE=+0.6 1Iev ancl
AE= -0.7 J l e v
for the thorium transformations, corresponding to values of p of about 1 : 2 and 1 : 24 for uranium and about 3 : 1 and 1 : 4 for thorium. Thus, we shall expect for uranium nI‘ = ! u 0 ;
uI“ = 8cru1,/25
and for thorium Thus, we shall expect an increase in fission yields of about a factor of two when comparing the effects of neutrons of a few million volts with While ui’ for thorium is only about ’$the value neutrons above ten million volts. for uranium, \ve see that the total cross sections As regards fission induced by deuterons, it n,’+”’’ become nearly equal for the two elef o l l o ~ sfrom simple theoretical considerations ments if cr approaches unity, as is to be expected (BIY, p. 448) t h a t a sufficient excitation of the from the high excitation (about 15 Mev) of the compound system can only be obtained bjr impacts compound system. The experiments of Jacobsen leading to a complete fusion of the deuteron and and Lassen, showing t h a t for 9-Mev deuterons the original nucleus. T h e yield of the reaction the fission yield for thorium amounts to about will, therefore, in the first place depend on the 0.7 of the uranium value, seem therefore to ease itith which the deuteron penetrates the confirm that we have here to d o with successive electrostatic field around the nucleus, and cross transformations. sections of the order of magnitude of nuclear In the fission effects i n uranium with fast dimensions can only be expected for deuteron neutrons and deuterons, the presence of the rare energies approaching 10 h4ev. This is in agreeuranium isotope 92U235will, in contrast to the ment with the experiments of Gant4who reported case with slow neutrons where it is responsible a threshold for the process in uranium of about for the \thole effect, be of negligible importance. 8 l l e v , without attempting measurements of In experiments Lvith separated uranium isotopes, cross sections. Such nieasurenients for uranium we shall, of course, also for 92U235 expect to observe as well as for thorium have recently been made successive transformations of the same kind as a t this Institute by Jacobsen and Lassens who those discussed here, b u t because of the fact that found for both elements a rapid rise in the yield for the compound nuclei 92uxJ6 and 93EkaRe237 of the process between 8 and 9.5 MeV, corredirectly formed by neutron and deuteron imsponding to cross sections of the order of pacts, we have from (1) the large negative values cm2 a t the latter energy. AE = - 1.2 and AE = - 2.3, corresponding to In deuteron induced fission of uranium and very small values for p , such effects will be far thorium, we shall expect progressive transformaless pronounced than in the cases considered tions involving the compound nuclei g3EkaRe240, above. Similar considerations apply to proto93EkaRe23g and 91Pa234, ,IPa233, respectively. From actinium fission by deuteron impact. ( I ) , we get From this brief discussion of successive trans-
AE= -0.4 Mev and
AE= - 1 . 7 hlev
D. 13. T.G a n t , Nature 144, 707 (1939). J . C. Jacobsen and N.0 . Lassen, Phys. Rev. 5 8 , 867
(1940), following paper.
formations in nuclear fission, i t will be seen t h a t the study of these phenomena offers a means of enlarging greatly the number of different nuclei in which the fission process may be investigated.
XLVII. DISINTEGRATION OF HEAVY NUCLEI [2] TUNGE ATOMKERNERS SQNDERDELING Overs. Dan. Vidensk. Selsk. Virks. Juni 1940 - Maj 1941, p. 38 Communication to the Royal Danish Academy on 10 January 1941 ABSTRACT TEXT AND TRANSLATION
See Introduction, sect. 5 , ref. 139.
NIELS BOHR giver en Meddelelse: Tunge Atomkerners Smderdeliiig. En Oversigt over d e sidste Aars Iagttagelser vedrsrende de tungeste Atomkerners Ssnderdeling vil blive givet, og det vil ))live vist, hvorledes disse Iagttagelser kan forklares ud fra simple Forestillinger om Atomkerneomdannelsers Forleb.
Vil blive trykt i Mat.-fys. Medd.
TRANSLATION Niels Bohr presents a communication: Disintegration of Heavy Nuclei. A review will be given of the last few years’ observations concerning the disintegration of the heaviest nuclei, and it will be shown how these results can be explained on the basis of simple ideas about the mechanism of nuclear reactions. This will be published in Mat.-fys. Medd.*
* [In fact,
it was not published.]
XLVIII. MECHANISM OF DEUTERON-INDUCED FISSION Phys. Rev. 59 (1941) 1042
See Introduction, sect. 5, ref. 136.
Reprinted from T H E PHYSICAL REVIEW,Vol. 59, No. 12, 1042, June 15, 1941 Printed in U. S. 4.
Mechanism of Deuteron-Induced Fission N. BOHR Inslilule of Theorelical Physics, Universily of Copenhagen. Copenhagen, Denmark M a y 8 . 1941
IN
nuclear transformations jnitiated b y deuteron impact, t\vo types of processes are, as well known, t o be t.iken into consideration. I n t h e process of t h e first t y p e (process J ) , the intermediate s t a t e is formed by t h e capture of the whole deuteron b y t h e nucleus; in t h e process of t h e second type (process I I ) , t h e deuteron breaks u p during t h e inipact with the result t h a t t h e proton escapes and only t h e neutron is taken up in t h e compound nucleus. As originall>, pointed o u t by Oppenheimer and Phillips' and more closel>.discussed b y Rethe,2 t h e cross section for t h e formation of t h e compound system niay, under certain circumCtcinceb be considerably larger in process I 1 than in process I . Still, il clear discrimination between t h e t w o types of processes by means of ordinary nuclear transformations s w m s so far t o have met with difficulties, a n d it m a y , therefore, tie of intereFt t o point o u t t h a t t h e study of tleu teron-induced fission of heavy nuclei offers new possiIlilities for such a discrimination. Not (Jnty i s fission easily distinguished from other possible trnniformations b u t , in particular, a certain critical ixcitat icdn energy different for different nuclei is necessary for fission t o occur. J u s t as regards t h e excitation of t h e c ~ ~ m p o u nnucleus, d t h e processes I and I 1 differ essentially. \Vhile the excitation obtained by process I will be far greater than the neutron binding energy for all nuclei conreriictl, it will, in process 11, on thc average he smaller t11,iii t1ii.q energy. Since, for t h e ktbundant uranium isotope, ;is \+el1 a s [or thorium, the critical fission enrrg!. is higher tli,in the neutron binding e n e r p , it was c o n c l t ~ t i e dt ~ hat a ct~ii~iilerable outpiit of nuclear fission in thorium and i i i I i i i i u i n cotil~l only lie expected in processes of t)'pe I . I:ven i f , i n certain deuteron energy regions, processes of t y i i c I I shoul(l he more prol)nIile, they woultl almost ent i r c s l y result i n r? permanent capture of a neutron with format ion of ratliriactive uranium a n d thorium isotopes with well-kno\vri periods. Oiic of t h e possibilities of teitiiifi these a r g ~ i m c n t s is offered by a comparison t)et \yeen t h e fission >.iel(ls in ur.iiiiiiin and thorium. This is possible because t h r probal)ilit>,t i f fission of t h e coiiipountl nucleus in process I niny lie estimated with a high degree of approximation. I n fact, the excitation energy in process I will not only be sufficient for fission t o occur in competition with neutron escape, litit even t h e excitation of t h e residual nucleus left after the escape of a neutron will be large enough t o make ;L fiasion quite probable. T h e total probability for fission of the compound nucleus in such successive transformations ivas thus estimated4 t o be nc;irly 1 f ( i r uranium ant1 about 0.8 for thorium. These expect;itions seemed confirmed by t h e experiments reported by Jacobsen a n d
Lassens who found t h a t t h e ratio of t h e fission cross sections in uranium a n d thorium a t 9-Mev deuteron energy was approximately 0.7.. I n a later discussion of these experiments,* however, i t has been realized t h a t t h e cross section for t h e formation of t h e compound system in process I , because of t h e smaller nuclear charge, must be expected t o be 25 percent greater in thorium than in uranium. If t h e whole fission effect in both elements was d u e t o processes of this type, t h e theoretically estimated ratio of t h e fission yields in thorium a n d uranium should, consequently, instead of 0.8, be a b o u t 1.0. T h e difference bet\veen this last figure a n d t h e measured value 0.7 seems too great to be explained, unless it is assumed t h a t a considerable p a r t of t h e effect, a t a n y r a t e in uranium, is d u e t o processes of t y p e 11. A support of this conclusion is also offered by a closer comparison of t h e fission effects in thorium a n d uranium for smaller deuteron energies. T h u s , in t h e experiments of Jacobsen a n d Lassen t h e fission cross section for deuteron energies about 8 Mev is rclatively higher in uranium t h a n i n thorium, as would he expected if a part of t h e effect in uranium sets in for lower energy values. A contribution of process I1 t o t h e fission effects which is relatively greater in uranium than in thorium niay lie expected from t h e fact t h a t t h e critical fission energy of t h e compound nucleus for thorium is almost 2 hlev higher t h a n t h e neutron binding energy, while, for the a b u n d a n t uranium isotope (238), t h e difference is smaller than 1 hlev. Moreover, in t h e energy region con. cerned, where t h e fission cross section is less t h a n 1 percent of t h e geometrical nuclear cross section, it is possible t h a t n not inconsiderable contribution is d u e t o t h e lighter rare uranium isotope (235). Since, for this isotope, t h e critical fission energy of t h e compound nucleus in process I 1 is a b o u t 1 M e v lower t h a n t h e neutron binding energv, t h e probability of fission m a y , for t h e low excitations obtained ti>. such a process, be far greater than for t h e heavy isotope. To clear u p the different questions raised, it would be very dcsirahle t h a t experiments on deuteron-induced fission be extended t o a region of greater deuteron energies, a n d , especially, t h a t such experiments be performed with separated uranium isotopes and with protactinium. for which the critical fission energy of t h e compound nucleus is nearly equal t o t h e neutron binding energy.' i
J . R.
Oppe'nheimer and M . Phillips, Phys. Rev. 48, 500 (1935). Rethe, Phys. Rev. 53, 39 (1938). S . Bohr and J. A . Wheeler, Phys. Rev. 56, 449 (1939). S . B ohr, Phys. Rev. 58. 864 (1940). J . C. Jncobsen and N . 0.Lassen, Phys. Rev. 58. 867 (1940). J . C. Jacohsm and N . 0 . Lassen. Det Kgl. Danske Vidensk. Selsk.
* H. A. 3 4
5 6
llath.-fys. Xledd. (Math.-phys. Comm., Acad. Sci. Copenhagen), in print. 7 N. Bohr and J. A . Wheeler. Phys. Rev. 56, 1065 (1939).
XLIX. ON THE TRANSMUTATIONS OF ATOMIC NUCLEI OM ATOMKERNERNES OMDANNELSER Overs. Dan. Vidensk. Selsk. Virks. Juni 1945 - Maj 1946, p. 31 Communication to the Royal Danish Academy on 19 October 1945 ABSTRACT TEXT AND TRANSLATION
See Introduction, sect. 5 , ref. 141.
XIELS BOHR gav en Meddelelse: dnniielser.
Om Afornkeriieriies Orn-
Der blev i Foredraget givet e n O ~ e r s i g to v e r d e n Udvikling af vort K r n d s k a b ti1 Atonikernernes Egenskaber, d e r h a r muliggjort e n Frigclrelse n f store Energimrpngder, h u n d n e i d e tungeste GrundstofTcrs A t om e r
TRANSLATION Niels Bohr presented a communication: On the Transmutations of Atomic Nuclei. The lecture gave a review of the development of our knowledge of the properties of atomic nuclei, which has made it possible to release large amounts of energy stored in the atoms of the heaviest elements.
L. ON THE MECHANISM OF TRANSMUTATIONS OF ATOMIC NUCLEI 11. PROCESSES IN THE CONTINUOUS ENERGY REGION OF THE COMPOUND STATE [l] (WITH R. PEIERLS AND G. PLACZEK) UNPUBLISHED MANUSCRIPT DRAFTED IN COPENHAGEN (INCOMPLETE) 1947
See Introduction, sect. 4, ref. 88.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
The folder “Mechanism of Transmutations of Atomic Nuclei”, 1947, contains carbon copies of two drafts of the unpublished Bohr-Peierls-Placzek paper. They are in English. The first is a draft of 19 pages, all dated 9 October 1947. There is a break after page 15 (where equation (34) is not filled in), indicated by the symbol I/on each side of the page numbers of the following pages. This is the draft reproduced here. The second draft, reproduced as document LI, runs to 21 pages, dated between 22 October 1947 and 29 October 1947. It has some amendments by Placzek, which have been incorporated here, whereas 6 numbered handwritten pages with further amendments by Placzek have not been included. The manuscripts are on microfilm Bohr MSS no. 17.
P A R T I: PAPERS A N D MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
9- 10-47.
ON THE MECHANISM OF TRANSMUTATIONS OF ATOMIC NUCLEI II. Processes in the Continuous Energy Region of the Compound State,
I . Typical Features of Nuclear Transmutations. As explained in earlier papers', nuclear transmutations initiated by impact of material particles or radiation may to a large extent be described as taking place in two well-separated stages. Of these, the first is the formation of a highly excited compound system of relatively long life-time, and the second the disintegration of this intermediate system or its transition with emission of radiation to a less excited state of still greater stability. In fact, because of the extreme facility of energy exchange between the densely packed particles within atomic nuclei, the excess energy will in the intermediate state be temporarily stored in some closely coupled motion of all the particles of the compound system. Any subsequent disintegration or radiative transition of this system can, therefore, to a high approximation be considered to be a separate process, and the final course of the transmutation will depend on a competition between all the disintegrative and radiative processes which the compound system in its intermediate stage can undergo. This picture of the course of nuclear transmutations leads immediately to the following formula for the cross-section 0 A - B of a transition process from the initial state A of the total system consisting of the original nucleus and an impinging material particle or radiation quantum to some final state B of the system in which either some particle has escaped or a radiation quantum is emitted from the intermediate state 0 of the compound nucleus:
where a, + o is the total cross-section for the formation of the compound nucleus from the state A , zo the mean life-time of the intermediate state of the compound system, and yo+B the probability per unit time of the disintegrative or radiative process of the compound system leading to B. The life-time ro is given by
' S e e N. Bohr, Nature 137, 344 and 351 (1937); Science 86, 161 (1937), and especially N. Bohr and F. Kalckar, Danske Vidensk. Selsk. math.-fys. Medd. XIV, [no.] 10 (1937) (in the text referred to as I ) .
MS,
2
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
M S . p. 3
MS,P 4
where the summation includes the probabilities of all possible disintegrative and radiative processes of the compound system, including the return to the state A . This last process is, of course, equivalent to what is usually termed “elastic scattering” of the impinging particle, but it must be observed that C T ~ , as ~ , defined by formula (1) for B = A , will in general not represent the total cross-section for elastic scattering, since part of this, the so-called “potential scattering”, may occur without the formation of a long-lived intermediate state of the compound system. To the complications to which this can give rise also for the unambiguous we shall come back later. definition of the quantity Quite apart from such complications, it is clearly necessary, for the quantities occurring in the formulae (1) and (2) to be sufficiently well defined, that the lifetime of the compound system be long compared with the time intervals involved in a thorough energy exchange between all its constituent particles. This again implies that the excitation energy of the compound system must be much smaller than the total energy necessary for its complete disintegration into elementary particles. While this condition prevents the strict application of the description of nuclear transmutations which we have outlined to collisions involving light nuclei built up of a few particles only, it will for heavier nuclei be well fulfilled, unless the kinetic energy of the colliding material particles or the energy of the incident radiation quanta is extremely high (amounting to 100 MeV or more). It is true that even for heavy nuclei special features regarding the formation of the compound system will have to be taken into account for a considerably smaller energy, because the impinging material particles, when their kinetic energy well exceeds the binding energy of individual nuclear particles (about 10 MeV), will have an appreciable probability of knocking a particle off the surface of the nucleus and, even of penetrating through this surface and throwing a particle directly out of the interior of the nucleus2. Such effects, however, d o not play any great r61e in the usual experiments on nuclear transmutations the typical feature of which is just the immediate establishing, through the interaction between the original nucleus and the impinging particle or light quantum, of a highly stable intermediate state of the compound system. Just on account of the long life-time of this intermediate state, the possibility of its formation is essentially a quantum mechanical problem which primarily depends on the distribution of energy levels of t.he quasi-stationary states of the compound system. For small excitation energies, any nucleus possesses a spectrum of well separated levels; even for heavy nuclei, the mutual distances of the lowest levels thus is of the order of magnitude of lo5 volts, while their widths, 2 F o r a closer discussion of such problems, see W. Heisenberg, Zs. f. Phys. [Ber. Sachs. Akad., math.-phys. KI. 89 (1937) 369-384; Naturwiss. 25 (1937) 749-750.1
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
determined by the probability of radiative processes, are only about lo-' volt. With increasing excitation energy, however, the level distance decreases rapidly and the level width begins markedly to increase as soon as the excitation is sufficient to make disintegration processes possible. Consequently, the level spectrum becomes practically continuous above a certain excitation energy which just falls within the region of excitation energies of the compound system with which we are concerned in the study of many typical nuclear transmutations. In the region where the compound system possesses discrete levels, the total cross-section 0, -o for the formation G f the intermediate state will be very small, except for energies in the immediate neighbourhood of each of the levels where we have t o do with a characteristic quantum mechanical resonance problem. If, for the moment, we disregard the potential scattering, usually very small compared with the proper resonance effects, and further assume the wavelength of the incident particle or light quantum to be large compared with nuclear dimensions - an assumption which at any rate for heavy nuclei is largely fulfilled in the region of discrete level distribution of the compound system - the problem is, in fact, quite analogous to the optical phenomenon of anomalous dispersion3. If EJ is the proper energy of a certain level of the compound system, of total angular momentum J , the theory gives for a total energy E close to E j (3) In this formula, To and r 0 - A are the so-called total and partial widths of the resonance level, defined by
where h is Planck's constant divided by 2z , while y o , are the probabilities entering in formulae (1) and (2) and referring to the energy E = E j . Furthermore, Q A J is an abbreviation given by
,i2
2J+1 -I I( 2 j + 1)(2s+ 1) '
AJ -
where
A is the wavelength of the incident particle, j the spin of the original
Cf. G. Breit and E. Wigner, Phys. Rev. [49 (1936) 519-5311. See also H. Bethe and G. Placzek, Phys. Rev. [51 (1937) 450-4841, where especially the spin factors in formula (5) are taken into account.
MS, P. 5
P A R T I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
nucleus, and s the spin of the impinging particle, the case of an incident light quantum being formally included by putting s = 4. For the case of maximum resonance, E=E,, we get from (3)
and for the mean value of the cross-section over an energy interval E large compared with robut small compared with the distance between the levels, we get further, by a simple integration,
As we shall see in the following, formula (6) is an immediate consequence of general quantum mechanical conservation laws, while (7)can be directly deduced from the well-known argument of detailed balancing in statistical equilibrium. In the energy region of continuous level distribution of the compound system, the cross-sections for the different possible transmutations will, of course, vary quite smoothly with the energy, and the estimation of o ~ presents , ~ us with a quantum mechanical problem essentially different from the simple resonance case. In fact, we must realize that the intermediate state of the compound nucleus is no longer represented by a single proper solution of the wave equation, but by the superposition of a multitude of such solutions, the relative amplitudes and phases of which may depend on the particular way in which the compound nucleus has been formed. In the continuous energy region, the disintegrative and radiative properties of the compound system, expressed by the various partial widths rO-A,fO+B, ... can, therefore, for the same total energy be essentially different for transmutation processes initiated by different agencies. In the treatment of this problem, for which analogies are well known from the application of the optical dispersion theory of the phenomenon of coherent scattering, it suggests itself, as a first approach, simply to generalize the cross-section formula of the type (3) to include the contributions from all the proper quantum states within the region of coherence4. This leads, at any rate if the potential scattering is neglected, to an expression for the cross-section of the form (7) in which To+, refers to a single proper quantum state in the region concerned, and A E represents the mean distance between the proper energies of such states. The lack of rigour of this procedure has given rise, however, to doubts as regards 4 C f . H.Bethe and G. Placzek, 1oc.cit.
PART I: PAPERS AND MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
the validity of such a formal generalization and it has even been proposed to disregard the coherence problem altogether and in the continuous energy region simply to use a cross-section formula of the type ( 6 ) holding for maximum resonance in an isolated level5. The apparent disagreement between the cross-section formulae obtained in the two ways has given rise to considerable confusion, especially because independent support of both types of formulae can be obtained from arguments based on conservation laws and detailed balancing, respectively. As we shall see, however, all paradoxes in this respect can be removed by a closer consideration of the definitions of the quantities occurring in th’e fundamental formula (1)6. For this purpose, we shall especially re-examine the application to nuclear processes of the general arguments of conservation and detailed balancing. In this connection, it will also be shown that the simple results arrived at by such considerations are in complete agreement with the more rigorous quantum mechanical treatment of the nuclear dispersion problem which has been recently developed’, but so far has not led to cross-section formulae for the continuous region sufficiently explicit to allow of final conclusions. Moreover, we shall discuss the application of our considerations to various nuclear processes which, hitherto, seemed to involve pronounced inconsistencies between theory and experiment. This refers especially to the nuclear photo-effects consisting in the liberation of neutrons from heavy nuclei by means of high frequency radiation. It will be seen that, far from presenting any disagreement with the theory, these effects provide important information about the mechanism of nuclear excitation, which fits in most satisfactorily with general quantum mechanical aspects of nuclear constitution.
2. Application of Conservation Theorems to Nuclear Processes. Without going into any detailed consideration of nuclear constitution, it is possible to arrive at certain important conclusions regarding the quantities entering into the formulae (1) and (2) simply by applying general conservation laws to any given transmutation process. For this purpose, it is sufficient to take account of the energy and angular momentum of the initial and final states of the nuclei concerned and, as regards the impinging and expelled material particles or light quanta, to consider the corresponding plane or spherical waves at distances from the centre of gravity of the system large compared with nuclear dimensions. Besides the well-known selection rules which follow from the conser-
’
F. Kalckar, J . Oppenheirner, and R. Serber, Phys. Rev. [52 (1937) 273-278.1 ‘ A brief account of the general ideas developed in this paper has already been published in Nature [N. Bohr, R . Peierls and G . Placzek, Nature 144 (1939) 200-201.1 [P.L.] Kapur and R . Peierls, Proc. Roy. SOC. A [166 (1938) 277-295.1
’
MS, p . 7
MS,P 8
P A R T I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
vation of angular momentum, we may in fact derive from the quantum mechanical continuity equation applied to each kind of particle a general relation between the cross-section for elastic scattering of the impinging particle and the total cross-section for the processes which involve an actual transmutation of the original nucleus. In order to avoid unessential complications, we shall for the moment assume that the s p i n j of the original nucleus as well as the intrinsic spin s of the incident particle are both zero. In a frame of reference in which the centre of gravity of the system is at rest, the wave-function of the incident and scattered particle at a distance r from the centre of gravity large compared with nuclear dimensions will then be simply given by
MS, p . 9
where Ak is its momentum, while 6 is the angle between the radius vector from the centre of gravity and the direction of incidence. The first term represents an incident plane wave of unit density, and the second the outgoing wave corresponding to the elastic scattering. Expanding in normalized zonal harmonics
and S,, 6, are the relative amplitude and phase of the scattered wave component of order 1. In formula (10) the two first terms in the brackets are the outgoing and ingoing wave, respectively, into which the component of order I of the incident plane wave may be resolved. The wave component v,/ may, thus, be regarded as the superposition of an ingoing wave
* Cf. Mott
[and Massey, Atomic Collisions, Oxford Univ. Press, 1933, p. 22.1
PART I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
and an outgoing wave
On account of the orthogonality of the zonal harmonics, the total radial flux corresponding to (8) will be given by the sum of the contributions R, of each term in (9). Obviously, we have
are the flux of the waves p/'"' and where Rl(i"),R/oUt) the velocity of the incident particle, we have
pI(OUL),
respectively. If u is
and respectively. I f , now, the only possible result of the collision was a simple elastic scattering of the incident particle, we would have R, = O and, consequently, get from (14) and (15) the well-known formula
between relative amplitude and phase-shift of the scattered wave in any simple scattering process. In this case we may, therefore, represent the resultant outgoing wave by the simple expression
of which we shall make use in the following. In case the collision can result in transmutation processes besides simple scattering, the net onward [inward] flux -R,, divided by u , will obviously be the total cross-section a, for all actual transmutation processes involving an intermediate state of angular momentum hl. From (14) and (15) we, therefore, get
MS, p .
10
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO N U C L E A R PHYSICS
\E, p I 1
Since, further, the contribution o ~ ~of the ( ~partial ~ ) wave ~7~ to the crosssection for elastic scattering is given by
we obtain for a given 1 the relation
between the total cross-section for all transmutation and scattering processes and the cross-section for elastic scattering. According to its deduction, the formula (20) involves no other assumption than that the spins of the original nucleus and of the impinging particle are equal to zero. This simplifying assumption may, however, be removed without difficulty by a slightly more complicated calculation involving the greater multiplicity of the wave-functions and their expansion in spherical harmonics of a more general character. For the mean values of the cross-sections over all directions of the spins of the nucleus and the particle, the resulting formula is
4
G
and dAJ are the where Q A j is just the quantity defined by ( 5 ) , while amplitude and phase of the scattered wave component corresponding to a given J . The consequences of this general relation are especially simple if we can neglect the potential scattering entirely in comparison with the processes which involve the intermediate state of the compound system. In this case, (21) reduces, in the notation of formula (l), to
MS, p. I 2
which, combined with (1) and (4),gives OA-o
= QAJ
r0-A
-sin2d A J . TO
Since, in this case,
where S A j is the amplitude of the scattered wave-component corresponding to a given J , we get further, from (22) and (23), the relation
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
between amplitude and phase of this wave-component. For well .separated levels, D ~ will , practically ~ vanish outside the resonance regions around each level. When, for increasing energy, we pass from one side of any such region to the other, the phase SAJ of the scattered wave will vary from 0 to 7 1 , according to the relation cotg ,a ,
Ej-E
=-
3r0
which, as is easily verified, simply follows from dispersion theory. From (23) we, therefore, just obtain the cross-section formula ( 5 ) . In particular, we see that maximum resonance which occurs for E = E j corresponds to d A j = ~ / 2 ,for which value (23) reduces simply to (6). In the continuous level region, where D ~ varies , ~ only very slowly, the phase of the scattered wave, if the potential scattering can be neglected, will keep the constant value S A j = 71/2 corresponding to maximum resonance for separated levels, In this case, we must therefore expect the formula (6) to have general validity if the potential scattering can be neglected. It must be reminded, however, that in contrast to the case of discrete levels the quantities &,A and ro will for continuous level distribution essentially depend on the way in which the compound system is formed, and we shall therefore, to avoid confusion, use the more precise notation DA+O
( A) rO-A
= QAJ (A)
r0
(27)
where the suffix ( A ) added to the T’s just refers to the dependence of the intermediate state of the compound system on its mode of formation. In case the potential scattering is not negligible in comparison to the other processes, the scattered wave in formula (8) may be regarded as built up of two coherent spherical waves
of which po corresponds to the process of escape from the compound system of a particle of the same kind and with the same energy as the incident particle, while pp corresponds to the direct reflection of this particle by the quasi-static potential field of the original nucleus. In this case, the general formula (21) does
\.IS,
p. 1 3
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
not immediately lead to a simple expression for o ~ , In ~ fact, . if for the wave components corresponding to a given J , we write
aOJ,
[ap,]
where SoJ, and S p J , represent the relative amplitudes and phases of the components of the waves po and p p in (28), we get from (21)
but since, now, M i , p.
I4
MS. p. I 5
we can obviously, without further assumption, not obtain in (30) any simple separation between the effects of the potential scattering and the processes involving the formation of an intermediate state of the compound system. Notwithstanding the interference effects in the two waves po and p p , it is possible, however, in actual nuclear problems - on account of the smallness of the coupling between the motions of the incident and the escaping particle and the collective motion of the particles of the compound system - to consider the mechanisms by which these waves are produced to a very large extent independent of each other. The problem is, in fact, closely analogous to that of an electromagnetic oscillator enclosed in a shell of large reflective power, and exposed to the effect of an infinite train of electromagnetic waves of a frequency closely coinciding with that of the oscillator. In this case, the reflection from the enclosure will, apart from any interference effect with the wave escaping from the interior, be almost independent of the resonance phenomenon giving rise to a high excitation of the oscillator. On the other hand, the larger the reflective power of the enclosing shell, the sharper is the resonance and the larger the excitation of the oscillator at maximum resonance. The amplitude and phase of the wave escaping from the interior will, of course, depend essentially on the enclosure, but not directly on the wave simultaneously reflected from it. In our nuclear problem, the amplitude and phase of the wave [pp] will similarly, to a high approximation, be independent of the excitation of the compound system, and the wave [pol, although its amplitude as well as its phase essentially depend on the field which gives rise to the potential scattering, will, nevertheless, be primarily determined by the state of this excitation. As a consequence of the extremely long life-time of the compound system compared with the time interval required for the incident particle to traverse a region of the same
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linear extension as the nuclear field, the wave would, in fact, persist practically unaltered for a considerable time after a stopping of the incident wave and, therefore, also of the directly reflected wave. On account of this situation, we may obviously to a very high approximation apply relations corresponding to (16) and (17) to the directly reflected wave [pol, separately, and obtain thus in the more general notation used in (26)
SpJ = sin dppJ, and for the total outgoing wave-component
Starting from this expression instead of (13), we evidently get, by exactly the same considerations which led to (18),
3. Arguments of Detailed Balancing and Conservation Laws. The possibility of a division of nuclear transmutations into two separate stages suggests at once the application of the well-known argument of detailed balancing to the processes of formation of the intermediate state of the compound system and the inverse processes of disintegration or radiation from this stateg. This argument demands that in statistical equilibrium the probability per unit time of any process of transition between two well-defined states must be exactly equal to the probability of the inverse transition processes, since otherwise circular processes would occur which with suitable arrangements could be used as power sources in contradiction to the second law of thermodynamics. In quantum theory, however, the application of this argument requires greater caution than in classical statistical mechanics, because the unambiguous definition of any transition process here obviously implies the possibility of a sharp separation between the initial and the final state and, consequently, the exclusion of all interference effects between these states. In particular, the intervention involved in the actual use of circular processes will in the field of quantum theory cause
’[L. Landau, Sov. Phys.
11, 556 (1937). V. Weisskopf, Phys. Rev. 52, 295 (1937). Oppenheimer, Kalckar & Serber, Phys. Rev. 52 (1937) 273-278.1
* [ I t was evidently intended to continue the discussion of the results including potential scattering, and therefore the pagination of the rest was marked as provisional.]
MS, p. 16
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MS. p 17
a disturbance of the original system which cannot be made arbitrarily small and, therefore, under certain circumstances, may make the whole argument illusory. Just in the case of nuclear transmutations we meet, as we shall see, with instructive examples of the necessity of the caution to be exercised in deriving conclusions from the argument of detailed balancing. Let us consider a statistical equilibrium between a number of nuclei and free particles as well as light quanta, all enclosed within a region of volume V very large compared with nuclear dimensions, and let us consider separately the collision processes between a certain kind of nuclei n, of spinj, and a particle a of the spin s (or light quantum), leading to the formation of an intermediate state 0 of the compound nucleus, of spin J , and of energy comprised between E and E + A E . On account of the finite life-time r0 of this state, the separation of any such process of formation from the inverse process claims, of course, that A E be large compared with ro= h / r o . Assuming, for simplicity, that the nuclei are at rest, the statistical weight of the state of the original nucleus will be g, = 2 j + 1 ,
(1')
and that of the intermediate state of the compound system
where nJ is the number of levels of spin J within the energy region.. . . Further, the statistical weight of the state of the impinging particle will be given by g, = ( 2 s
477 VAE + 1) h-3 V . 4 n p ~ A p =, ( 2 s + 1) ~, A2v,h
(3')
where p a is the momentum of the particle, v , its velocity, and A its wavelength. The condition of detailed balancing can now, in the notation of formula (l), be expressed by gag,
where
va aA-O V
=
gOYO+A,
(4')
ay!A denotes, like in formula (7), the mean value of the cross-section
T ~ over ~ ~ the , energy interval A E . On account of (l'), (27, and (3'), the formula (4') gives
C
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using the notations introduced by (4) and ( 5 ) . In case the potential scattering has only a negligible influence on the process of formation of the compound system and its disintegration, the formula ( 5 ’ ) allows of very simple applications. In the first place, we may for well separated levels of the compound system take nJ = 1 and obtain again formula ( 7 ) , as was to be expected. If, however, we have to d o with the continuous level region of the compound system, we may write
MS, P. 18
where DJ can be regarded as the average “distance” between neighbouring levels of angular momentum J . For the slowly varying cross-section oA+o = we get, therefore, from ( 5 ’ )
;01‘:
where the suffix ( M )added to r 0 - A serves to distinguish the partial width r’y’, referring to statistical equilibrium from the quantity r’JA in (24), which refers to the intermediate state formed exclusively from the initial state A . Comparing ( 7 ’ ) and (24), we obtain
which shows that the quantity r$!JA may be many times larger than r ’:L if the level width r$!) is large compared with the level distance D J . Such a large difference between the two partial widths rfJA and which, as already mentioned, is of decisive importance in the discussion of experiments, originates in the entirely different phase relations in the two cases between the proper wave-functions of which the intermediate state of the compound system is built up. The situation is, in fact, closely analogous to the classical problem of the radiation from a large number of oscillators enclosed within a region small compared with the wave-length. If the system is excited by an incident monochromatic wave ( A ) , all the oscillators will perform forced vibrations in phase with the incident wave, and the ratio of the intensity of the radiation reemitted by the oscillators to their total vibration energy at any moment will be much larger than the value of the corresponding ratio when the excitation is due to a thermal equilibrium radiation, in which case the vibrations would have phases distributed at random. For n oscillators all alike, yy) would, as is well
r’yL
yy)
yiMi””
MS,p. 19
PART I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
yiM),
known, be just n times larger than which would have the same value as for a single oscillator. A still closer comparison with the case of nuclear transmutations in the continuous energy region is, of course, offered by an ensemble of oscillators with closely distributed proper frequencies, and each coupled, besides to the radiation field, to some other agency ( T ) . In this case, we get in fact, in complete correspondence with (8’)
where d is the average difference between neighbouring proper frequencies, and y ( A ) = y i A ) + y k M ) the total damping factor of the system, arising from the coherent radiation damping and the average supplementary damping ykMM’. The interpretation of the general formula ( 5 ’ ) , when the potential scattering has to be taken into account, presents more intricate problems. At first sight, one might be tempted to conclude that in statistical equilibrium all effects of the potential scattering would be completely compensated,
yiA)
LI. ON THE MECHANISM OF TRANSMUTATIONS OF ATOMIC NUCLEI 11. PROCESSES IN THE CONTINUOUS ENERGY REGION OF THE COMPOUND STATE [ 2 ]
(WITH R. PEIERLS AND G. PLACZEK) UNPUBLISHED MANUSCRIPT DRAFTED IN BIRMINGHAM 1947
See Introduction, sect. 4, ref. 89.
PART I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
See the editorial note to document L.
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
22.10.47
ON THE MECHANISM OF TRANSMUTATIONS OF ATOMIC NUCLEI II. Processes in the Continuous Energy Region of the Compound State. N . Bohr R.E. Peierls G. Placzek 1. Introduction.
The present paper presents the results of discussions in Copenhagen in 1938-39, some of which have already been published as a brief note in Nature.' The completion of the work was interrupted by the separation of the authors and circumstances have made it impossible until now to take these problems up again. Meanwhile papers have been published on the general subject of nuclear reactions by several other authors, but we felt that it might still be worthwhile to give a brief account of the conclusions we had reached and of simple arguments by means of which they can be justified. The present paper substantially describes the state that the work had reached in 1939 and we are not attempting to take account of other work published since then.
2. Typical Features of Nuclear Transmutations. As explained in earlier papers2, nuclear transmutations initiated by impact of material particles or radiation may to a large extent be described as taking place in two well-separated stages. Of these, the first is the formation of a highly excited compound system of relatively long life-time, and the second the disintegration of this intermediate system or its transition with emission of radiation to a less excited state. In fact, because of the extreme facility of energy exchange between the densely packed particles within atomic nuclei, the excess energy will in the intermediate state be temporarily stored in some closely coupled motion of all the particles of the compound system. Any subsequent disintegration or radiative transition of this system can, therefore, to a high approximation be considered to be a separate process, and the final course of the transmutation will depend on a competition between all the disintegrative and radiative processes which the compound system in its intermediate stage can undergo.
' Nature 144, 200 (1939). 'See N. Bohr, Nature 137, 344 and 351 (1937); Science 86, 161 (1937). and especially N. Bohr and F. Kalckar, Dansk Vidensk. Selsk. math.-fys. Medd. XIV, [no.] 10 (1937) (in the text referred to as I).
M S , ~ . ~
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This picture of the course of nuclear transmutations leads immediately to the following formula for the cross-section CTABof a transition process from the initial state A of the total system consisting of the original nucleus and an impinging material particle or radiation quantum to some final state B of the system in which either some particle has escaped or a radiation quantum is emitted from the intermediate state 0 of the compound nucleus:
hlS, p 3
MS. p . 4
where oA0is the total cross-section for the formation of the compound nucleus from the state A and T~ the mean life-time of the intermediate state of the compound system, while yos is the probability per unit time of the disintegrative or radiative process of the compound system leading to B. The life-time T~ is given by
where the summation includes the probabilities of all possible disintegrative and radiative processes of the compound system, including the return to the state A . This last process is, of course, equivalent to what is usually termed “elastic scattering” of the impinging particle. It must be observed that we can describe in this manner only reactions which proceed through the formation, as an intermediate state, of a compound nucleus, and there exist also collisions which cannot be so described, but in which the impinging particle never joins the initial nucleus completely so as to form a compound nucleus with it. A typical example of this is the ordinary Coulomb scattering of charged particles which takes place at distances greater than the range of the nuclear forces. This process of scattering without the formation of a compound nucleus is usually referred to as “potential scattering” and it is particularly important for the elastic scattering. It may, however, also contribute to inelastic scattering, since, for example, a charged particle which passes the nucleus at a fairly large distance gives rise to a field at the nucleus which varies with time and is, therefore, capable of exciting the nucleus. To the complications to which this can give rise also for the unambiguous definition of the quantity yoA we shall come back later. Quite apart from such complications, it is clearly necessary, for the quantities occurring in the formulae (1) and ( 2 ) to be sufficiently well defined, that the lifetime of the compound system be long compared with the time intervals involved in a thorough energy exchange between all its constituent particles. This again implies that the excitation energy of the compound system must be much smaller than the total energy necessary for its complete disintegration into elementary
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particles. While this condition prevents the strict application of the description of nuclear transmutations which we have outlined, to collisions involving light nuclei built up of a few particles only, it will for heavier nuclei be well fulfilled, unless the kinetic energy of the colliding material particles or the energy of the incident radiation quanta is extremely high. It is true that even for heavy nuclei special features regarding the formation of the compound system will have to be taken into account for a considerably smaller energy, because the impinging material particles, when their kinetic energy well exceeds the binding energy of individual nuclear particles (about 10 MeV), will have an appreciable probability of knocking a particle off the surface of the nucleus and, even of penetrating through this surface and throwing a particle directly out of the interior of the nucleus3. Such effects, however, do not play any great role in the usual experiments on nuclear transmutations, the typical feature of which is just the immediate establishing, through the interaction between the original nucleus and the impinging particle or light quantum, of a highly stable intermediate state of the compound system. Just on account of the long life-time of this intermediate state, the possibility of its formation depends primarily on the distribution of energy levels of the quasi-stationary states of the compound system. For small energies, any nucleus possesses a spectrum of well separated levels; even for heavy nuclei, the mutual distances of the lower levels thus is of the order of magnitude of lo5 volts, while their widths, determined by the probability of radiative processes, amount to only a small fraction of a volt. With increasing excitation energy, however, the level distance decreases rapidly and the level width which to begin with remains small, will begin to increase rapidly as soon as the excitation is sufficient to make disintegration processes probable. Consequently, the level spectrum becomes practically continuous above a certain excitation energy which just falls within the region of excitation energies of the compound system with which we are concerned in the study of many typical nuclear transmutations. Within the region of energies in which the concept of a compound nucleus can be usefully applied, we are meeting particularly simple conditions if the compound system possesses discrete levels. In this case considerations very similar to those familiar from the discussion of the optical phenomena of anomalous dispersion lead to a simple expression for the cross-sections in the neighbourhood of resonance4. This “dispersion formula” is very largely independent of any assumptions about the model used to describe the nucleus and we shall show in 3 F o r a closer discussion of such problems, see W. Heisenberg, Zs. f . Phys. [Ber. Sachs. Akad., math.-phys. K1. 89 (1937) 369-384; Naturwiss. 25 (1937) 749-750.1 ‘Cf. G. Breit and E. Wigner, Phys. Rev. 49, 519 (1936). See also H . Bethe and G. Placzek, Phys. Rev. 51, 540 [450] (1937), where especially the spin factors are taken into account.
MS, p. 5
MS, p. 6
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the next section that it follows directly from a few simple arguments of a general validity. These include the well-known principle of detailed balancing and also bear a close relation to a general conservation theorem of wave mechanics. These two important principles will be discussed further in sections 4 and 5 respectively, and we shall then show that while they are still valid in their general form if we go from the discrete spectrum to the case of a continuous spectrum, more care is needed in the latter case in defining precisely the quantities which enter into these relations. 3. The Dispersion Formula f o r Discrete Levels. In the case in which the width of each of the levels of the compound nucleus is less than the distances between different levels the one level resonance formula is applicable. This was first put forward by Breit and Wigner5 and justified by means of a model in which the coupling between different particles inside the nucleus may be regarded as weak. It has since then been derived in other ways6. We want to show that this formula follows quite directly from the application of very general principles. The formula follows, in fact, from the following three statements: (a) The total cross-section, integrated with respect to energy, over the region in which a certain resonance state of the compound nucleus is important, can be identified with the integral over the same region, of the cross-section for the formation of a compound nucleus in that state, since in the resonance region the “potential scattering” is negligible. The integrated cross-section for the formation of a compound nucleus is
where
is the width of the state 0 of the compound nucleus for disintegration by the process A , and
A2
QAJ =
( 2 J + 1)
n ( 2 j + 1)(2s+ 1)
*
’ G . Breit and E. Wigner, 1. c. 6 P . L . Kapur and R . Peierls, Proc. Roy. SOC. A 166, 277 (1938); Wigner, Phys. Rev. 70, 15 (1946); 70, 606 (1946), Wigner and Eisenbud, Phys. Rev. 72, 29 (1947); Feshbach, Peaslee and Weisskopf, Phys. Rev. 71, 145 (1947).
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Here A is the wavelength of the incident particle (in the frame of reference in which the centre of gravity is at rest), J the spin of the compound nucleus, j that of the original nucleus, and s that of the incident particle. For an incident photon, one has to take formally s = + in order to get the correct statistical weight. Equation (3) expresses the law of detailed balancing applied to the processes of formation and disintegration of the compound nucleus and will be derived in Section 4 of this paper. (b) The variation of this total cross-section with energy is of the form: OAO =
const. ( E- E0)2+ (T0/2)*
where E is the energy of this system and Eo that of the resonance level. This law follows from the fact that, in the case of discrete levels, the energy of the compound nucleus can, within its life time be taken to be sufficiently sharply defined to determine its quantum state uniquely. In that case the disintegration probability per unit time of the compound nucleus is also uniquely determined and is, in particular, independent of the time that has elapsed since its formation. The probability of survival of the compound nucleus is, therefore, an exponential function of time, and the amplitudes of the waves emitted from it must also vary with time by an exponential law: e-(i/h)E,r
-r0//2
MS, p.
s
(7)
From the well-known rules of quantum mechanical transformation theory it follows then that the contribution of the process in which the energy is exactly E , is given by the Fourier transform of ( 7 ) which leads to the law (6). By means of (3) one can find the value of the constant in (6) and thus obtain the result: OAO
= +QAJ
rOA rO
( E - E0)2+ (r0/2)2 *
(c) The fact that the properties of the compound nucleus are unambiguously determined by its energy has also the consequence that the ratios of the probabilities of its disintegration in different ways are uniquely determined, and, in particular, independent of the manner in which the compound nucleus has been formed. We can, therefore, write the cross-section for the process leading to the final
MS, p . 9
PART I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
state B of the system in the form GAB = ‘JAO
rOB
-
(9)
r0
as in equation (1). Using this and (8) ‘JAB =
SQAJ
rOA rOB
( E- E
~+ (r0/2)2 ) ~
*
This is the equation of Breit and Wigner. At full resonance, E = E o , we have, in particular: ~ A = O QAJ
rOA ~
r0
,
~ A = B QAJ
rOArOB ~
To2
and for the special case B = A , which represents elastic scattering:
At maximum resonance, we have therefore:
This relation will later be seen to have a close connection with the general conservation laws of wave mechanics which we shall discuss in Section 5 . 4. Detailed Balancing. MS. p.
10
The possibility of a division of nuclear transmutations into two separate stages suggests at once the application of the well-known argument of detailed balancing to the processes of formation of the intermediate state of the compound system and the inverse processes of disintegration or radiation from this state.’ This argument demands that in statistical equilibrium the probability per unit time of any process of transition between two well-defined states must be exactly equal to the probability of the inverse transition process, since otherwise cycle processes would occur which with suitable arrangements could be used ’ L . Landau, Sov. Phys. 11, 556 (1937). V. Weisskopf, Phys. Rev. 5 2 , 295 (1937). Oppenheimer, Kalckar & Serber, [Phys. Rev. 52 (1937) 273-278.1
PART I : PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
as power sources in contradiction to the second law of thermodynamics. In quantum theory, however, the application of this argument requires greater caution than in classical statistical mechanics, because the unambiguous definition of any transition process here obviously implies the possibility of a sharp separation between the initial and the final state and, consequently, the exclusion of all interference effects between these states. As long as the initial and final states are, however, well-defined states in the sense of quantum mechanics, the theorem can be applied without ambiguity. Consider a statistical equilibrium between a number of nuclei and free particles as well as light quanta, all enclosed within a region of volume V very large compared with nuclear dimensions, and consider separately the collision processes between a certain kind of nuclei n , of s p i n j , and a particle a of the spin s (or light quantum), leading to the formation of an intermediate state 0 of the compound nucleus, of spin J , and of energy comprised between E and E + A E . On account of the finite life-time T~ of this state, the separation of any such process of formation from the inverse process requires, of course, that A E be large compared with T o = h / r o . Assuming, for simplicity, that the nuclei are at rest, the statistical weight of the state of the original nucleus will be gn = 2 j + 1
(14)
and that of the intermediate state of the compound system
where ( n J ) A Eis the number of levels of spin J within the energy region A E . Further, the statistical weight of the state of the impinging particle will be given by 477 V A E P,2 A P , g U = ( 2 s + 1 ) V - 4 n-- ( 2 s + 1) h3 A2v,h ~
where p a is the momentum of the particle, u, its velocity, and A its wavelength. The condition of detailed balancing can now, in the notation of formula ( l ) , be expressed by
where
(oA0)dE
denotes the mean value of the cross-section D~~ over the energy
MS, p . I I
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interval A E . On account of (14), (15), and (16), the formula (17) gives
\1s, p I2 I I I 47.
using the notations introduced by (4) and (5). In case the potential scattering has only a negligible influence on the process of formation of the compound system and its disintegration, the formula (18) allows of very simple applications. In the first place, we may, for well-separated levels of the compound system, take nJ = 1, and again obtain formula (7), as was t o be expected. If, however, we have t o do with the continuous level region of the compound system, we may write
n,
AE
=-
DJ
where l/DJ is the number of states per unit energy, and hence D j may be regarded as the average “distance” between neighbouring levels of angular momentum J . In this case we expect the cross-section to vary slowly with energy, and may therefore identify the actual cross-section aA0with its average a , ,( A E ). It must also be remembered that, in contrast to the case of discrete levels the quantities roA will now depend essentially on the way in which the compound system is formed, and we shall therefore, to avoid confusion, add a superscript indicating the mode of formation. In (18), the partial width refers to a compound system in statistical equilibrium, which we shall denote by the letter M.Then (18) becomes:
We shall see later that the precaution of taking into account the mode of formation of the compound nucleus is not unnecessary, and that, in the continuous level region, rh?)is substantially different from the corresponding quantity for compound states formed in other ways. 5 . Application of Conservation Theorems to Nuclear Processes.
Without going into any detailed consideration of nuclear constitution, it is possible to arrive at certain important conclusions regarding the quantities
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entering into the formulae (1) and (2) simply by applying general conservation laws to any given transmutation process. For this purpose, it is sufficient to take account of the energy and angular momentum of the initial and final states of the nuclei concerned and, as regards the impinging and expelled material particles or light auanta, to consider the corresponding plane or spherical waves at distances from the centre of gravity of the system large compared with nuclear dimensions. Besides the well-known selection rules which follow from the conservation of angular momentum, we may in fact derive from the quantum mechanical continuity equation applied to each kind of particle a general relation between the cross-section for elastic scattering of the impinging particle and the total transmutation of the original nucleus. In order to avoid unessential complications, we shall for the moment assume that the s p i n j of the original nucleus as well as the intrinsic spin s of the incident particle are both zero. In a frame of reference in which the centre of gravity of the system is at rest, the wave-function of the incident and scattered particle at a distance r from the centre of gravity large compared with nuclear dimensions will then be simply given by
where hk is its momentum, while 8 is the angle between the radius vector from the centre of gravity and the direction of incidence. The first term represents an incident plane wave of unit density, and the second the outgoing wave corresponding to the elastic scattering. Expanding in normalized zonal harmonics
where
we obtain’
where QA/ =
/I2 7 (21 + 1) = 4 ~ ( 2 / +l ) / k 2
Mott & Massey, Atomic Collisions, Oxford 1933, p . 22.
MS. p . ~ 4
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and the complex quantity
determines the scattered wave of order I, sl being the amplitude and d1 its phase. The two first terms in the bracket of (23) are the outgoing and incoming wave respectively into which the component of order I of the incident wave may be resolved. The wave component q may, thus, be regarded as the superposition of an ingoing wave
and an outgoing wave
Because of the orthogonality of the zonal harmonics, the total radial flux corresponding to (20) will be given by the sum of the contribution RI from each term in (21). Obviously we have:
R I - R ( IO u t ) - R:'"'
\1s, p . 15
(28)
where I?:'"', R:Out) are the contribution of the waves q,(in), q , ( O u t ) respectively. i f u is the velocity of the incident particle,
and
respectively, where the asterisk denotes the conjugate complex quantity. If the only possible result of a collision were a simple elastic scattering of the incident particle, we would have RI = 0, and consequently from (28) and (29)
and using (25) we obtain the well-known formula
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between amplitude and phase-shift of the scattered wave. If the collision can also be inelastic, resulting either in scattering with loss of energy, or in a transmutation, the net inward flux -RI divided by the velocity, will obviously be the total cross-section oATIfor all such inelastic processes involving an intermediate state of angular momentum hl. From (28) and (29) we get therefore
Since, further, the contribution aASof the partial wave q, to the cross-section for elastic scattering is given by:
we obtain for any given [ I ] the relation
between the total cross-section for all inelastic and elastic processes and that for elastic scattering. The consequences of this general relation are particularly simple if we can neglect the potential scattering entirely in comparison with the processes which involve the intermediate state of the compound system. In this case, (34) reduces, using the notation of section 3 to:
We are still restricted to the case in which incident particle and initial nucleus have no spin, hence the quantity (24) appears in place of (5). Combining (35) with (1) and (4)
If the potential scattering is not negligible, we have to consider the scattered wave in equation (20) as built up of two coherent spherical waves:
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s = s,, + so,
(37)
in which Spl is due to the potential scattering and the remainder Sol represents the effect of the escape from the compound nucleus of a particle of the same kind, and with the same energy as the incident one. In this case (32) has to be written
h 1 i . 1 1 17
Now S,, represents the solution of a possible mechanical problem, in which only the quasi-static potential of the nucleus is present, but in which the nucleus is replaced by an object in which no transmutations can take place. Hence the conservation theorem (32) must also apply to the result of potential scattering separately:
where oiTI denotes the cross-section for inelastic potential scattering of a particle with angular momentum lh. As we have pointed out in section 2, the elastic scattering may have to be included in the potential scattering. I f , however, we disregard this effect, we have from (39)
or, if we write
(40) becomes equivalent to S l ,l
=
sin&,/.
We can then write (38) in the form
provided we define the phase do, by means of the relation
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Equation (43) is the same as (32), but applied separately to those processes that proceed by way of the formation of a compound nucleus only. (44) shows that the quantity that plays the part of a phase is modified by the presence of the potential scattering. If the potential scattering can also cause inelastic collisions, it will also contribute to the left-hand side of (38), while (40) will also have to be replaced by the more complicated relation (39). In these circumstances it is still reasonable to expect a relation of the type (43), but a more detailed investigation would be required to confirm this. We can then use the relations (35) and (36) even in the presence of potential scattering. Equation (35) evidently implies the inequality
MS, P. 18
in which the equality sign applies in the case when SA, = 0. As we shall see in the next section, this is the case of full resonance. If we can regard the nucleus as a sphere of radius R and if the wavelength is small compared to R it is well-known that only those angular momenta can occur with appreciable probability in a collision for which
2rtR IjkR=-. 1,
Then the total collision cross-section and that for elastic scattering are, respectively,
Inserting from (34):
or
The square of the sum of products is less than the product of the sums of squares:
MS, p , 19
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Using (24) and (47):
MS, p. 20
It follows from this by elementary algebra that the inelastic cross-section total - oAScan never exceed the value n R and can reach this value only if the elastic cross-section oAshas the same value. This last result appears at first sight strange in the case of a macroscopic black sphere which evidently has an inelastic cross-section of n R 2 but which one does not usually picture as having also an elastic cross-section of the same magnitude. The solution of the apparent difficulty lies in the fact that the incident plane wave plus the scattered wave must give account of the shadow behind the body, and therefore the main function of the scattered wave is to extinguish that part of the incident plane wave which lies behind the body. It is obvious that for this purpose one just requires a wave of intensity n R 2 . Nevertheless, one can still apply the usual argument according to which 1SI2may be interpreted as a scattered wave. One must only keep in mind that this scattered wave is concentrated in a forward cone of opening angle of the order A/R and one can easily see from the uncertainty principle that this scattering can only be observed as such at distances greater than R2/A from the scattering centre. For macroscopic objects this is usually beyond the range of practical interest, but the scattering by nuclei is always observed far beyond this critical distance. One may therefore, without ambiguity interpret the whole of the cross-section / S I 2 as due to elastic scattering, but one has to keep in mind that for short waves part of this scattering will be through comparatively small angles and can therefore only be observed if one uses fairly well defined beams. The results of this section can also be generalized to the case in which the incident particle and the initial nucleus have spins. In that case the wave function (20) must be replaced by a set of functions describing the possible orientation of the spins. In that case, we have to count as elastic only such collisions in which the particle is scattered with unchanged spin direction, as well as with unchanged energy. The cross-sections have to be averaged over the initial spin orientations of particle and nucleus. One then can again derive relations similar to (45) and (9, except that QA, has to be replaced by the quantity QAj which is defined in ( 5 ) . 6. Consequences of the General Theorems. In the case of well-separated levels, the inequality (45) is a consequence of the one level formula (lo), and (13) shows, in particular, that the equality sign holds at maximum resonance. In the continuous level region, we have already pointed out that the quantities
PART I : PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
and ro may depend on the process by which the compound nucleus has been formed, and we shall again indicate this process by a superscript. Then, (1) becomes more precisely
rOA
MS, p. 21 29.10.47.
Comparing (51) and (52) with (45) generalized to cover spin degeneracy, we find:
rg)
and r;;) is important since We see therefore that the distinction between the ratio between them must become very large when the width r$')exceeds the level distance. r') is the greater of the two, since the particular combination of the wave functions belonging to a given energy which is produced by process A will also be more suitable for the disintegration by process A than for other processes. The application of this general result to the discussion of the nuclear photoeffect has already been given e l ~ e w h e r e . ~
' N . Bohr, G . Placzek and R.E. Peierls, 1 . c.
LII. TENTATIVE COMMENTS ON ATOMIC AND NUCLEAR CONSTITUTION UNPUBLISHED MANUSCRIPT 1949
See Introduction, sect. 6, ref. 147.
P A R T I: PAPERS A N D MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
The folder “Comments on Atomic and Nuclear Constitution”, 1949, contains 3 typewritten drafts and 2 carbon copies, of 4 pages each, of an unpublished note, with minor handwritten amendments in pencil and ink. The manuscripts are in English. One version contains a re-draft of one paragraph. This re-draft is dated 15 August 1949, and contains an additional sentence about the absence of rotational states. In the version reproduced here this amendment has been included. Otherwise the differences between the different drafts are purely textual. The manuscript is on microfilm Bohr MSS no. 19.
PART I: PAPERS AND MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
TENTA TIVE COMMENTS ON A TOMIC AND NUCLEAR CONSTITUTION. From the point of view of classical mechanics pictures of atoms and nuclei are essentially different, the former resembling a planetary system with spatial dimensions large compared with the size of the constituent particles, while the latter exhibit a close packing more like the molecules in a liquid drop. These pictures offer also an immediate explanation of some characteristic features regarding collisions between atoms or nuclei and swift particles. In quantum mechanics, however, all pictorial considerations are essentially limited and, above all, the remarkable stability of atoms and nuclei is accounted for only by the inherent individuality of elementary processes completely foreign to classical physical ideas. As regards the problem of atomic constitution, the application of quantum mechanics has been greatly facilitated by the possibility - notwithstanding all novel features - of retaining a certain simple correspondence with the pictorial representation. Thus, in the first place, it is possible with a high approximation to compare the state of binding of each electron in the atom with that of a particle in the force field originating from the nucleus and the electronic charge distribution, and only in the enumeration of these states to introduce the exclusion principle involving the spin properties of the electron. In nuclear constitution we meet with a new situation in that respect that the consequences of quantum mechanics imply a still more far-reaching change of the classical pictures, extending to almost every aspect of the problem. The great progress as regards the account of many nuclear properties which has recently been obtained by representing the state of binding of each proton and neutron in a similar way as that of an electron in an atom might indeed at first sight seem to involve assumptions inconsistent with the experiences regarding nuclear reactions in collisions, showing the impenetrability of nuclear matter for particles of energy comparable with the kinetic energies of the nuclear constituents. At closer consideration it appears, however, that such arguments are not appropriate. In fact, as regards the stationary state of a nucleus of high mass number the indeterminacy of the position of the individual nucleons will imply an averaging concerning the specification of the interaction between the individual nucleons with the result that such interaction can to a high approximation be represented as that of a force field with a potential varying smoothly inside the nucleus. This force field is primarily determined by the density and charge distribution within the nucleus and is thus in itself dependent on the general features of the nucleon binding. As a calculation shows, the binding energies corresponding to the semi-
MS, p. 2
PART I : PAPERS AND MANUSCRIPTS RELATING T O NUCLEAR PHYSICS
CIS, p . 3
independent states of the individual nucleons will depend on the quantum numbers in a somewhat other way than for the electron bindings in an atom and, in particular, will the majority of the binding energies be of the same order of magnitude. As regards finer details we must reckon with exchange effects in which particles interchange their states but, although such effects must be expected to have a greater influence than in the constitution of isolated atoms, the exchange periods will probably be long compared with the orbital periods, and effects of this kind should therefore only to a smaller extent impede the conclusions regarding nuclear properties estimated on the assumption of separate bindings. As regards the excitation of nuclei we meet with analogies as well as with peculiar differences from the excitation of atoms. On the one hand, we may have higher energy states in which one or more nucleons have quantum numbers different from those corresponding to the lowest energy states. On the other hand, we may have excited states of the nucleus corresponding to oscillation of its boundary, the periods of which will in general be long compared with the orbital periods of the nucleons, with the result that their motions will in the first approximation only be adiabatically influenced. In particular, it is under these circumstances evident that there cannot be question of stationary states corresponding to the rotation of the whole nucleus as a solid body and that the angular momentum and spin of the nucleus will be determined directly by the specification of the binding states of the individual nucleons. In the problem of a collision between a nucleus and a free nucleon we meet with essential differences in the cases where the energy of the impinging particle is large or small compared with the kinetic energies of the bound nucleons. For high energies, we may, in analogy with the penetration of high-speed electrons through atoms, reckon with a simple penetration through the nucleus and violent collisions with individual nucleons, effects which to some extent allow pictorial representation due to the possibility of describing the motion approximately by means of wave-packets small compared with nuclear dimensions. For smaller energies, all pictorial representations fail and, instead of the often used comparison with the capture of a molecule by a liquid drop, we may more appropriately sketch the stages of the incorporation of the particle in the compound nucleus as follows. In the first stage we have a semi-stationary binding of the particle within the nuclear potential, of a duration long enough to permit exchanges of states with the other nucleons, resulting in a state in which none of the individual particles has energy enough to leave the nucleus. A further stage is the transformation of the surplus energy into a vibrational excitation of the whole nucleus, from which state a disintegration demanding a reversal of the whole process is still more improbable.
P A R T I: PAPERS A N D MANUSCRIPTS RELATING TO NUCLEAR PHYSICS
In quantum mechanics such a separation of stages can of course not be taken literally, and only in the case where the total energy of the free particle and the original nucleus corresponds to a stationary state of the compound nucleus we can have resonance effects and considerable cross-sections for nuclear reactions. Still, for the remarkable simplicity of the laws governing such reactions, it is only decisive that the life-times of the excited states are extremely long compared with the orbital periods of the bound nucleons, and the primary aim of these comments is just to point at the consistency of this condition with the general concepts of nuclear constitution.
MS, p. 4
LIII. DISCUSSION REMARKS AT THE INTERNATIONAL PHYSICS CONFERENCE IN COPENHAGEN, 3-17 JUNE 1952
See Introduction, sect. 6 , ref. 158.
P A R T I : P A P E R S A N D M A N U S C R I P T S RELATING TO N U C L E A R P H Y S I C S
Reproduced from the cyclostyled Conference Report, edited by 0. KofoedHansen, P. Kristensen, M. Scharff and A . Winther (with a short preface by Bohr, p. 3 ) . 66 pages. Further discussion remarks by Bohr are found on p. 21 (report by R. Wilson), pp. 36-37 (report by W. Heisenberg), p. 52 (report by C. M ~ l l e r )and p. 57 (report by A . Wightman).
P A R T I : P A P E R S A N D M A N U S C R I P T S R E L A T I N G T O N U C L E A R PHYSICS
Remarks by Niels Bohr during Discussions at the Copenhagen Conference, 1952. W. Kohn, Scattering of Fast Electrons by Nuclei, pp. 14-16. Discussion, p. 16.
N. Bohr (Copenhagen) and Wilson (Cornell) stressed the latitude in the definition of the nuclear radius. The effective radius may depend strongly on the phenomenon in question. B. Mottelson, Collective Motions in Nuclei, pp. 17-18. Discussion, pp. 18-20 (here p. 19).
Rosenfeld (Manchester) asked how far this model is based on first principles. N. Bohr (Copenhagen) answered that it appeared difficult to define what one should understand by first principles in a field of knowledge where our starting point is empirical evidence of different kinds which is not directly combinable. So far it has not been easy to deduce the conditions for the binding of the individual nucleons in an atomic nucleus from the evidence obtained by collisions between free nucleons. Moreover, as regards the problems of deformation of the nuclear shape, it is to be remembered that, quite apart from the evidence discussed here, the discovery of nuclear fission clearly shows the possibility of even large deformations of nuclei. The present attempt of developing the shell model to take into account deformations of the nuclear field associated with collective types of motions would seem t o indicate a way for a rational description of the various types of nuclear phenomena.
INTRODUCTION
The letters t o and from Bohr, quoted in the Introduction to Part I, are reproduced here in the original language, arranged in alphabetical order according to correspondents. Two letters exchanged between Rosenfeld and Delbruck have been included. Letters in the Scandinavian languages are followed by a translation. As in the previous volumes, this also applies to the few German letters in the Heisenberg and Pauli correspondences. The editors have used their discretion t o correct tacitly “trivial” mistakes, e.g., in spelling and punctuation. We have tried, however, to preserve “characteristic” mistakes. In the reproduction we have attempted to make the lay-out of letterheads etc. correspond as nearly as possible t o that of the original letters. The list preceding the letters contains references to the pages in the Introduction where the letters are quoted so that the reader can readily find the context in which a particular letter has been quoted. Footnote numbers are repeated in the translations and, occasionally, in later letters belonging to the same correspondence.
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E
(1929- 1949)
CORRESPONDENCE INCLUDED
Reproduced p. Translation p.
Quoted p.
HANS A . BETHE Bohr to Bethe, 23 November 1936
539
-
39
540 542 543
541 542
-
14 44 44
544 545 545 546
-
22 23 24 24
547 548
-
550 552 552 553 554
-
555
-
FELIX BLOCH Bohr to Bloch, 17 February 1934 Bohr to Bloch, 1 February 1938 Bloch to Bohr, 15 February 1938
MAX DELBRUCK Bohr to Delbriick, 18 March Delbriick to Bohr, 20 March Rosenfeld to Delbriick, 22 [?] March Delbriick to Rosenfeld, 25 March
1936 1936 1936 1936
PAUL A.M. DlRAC Bohr to Dirac, 24 November 1929 Dirac to Bohr, 26 November 1929
-
ENRICO FERMl Bohr to Fermi, 1 February 1939 Bohr to Fermi, 2 February 1939 Bohr to Fermi, 17 February 1939 Fermi to Bohr, 1 March 1939 Bohr to Fermi, 2 March 1939
-
-
60, 66 60 66 62 63
RALPH H . FOWLER Bohr to Fowler, 14 February 1929
6
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E
(1929-1949)
Reproduced p. Translation p.
Quoted p.
556 559
551 -
(55) 59
5 60 58 58 563
56 1 -
(55) 58 58 59
565
-
(60)
561 568 570 572
567 569 51 1 513
36 (8) 8 20
513 575 571 578 519 582 585
514 516 511 579 581 583 586
(12) 12 (12) 13 19, (76) 34 45
OTTO ROBERT FRISCH
20 Bohr to Frisch, Frisch to Bohr, 22 Bohr to Frisch, 24 Frisch to Bohr, 31 Frisch to Bohr, 1 Bohr to Frisch, 3 Frisch to Bohr, 15/18
January 1939 January 1939 January 1939 January 1939' February 1939' February 1939 March 1939
GEORGE GAMOW Gamow Gamow Bohr to Bohr to
to Bohr, to Bohr, Gamow, Gamow,
6 31 21 26
January 1929 December 1932 January 1933 February 1936
WERNER HEISENBERG Heisenberg to Bohr, Bohr to Heisenberg, Bohr to Heisenberg, Bohr to Heisenberg, Bohr to Heisenberg, Bohr to Heisenberg, Heisenberg to Bohr,
18 July [1932] 1 August 1932 2 August 1932 20 April 1934 8 February 1936 2 May 1936 9 February 1938
INSTITUTE FOR THEORETICAL PHYSICS' Bohr to Institute, Bohr to Institute, Bohr to Institute, Bohr to Institute, Bohr to Institute, Institute to Bohr, Bohr to Institute, Bohr to Institute, Institute to Bohr, Bohr t o Institute,
30 30 31 3 9 15 16 19 13 15
January 1939 (1) January 1939 (2) January 1939 February 1939 February 1939 February 1939 February 1939 February 1939 March 1939 March 1939
51 51 58 59 588 588 589 589 589 590
' Telegram.
' These are telegrams or drafts of telegrams. See also Frisch, Jacobsen and
Rasmussen.
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E
(1929-1949)
Reproduced p. Translation p.
Quoted p.
590
59 1
(68)
591
-
592 595
594 595
JACOB CHRISTIAN JACOBSEN Bohr to Jacobsen, 13 February 1939
FREDERIC AND IRENE JOLIOT-CURIE Bohr to the Joliot-Curies, 30 April 1932
OSKAR KLEIN ~ Klein to Bohr, 2 [ D e ~ e m b e r ]1935 Bohr to Klein, 9 January 1936
18 18
HENDRIK A . KRAMERS Bohr to Kramers, Kramers to Bohr, Bohr to Kramers, Kramers to Bohr,
30 November 1929 1 1 March 1936 14 March 1936 20 March 1936
Vol. 6, p. [425] Vol. 6, p. [4271 7 596 597 25 598 600 ( 1 3 , 25 602 603 25
JOHANN KUDAR Bohr to Kudar, 28 January 1930
605
-
7
WOLFGANG PAUL1 Bohr to Pauli to Pauli to Bohr to
Pauli, 1 July 1929 Bohr, 17 July 1929 Bohr, 11 February 1938 Pauli, 15 August 1949
Vol. 6, p. [441] Vol. 6, p. [443] 5 Vol. 6, p. [444] Vol. 6, p. (4461 5 606 608 44 Vol. 7 Vol. 7 79
Dated (probably in error) February. See the Introduction, ref. 33.
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E
(1929- 1949)
Reproduced p . Translation p.
Quoted p.
RUDOLF PEIERLS Bohr to Peierls, Bohr to Peierls, Peierls t o Bohr, Bohr to Peierls, Peierls to Bohr, Peierls to Bohr, Bohr to Peierls, Peierls to Bohr, Peierls to Bohr, Bohr to Peierls,
9 September 1936 17 October 1936 8 February 1938 6 June 1939 2 November 1947 6 February 1948 22 August 1949 26 August 1949 7 December 1949 17 December 1949
609 610 61 1 612 613 615 616 617 619 620
EBBE RASMUSSEN Bohr to Rasmussen, Ramussen to Bohr, Rasmussen t o Bohr, Rasmussen to Bohr, Bohr to Rasmussen, Rasmussen to Bohr,
14 February 1939 20 February 1939 24 February 1939 3 March 1939 10 March 1939 24 March 1939
62 1 625 629 632 633 638
623 627 630 632 635 639
64 1 644 646 648
642 645 647 650
LEON ROSENFELD4 Bohr to Rosenfeld, Bohr to Rosenfeld, Rosenfeld to Bohr, Bohr to Rosenfeld,
8 January 1936 16 August 1949 19 August 1949 29 August 1949
19 80 80 81
ERNEST RUTHERFORD Bohr to Rutherford, 30 June 1934
65 1
14
B J 0 R N TRUMPY Trumpy to Bohr, 12 February 1943 Bohr to Trumpy, 16 February 1943
See also Delbruck.
653 656
654 656
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E
(1929- 1949)
Reproduced p. Translation p . JOHN A . WHEELER Bohr to Bohr to Bohr to Bohr to Wheeler Wheeler Bohr to Bohr to Wheeler Wheeler Bohr to
Wheeler, Wheeler, Wheeler, Wheeler, to Bohr, to Bohr, Wheeler, Wheeler, to Bohr, to Bohr, Wheeler,
20 July 1939 4 October 1939 (1)' 4 October 1939 (2) 16 December 1939 19 January 1940' 12 February 1940' 4 July 1949 13 July 1949 3 September 1949 12 December 1949 24 December 1949
651 72 66 1 662 13 13 665 665 667 668 670
Quoted p.
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E
(1929- 1949)
HANS A. BETHE BOHR TO BETHE,
23 November 1936
[Carbon copy] [Kobenhavn,] November 23rd [19]36. Dear Bethe, I thank you very much for your kind letter with the manuscript of yours and Placzek's paper5, in which Kalckar and I have been very interested. At the moment we are busy in preparing the account of our work on the nuclear reactions, the publication of which has been so much delayed due to my many other duties and my overstrain last summer which also to my great regret prevented me in attending the Harvard symposium. As you will have heard from Placzek, we have above all been interested in showing how the extreme energy exchange in nuclear processes can be taken into account in a rational quantum mechanical treatment leading especially to the establishment on a general basis of formulas of similar type as that deduced by Breit and Wigner6 by help of a simplified nuclear model and utilized in a more comprehensive way in yours and Placzek's work. Further we have discussed a number of features of nuclear reactions, for which the extreme facility of energy exchange allows to understand various experimental results which hitherto were quite unexplained. While the former part of our work will be published in the Proceedings of the Copenhagen Academy', we have found it more practical first to publish a more qualitative discussion of the latter problems in a paper to appear in the Proceedings of the Royal Society', the manuscript of which we are just finishing, and of which we hope to be able to send you a copy in a few weeks. By the way I have recently exchanged some letters with Peierlsg regarding the problem of excitation and radiation of nuclei, and as I understand we all agree as regards the great difficulty in arriving to any reliable estimate about the level scheme of excited nuclei by comparison of the nucleus with a Fermi gas in the way you attempted in your recent interesting paper". It seems to me that the only rational way to treat this problem is to consider the collective modes of motions of the nuclear particles and their more or less independent combinations, as indicated in my Nature article. In fact, it follows from simple considerations, as I suppose you have also convinced
' Introduction, ref. 49. ' Introduction, ref. 48. Introduction, ref. 46. This paper was not published. See the Introduction, p. [39]. See the Bohr-Peierls correspondence. '(I Introduction. ref. 44.
'
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E ( 1 9 2 9 - 1 9 4 9 )
yourself, that as well the distribution of the levels as the probabilities of radiative transitions between them obtained in this way agrees approximately with experiments. As Placzek may also have told you, Kalckar and I intend to come to America in the early spring, where we not least look forward to meet you at the conference in Washington which Gamow is arranging in February, and to the opportunity for a closer discussion of all the problems mentioned. With kind regards from us both Yours, [Niels Bohr]
FELIX BLOCH BOHR TO BLOCH,
17 February 1934
[Carbon copy] [Kerbenhavn,] 17. Februar [19]34. Kzere Bloch, Det var forfmdelig rart at herre fra Dem, og jeg haaber, at De vil have G l z d e af Deres Rejse ti1 Amerika. Stanford er et dejligt Sted med mange sympatiske Mennesker, og i Kalifornien er der jo ikke alene megen god Fysik, men ogsaa den skernneste Natur. Min Kone og jeg tror sikkert, at vi kommer dertil i Sommeren 1935. Jeg har netop skrevet ti1 Nishina for at herre nzermere om, hvordan Forholdene er i Japan, og saa mart vore Rejseplaner er fastlagte, skal jeg skrive ti1 Dem i Stanford. Det skal blive vzldig morsomt at trzeffes igen derovre, og jeg behaver jo ikke at sige, at De altid er mere end velkommen i Kerbenhavn, hvis det skulde komme paa Tale, at De ernsker at tilbringe Resten af Deres Rockefellertid her. Hvad Fysikken angaar, er vi j o naturligvis alle begejstrede for de stadig lige vidunderlige Fremskridt med Hensyn ti1 Atomkernerne; ikke mindst har j o den sidste Opdagelse i Paris aabnet helt nye Perspektiver. Vi har naturligvis ogsaa alle vzeret meget interesserede i Fermis nye Arbejde", der utvivlsomt vil virke meget stimulerende paa Arbejdet med de elektriske Kerneproblemer, selv om jeg maa tilstaa, at jeg endnu ikke ferler mig fuldt overbevist om Neutrinoens fysiske Eksistens. Paa Baggrund af den rivende Udvikling maa det j o ofte forekomme noget trivielt at spekulere over Elektron-
"
Introduction, ref. 21a.
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E
(1929- 1 9 4 9 )
teoriens Paradoxier; men helt glemt dem har jeg ikke, og som et lille Budskab fra vort gamle f d l e s Vzerksted sender jeg indlagt en Kopi af et Brev, som jeg i Gaar sendte ti1 Pauli12, og som jeg er spzndt paa, om han vil betragte som det rene Dilettanteri. Jeg skal jo ogsaa vaxe glad for at herre et Par Ord om Deres Mening derom. Med mange venlige Hilsener fra 0s alle, ogsaa ti1 Fermi, Deres [Niels Bohr]
Translation [Copenhagen,] 17 February 1934 Dear Bloch, It was terribly nice to hear from you, and I hope you will enjoy your trip to America. Stanford is a charming town with many attractive people, and California has not only much good physics but also very beautiful nature. My wife and I firmly believe that we shall be there in the summer of 1935. I have just written to Nishina to find out more about the situation in Japan, and as soon as our travel plans are fixed I shall write to you in Stanford. It will be very pleasant to meet again over there and I surely need not say that you will always be more than welcome in Copenhagen if it should turn out that you want to spend the rest of your Rockefeller time here. As regards physics, we are of course all very enthusiastic about the continuing wonderful progress with the atomic nuclei; not least about the latest discoveries in Paris which have opened new perspectives. We have of course also all been very interested in Fermi’s new paper” which no doubt will be very stimulating for the work on electric nuclear problems, although I must confess that I don’t yet feel fully convinced of the physical existence of the neutrino. Against the background of this rapid development it may seem somewhat trivial to speculate about the paradoxes of the electron theory; but I have not quite forgotten them, and as a little reminder from our old joint workshop I enclose a copy of a letter which I sent yesterday to Pauli12, and I am curious to know whether he will regard this as pure dilettantism. I shall of course also be glad to hear from you a few words about your opinion of this. With many kind regards from us all, also to Fermi, Yours, [Niels Bohr]
”
Bohr to Pauli, 15 February 1 9 3 4 . BSC, microfilm no. 24.
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E
BOHR TO BLOCH,
(1929-1949)
1 February 1938
[Carbon copy] [Kerbenhavn,] 1. Februar [19]38. Kiere Bloch, Mange Tak for Deres venlige Brev. Jeg vidste j o at De ogsaa vilde blive meget bedrervet over at herre om Kalckars pludselige D0d og baade for hans Familie og mig selv var det en vardifuld Oplysning at faa at vide om det tidligere Tilfielde af Bevidstlershed som han fik paa Udflugten sammen med Dem og som han uden at nogen andre vidste det havde haft paa Udflugter med sine Brerdre for Aar tilbage. - Med hensyn ti1 Houtermans og hans Familie vil det glzde Dem og Pauli at herre at det lykkedes at skaffe Fru Houtermans og Berrnene Pasvisum ti1 England hvor the Society for the Protection of Science and Learning har taget sig kraftigt af hans Sag og har tilbudt ham en Understerttelse der, saasnart det lykkes at overvinde Vanskelighederne ved hans Udrejse, vil tillade ham for den nzrmeste Fremtid at fortsztte sit videnskabelige Arbejde i England. - Jeg skal viere meget interesseret [i] at herre om hvad der kommer ud af Deres fortsatte Diskussioner med Pauli og Fierz. I Forbindelse med Diskussionerne med Bothe i Bologna vil det maaske ogsaa interessere Dem og Pauli at se den lille Note om Kernef~toeffekterne’~ som jeg netop har afsendt ti1 “Nature” og hvoraf jeg vedliegger en Kopi i dette Brev. Argumentationen forekommer mig ikke alene meget naturlig fra et teoretisk Synspunkt men synes mig ogsaa at viere en utvungen Beskrivelse af de eksperimentelle Kendsgerninger og jeg skal jo viere meget glad for at herre de mere l a r d e Herrers Kritik og sender Dem og Paulis og alle andre Venner i Zurich de venligste Hilsener fra 0s alle. Deres [Niels Bohr]
Translation [Copenhagen,] 1 February 1938 Dear Bloch, Many thanks for your kind letter. I realised that you would also be very distressed to hear of Kalckar’s sudden death, and both for his family and for myself it was valuable information to get to know of the earlier incident of his fainting on his excursion with you, similar to attacks he had on excursions with his brothers years ago, and which nobody else knew about. As regards Houtermans and his family, both you and Pauli will be glad to hear l3
Introduction. ref. 79
P A R T 1 1 : S E L E C T E D C O R R E S P O N D E N C E (1929-
1949)
that it has been possible to obtain a visa for Mrs. Houtermans and the children to go to England, where the Society for the Protection of Science and Learning has taken up his case with great energy and has offered him a grant which will allow him to continue his scientific work in England as soon as the difficulties with his exit permit can be overcome. I shall be very interested to hear the outcome of your continued discussions with Pauli and Fierz. In connection with the discussions with Bothe in Bologna it may interest you and Pauli to see the little note on nuclear photo-effectsI3 which I have just sent to “Nature” and of which I enclose a copy. It seems to me that the argumentation is not only very natural from a theoretical standpoint, but also a very plausible description of the experimental facts, and I shall be very happy to hear the criticism of the more learned gentlemen, and I send the kindest regards to you and the Paulis and all other friends in Zurich. Yours, [Niels Bohr]
BLOCH TO BOHR,
15 February 1938
[Handwritten] Zurich, 15.II.38. Lieber Professor Bohr, Vielen herzlichen Dank fur Ihren letzten Brief und die Zusendung des Manuskripts uber den Kernphotoeffekt. Ich habe mich naturlich im Anschluss an unsere fruheren Diskussionen uber Strahlungseigenschaften der Kerne sehr dafur interessiert und hatte auch jetzt mehrere Diskussionen daruber mit Wentzel und Pauli. Von Anfang an lag fur uns die grosste Schwierigkeit darin, zu wissen, was wir uns unter den “special vibratory motions with singular radiation properties” eigentlich vorstellen sollen, und Pauli hat Ihnen j a im beiliegenden Brief sein Herz daruber ausgeschuttet. Ich bin vielleicht insofern positiver eingestellt, als ich durchaus einsehe, dass die Versuche von Bothe und GentnerI4 empirisch im Kontinuum der hochangeregten Kernniveaus wohldefinierte Zustande oder Zustandsgruppen verlangen, die besonders stark mit der Strahlung wechselwirken; deshalb gebe ich auch zu, dass Sie in Ihrer Note eine naturliche Beschreibung des Sachverhaltes gefunden haben. Fur eine “Theorie” fehlt mir aber wirklich das Verstandnis des zugrundeliegenden Mechanismus, und ich befinde mich da in einer ahnlichen Lage, wie Introduction, ref. 78
‘I
P A R T 1 1 : S E L E C T E D C O R R E S P O N D E N C E (1929-
1949)
damals, als wir uber die Dipol- und Quadrupolstrahlung der Kerne sprachen. Wenn man naturlich den Kern als Tropfchen mit vollig ausgeschmierter Ladung behandelt, so werden dessen Schwingungen nur durch ein Quadrupolmoment mit der Strahlung verknupft sein und falls die “special vibratory motions” ein Dipolmoment haben sollen, so durften sie eben nicht nach dem Tropfchenmodell behandelt werden. Mir scheint aber dieses Model1 uberhaupt nicht zuverlassig genug, um seine Konsequenzen betreffend das Verschwinden des Dipolmomentes als bindend betrachten zu konnen, und wenn man schon fur spezielle Schwingungen Ausnahmen zulasst, dann mochte ich allerdings auch mit Pauli gerne wissen, worin denn ihre Spezialitat zu suchen ist. - Aber vielleicht meinen Sie uberhaupt etwas ganz anderes, und ich bin jedenfalls auf Ihre ausfuhrlichere Veroffentlichung sehr gespannt. In 10 Tagen werde ich von hier verreisen; es tut mir schrecklich leid, dass ich meinen diesmaligen Aufenthalt in Europa nicht zu einem langeren Besuch bei Ihnen benutzen konnte, und ich bin Ihnen doppelt dankbar dafur, aus Ihren Briefen etwas vom “Kopenhagener Geist” erfahren zu haben. Mit vielen herzlichen Grussen Ihr Felix Bloch. NS. Es scheint, dass diesen Sommer eine kleine Gesellschaft von Physikern, bestehend aus Weisskopf, Placzek und Rabi in Stanford zusammen sein wird. Darauf freu’ ich mich naturlich schon sehr!
MAX DELBRUCK BOHR TO DELBRUCK,
18 March 1936
[Carbon copy] [K~benhavn,]18. Marts [19]36. Lieber Delbruck, Gestern morgen empfing ich die Korrektur Ihrer und Herrn Reddemanns Ubersetzung meines Artikels fur “Die Naturwissenschaften””, die ich hiermit zuruckschicke, nachdem Kalckar, Rosenfeld und ich zusammen sie sorgfaltig durchgesehen haben. Wir fanden die Ubersetzung sehr schon, haben uns aber erlaubt, eine Anzahl kleiner Anderungen vorzuschlagen, wobei es sich vor allem Is
Introduction, ref. 41.
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darum handelt, einige Satze, deren Sinn in der englischen Fassung nicht ganz deutlich war, etwas klarer zu machen. Ich hoffe auch nicht, dass Ihr Kunstlergewissen allzu stark dabei leiden wird, dass wir an einigen Stellen zwei Satze wieder zu vereinigen vorgeschlagen haben, die Sie mit Ihren im allgemeinen sehr erfolgreichen und willkommenen Bestrebungen getrennt haben. Wenn Sie mit diesen Vorschlagen einverstanden sind, brauchen wir naturlich keine weitere Korrektur zu sehen. Wie ich gleichzeitig Dr. Matthee geschrieben habe, mochte ich nur noch erwahnen, dass der zugefugte Hinweis in der Note zu der Uberschrift nicht nur litterarisch zweckmassig sein durfte, sondern auch eine Voraussetzung fur die freundliche Zustimmung der Redaktion von “Nature” zum Erscheinen der Ubersetzung bildet. Mit herzlichen Grussen von uns allen und auf baldiges Wiedersehen. Ihr [Niels Bohr]
DELBRUCK TO
BOHR,20 March 1936 (postmark)
[Postcard] Lieber Professor Bohr, uber Ihre Korrekturen bin ich sehr erbittert und halte sie fur ein Verbrechen am Lesepublikum. Da ich es aber fur aussichtslos hielt, Sie von der Mangelhaftigkeit Ihres Gebrauchs der deutschen Sprache zu uberzeugen, habe ich die Korrektur unverandert weitergegeben und mich darauf beschrankt, meiner Missbilligung “symbolisch” dadurch Ausdruck zu verleihen, dass ich meinen Namen als Ubersetzer gestrichen habe. Die besten Grusse Ihr M. Delbruck
DELBRUCK, 22[?] March 1936 [Typewritten copy]
ROSENFELD TO
[K@benhavn,]22[?]/3 1936. Lieber Max, Bohr hat mir Deine Karte gezeigt, und wir beide beklagen sehr, dass unsere Vorschlage zu Anderungen in Deiner Korrektur Dich so vie1 erbittert haben, dass Du sogar daran denken konntest, jede Verantwortung fur die Ubersetzung abzulehnen, was Bohr, der fur Dein Interesse fur seinen Artikel sehr dankbar war, eine wirkliche Sorge bereiten wurde. Was die Anderungsvorschlage betrifft, glau-
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ben wir auch, dass Du gewissermassen unsere Absicht missverstanden hast. Als Auslander konnten wir ja keineswegs daran denken, Deinen Stil kritisieren oder gar verbessern zu wollen, zumal wir alle ihn im Allgemeinen ganz besonders schatzen. Es handelt sich aber vor allem um die Klarstellung des Inhalts einiger Satze, deren Sinn vielleicht auch nicht ganz deutlich in der englischen Fassung war, wo wir aber furchteten, dass die von Dir vorgeschlagene, sicherlich sprachlich bessere Fassung sich zu weit von den gewunschten Nuancierungen entfernte, besonders wo es das Verhaltnis zur fruheren Literatur, welche nach der Art des Artikels nur indirekt beruhrt werden konnte, betraf. Alle unsere Anderungen, was Bohr vielleicht in seinem Brief nicht deutlich genug betont hatte, waren naturlich auch nur als Vorschlage zu Dir und Reddemann gemeint, damit Ihr sehen konntet, in welcher Richtung unsere Bedenken lagen. Bohr wurde sich selbstverstandlich ganz besonders freuen, wenn Du diese Anderungsvorschlage so umarbeiten wolltest, dass auch die entsprechenden Stellen in sprachlicher Hinsicht so schon auszusehen kommen wie der Rest der Ubersetzung, welche von uns allen als ganz vorzuglich beurteilt wurde. Es ware sehr schade, gerade bei diesen schwierigeren Punkten auf Deine Hilfe verzichten zu mussen. Was die in dieser Hinsicht ganz untergeordneten Punkt der Wiedervereinigung der gespalteten Satze betrifft, verstehe ich wohl, dass Du denkst, dass wir zu weit gegangen sind. Aber aus personlicher Erfahrung (mit der franzosischen Ubersetzung des Bohrschen Buches) weiss ich ganz genau, wie man zunachst tapfer darangeht, die Bohrschen Satze zu zerstuckeln, um dann aber bei naherer Uberlegung zu finden, dass es nicht so leicht gemacht werden kann, ohne deren Sinn abzuschwachen. Ich glaube, es hilft nichts; das Lesepublikum sol1 sich lieber damit abfinden, dass es eben zu den Bohrschen Gedanken keine “via regia” gibt. Vor allem hoffe ich, dass dieser Brief das uns allen unerwartete Missverstandnis beseitigen wird, und dass Du infolgedessen sowohl Deine direkte Hilfe wie die formale Teilnahme an der Ubersetzung nicht mehr verweigern wirst, wodurch Du uns allen und insbesondere Bohr eine grosse Freude bereiten wurdest. Rosenfeld
DELBRUCK
TO ROSENFELD,
25 March 1936
[Handwritten] Grunewald 2 5 . Marz 1936 Lieber Leon, eben dieses: die Mitarbeit an den Nuancen will ich auf alle Faille vermeiden. Denn den Sinnunterschied dieser Nuancen vermag ich nicht zu erkennen; ihr
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kunstlerischer Wert ist mir gleichgultig, und unter dem Gesichtspunkt der Klarheit und Eindringlichkeit halte ich sie fur abtraglich. Es ist naturlich Bohrs gutes Recht, in seiner Manier zu schreiben, aber er kann nicht verlangen, dass ich mich mit ihm uber Nuancen streite, wenn ich diese Nuancierung auf Kosten der Eindringlichkeit als solche fur verfehlt halte. Ich habe deshalb Eure Fassung, die unfehlbar jeden Leser aufs ausserste ermudet, unverandert abgeschickt.* Da der Grundgedanke der Arbeit so einfach ist, wird es ja wohl auch so den meisten Lesern gelingen, ihn schliesslich herauszufinden. Aus diesem Grunde scheint mir auch der ganze Streit des ernsthaften Streites nicht wert. Ich bin aber gern bereit, ihn nachste Woche (d.h. den Streit uber das Prinzip, nicht uber die Nuancen) in Kopenhagen fortzusetzen. In den ersten Apriltagen kommt auch die zweite Korrektur, bis dahin kann sowieso nichts geschehen. Friede sei mit Euch! M.D. P.S. zu Trauer und Sorge, die aus Deinen ruhrenden Zeilen spricht, scheint mir kein Anlass. Was kann es erfreulicheres geben als einen kraftigen Streit. Danach durste ich schon lange! * Ihr braucht nicht zu befiirchten, dass Euer Deutsch nicht korrekt sei. Die identische Nachahmung der seit zwanzig Jahren bewahrten Satzbildungen ist eine sichere Garantie dafur.
PAUL A.M. DIRAC BOHR TO DIRAC,
24 November 1929
[Carbon copy] [K~benhavn,]November 24. [19]29. Dear Dirac, From Gamow I hear that you are now back in England again, and that you have made progress with the mastering of the hitherto unsolved difficulties in your theory of the electron. As we have not yet heard about any details Klein and I should be very thankful if you would be so kind to tell us something of your present views. Recently I have been very interested in these problems and have thought that the difficulties in relativistic quantum mechanics might perhaps be connected with the apparently fundamental difficulties as regards conservation of energy in @ray disintegration and the interior of stars. My view was that the difficulties in your theory might be said to reveal a contrast between the claims of conservation of energy and momentum on one side and of the conservation of the individual particles on the other side. The possibility of fulfilling both
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these claims in the usual correspondence treatment would thus depend on the possibility of neglecting the problem of the constitution of the electron in non relativistic classical mechanics. It appeared to me that the finite size ascribed to the electron on classical electrodynamics might be a hint as to the limit for the possibility of reconciling the claims mentioned. Only in regions where electronic dimensions do not come into play, the classical concepts should present a reliable fundament for the correspondence treatment. Of course you are aware yourself of the great difficulties which just in Lhis respect encounter the unambiguous interpretation of the unsatisfactory consequences of your earlier theory as regards transitions connected with a change of “sign” of the electric charge. This refers just as much to the transition in static fields as to those connected with radiation. As regards the latter the difficulty of the correspondence with usual radiation ideas appears not least therein that the uncertainty of the energy due to the shortness of the lifetime would even be larger than mc2. I was therefore prepared that we might have to face an essential limitation of the principles of conservation of energy and momentum in nuclear problems, and I am very interested to learn whether your new work leads to such consequences or proceeds on different lines. With the kindest regards from us all. Yours very sincerely, [Niels Bohr]
DIRAC TO BOHR,
26 November 1929
[Handwritten] St. John’s College, Cambridge. 26- 1 1-29. Dear Professor Bohr, Many thanks for your letter. The question of the origin of the continuous 0ray spectrum is a very interesting one and may prove to be a serious difficulty in the theory of the atom. I had previously heard Gamow give an account of your views at Kapitza’s club. My own opinion of this question is that I should prefer to keep rigorous conservation of energy at all costs and would rather abandon even the concept of matter consisting of separate atoms and electrons than the conservation of energy. There is a simple way of avoiding the difficulty of electrons having negative kinetic energy. Let us suppose the wave equation
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does accurately describe the motion of a single electron. This means that if the electron is started off with a + ve energy, there will be a finite probability of its suddenly changing into a state of negative energy and emitting the surplus energy in the form of high-frequency radiation. It cannot then very well change back into a state of + ve energy, since to do so it would have to absorb high-frequency radiation and there is not very much of this radiation actually existing in nature. It would still be possible, however, for the electron to increase its velocity (provided it can get the momentum from somewhere) as by so doing its energy would be still further reduced and it would emit more radiation. Thus the most stable states for the electron are those of negative energy with very high velocity. Let us now suppose there are so many electrons in the world that all these most stable states are occupied. The Pauli principle will then compel some electrons to remain in less stable states. For example if all the states of - ve energy are occupied and also a few of + ve energy, these electrons with + ve energy will be unable to make transitions to states of -ve energy and will therefore have to behave quite properly. The distribution of - ve electrons will, of course, be of infinite density, but it will be quite uniform so that it will not produce any electromagnetic field and one would not expect to be able to observe it. It seems reasonable to assume that not all the states of negative energy are occupied, but that there are a few vacancies or “holes”. Such a hole which can be described by a wave function, like an X-ray orbit would appear experimentally as a thing with +ve energy, since to make the hole disappear (i.e. to fill it up), one would have to put -ve energy into it. Further, one can easily see that such a hole would move in an electromagnetic field as though it had a +ve charge. These holes I believe to be the protons. When an electron of +ve energy drops into a hole and fills it up, we have an electron and proton disappearing simultaneously and emitting their energy in the form of radiation. I think one can understand in this way why all the things one actually observes in nature have a positive energy. One might also hope to be able to account for the dissymmetry between electrons and protons. So long as one neglects interaction one has complete symmetry between electrons and protons; one could regard the protons as the real particles and the electrons as the holes in the distribution of protons of - ve energy. However, when the interaction between the electrons is taken into account this symmetry is spoilt. I have not yet worked out mathematically the consequences of the interaction. It is the “Austausch” effect that is important and I have not yet been able to get a relativistic formulation
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of this. One can hope, however, that a proper theory of this will enable one to calculate the ratio of the masses of proton and electron. I was very glad to hear that you will visit Cambridge in the spring and I am looking forward to your visit. With kind regards from Yours sincerely, P.A.M. Dirac.
ENRICO FERMI BOHR TO FERMI,
1 February 1939
[Carbon copy] [Princeton,] February 1, 1939. Dear Fermi, When I came back from Washington I received confirmation of what I told you there was my presumption, that Professor Meitner and Dr. Frisch in their note to appear in Nature’6 had actually suggested the very same experiment of which you spoke as well as a number of others; and also in a letter from my son dated January 16, I learned that Frisch had then already succeeded in verifying the presence of the high energy splitters [splinters?]. I felt therefore most strongly how justified I had been in urging so insistently that Tuve and you should not publish anything before the actual text of Meitner and Frisch’s note was at hand, since the whole idea was brought to the notice of scientists in this country only by the authors’ kind and confidential communication to me. I telephoned immediately to Tuve to stress this and tell him about Frisch’s own experiments. To my great concern Tuve told me that the connection with the press had already gone too far to stop publication, and especially that steps had already been taken by Columbia to publish your results in the New York Times. I then called Pegram, who at once agreed about the necessity that any newspaper account of the effect predicted by Frisch and Meitner should contain a reference to Frisch’s original proof of the existence of this wonderful phenomenon. At the same time I sent a telegram to Copenhagen, asking for immediate information about the progress of Frisch’s experiments. As you know, Pegram’s attempts to get the newspaper articles altered in the way desired were unsuccessful. When he called yesterday morning to explain this, I had not yet received any answer from Copenhagen to my cable, and I therefore arranged with him to postpone any further step to put the matter straight until 16
Introduction, ref. 98.
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I should get full information from Copenhagen. This morning I have just received the following telegram from Frisch: LINEAR AMPLIFIER DEMONSTRATES DENSELY IONISING SPLIT NUCLEI BOTH URANIUM THORIUM DETAILED INFORMATION POSTED TWENTYSECOND N E W EXPERIMENTS DEMONSTRATE SPLITTING WITHIN FIFTIETH SECOND
I hope to receive the letter mentioned in this telegram before I see you on Saturday, and then we shall be better able to discuss with Pegram the proper way to remedy this most unfortunate situation which, I am afraid, has in the meantime caused great dismay in Stockholm and Copenhagen. Any such sensational news from America is in fact generally telegraphed at once to the newspapers there, which will most probably not have heard anything as yet of the original discoveries of Meitner and Frisch, since it is not the custom of our laboratories to send any communication directly to the press. The best solution might perhaps be that I write an article in Science about the whole new development from the experimental as well as the theoretical viewpoint, which would offer me the opportunity to give everyone concerned proper credit. Tuve, with whom I have just had a telephone conversation, also strongly advised this, and I will therefore try to have such an article ready for Saturday. Since we met in Washington, I have myself got considerably further as regards the estimation of the barrier effects for the heavy elements. Especially has the consideration of the stability, not only of U238,but also of all the other isotopes of this and the other heavy elements lent strong support to the views I presented in Washington. Probably I shall very soon be in a position to publish with Wheeler a more elaborate account of the ideas indicated in my Nature note”. I need not say how much I look forward to discussing these problems with you when we meet in New York. With kindest regards, Yours, Niels Bohr
P.S. From my telephone conversation with Pegram this afternoon you may already know most of the content of this letter. But thinking that it may be of interest for you to have a direct copy of Frisch’s telegram, I still decided to send it to you. Pegram and I talked also about the advisability of sending additional information at once to the American press, and he said he would discuss this very delicate question with you. Since I have not heard from him again, I presume that you both found it better to postpone a decision about this point until Saturday, when more information from Copenhagen will be at hand. Introduction, ref. 99.
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BOHR TO FERMI,
2 February 1939
[Carbon copy] [Princeton,] February 2 , 1939. Dear Fermi, It was a great relief to me this morning to receive from Tuve the Science Service" of January 30, in which through his kind intervention reference to the first experiments at Copenhagen was introduced in direct connection with the account of the explanation of Hahn's results proposed by Frisch and Meitner. I feel indeed that through the kind understanding shown me from all sides proper credit is now secured for everyone concerned. I know that you realize that it has not been my intention unduly to stress personal matters, but that I was only afraid that an unhappy concourse of circumstances, each most pleasant in itself, should lead to discomfort for my friends and collaborators who had confided in me. With kindest regards to Professor Pegram and yourself, and looking forward t o meeting you both on Saturday morning, Yours, Niels Bohr
BOHR TO FERMI,
17 February 1939
[Carbon copy] [Princeton,] February 17, 1939. Dear Fermi, It was a great pleasure to me on my visit to Columbia to learn about the progress with the experiments there, and I thought it might interest you to learn that I just received a telegram from Copenhagen, with the following information: JACOBSEN ACTIVATED URANIUM W I T H 4.5 MEV DEUTERONS AND COLLECTED RECOILMATERIAL
SHOWING
SAME
DECAY
STOP
HIGHVOLTAGE
DEPARTMENT
LITHIUM DEUTERON NEUTRONS SPLIT URANIUM THORIUM BUT NONE FROM BISMUTH TO PLATINUM INCLUSIVELY
STOP LITHIUM PROTON
GAMMAS POSSIBLY SPLIT
URANIUM EXPERIMENTS CONTINUED STOP
I need hardly add that it was also a great pleasure to get the opportunity once again to discuss with you the theoretical aspects of the fission problem. Of course, I quite realize the soundness of your arguments for doubting my conception of the fission mechanism, until further experiments as regards a comparison l8
Introduction. ref. 108a.
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of the statistical distributions of the nuclear fragments produced by thermal and by fast neutrons have been carried out. I hope that such experiments will soon be at hand; at any rate I have also sent a copy of my noteIg to Copenhagen and urged that a minute search for eventual [possible] differences between these distributions be carried out there as soon as possible. As regards the variation of the fission probability with energy and mass and charge numbers, I hope also that they soon shall have made sufficiently accurate measurements in Copenhagen about the variation with neutron velocity of the ratio between the fission in Uranium and Thorium, so as to know more about how the fission probability varies with energy in the region of fast neutrons. In this connection I suppose that new important evidence will also have resulted from the experiments of the Columbia group before we meet again at the occasion of the American Physical Society congress in New York. With kindest regards also to Pegram and Dunning Yours, [Niels Bohr] FERMI TO BOHR,
1 March 1939
[Typewritten] 450 Riverside Drive New York, March 1, 1939
Dear Professor Bohr, Both Dunning and I would have been of course very glad to introduce in the letter that we sent t o the Physical Review2’ the changes that you suggested to Dunning on Saturday. Unfortunately we were informed by Miss Mitchell that it was already too late, since the proofs had been already licenced last friday. For this reason the letter shall be printed as the original manuscript. In any case it seems to me that the short account of the “history” of the problem that we gave was fairly accurate and I can assure you that both Dunning and I were very careful to give t o Hahn, Strassmann, Frisch and Meitner their credit. According to what Dunning told me of the conversation he had with you, it seems that you dont consider as quite fair to give to Hahn the credit for the discovery of the splitting process and to Frisch and Meitner the credit for clearing up the energetic relations that make such a splitting process understandable. Now I reread Hahn’s paper2’ and I found there a very clear suggestion that the process 19
21
Introduction, ref. 115. Introduction, ref. 110. Introduction, ref. 96.
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should consist in a division of the uranium nucleus into two approximately equal parts. How far this statement of Hahn has been influenced or determined by the correspondence that he had on the subject with Lise Meitner and with Frisch, I am of course unable to say, since he does not mention it. But, judging from the evidence of the papers that have been written, it seems to me that what we said was quite accurate. I am really very sorry that you should take a different point of view. And I hope in any case that you will agree that we did not try to give the impression that we had contributed to the problem more than we actually did, which is of course very little. With best regards Yours sincerely Enrico Fermi
BOHR TO FERMI,
2 March 1939
[Carbon copy] [Princeton,] March 2, 1939. Dear Fermi, Thanks for your kind letter. As I said to Dunning, during my conversation with him last Saturday, I appreciated most fully the fairness and liberality with which, in your letter to Physical Review, credit was given to everyone concerned with the new wonderful development, to which you and he have yourselves contributed so greatly. My only reason for suggesting a few quite unimportant changes was Dunning’s direct request in his letter of 20 Feb. The point which I discussed at length with him and as regards which I am afraid from your letter that he did not quite understand me was the question of what may be said to be the merit of Meitner and Frisch in this matter. In your letter to Phys. Rev. they are credited with the remark about the release of energy, and I felt that it was in some way almost too much, since this point by itself would be clear t o everyone who first believed in the fission-phenomenon. To my mind their merit was rather to have grasped the fission idea so thoroughly and given so reasonable an explanation of the mechanism of energy-release that it would appeal immediately to the interest of all physicists. That was in any case my personal experience and also the impression of the circle here in Princeton. As Placzek will probably have told you himself the whole phenomenon appeared indeed so strange and impossible to explain even to a man with his great experience in nuclear theory that he refused to believe in Hahn’s discovery when he first heard about it.
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As regards the credit due to Hahn and Strassmann, I agree of course entirely with you and Dunning, and I do not understand what may have induced you to believe that I should take a different point of view. Even if, as I without any firsthand knowledge suggested as a possibility in the talk with you in Washington, Meitner and Frisch’s enthusiastic interest might have fortified Hahn’s confidence in his surprising findings, this would be entirely a matter of exchange of views between intimate friends and would have no influence whatsoever on the merit of Hahn and Strassmann for their great discovery. With the kindest regards to you and Dunning Yours, [Niels Bohr]
RALPH H . FOWLER BOHR TO FOWLER,
14 February 1929
[Carbon copy] [K~benhavn,]February 14. [19]29. Dear Fowler, First of all I want to congratulate you to the completion of your great work” which you were so kind to send me. It is a tremendous undertaking which will surely be most welcome to all physicists. I look forward myself to learn much from it, and here in the institute we have already had experience how useful your work is to students who want to specialize in statistics. Gamow, who has enjoyed his visit to Cambridge most intensely, returned to Copenhagen the day before yesterday and has been telling us about all his new experience. In connection with Rutherford’s new experiments on the expulsion of protons by bombardment of atomic nuclei with a-rays, I have been wondering whether he thinks it excluded that the observed velocity distribution of the protons may arise from different discrete stages of excitation of the resulting nucleus, and if an emission of y-rays accompanying this excitation would escape observation. If even in proton transformations we witness a want of definition of energy, new aspects indeed seem to open. Lately I have been thinking a good deal of the possible limitation of the conservation theorems in relativistic quantum theory, and we have just been discussing, if in the reversal of P-ray transformations we might find the mysterious source of energy claimed by Eddington’s theory of constitution of stars. 22
R . H . Fowler, Statistical Mechanics, Camb. Univ. Press, 1 9 2 9 .
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For the rest I am trying in these days to finish a small note of the philosophical aspects of quantum theory23which I hope will not be considered to be too metaphysical. As soon as I have finished it l shall write again and tell more about things. To-day I wanted first of all to thank you for your book. With kindest regards to Eileen and yourself and Rutherfords from Margrethe and yours, [Niels Bohr]
OTTO ROBERT FRISCH BOHR TO FRISCH,
20 January 1939
[Carbon copy] Institute for advanced study Princeton Januar 20 1939 K z r e Frisch, Paa Vejen over har jeg t a n k t en he1 Del paa de'vidunderlige nye Udsigter, der er aabnede ved Hahn's F o r s ~ gmed de tunge Kerner, og hvis Resultater jeg nu haaber helt er sikrede. Lige fra den f ~ r s t eGang De fortalte mig om det har jeg jo varet enig med Tendensen i Deres og Deres Tantes Betragtninger, men jeg f ~ l t edet alligevel et 0jeblik paa Rejsen svzrt at forstaa, hvordan en forholdsvis ringe Forstyrrelse saa fuldstzndigt kunde forandre en tung Kernes Stabilitet. Det ferrste Stadium efter Neutronsammenst~detvil jo utvivlsomt ogsaa her v z r e en forholdsvis ringe Opvarmning af Totalkernen. Den simple Lersning er imidlertid naturligvis den, at vi ved Kernens senere Deling har at gore med Resultatet af en Fluktuation af Energifordelingen mellem Kernens Frihedsgrader, der, selv om Resultatet er saa forskelligt, ikke i Princip er vzsentligt anderledes end de Fluktuationer i Energifordelingen, der betinger de szdvanlige Disintegrationer. Da jeg kunde t a n k e mig, at dette Synspunkt kunde have Interesse for Laserne af Deres og Deres Tantes Note, har jeg straks da jeg kom her ti1 Princeton skrevet en lille Note ti1 NATURE24, som jeg indlagt sender, sammen med et Brev ti1
'' Probably, N.Bohr, Wirkungsquantum und Naturbeschreibung, Naturwiss. 17 (1929) 483-486.
Vol. 6, p . [201]. 24 Introduction, ref. 99.
See
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Redakt~ren,og som jeg beder Dem at lade Fru Schultz videresende dersom, som jeg haaber, Hahn’s Artikkel allerede er udkommet, og Deres og Deres Tantes Note allerede er indsendt ti1 NATURE. Jeg glieder mig meget ti1 at hrare fra Dem, baade om det sidste nyt i denne Forbindelse og hvordan det er gaaet med Undersogelserne paa Instituttet, hvor jeg jo trods Afstanden fdger alt med saa mange Tanker. Jeg haaber ogsaa inderligt, at De mart har gode Efterretninger om Deres egen Familie og sender sammen med Rosenfeld Dem og alle paa Instituttet de hjerteligste Hilsner, Deres hengivne [Niels Bohr] P.S. Som jeg har skrevet i Brevet ti1 Mr. Gale, vil jeg gerne bede Dem om at rette Korrekturen og tilbagesende den ti1 NATURE, dersom Sagen ikke i Mellemtiden tager nogen uventet Udvikling. I saa Fald vil jeg gerne, at De enten straks skriver ti1 mig derom, saa at jeg kan naa at ware Dem fOr De modtager Korrekturen, eller at De paa et hvilket som helst senere Tidspunkt beder Fru Schultz om at sende mig et “langsomt” Telegram med de nerdvendige Oplysninger.
P.S. Jeg har lige set Hahns og Strassmanns Artikkel i Naturwiss.2s, der naturligvis straks har givet Anledning ti1 megen Diskussion her i Instituttet, hvor man paatamker at gare F o r s ~ gpaa at finde de hurtige 6-Straaler svarende ti1 de kortlevende Produkter der umiddelbart skulde fremkomme ved Urankernens Deling. Jeg skal skrive niermere om det med n m t e Post.
Translation Princeton, 20 January 1939 Dear Frisch, On the way over I have thought a great deal about the marvellous new prospects which have been opened up by Hahn’s experiments with the heavy nuclei, and whose results I now hope are completely certain. Right from the first time when you told me about this I agreed with the trend of your and your aunt’s considerations, but for a moment during the voyage I found it difficult to under25
Introduction, ref. 96.
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stand how a relatively small disturbance could alter the stability of a heavy nucleus so completely. The first stage after the neutron impact will surely also in this case consist of a relatively slight heating of the compound nucleus. However, the simple solution is, of course, that in the later behaviour of the nucleus we have to d o with the result of a fluctuation in the energy distribution between the degrees of freedom of the nucleus which, in principle, is not essentially different from those fluctuations in the energy distribution which are responsible for the ordinary disintegrations, although the result is so very different. I could imagine that this point of view could be of interest to the readers of the note by you and your aunt, and I have therefore immediately on arriving here in Princeton written a little note to Nature24, which I enclose, together with a letter to the editor. I would like you to ask Mrs. Schultz to send these on if, as I hope, Hahn’s article has already appeared, and the note by you and your aunt has already been sent in to Nature. I shall be very glad to hear from you, both about the latest news on this subject, and how it goes with the investigations in the Institute, which I follow with so much concern in spite of the distance. I sincerely hope also that you will soon have good news about your own family, and I am sending, jointly with Rosenfeld, the warmest greetings to you and everybody in the Institute. Yours sincerely, [Niels Bohr] P.S. As I wrote in the letter to Mr. Gale [Editor of Nature] I would ask you to correct the proofs and return them to Nature, provided there have not been any unexpected developments in the meantime. In that case I would like you either to write to me about it immediately, so that I can reply before you receive the proofs, or at some later time to ask Mrs. Schultz to send me a “delayed” telegram with the relevant information. P.S. I have just seen Hahn and Strassmann’s article in N a t u r w i ~ s .which ~ ~ , naturally has at once led to much discussion here in the Institute, where people are thinking of doing experiments to find the fast P-rays corresponding to the short-lived products which should result immediately from the splitting of the uranium nucleus. I shall write more about this with the next mail.
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22 January 1939 [Typewritten with handwritten addition]
FRISCH TO BOHR,
Copenhagen, 22.1.1939. Modtaget [Received] 2-2 1939 Dear Professor Bohr, Please excuse my writing english, but although I speak danish quite easily I find it rather difficult to write it, especially about scientific things. (And then my machine has no danish types.) Enclosed I send you copies of two letters which I sent to NATURE a few days agoz6.The first one you have seen before you left; it has increased somewhat by adding details but I hope otherwise to have followed, more or less, the suggestions you gave me on our talk in Carlsberg. The second paper contains the report of an experiment, which I decided to undertake on Thursday Jan. 12th; I was so lucky as to get a positive result the next day, which I confirmed, and got details of, during the next three days, and on Monday night I sent off the letters. Yesterday I got the proofs and sent them back last night; so I hope both papers will come out very soon. (Of course, there is no “Tavshedspligt” [secrecy] any longer!; Hahn’s paper came out the day you left.) It was great fun to get this experiment done so quickly, but now of course there are a lot of things for more detailed study. The next thing, I shall try to do the experiment with a very thin layer of uranium (or thorium) so as to have practically no energy loss of the particles emerging from it; this should permit the determination of energy groups, by recording the size of the ionization pulses, and thereby of the mode of division (mass ratio of the two parts; whether there is a nearly unique “division line” or whether a broad range of mass ratios occurs). Furthermore this experiment should permit the determination of the cross-section of the uranium nucleus effective with respect to these “fission” processes (I wonder how you like this word; it was suggested by the biochemist Dr. Arnold, who told me it was the usual term for the division of bacteria). From my present experiments with a thick layer of uranium and under the assumption of a range of 4 mms in air for the particles resulting from the fission, a cross-section of 1.5. cm2 is obtained which agrees exactly with the value found by Hahn, Meitner etc, for all the activities obtained in uranium (including the “transuranium” activities, which are the strongest). The cross-section is, however, much less than the total cross-section (about 15. of uranium. I was first surprised at this, but one should perhaps expect it from the “liquid drop” model, since a particle hitting a droplet will excite many different oscillations, of which only the ones cor”’ Introduction, ref. 98.
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responding to the lowest order spherical harmonics will favour the division of the droplet in two. Of course one must see if elements beside uranium and thorium show this phenomenon. I have had lead in the chamber, with negative result, but this experiment (and experiments with Bi, T1, H g , A u etc) will be repeated more carefully and, perhaps, with the fast neutrons from Li + D from our High-tension tube, which will be ready to work in a few days, from what Bjerge tells me. We also thought of looking for fission induced by the hard gamma-rays from Li + H . Furthermore we intend to carry out some experiments of the kind indicated at the end of my letter to NATURE, probably in collaboration with Prof. Meitner by sending her the irradiated samples (air mail) for physical and chemical investigation. So it seems that this new phenomenon opens possibilities for quite a bit of work. But of course the other things are not being neglected. The cyclotron is working again after a period of general repair; I think Dr. Jacobsen has written to you about this. The magnet for the neutron magnetic moment is being cast these days. Dr. Simons, of Helsingfors, has started work; he is going to measure the scattering cross-section of protons (in water) relative to resonance neutrons of silver and iodine, which have energies high in comparison t o the chemical binding of the protons. With my best regards, also t o Erik, Yours sincerely, O.R. Frisch BOHR TO FRISCH,
24 January 1939
[Carbon copy] [Princeton,] January 24, 1939. K z r e Frisch, Jeg haaber at De har faaet det Brev, som jeg sendte forleden sammen med en lille Note o m de nye Kerne-Sranderdelingsprocesser. Jeg har endnu slet ikke modtaget noget Brev fra Instituttet og Ianges i s z r efter at se den endelige Form af Deres og Deres Tantes Note ti1 NATURE, hvoraf De lovede at sende mig en Kopi. Jeg ved derfor ikke, o m De selv i Deres Note kommer ind paa lignende Betragtninger over Sranderdelingens Mekanisme, som de, der antydes i min Note og hvorvidt denne sidste bringer noget tilstrakkelig nyt for en Offentligg~relse. Min Hensigt var imidlertid ogsaa i frarste Linie kun a t g m e det klart for migselv og andre, at der ikke er nogen Modstrid mellem Deres Forklaring af de nye Processer og de almindelige T r z k i Kernereaktionernes Forlrab, som d e sadvanlige S~nderdelingsprocesseraabenbarer.
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En Sztning i min Note, som maaske kunde give Anledning ti1 Misforstaaelser er Sammenligningen mellem Hyppighederne for de to Slags Processer for de tunge Kerner. Jeg mente j o dermed kun at visse TrEk i de tidligere Undersergelser over “Transuranerne” vel stadig maa vzere rigtige, og at derfor i det mindste Hyppigheden for Neutronindfangninger med Straalingsudsendelse maa vzere sammenlignelig med Hyppigheden for de nye Smderdelingsprocesser. Iervrigt er jeg ved at tzenke nzrmere over Aarsagen bleven mere og mere klar over at man i alle Betragtninger over Overfladespzmdingen maa udvise stor Forsigtighed ved Sammenligningen imellem Virkningerne af de typiske short range Kernekrzefter og de elektriske Frasterdninger, hvis Indflydelse paa Kernens Stabilitet er af vzsentlig anden Karakter. Skal Noten overhovedet offentliggerres vil jeg i hvert Fald bede Dem om i Korrekturen at indferre de smaa Endringer, vedr~rendede omtalte Punkter som er anferrt i Margen paa den Kopi som jeg vedlzgger. Jeg vil gerne bede Dem om at vente med Korrekturens Tilbagesendelse ti1 jeg skriver igen saa mart jeg har faaet herrt fra Dem og set Kopien af den Note, De og Deres Tante selv har indsendt. Som jeg nzevnte sidst i mit forrige Brev er Fysikerne her i Instituttet meget optagne af hele Sperrgsmaalet og jeg har allerede truffet Forberedelser ti1 at gerre Forserg paa at paavise de radioaktive Stoffer med meget kort Levetid, hvis Fremkomst skulde v z r e et umiddelbart Resultat af den nye Type af Kernesernderdelinger. Hvis en saadan Paavisning lykkes vil [det] jo v z r e den allersimpleste og mest direkte Maade ti1 at underserge mange Problemer vedrrarende Betingelserne for Kernesernderdelingernes Fremkomst. I Samarbejde med Wheeler er jeg ogsaa begyndt paa en mere indgaaende Undersergelse af de forskellige teoretiske Problemer, som de nye Kernesernderdelinger stiller 0s overfor. Naturligvis er jeg meget interesseret i at herre nzrmere om, hvad De selv baade i den ene og i den anden Retning har tzenkt paa, lige som jeg jo er meget spzndt paa at herre om, hvorledes det gaar med alle Undersergelserne paa Instituttet. Med mange venlige Hilsner Deres hengivne [Niels Bohr]
Translation [Princeton,] 24 January 1939 Dear Frisch, I hope you have received the letter I sent you the other day with a little note on the new nuclear splitting processes. I have not yet had any letter at all from the Institute, and am particularly anxious to see the final form of your and your
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aunt’s letter to Nature of which you promised to send me a copy. I therefore do not know whether in your note you go into similar considerations about the mechanism of the transmutation to those which are sketched in my note and whether the latter contains sufficient new material for publication. My intention was however also in the first place only to make it clear to myself and others that there is no contradiction between your explanation of the new processes and the general features of the mechanism of nuclear reactions shown by the usual transmutation processes. One sentence in my note, which could perhaps give rise to misunderstandings, is the comparison between the frequencies of occurrence of the two kinds of processes in heavy nuclei. I meant with this only that certain features of earlier investigations on the “transuranics” ought still to be correct, and that therefore at least the frequency of radiative neutron capture must be comparable with the frequency of the new splitting process. Besides, as I think more about the causes it becomes more and more obvious to me that in all considerations of surface tension one has to be very cautious in comparing the effects of the typical shortrange nuclear forces and the electric repulsions whose influence on the stability of the nucleus is of an essentially different character. If the note is going to be published at all, I would ask you at least to insert in the proofs the small corrections concerning the mentioned points as given in the margin of the enclosed copy. I would ask you to wait with returning the proofs until I write to you again as soon as I have heard from you and have seen a copy of the note sent in by you and your aunt. As I already mentioned in my last letter, physicists here in the Institute are very excited about the whole question, and I have already made preparations for experiments to demonstrate the very short-lived radioactive substances whose formation should be an immediate result of the new type of nuclear splitting process. If such a demonstration succeeds it would be the simplest and most direct method for investigating many problems concerning the conditions for the occurrence of nuclear splitting. I have also started, in collaboration with Wheeler, a more thorough investigation of the various theoretical problems with which we are confronted by the new nuclear transmutation. I am of course very interested to hear more of what you yourself have thought about in one or other direction, just as I am eagerly waiting to hear how it goes with all the research in the Institute. With many kind regards, Yours sincerely, [Niels Bohr]
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BOHR,31 January 1939 [Telegram]
FRISCH TO
See p. [58]. FRISCH TO BOHR,
1 February 1939
[Telegram] See p. [ 5 8 ] .
BOHR TO FRISCH,
3 February 1939
[Carbon copy] [Princeton,] February 3, 1939 Dear Frisch, I need not say how extremely delighted I am by your most important discovery, on which I congratulate you most heartily. The two notes of your aunt and yourself, of which I have just received copies together with your letter of the 22nd, are indeed most excellent as well in form as in content, and I am of course extremely interested in the whole program of experiments mentioned in your letter. I have myself been thinking a good deal over the theoretical explanation of the result and what further experiments will be desired for the elucidation of the “fission” mechanism. The point which struck me when thinking over the whole matter as soon as I got a quiet time on board was the essential importance of the fluctuations in the statistical distribution of the energy between the more or less coupled modes of vibration of the compound nucleus for an understanding of the contrast between the stability of the heavy nuclei and the ease with which they are split by comparatively small excitations. I was indeed thinking of just the same point as mentioned in your letter about the way in which special modes of vibration may be excited by direct impact, and realized that the probability of fission estimated in this way was far too small. I wrote a note2’ in order to call attention to this point, which may be decisive for suggestions of further experimental research, as well as to stress the importance of the new discovery, which may hardly be necessary as later experience has shown. The experiments of Hahn, together with your aunt’s and your explanation have indeed raised quite a sensation not only among physicists, but in the daily press in America. Indeed, as you may have gathered from my telegrams and perhaps even, as I
’’ Introduction, ref. 115.
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feared, from the Scandinavian press, there has been a rush in a number of American laboratories to compete in exploring the new field. On the last day of the conference in Washington (January 26-28), where Rosenfeld and I were present, the first results of detection of high energy splitters [splinters?] were already reported from various sides. Unaware as I was, to my great regret, of your own discovery, and not in possession even of the final text of your and your aunt’s note t o Nature, I could only stress (which I did most energetically) to all concerned that no public account of any such results could legitimately appear without mentioning your and your aunt’s original interpretation of Hahn’s results. When Hahn’s paper appeared, information about this could of course, for your own sake, not be withheld and was, in fact, the direct source of inspiration for all the different investigators in this country. When I came back to Princeton I learned from an incidental remark in a letter from Hans the first news of the success of your experiments. I at once telephoned this information to Washington and New York, and succeeded in obtaining a fair statement in a Science Service circular2* of January 30, of which I have sent a copy to my wife, but I could not prevent various misstatements in newspapers. This is of course regrettable but without any importance for the judgment of the scientific world, which here even more than in Denmark is accustomed to such happenings. As you know from my cable and letters, I have been very uncertain as regards the advisability of publishing my own note, and above all I felt it of course impossible to determine the final text before I had received the copy of your and your aunt’s note, which from our talk I supposed was sent in immediately after the appearance of Hahn’s article. After receiving the copies of your notes I have made a few corrections in the last version which I sent you. I enclose a new copy of the whole note, in which for convenience the new alterations are marked in red ink, and I ask you, possibly with the help of Miss Schultz or Miss Hellmann, kindly to take care that all corrections of the original note be introduced clearly in the proof, so that no further proof will be required. Quite apart from the question how much or little new the note contains, I think that its appearance at the earliest possible opportunity will contribute essentially to clear up the confusion as regards the history of the discovery and its theoretical significance. I need not add how happy I have been to learn that your father came back to your mother in Vienna, and I hope that they will be in Sweden already, or at any rate in the nearest future. With kindest regards to the whole Institute from Rosenfeld and myself, Yours, [Niels Bohr] 28
Introduction. ref. 108a.
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15 and 18 March 1939 [Typewritten with handwritten addition]
FRISCH TO BOHR,
Copenhagen, March 15, 1939 Dear Professor Bohr, I am awfully sorry for the long time which has elapsed since I wrote you last, and my only excuse is that we have been working a lot in these days. Actually I had written most of a letter to you when your letter of Feb. 3. arrived and necessitated writing the letter anew; and ever since I had the intention to write but had to postpone it again and again, for some reason or other. I am very sorry, too, for the trouble I caused to you by my slowness in communicating my results on uranium fission to you. This was partly due to a lack of imagination on my side, as I did not imagine that the appearance of Hahn and Strassmann’s paper would raise such a run as it did. And then I was pretty tired after the experiment (I had been working long after midnight for several nights in track) and instead of sending you the manuscripts at once (the obvious thing to do) I kept them until I managed to write you a letter, which meant about six days delay. When I think it over now I can hardly find an excuse for my letting you without information as I did, but, you see, I did not think my experiment so terribly important (it seemed to me just additional evidence of a discovery already made) and the idea of cabling to you would have appeared unmodest to me. Of course now I know it was wrong not to cable. But I shall stop apologizing now and rather tell you how grateful I am for your energetic and successful efforts in telling the Americans about Prof. Meitner’s and my work. It was unfortunate that our papers in NATURE came out so late, probably o n account of an accidental increase in the number of letters and, perhaps, because we had not sufficiently stressed the importance of quick publication, when writing to the editor. (I intended to send you the whole correspondence with the editor and laid all the letters aside in a map [folder], but then I mislaid the map and have not been able to find it ever since!) But from the Phys. Rev. of Feb. 15. which arrived yesterday I see that our papers are quoted, and your note contains another very clear account of the history of the discovery, in which also Hahn and Strassmann are given the honour which they deserve, in contrast to some papers (especially some French ones) where Hahn and Strassmann are quoted either in a misleading way or not at all. On March 6, Prof. Meitner and I sent you a telegram saying that we had identified, by chemical separation combined with decay measurements, the “transuranium” elements among the active recoil nuclei from uranium fission under neutron bombardment, collected on a surface of water, one mm below the uranium layer bombarded. On the same day, we posted a note to the editor of
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NATURE2', and a copy of the note to you. This time the editor did his best to speed up publication and promised that the paper would appear in the issue of March 18. Had our first papers appeared so fast, much trouble would have been saved. Anyhow, we are glad that this paper comes out soon. Prof. Meitner has corresponded with Prof. Hahn about our results and he admits that our experiments are convincing. He is not convinced, however, of the correctness of the assignment made by Abelson (Phys. Rev. Feb. 15). We plan to make a few more experiments of a similar kind with thorium in order to see how far goes the similarity of the fission products of thorium and uranium. Prof. Meitner is going to stay for another few days and trying to give help and advice in the experiments which you suggested, of comparing the decay curves of the fission products of uranium, obtained by fast and slow neutrons respectively. March 18. Two days ago Dr. Simons and I sent you a manuscript by Dr. Simons (on the neutron-proton scattering cross-section) and two letters, one by each of us, which I hope have arrived in due time. It is now two months that I wrote you last, but there is not very much to report, apart from the experiments with Prof. Meitner. In the beginning I spent a week constructing an arrangement for recording the sizes of the ionisation burst due to nuclear fission and got some very doubtful indications of group structure; but then I abandoned this line again because I thought this could be done much better with the help of the high-tension plant. Then (following your inquiry) I made some experiments with a neutron source moving past the uranium chamber, in order t o detect possible delays; I found very quickly that no appreciable fraction of fissions could occur with a delay of more than a twentieth of a second, but when I tried to improve the sensitivity of the method I got all kind of spurious effects and finally gave it up when I was informed that my parents were on the way to Sweden. Now I shall stop and get this letter posted, and this time I shall not let you wait two months for the next one. With kindest regards and with many thanks for your letter, Yours, O.R. Frisch Viele herzlichste Griisse. Ich bin so froh iiber die schone Arbeitszeit hier. Deine Lise Meitner L. Meitner and O.R. Frisch, Products of the Fission of the Uranium Nucleus, Nature 143 (1939) 471-472. 29
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GEORGE GAMOW GAMOW TO BOHR,
6 January 1929
[Handwritten] Leiden, 6 Januar 1929 K m e Prof. Bohr, Mange Tak fra Deres venelige Brev. Am Grznsen var det virkelig “ganske god”: Telegramerne fra Kabenhavn og ogsaa fra den Haag, fordi Ehrenfest har gare en lille Skandal der. Jeg har ikke trzffet Jordan i Hamburg - tro jeg han er nu ikke der. Jeg har kommet i Leiden i Gaar Aften og blive nu i Ehrenfest’s Hus. I Morgen rejse jeg ti1 Rotterdam i engeske Passkontoret og maaske ti1 Amsterdam for Rembrand. Tirsdag Aften skall jeg rejse ti1 London. Ehrenfest er meget interesieret i “Tropfchenmodell”; han mener det maaske maa man betrage ogsaa “Kapilare Tropfchenschwingungen” for y-Termen Erklaring. Men jeg maa ikke tale over “6-y” ti1 jeg skal komme ti1 Cambridge; uden Experimentalmaterial er det noget farligt. Med mange Hilsener ti1 Fru Bohr og Barnen ogsaa ti1 Frk. Schultz Deres hengivne G. Gamow.
Translation Leiden, 6 January 1929 Dear Professor Bohr, Many thanks for your kind letter. At the border things were really “quite good”: There were telegrams from Copenhagen and also from The Hague because Ehrenfest made a little row there. I did not meet Jordan in Hamburg - I believe he is not there now. I arrived in Leiden last night, and am now staying in Ehrenfest’s house. Tomorrow I go to Rotterdam for the English visa office, and maybe to Amsterdam for Rembrandt. O n Tuesday evening I shall travel to London. Ehrenfest is very interested in the “liquid-drop model”; he thinks one should perhaps also consider “capillary vibrations” in the explanation of y-ray levels. But I should not talk about “p-y” until I get to Cambridge; without experimental material this is quite dangerous. With many regards to Mrs. Bohr and the children, and also to Miss Schultz, Yours sincerely, G. Gamow
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KEre Prof. Bohr! Jeg skriver for at Hilse Dem med Nyt Aar, jeg vilde sende telegram, men desvzere det er umuligt fra det Sted. Her er ingen Telegraph, ingen Electrizitat ingen Biographer men vi har mange Snee, Hirschen-Taxi og Polarlys. Vi er kommet her for et Uge for at m0de Nytaar paa noget usedvanlige Mode og for at staa lit paa Ski.* Det lille Lapar-Landsby liger paa Kuste af en store See Imandra i Hjerten af Kola-Peninsula og omkig vi har temelig store Bjergerne (ti1 2400 m). Landskaper liger meget Daambos men er naturligvis lit nordisker, Solen kommer slet ikke vi har kun fem eller seks Timer Dammerung. Herfra vi tzenker at besrage Murmansk og saa rejse Hjeme. I Begundelse at December jeg har vzeret at Charkow Institutet for at see hurtige Protoner som man har foet der. Der var ogsaa Ehrenfest, Landau og nogen ander Theoretiker saa vi har organiseret en lille Konferensen. Vi har diskuteret mange Sp~rgsmaalerog har klaret op en Ting som, tro jeg, maa vzere serlig interesant for Dem. Det see so ud at Unerhaltung der Energie er i en Wiederspuch med Gravitationsligninger for lehre Raum. Hvis Grav.lig. er rigtig for Gebiet B saa betynder det at sammtmasse i Gebiet A (hvor vi kenner ikke Loverne) maa v z r e konstant. Hvis i A vi har, skal vi sige, et RaE-Kern og andert sammtmasse med Hop i Omdanelseprocesse saa maa vi ikke skrive i B sedvanlige Grav.ligninger. Paa hvilken maade maa vi verandern det Ligninger er ikke klart men det maa g0res. Hvad tzenker De om det? Nu maa jeg sige farvel og at go paa Kerken for at hjelpe med preparation af Mad og Glyntvein. Mange Hilsener ogsaa ti1 Fru Bohr og Drengerne fra Deres G. Gamow.
@
P.S. Min Kone be sender ogsaa henes Hilsener. * Og naturligvis for
at spile Pokker.
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Translation Chibin Mountains, 31 December 1932 Dear Professor Bohr, I write to send you greetings for the New Year. I wanted to send a telegram, but unfortunately this is impossible from this place. There is no telegraph here, no electricity, no cinema, but we have lots of snow, reindeer taxis, and the aurora borealis. We have come here for a week to meet the New Year in a somewhat unusual manner, and to ski a little.* This little Lapp village lies on the shore of a large lake, Imandra, in the heart of the Kola peninsula, and is surrounded by fairly high mountains (up to 2400 m). The landscape greatly resembles Dimbos but is naturally a bit more northerly. The sun does not rise, we have only five or six hours of twilight. From here we plan to visit Murmansk and then to go home. In the beginning of December I was at the Institute in Kharkov to look at the fast protons which they got there. Ehrenfest, Landau, and some other theoreticians were also there, so we organised a small conference. We discussed many problems, and cleared up one matter which I believe will be especially interesting for you. It looks as if non-conservation of energy is in contradiction with the equations of gravitation for the vacuum. If the gravitational equations are correct for region B, this implies that the total mass in .B. region A (where we do not know the laws) must be constant. If in A we have, for example, a RaE nucleus, and alter its total mass with a jump in a transmutation process, we can no longer apply the usual gravitational equations in region B. In what way we have to change the equations is not clear, but it must be done. What do you think about this? Now I must say farewell and go to the kitchen to help with the preparation of dinner and mulled wine. Many greetings also to Mrs. Bohr and the boys from your G. Gamow
@
P.S. My wife also sends her greetings. * And of course to play poker
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BOHR TO GAMOW,
1949)
21 January 1933
[Carbon copy] [Kerbenhavn,] 21. Januar [19]33. K a r e Gamow, Allerferrst vil vi alle sende Dem og Deres Kone mange gode 0nsker for det ny Aar. Vi var meget rerrte over, at De saa venligt havde t a n k t paa Drengene, der var henrykte for de smukke Ksker, som kom ti1 Jul. Vi haaber alle snart at se Dem igen, og i s a r at det skal v z r e muligt for Dem at komme og deltage i vor aarlige Konferens, der vil finde Sted i de ferrste Uger af April, og hvortil vi forventer Deltagelse af de fleste af de gamle Medarbejdere. Instituttet har Midler ti1 at bestride Udgifterne ved Deres Rejse og Ophold her, og jeg vil meget gerne paa enhver Maade hjalpe ti1 at skaffe Dem Rejsetilladelse og beder Dem saa hurtigt som muligt og saa nerjagtigt som muligt fortalle mig, paa hvad Maade det bedst lader sig g ~ r e og , i s z r ti1 hvem jeg skal henvende mig med Hensyn ti1 den officielle Indbydelse fra Instituttet. Paa Konferensen vil vi paa vor szdvanlige informelle Maade naturligvis f ~ r s tog fremmest diskutere Kerneproblemerne, men ogsaa de almindelige Kvanteproblemer. Jeg var meget interesseret i, hvad De skrev om Diskussionerne i Charkow og fuldstandig enig i, at en Afvigelse fra Energiszetningen vil medferre lignende gennemgribende Konsekvenser for Einsteins Gravitationsteori, som en eventuel Afvigelse fra Elektricitetsmangdens Bevarelse vilde have for den Maxwellske Teori, hvor Elektricitetsbevarelsen j o er en umiddelbar Konsekvens af Feltligningerne. I denne Forbindelse vilde det maaske interessere Dem at herre, at det i Lerbet af Efteraaret er lykkedes Rosenfeld og mig i et Arbejde3', som mart vil udkomme i Zeitschrift fur Physik, at eftervise en fuldstandig Overensstemmelse mellem Grundlaget for den kvanteelektrodynamiske Formalisme og de elektromagnetiske Feltsterrrelsers Maalelighed. Jeg haaber, at det vil v a r e en T r ~ s for t Landau og Peierls, at de Dumheder, som de i denne Henseende har begaaet, ikke er v a r r e end de, som vi alle, indbefattet Heisenberg og Pauli, paa dette omstridte Gebet har gjort 0s skyldige i. Vi venter Besag af Peierls ti1 Konferensen, og det var j o morsomt, om ogsaa Landau kunde komme. Paa vor sidste Konferens, hvor vi maatte savne Dem, havde vi, som De vist har herrt, meget livlige Diskussioner i s a r med Dirac om mulige Endringer af Formalismen. Vi havde ogsaa, i s a r takket v z r e Delbruck, en meget morsom Afslutningsfest paa Instituttet. De har vist ogsaa h ~ r t at , vi siden den Tid er flyttet fra Instituttet og nu bor paa Carlsberg, hvor der er mere Plads og Lejlighed ti1 saadanne sp~gefuldeSammenkomster, og hvor
3"
See V O I . 7.
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min Kone og jeg haaber, at Konferensen vil finde en festlig Ramme trods de morke Tider. Med mange venlige Hilsener fra 0s alle, Deres [Niels Bohr]
Translation [Copenhagen,] 21 January 1933 Dear Gamow, First of all we all want to send you and your wife many good wishes for the New Year. We were very touched by your so kindly remembering the boys, who were delighted with the beautiful boxes which arrived for Christmas. We all hope to see you again soon, and particularly that you could be able to come and participate in our yearly conference, which will be held in the first weeks of April, and in which we expect most of the old collaborators to take part. The Institute has the means to cover the cost of your journey and of your stay here, and I shall with great pleasure help in every way with obtaining your travel permit. Let me know as soon and as precisely as possible in what way this could best be done, and particularly to whom I shall address myself with respect to the official invitation from the Institute. In the conference we shall of course, in our usual informal way, discuss the nuclear problems above all, but also the general quantum problems. I was very interested in what you wrote about the discussions in Kharkov, and I fully agree that a renunciation of energy conservation will bring with it equally sweeping consequences for Einstein's theory of gravitation, as a possible renunciation of conservation of charge would have for Maxwell's theory, where the charge conservation is after all an immediate consequence of the field equations. In this context you may be interested to hear that in the course of the autumn Rosenfeld and I have succeeded, in a paper soon to appear in Zeitschrift fur Physik3', in verifying the complete correspondence between the basis of the formalism of quantum electrodynamics and the measurability of the electromagnetic field quantities. I hope it will be a comfort for Landau and Peierls that the stupidities they have committed in this respect are no worse than those which we all, including Heisenberg and Pauli, have been guilty of in this controversial subject. We expect a visit from Peierls for the conference, and it would be nice if also Landau could come. At our last conference, at which we had to miss you, we had many lively discussions especially with Dirac about possible changes in the formalism, as you have probably heard. We also had, largely thanks to Delbruck, a very amusing closing party in the Institute. You will
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also have heard that we have since then moved out of the Institute and now live at Carlsberg, where there is more room and opportunity for such jocular gatherings, and where my wife and I hope that the conference will find a festive framework in spite of the dark times. With many kind regards from all of us, Yours, [Niels Bohr]
BOHR TO GAMOW,
26 February 1936
[Carbon copy] [Kabenhavn,] 26. Februar [19]36. K a e Gamow, Tak for det rare Brev, som jeg lige har faaet efter Hjemkomsten fra England, hvor jeg navnlig har haft stor Fornajelse af sammen med Rutherford at diskutere nogle almindelige Synspunkter vedrarende Kernebygningen, som jeg i de sidste Maaneder har udviklet, og som virkelig synes at v z r e nyttige for Tydningen af det experimentelle Materiale vedrarende Kernernes Keaktioner. Som De vil se af den indlagte Artikel, som mart fremkommer i “ N a t ~ r e ” ~ ’drejer , det sig om Forfalgelsen af en Tanke, som jeg allerede kom ind paa ved den sidste Konferens i Kabenhavn i Efteraaret 1934 straks efter Fermis farste Forsag over Indfangning af hurtige Neutroner, og som jeg har taget op igen efter de seneste vidunderlige Opdagelser vedrarende langsomme Neutroners Indfangning. Kalckar og jeg er i 0jeblikket beskzftiget med Udarbejdelsen af en udfarlig Fremstilling af Teoriens K o n ~ e k v e n s e r ~og~ ,saa mart vort Manuskript er fzrdigt, skal vi sende en Kopi ti1 Dem. Med Hensyn ti1 Deres venlige Spargsmaal om Planerne for min Amerikarejse ti1 Sommer haaber jeg meget, at jeg faar Lejlighed ti1 at komme ned ti1 Washington og besage Dem, men jeg er bange for, at jeg rnaa skynde mig hjem, saa snart at Harvard-Festlighederne er forbi, og at jeg derfor ikke saa godt kan komme ti1 en Konferens i Washington paa den Tid. Jeg skal imidlertid om nogle Uger skrive nzrmere om mine Rejseplaner. I Dag vil jeg blot sende mange Hilsener og gode 0nsker fra 0s alle ti1 Deres Kone og lille Igor og Dem selv samt ti1 fzlles Venner i Washington. Deres [Niels Bohr] 3’
32
Introduction, ref. 24. Introduction. ref. 46.
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Translation [Copenhagen,] 26 February 1936 Dear Gamow, Thank you for your good letter, which I just received on my return from England, where I especially had the great pleasure of discussing with Rutherford some general points of view concerning nuclear structure which I have developed in the last few months, and which really seem useful for the interpretation of the experimental material concerning nuclear reactions. As you will see from the enclosed article, which will soon appear in “ N a t ~ r e ” ~ this ’ , is a development of a thought which I already brought up at the last Copenhagen conference in the autumn of 1934, immediately after Fermi’s first experiment on the capture of fast neutrons, and which I have taken up again after the latest wonderful discoveries about the capture of slow neutrons. Kalckar and I are at this moment engaged in working out a detailed formulation of the consequences of the theory3’, and we shall send you a copy of the manuscript as soon as it is ready. As regards your kind question about the plans for my trip to America for the summer, I very much hope to have an opportunity to come down to Washington and visit you, but I am afraid that I may have to rush home immediately after the Harvard festivities are over, and that therefore I shall not be able to come to a conference in Washington at that time. However, I shall write more precisely about my travel plans in a few weeks’ time. Today I only want to send many greetings and good wishes from all of us to your wife and little Igor and yourself, and also to mutual friends in Washington. Yours, [Niels Bohr]
WERNER HEISENBERG HEISENBERG TO
BOHR,18 July [1932]
[Handwritten] 18.7. [ 19321 Lieber Bohr! Vielen Dank fur Deinen Brief, den ich sofort beantworte. Uber die y-Strahlstreuung hab ich mir folgendes uberlegt: Es gibt zwei Arten von Streuung: Erstens wird die Bewegung der Neutronen und Protonen im Kern durch das einfallende Licht gestort - dies gibt aber im allgemeinen eine vie1 zu schwache Streuung, hochstens an den Resonanzstellen konnte die merkbar werden. Zweitens
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wird das einzelne Neutron, d.h. die negative Ladung in ihm, streuen. Uber die Intensitat dieser Streuung weiss man von vornherein nichts, man wird hochstens erwarten durfen, dass sie schwacher ist, als fur freie Elektronen. Nun gibt es zwei Moglichkeiten: 1 .) Die Neutronenstreuung ist eine koharente Rayleighstreuung. Dann ist ihre Intensitat UKern = UNeutr . n: ; nl = Neutronenanzahl. 2.) Sie ist inkoharent. Dann wird ihre Intensitat UKern = UNeutr . n l . Mit den Experimenten ist die erste Annahme U K ~ ~ ,= , UNeutr . n? gut vertraglich (die Messungen sind ja sehr unsicher), wenn man vorher den Photoeffekt abzieht. Ich mochte also mit Frl. Meitner glauben, dass die Streuung koharent ist. Du hast also ganz recht mit Deiner Annahme, dass die Streuung doch sehr regelmassig von der Ordnungszahl abhangt, die Theorie lasst sich auch mit Jacobsens Messungen am besten vereinigen. Man bekommt bei X = 4,7 XE fur UNeutr den Wert 1,5 . cm2. Das ist etwa 4000 ma1 weniger, als ein freies Elektron gabe. Ein klassischer harmonischer Oszillator der Eigen-Frequenz hv = 43 mc2 wurde soviel streuen, wie das Neutron. - Ich war mir nicht ganz klar, ob Du a n Ostern nicht im Grund dies alles schon gewusst hast, was ich hier uber die Streuung schreibe. Ich hab die Diskussionen in Kopenhagen in meiner Arbeit so allgemein erwahnt und geschrieben, dass ich daraus gelernt hatte. Wenn Du aber das Wesentliche schon genau wusstest, mochte ich das gern ganz klar in meiner Arbeit schreiben. Vielleicht konntest Du mir ein paar Zeilen druber schreiben. - Sonst gibts wenig Neues, ich freue mich am meisten auf die Heimreise und die Zeit in Kopenhagen; es ist hier so heiss, dass man nicht recht arbeiten kann, und von Physik hort man auch zu wenig. - Ubrigens ist meine Mutter diesmal mit nach Amerika gefahren und lasst Dich sehr herzlich grussen. Die besten Wunsche fur einen schonen Sommer und viele, viele Grusse Dein Werner Heisenberg.
Translation 18 July [ 19321 Dear Bohr, Many thanks for your letter, to which I am replying immediately. About y-ray scattering I have the following thoughts: There are two kinds of scattering: Firstly the motion of the neutrons and protons in the nucleus is perturbed by the incident light - but this gives in general much too weak a scattering, this could be noticeable at most at the resonance positions. Secondly the individual neutron, i.e., the negative charge contained in it, will scatter. About the intensity of this scattering nothing is known in advance, one might expect at most that it is weaker than for free electrons. Now there are two possibilities: 1. The scattering
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by neutrons is coherent Rayleigh scattering. Then its intensity is unucl = uneutr . n: ; nl = number of neutrons. 2. It is incoherent. Then its intensity becomes unucl - uneutr. n l . The first assumption, unucl = uneutr. n? is well compatible with the experiments (the measurements are still very uncertain) if one first subtracts the photo-effect. I am inclined, therefore to believe with Miss Meitner that the scattering is coherent. You are therefore quite right in your assumption that the scattering does depend very regularly on the atomic number, the theory is also best compatible with Jacobsen’s measurements. One obtains at X = 4.7 X-ray units the value of 1.5 x cm2 for uneurr.This is about 4000 times less than for a free electron. A classical harmonic oscillator of characteristic frequency hv = 43 mcz would scatter as much as a neutron. It was not quite clear to me whether at Easter you did not in essence know already all that I write here about scattering. I have mentioned the Copenhagen discussions in my paper in general and written that I have learned from them. But if you already knew the essential part exactly, I would like to make this quite clear in my paper. Perhaps you can write me a few lines about this. Otherwise there is little news. I look forward particularly to the journey home and to the time in Copenhagen; here it is so hot that one cannot work very well and of physics one hears very little. Incidentally, my mother came with me to America this time and sends you her best regards. With best wishes for a good summer and many, many greetings, Yours, Werner Heisenberg
HEISENBERG, 1 August 1932 [Carbon copy]
BOHR TO
[K~benhavn,]1. August [19]32. Kzere Heisenberg! Mange Tak for Dit rare Brev. Jeg forstaar, at Dine Betragtninger om yStraalespredningen er et vzsentligt Bidrag ti1 Dit Arbejde om Atomkernebygningen, og det glaedede mig, at Du syntes, at Diskussionerne i Kerbenhavn havde hjulpet lidt ti1 Klarlzeggelsen af Sperrgsmaalet. Disse Diskussioner var j o kun af orienterende Karakter, og Hensigten med mine Bemaerkninger var mere at paapege de forskellige Muligheder end at tage bestemt Stilling ti1 Problemet. I ~ v r i g ter jeg ikke helt klar over Berettigelsen i at antage, at Spredningen pr. Neutron altid er den samme. Den Energi, hvormed Neutronerne og Protonerne bindes sammen i a-Partikler, er jo ikke ubetydelig i Forhold ti1 Bindingsenergien
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maalt ved Massedefekten af Elektronen i en fri Neutron. Jeg kunde derfor t z n k e mig, at det var ligesaa korrekt at s z t t e Spredningen proportional med Kvadratet af a-Partikler som med Kvadratet af Neutroner; men Maalingerne er vel knapt paalidelige nok ti1 at a f g ~ r edette. Jeg er meget spamdt paa at se den nzrmere kvantitative Udfmelse af Dine Betragtninger, og baade herom og om mange andre Ting glseder jeg mig ti1 at snakke nzrmere, naar Du kommer ti1 K~ benhavn. Jeg skal v z r e glad for at h ~ r fra e Dig, saa snart Du ved nzrmere om Dine Rejseplaner. Rutherfords kommer her fra 12. ti1 22. September. Det var jo morsomt, om Du kunde v z r e her noget af den Tid, men navnlig haaber jeg, at Du kan blive lidt lzngere, og at vi ligesom i Forfjor kan g ~ r en e lille Sejltur sammen med Bjerrum. Det vilde gl z de min Kone og mig, om Din Moder, som vi talte om i Leipzig, havde Lyst ti1 igen engang at komme paa et lille Bescag ti1 K ~ b e n h a v n .Medens Rutherfords er her, kan vi ikke saa godt have hende boende, men ellers vil det v z r e en stor Forn~je lsefor 0s begge. Med mange venlige Hilsener ti1 Din Moder og Dig selv fra min Kone og Din [Niels Bohr]
Translation [Copenhagen,] 1 August 1932 Dear Heisenberg, Many thanks for your good letter. I understand that your considerations on y-ray scattering are an essential contribution to your work on nuclear structure, and I am pleased that you think the discussions in Copenhagen have helped a little in clarifying the question. These discussions were only of an exploratory character, and the intention of my remarks was more to point out the various possibilities than to take a definite position on the problem. Moreover I am not quite clear about the justification for the assumption that the scattering per neutron is always the same. The energy with which neutrons and protons are bound together in a-particles is after all not insignificant in relation to the binding energy measured by the mass defect of the electron in a free neutron. I could therefore believe that it might be as correct to set the scattering proportional to the square of the number of a-particles, as to the square of the number of neutrons; but the measurements are not yet reliable enough to decide this. I am very curious to see the more detailed quantitative results of your considerations, and look forward t o talking with you about this and many other things more fully when you come to Copenhagen. I shall be glad to hear from you as soon as you know more about your travel plans. The Rutherfords are coming from 12 t o 22 September. It would be wonderful if you could be here some of that time,
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but I hope in particular that you can stay a little longer, and that we can go on a little sailing trip with Bjerrum, like the year before last. My wife and I would be very pleased if your mother would like to come again for a short visit to Copenhagen, as we discussed in Leipzig. While the Rutherfords are here we could not very well have her stay here, but otherwise it would be a great pleasure for us both. With many friendly greetings to your mother and yourself from my wife and Yours, [Niels Bohr]
2 August 1932 [Draft in Margrethe Bohr’s handwriting]
BOHR TO HEISENBERG,
Tisvilde, 2/8 1932. Kz r e Heisenberg, I det Brev jeg sendte ti1 Dig i Gaar er der en Linie, der kan misforstaas. Det var jo ikke Meningen, at en a-Partikel skulde sprede mere end 2 koharente Neutroner, men snarere adskilligt mindre. Maaske kan det forklare nogle af Uregelmzssighederne i Kurverne. Det har Du dog vist altsammen selv t a x k t nzrmere over. Med mange venlige Hilsener fra 0s alle herude ti1 Din Mor og alle fzlles Venner i Ann Arbor. Din N. Bohr
Translation Tisvilde, 2 August 1932 Dear Heisenberg, In the letter I sent you yesterday there is a line which might be misunderstood. It was of course not the intention that an a-particle should scatter more than 2 coherent neutrons, but rather considerably less. Maybe this explains some of the irregularities in the curves. You probably already gave all this some further consideration yourself. With many friendly greetings from all of us out here to your mother and all mutual friends in Ann Arbor. Yours, N . Bohr
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HEISENBERG, 20 April 1934 3 3 [Typewritten]
BOHR TO
UNIVERSITETETS INSTITUT
FOR
BLEGDAMSVEJ DEN
15,
KQBENHAVN 0 .
20. April 1934.
TEORETISK FYSIK
K z r e Heisenberg, Mange Tak for Dit rare Brev. Vi er j o alle kede af, at Du ikke kunde komme nu ti1 Kerbenhavn, men vi haaber i det mindste at se Dig her igen ti1 Efteraaret. Iervrigt rejser jeg selv om en Ugestid ti1 Rusland for at holde nogle Foredrag og l z r e Forholdene at kende. Du faar sikkert en morsom Tid i Cambridge, og jeg deler saa fuldtud Din Begejstring over de Linier, hvorefter Kernefysikken udvikler sig. Jeg er ogsaa ganske enig med Dig med Hensyn ti1 den formelle Analogi mellem Atomfysikken og Kernefysikken, som Du skriver om, og vi er j o sikkert paa den anden Side ogsaa enige om den Forskel, der er betinget af den forskellige Rolle, som Konstanterne e2/hc og m / M spiller paa de to Omraader. Med Henblik paa den fuldkomne Symmetri med Hensyn ti1 Ladningsfortegnet, som kendetegner Elektronteoriens nuvzrende Standpunkt, har vi i ~ v r i g tspekuleret en Del over, hvorvidt denne Symmetri ogsaa viser sig indenfor Kerneproblemerne, og jeg sender indlagt to Afhandlinger af gar no^^^ og Williams35, som netop er sendt ti1 Physical Review, og hvori de diskuterer Muligheden af Eksistensen af negative Protoner saavel indenfor Kernerne som i de kosmiske Straaler. Navnlig i ferrste Henseende er Sp~rgsmaaletj o endnu meget hypotetisk, og sommetider er jeg endda tilb~jeligti1 at tznke, at vi med Hensyn ti1 Kernerne strengt taget kun kan tale om en samlet Ladning af hele Systemet, paa lignende Maade som vi for det omgivende Elektronsystem kun eentydigt kan tale om dets samlede Vinkelmoment. Dette skal dog ikke give Udtryk for nogen Skepsis overfor Vzrdien af Dit saa frugtbare Angreb paa Kerneproblemerne, som vi her hver Dag glieder 0s over i Forbindelse med Diskussionen af de nye radioaktive Fienomener, som er opdaget i Paris og Rom, og som vi ogsaa her i Laboratoriet under Francks Ledelse har taget o p med stor Energi i den sidste Tid. Med mange hjertelige Hilsener fra 0s alle ti1 Dig selv og alle fzlles Venner i Cambridge, Din Niels Bohr 3 3 We are grateful to Dr. Helmut Rechenberg of the Heisenberg Archive in Munich for providing us with copies of these letters. 34 Introduction, ref. 18. 3 5 Introduction. ref. 19.
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Translation Copenhagen, 20 April 1934 Dear Heisenberg, Thank you for your good letter. We are of course all sorry that you could not come to Copenhagen at this time, but we hope at least to see you here again in the autumn. Incidentally, I myself will leave for Russia in a week’s time to give some lectures and learn about the situation there. You will no doubt have a pleasant time in Cambridge, and I share so fully your enthusiasm about the way in which nuclear physics is developing. I also agree entirely with you about the formal analogy between atomic and nuclear physics which you mention, and on the other hand we are surely also agreed about the difference arising from the different roles played in these two areas by the constants e2/hc and m / M . As regards the complete symmetry with respect to the sign of the charge, which characterises the present point of view of electron theory, we have also speculated somewhat whether this symmetry also appears in nuclear problems, and I enclose two papers by gar no^^^ and Williams35 which have just been sent to the Physical Review, and in which they discuss the possibility of negative protons existing both inside nuclei and in the cosmic radiation. Particularly in respect of the former the question does seem very hypothetical, and sometimes I am inclined to think that in the nucleus we may, strictly speaking, talk only of the total charge of the whole system, just as in the surrounding electron system we can talk unambiguously only about the total angular momentum. This should not imply any scepticism concerning the value of your so productive attack on the nuclear problems, in which we delight every day in connection with the discussion of the new radioactive phenomena discovered in Paris and Rome, which lately we have also taken up with great energy here in the laboratory under the leadership of Franck. With many sincere greetings from all of us to yourself and to all mutual friends in Cambridge, Yours, Niels Bohr BOHR TO HEISENBERG,
8 February 1936
[Carbon copy] [Kabenhavn,] 8. Februar [19]36. K a r e Heisenberg, Mange Tak for Dit rare Brev. For baade Hans36og mig vilde det viere en stor Bohr’s son.
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G l a d e og Styrkelse, om vi ogsaa kan v a r e med paa Skituren i Aar. Jeg maa imidlertid vente et Par Dage med at give bestemt Svar paa Din venlige Indbydelse, da Hans ferrst maa sperrge paa Skolen om Tilladelse, og jeg ikke selv i 0jeblikket helt overser mine Forpligtelser. Min Kone og jeg skal nemlig lige om et 0jeblik tage Toget ti1 England, hvor jeg skal v a r e i 14 Dage og holde et Par Forelzsninger i London og Cambridge. Jeg har lige ti1 det sidste slidt med at gerre den lille Afhandling om Kernereakti~nerne~’ fardig, som jeg forlangst havde lovet at sende Dig, men Sagen har vzret i stadig Udvikling for mig, og det er efterhaanden blevet ti1 et mere omfattende Synspunkt, som jeg tror vil blive ti1 Nytte for Forstaaelsen af mange forskellige af Kernernes Egenskaber. Enkelthederne vedrerrende Kernereaktionerne og de Lettelser, som den nye Opfattelse indeholder overfor den tidligere, vil blive diskuteret i en mere udferrlig Afhandling, som jeg samtidig har arbejdet paa sammen med K a l ~ k a r Den ~ ~ . lille Note, hvoraf jeg sender Manuskriptet, og som jeg tznker vil komme frem i Nature, er blot en omtrentlig Gengivelse af et Foredrag, hvor jeg har gjort Rede for de Angrebspunkter paa Problemet, som Neutronindfangningen frembyder. Jeg skal v z r e meget glad, om Du vil skrive et Par Ord, om hvad Du tznker om det hele, ti1 Cambridge, hvor jeg skal bo hos Rutherford, Newnham Cottage, Queens Road. Du skal ikke sarlig bryde Dig om mine Bemzrkninger om Kernernes Byggestene, der i denne Forbindelse er af underordnet Betydning. Det drejer sig heller ikke her om nogen Mange1 paa Forstaaelse af Din og Fermis store Indsats, men blot om en vis Skepsis verdrerrende Enkeltheder ikke mindst ved Anvendelsen af Pauli-Princippet, som de nye Synspunkter gradvis har fart med sig. Herom skal jeg snart skrive narmere, ligesom jeg ogsaa ferrst paa Rejsen faar Tid ti1 i Enkeltheder at forfine de Smaabemzrkninger i Afhandlingen, der tager Sigte derpaa. I Dag ernskede jeg blot foruden at sende Dig Manuskriptet i sterrste Hast at takke Dig for Dit venlige Brev, som jeg som sagt skal narmere besvare, naar jeg i England har herrt fra Hans og lidt bedre kan overse Mulighederne for de narmeste Uger. Med mange venlige Hilsener ti1 Dig selv og alle Venner i Leipzig, Din [Niels Bohr]
”
Introduction, ref. 24. Introduction, ref. 46.
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1949)
Translation [Copenhagen,] 8 February 1936 Dear Heisenberg, Many thanks for your good letter. Both for Hans36and for me it would be a great pleasure and very refreshing if we could also join the skiing tour this year. However I must wait a few days before giving a definite answer to your kind invitation, as Hans must first ask the school for permission, and at this moment I cannot myself yet see my commitments clearly. This is because my wife and I are about to take the train to England, where I shall stay for a fortnight and give a few lectures in London and Cambridge. For this reason I worked hard to the last minute finishing the small article on nuclear reactions3’ which I promised you long ago, but the matter was continuously developing for me, and it gradually became a more comprehensive point of view, which I believe to be of use for the understanding of many different nuclear properties. The details concerning nuclear reactions and the help which the new understanding provides compared with the earlier one, will be discussed in a more complete paper on which I have been working at the same time with Kalckar3’. The small note of which I enclose a manuscript, and which I think will appear in Nature, is only an approximate reproduction of a lecture in which I have talked about the opening which the neutron capture has provided for an attack on this problem. I shall be very glad if you can write a few words on what you think of all this to me in Cambridge, where I shall stay with Rutherford, Newnham Cottage, Queens Road. You should not worry too much about my remarks on the constituents of the nucleus, which in this context are of minor importance. This does not imply any lack of understanding of your and Fermi’s great contributions, but only a certain scepticism concerning the details, not least in the application of the Pauli principle, which the new points of view have introduced. About this I shall write further, just as soon as I get time on my trip to refine in detail the minor remarks in the article which relate to this. Today I wanted only to send you the manuscript in a great hurry, and to thank you for your kind letter which, as I said, I shall reply to when I have heard in England from Hans, and when I can also judge a little more clearly the possibilities for the next few weeks. With many kind regards to you and all friends in Leipzig, Yours, [Niels Bohr]
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E (1929-
BOHR TO HEISENBERG,
1949)
2 May 1936 3 3
[Typewritten] UNIVERSITETETS INSTITUT FOR
BLEGDAMSVEJ
DEN
15, K0BENHAVN 0.
2 . Maj 1936.
TEORETISK FYSIK
K z r e Heisenberg, Tidspunktet for vor lille Konferens er nu endelig fastsat ti1 Ugen fra 14.-20. Juni, og vi haaber, at ikke alene Du, men ogsaa Weizsacker og Euler vil kunne komme. Hele Familien glzder sig ti1 at have Dig boende hos 0s igen, og Weizsacker og Euler vil under deres Ophold i Kerbenhavn v z r e Instituttets Gzster, der vil serrge for deres Anbringelse sammen med forskellige andre Gzster ti1 Konferensen. Jeg haaber, at vi skal have mange lzrerige Diskussioner, og navnlig lznges jeg meget efter at snakke rigtigt ud med Dig selv o m Grundlaget for Teorien for Kernebygningen, som jeg har t z n k t meget over i den sidste Tid i Forbindelse med Arbejdet med Kalckar, som jeg haaber vil foreligge fzrdigt ti1 Konferensen. Efter megen Vaklen frem og tilbage tror jeg, at jeg nu bedre forstaar, hvorledes de Resultater, som er vundne ved Dit Arbejde over Kernebygningen, kan forenes med de Synspunkter over Kernereaktionerne, som jeg udviklede i min NatureArtikel. Paa den ene Side forstaar jeg fuldstzndigt, hvor vzsentlig Din Anvendelse af Pauli-Princippet paa Protoner og Neutroner er for Ligevzgten mellem den kinetiske og potentielle Energi i Kernerne, der i ferrste Linie er bestemmende for Massedefekten, og hvorledes den paa utvungen Maade ferrer ti1 en Antagelse om de stzrke Ombytningskrafter mellem Neutroner og Protoner. Paa den anden Side tror jeg ikke, at man ved H j z l p af en Fremgangsmaade, hvor Neutroner og Protoner i ferrste Tilnzrmelse antages som fri, kan naa ti1 en Redegerrelse for saadanne Egenskaber af Kernerne, som de for Reaktionerne bestemmende mulige stationare Tilstande og Overgangssandsynligheder. Her tror jeg, at den eneste Fremgangsmaade er at gaa ud fra en vzdskelignende Kernesubstans og uden direkte Brug af Pauli-Princippet for Kernedelene sammenligne de anslaaede Tilstande med en Draabes Svingninger under Indflydelse af Elasticitet eller Overfladespznding. For at tage et extremt Tilfzlde, lad 0s t z n k e paa en Draabe af flydende Helium indeholdende 100 Atomer. Ud fra Draabens Sterrrelse kan man j o beregne den kinetiske Energi svarende ti1 en Fermifordeling af 200 Elektroner og finder en Middelenergi af ca. 20 Volt for hver af disse. Ud fra Lersrivelsesarbejdet for Elektroner fra Draaben kan man dernzst bestemme den potentielle Energi pr. Elektron og vil da finde Vzrdier svarende ti1 Coulombkrzfterne i Helium-
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E
(1929- 1949)
atomerne, ligesom den omtalte kinetiske Energi omtrentlig vil ware ti1 Nulpunktsbevagelsen af Elektronerne i Heliumatomernes Normaltilstand. Draabens mekaniske Egenskaber vil derimod v a r e bestemte ved de Van der Waalske Krafter imellem Atomerne, og de mulige Svingningstilstande vil hverken have noget at g0re med Anslagsenergierne for de enkelte Atomer eller med de Energivardier, man vil beregne ud fra den betragtede Fermifordeling af Elektronerne indenfor Draabens Omraade. Denne Sammenligning er naturligvis alt for grov, fordi vi i Kernerne langtfra har en saa strengt lokaliseret Underdeling som Atomerne i Heliumdraaben. Men jeg har alligevel Mistanke om, at der i Kernerne findes en virtue1 Underdeling, der gaar vasentlig udover den, der svarer ti1 Ombytningskrafterne mellem Neutroner og Protoner. Det forekommer mig nemlig n a p p e muligt at forklare den ejendommelige Vekslen mellem Spinog Stabilitetsegenskaberne hos “lige” og “ulige” Kerner uden at antage “Ombytningskrafter” imellem Partikler af samme Ladning men forskelligt Spin, hvis Virkning vel ikke er n a r saa stor som Ladningsombytningskrafternes, men som alligevel har en forholdsvis langt s t ~ r r eIndflydelse end Spinkrafterne mellem Atomelektronerne. I Afhandlingen med Kalckar tanker vi vasentligt at holde 0s ti1 en halvempirisk Beskrivelse af Kernernes Egenskaber, medens jeg agter at komme narmere ind paa de principielle Sp~rgsmaali den Beretning, som jeg forbereder ti1 mit Foredrag i Harvard i Sommer, hvis Titel jeg nylig har andret efter de narmere Oplysninger om Organisationen af Symposiet i Fagsektioner. Men, som sagt, haaber jeg fOr den Tid at faa Lejlighed ti1 narmere at diskutere disse Spcargsmaal indgaaende med Dig, ligesom jeg langes efter mart igen at kunne tale rigtigt med Dig om en he1 Mangde andre Problemer. Den mere filosofiske Kongres om Kausalitetsproblemerne, som jeg skrev om sidst, vil finde Sted umiddelbart efter vor lille Konferens, nemlig i Dagene fra 21. ti1 28. Juni, og vi haaber jo alle, at Du ogsaa vil kunne deltage deri. Iplvrigt har Du sikkert allerede hmt, at Solvaymerdet ti1 Efteraaret paa Grund af Langevins Sygdom desvzerre har maattet udsattes ti1 naste Aar. Med mange venlige Hilsener fra 0s alle, Din Niels Bohr
Translation Copenhagen, 2 May 1936 Dear Heisenberg, The date for our little conference has now finally been fixed for the week of 14 to 20 June, and we hope that not only you, but also Weizsacker and Euler
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will be able to come. The whole family looks forward to having you stay with us again, and Weizsacker and Euler will during their stay in Copenhagen be the guests of the Institute, which will arrange their accommodation together with various other visitors to the conference. I hope we shall have many instructive discussions, and in particular I am very anxious to talk properly with you about the basis for the theory of nuclear structure, to which I have lately given much thought in connection with the paper with Kalckar, which I hope will be ready for the conference. After much vacillation I now believe that I understand better how the results obtained in your paper on nuclear structure can be reconciled with the point of view about nuclear reactions which I developed in my Nature article. On the one hand I understand completely how essential your use of the Pauli principle for neutrons and protons is for the equilibrium between kinetic and potential energy in the nuclei, which in the first place determines the mass defect, and how this leads naturally to an assumption about the strong exchange forces between neutrons and protons. On the other hand I do not believe that one can get to an explanation for such nuclear properties as the possible stationary states and transition probabilities which dominate the nuclear reactions, from a procedure which treats the neutrons and protons in first approximation as free. Here, I believe, the only procedure is to start from a liquid-like nuclear substance, without a direct use of the Pauli principle for the nuclear constituents, comparing the excited states with the vibrations of a drop under the influence of elasticity or surface tension. To take an extreme case, let us consider a drop of liquid helium containing 100 atoms. From the size of the drop one can then calculate the kinetic energy corresponding to a Fermi distribution of 200 electrons, and find an average energy of about 20 volts per electron. From the energy of separation of electrons from the drop one can then determine the potential energy per electron, and will find values corresponding to the Coulomb force in the helium atom, and similarly the kinetic energy mentioned will roughly correspond to the zero-point motion of an electron in the ground state of the helium atom. Nevertheless the mechanical properties of the drop will be determined by the van der Waals force between the atoms, and the possible vibrational states will have to do neither with the excitation energies of a single atom, nor with the energy values calculated from the consideration of the Fermi distribution of electrons in the volume of the drop. This analogy is of course much too crude, since in the nuclei we are very far from having as close a localised substructure as in the atoms in the helium drop. Yet I have a suspicion that we have in the nucleus a virtual substructure which goes far beyond that due to the exchange forces between neutrons and protons. This is because it seems to me hardly possible to explain the peculiar alternation between the spin and stability properties of “even” and “odd” nuclei without
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assuming “exchange forces” between particles of the same charge but different spin, whose effect will be not nearly as strong as the charge exchange forces, but which nevertheless have a much greater influence than the spin-dependent forces between atomic electrons. In the paper with Kalckar we intend essentially to keep to a semi-empirical description of nuclear properties, while I plan to examine more closely the fundamental questions in the account which I am preparing for my Harvard lecture in the summer, whose title I have changed recently after getting more detailed information about the organisation of the symposium in specialist sections. But, as I said, I hope before then to have the opportunity to discuss these questions thoroughly with you, just as I a m anxious soon to be able to talk properly with you about a whole lot of other problems. The more philosophical congress about the causality problems about which I wrote last time, will take place immediately after our little conference, namely in the week of 21 to 28 June, and we certainly all hope that you will be able to take part in it too. Incidentally you have surely heard already that the Solvay meeting in the autumn unfortunately had to be postponed until next year, because of Langevin’s illness. With many kind regards from all of us, Yours, Niels Bohr HEISENBERG TO BOHR,
9 February 1938
[Handwritten]
9.2.38. Lieber Bohr! Hab vielen Dank fur Deinen Brief, uber Eure Gluckwunsche haben wir uns sehr gefreut. Es geht Elisabeth und den Kindern sehr gut. - Uber die Nachricht vom Tode des jungen Kalckar war ich sehr traurig; ich fand ihn immer einen der anziehendsten und feinsten Menschen des Kopenhagener Instituts, und er war doch gerade in der letzten Zeit in wirklich gute wissenschaftliche Arbeit gekommen. Er wird Dir sicher sehr fehlen und fur Kalckars arme Mutter wird es besonders schwer sein. Hab vielen Dank auch fur Dein Manuskript. Man kann ja garnicht zweifeln, dass Deine Erklarung der starken Photoeffekte die richtige ist; wenn ich recht verstehe, vergleichst Du also diese selektiven Photoeffekte etwa mit den ultraroten “Reststrahlen” eines Kristalls, die j a auch zu einer Schwingung fuhren, die nichts mit gewohnlicher Temperaturstrahlung zu tun hat. Etwas unklar war mir noch, warum die Grosse r c l O I 9 sec-’ etwa hundertmal kleiner ist als gewohnliche Kernfrequenzen. Dies bedeutet eine recht erhebliche Stabilitat der betref-
-
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E
(1929-1949)
fenden Schwingung, wahrend bei den Reststrahlen r c fast von der Grossenordnung v ist. Fur wie sicher kann man das Verhaltnis Fc/v - 1/100 halten? Die Rechnungen uber die Kernzertriimmerungen durch schnelle Protonen hab ich fertiggemacht, Du bekommst in diesen Tagen einen Sonderabdruck. Inzwischen habe ich von Blau u. Wambacher das Material iiber etwa 30 Sterne bekommen. Dabei hat sich einiges Interessantes herausgestellt: erstens scheinen die meisten Zertriimmerungen an leichten Kernen stattzufinden, da sehr haufig auch Protonen kleiner Energie vertreten sind. Nur einige wenige Aufnahmen zeigen Sterne, bei denen alle Protonen mehr als ca 5 Mill Volt Energie besitzen. Auch bei diesen ist die Energie der Protonen so klein, dass man annehmen muss - sofern es sich um einen schweren Kern handelt - dass der Kern durch Erhitzung nach Neutronenverdampfung stark aufgeblaht war, wodurch der Gamowberg verkleinert wurde. In den meisten anderen Fallen aber handelt es sich offenbar um leichtere Kerne (C, N, S). Dazu passt erstens die Tatsache, dass ziemlich viele Protonen emittiert werden, ferner auch der Umstand, der bei genauerer Untersuchung der Energieverteilung herauskommt, dass etwa % aller Protonen durch direkten Stoss den Kern verlassen, nur % durch nachtragliche Verdampfung. Die Energieverteilung der ersteren stimmt sehr gut mit der Theoretischen, wenn man die Reichweite der Kernkrafte als 0,85 e2/mc2ansetzt. Die Versuche von Blau u. Wambacher scheinen mir die bisher beste Bestimmung dieser Reichweite zu liefern. Sobald ich das empirische Material genau verarbeitet habe, werd ich Dir einen Abzug schicken. - - Was haltst Du eigentlich von der jetzt so modernen Yukawa-Theorie? -
*..
Nun viele herzliche Grusse von Elaus zu Haus Dein Werner Heisenberg.
Translation 9 February 1938 Dear Bohr, Many thanks for your letter, we were very pleased with your good wishes. Elisabeth and the children are very well. The news of the death of the young Kalckar has made me very sad; I always found him one of the most attractive and finest human beings of the Copenhagen Institute, and lately he really started to do excellent scientific work. You will surely miss him and for Kalckar’s poor mother it will be very hard to bear. Many thanks to you also for your manuscript. One cannot doubt that your explanation of the strong photo-effect is the right one; if I understand correctly you
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E ( 1 9 2 9 -
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liken these selective photo-effects perhaps to something like the infrared “Reststrahlen” of a crystal, which also lead to a vibration which has nothing to do with ordinary thermal radiation. I am still not very clear why the quantity r c 1019 sec-’ is a hundred times smaller than ordinary nuclear frequencies. This means a considerable stability of that mode of vibration, whereas in the Reststrahlen I‘c is almost of the order of u . How reliable is the estimate r C / u 1/100? The calculations of the disintegration of nuclei by fast protons have been finished, one of these days you will get a reprint. Meanwhile I have received from Blau and Wambacher data about some 30 stars. From this a few interesting facts have emerged: in the first place most disintegrations seem to involve fight nuclei, since there appear frequently protons of low energy. Only a few photographs show stars in which all protons have energies above about 5 MeV. Even in these the proton energy is so low that one has t o assume - if this relates to a heavy nucleus - that the nucleus was strongly blown up by heating after neutron evaporation, and the Gamow barrier thus reduced. But in most other cases one is evidently concerned with lighter nuclei (C, N, S). In the first place this fits with the fact that rather many protons are emitted and also with the fact that a detailed investigation of the energy distribution shows that about % of the protons are ejected from the nucleus by a direct collision, and only % by later evaporation. The energy distribution of the former agrees well with the theoretical one if one takes the range of the nuclear forces as 0.85 e2/mc2.The experiments of Blau and Wambacher seem to me to yield so far the best determination of this range. As soon as I have gone through the empirical material I shall send you a copy. What do you really think of the now so fashionable Yukawa theory?
-
-
With kindest regards from house to house, Yours, Werner Heisenberg INSTITUTE FOR THEORETICAL PHYSICS INSTITUTE, 30 January 1939 (1) [Draft telegram]
BOHR TO
See p. [57].
INSTITUTE, 30 January 1939 (2) [Draft telegram]
BOHR TO
See p. [ 5 7 ] .
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E
BOHR TO INSTITUTE,
(1929-1949)
31 January 1939
[Telegram] See p. [58]. BOHR TO INSTITUTE,
3 February 1939
[Telegram] See p. [59]. BOHR TO INSTITUTE,
9 February 1939
[Telegram] PRINCETON,
9 [February 19391
SCHULTZ INSTITUT TEORETISK FYSIK BLEGDAMSVEJ K H EXPLAINED RESONANCE URANIUM NOTE APPEARS PHYSICAL REVIEW FEBRUARY FIFTEENTH STOP DESIRE EARLIEST APPEARANCE MY NATURE NOTE W I T H ALTERATIONS SENT FRISCH LETTER FEBRUARY THIRD BOHR
INSTITUTE TO BOHR,
15 February 1939
[Telegram] COPENHAGEN,
15 [February 19391
BOHR VANSTITUTE PRINCETON N E W JERSEY JACOBSEN ACTIVATED URANIUM W I T H
4.5
MEV DEUTERONS AND COLLECTED
RECOILMATERIAL SHOWING SAME DECAY STOP HIGHVOLTAGE DEPARTMENT LITHIUM DEUTERON NEUTRONS SPLIT URANIUM THORIUM BUT NONE FROM BISMUTH TO PLATINUM INCLUSIVELY STOP LITHIUM PROTON GAMMAS POSSIBLY SPLIT URANIUM EXPERIMENTS CONTINUED STOP YOUR DISINTEGRATION NOTE WILL APPEAR NATURE FEBRUARY TWENTYFIFTH STAFF
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E
BOHR TO INSTITUTE,
(1929-1949)
16 February 1939
[Telegram] PRINCETON,
16 [February 19391
INSTITUTE TEORETISK FYSIK BLEGDAMSVEJ K H TELEGRAM MOST INTERESTING STOP EXAMINE VELOCITY VARIATION RATIO FAST NEUTRON EFFECTS URANIUM THORIUM STOP SEARCH MINUTELY STATISTICAL DIFFERENCES RELATIVE ABUNDANCE URANIUM PRODUCTS FOR THERMAL AND FAST NEUTRONS STOP DISCUSS HEVESY POSSIBILITY EXPERIMENTS MESOTHORIUM AND ACTINIUMLEAD STOP FREQUENT
TELEGRAPHIC
INFORMATION DESIRED MAIL ALSO
MANUSCRIPTS STOP PUBLISH RAPIDLY BECAUSE INTENSE COMPETITION GENERALSTAFF BOHR TO INSTITUTE,
19 February 1939
[Telegram] PRINCETON,
19 [February 19391
INSTITUTE FOR TEORETISK FYSIK BLEGDAMSVEJ K H HOW LARGE IS CROSSECTION
DEUTERON URANIUM EFFECT STOP DEUTERON
THORIUM EFFECT EXPECTED NULL SHOULD BE TESTED STOP COMPLETE ACCOUNT RESEARCH RESULTS URGENTLY DESIRED STOP CABLE ALSO DETAILED EXPLANATION REGRETTABLE DELAY PUBLICATION FRISCH NATURELETTER BOHR
INSTITUTE TO BOHR,
13 March 1939
[Telegram] COPENHAGEN,
13 [March 19391
BOHR VANSTITUTE PRINCETON NJ THORIUM BOMBARDED WITH
6 MEV
DEUTERONS GIVES NO EFFECT STOP SHALL WE
PUBLISH STOP FRISCH MEITNER NOTE APPEARS NATURE EIGHTEENTH STAFF
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E (1929-
BOHR TO INSTITUTE,
1949)
15 March 1939
[Telegram] PRINCETON,
15 [March 19391
INSTITUT TEORETISK FYSIK BLEGDAMSVEJ COPENHAGEN PUBLISH ALL DEUTERON FISSION EXPERIMENTS NATURE STOP SEND COPY EXPRESS PRINCETON STOP HAVE ASKED EDITOR QUICK PUBLICATION COPENHAGEN NOTES BOHR
JACOB CHRISTIAN JACOBSEN3’ BOHR TO JACOBSEN,
13 February 1939
[Carbon copy] [Princeton,] Februar 13, 1939 K z r e Dr. Jacobsen, Tak for Deres venlige og interessante Brev af den j t eFeb.40. Det var j o i s z r rart at herre at De stadig har saa gode Erfaringer med den nye Konstruktion af Cyklotronen. Deres Overslagsregning over Udbyttet forekommer mig meget rigtig og jeg ved ikke hvordan Lawrence kan faa saa store Strermme, men jeg husker at han i den Henseende altid fremhavede Betydningen af den sterrst mulige Volumen af Duanterne. Det er jo imidlertid i s a r spandende om De kan faa Partikkelenergien saa herjt op sorn muligt; alligevel er det j o dog i den farste Tid af allersterrste Betydning at gennemfsre alle tznkelige Forserg med de nye Kernespaltninger, men det taler De j o sikkert narmere om med Dr. Frisch. Det er jo kedeligt, at der er saa lille Tilgang af Fysikstuderende, der kunde hjalpe ti1 med Arbejdet, men vi maa jo, som jeg ogsaa har skrevet ti1 Dr. Rasmussen, se at gnre alt hvad vi kan for at skaffe den fornerdne Arbejdskraft ti1 Undersergelserne paa Instituttet. Med mange venlige Hilsner ti1 Deres hele Familie og alle paa Instituttet Deres hengivne [Niels Bohr] For a biographical note o n Jacob Christian Jacobsen, see Vol. 5 , p . [ 9 5 ] . Probably the letter from Jacobsen to Bohr of 26 January 1939 (received 5 February ?). Not yet microfilmed. 39
40
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Translation [Princeton,] 13 February 1939 Dear Dr. Jacobsen, Thank you for your kind and interesting letter of 5 February4'. It was particularly good to hear that you still have such good experience with the new construction of the cyclotron. Your estimate of the yield seems to me entirely correct, and I do not know how Lawrence can get such big currents, but I remember that he always emphasised in this connection the importance of the greatest possible volume of the dees. However, it will indeed be very interesting to see if you can get the particle energy as high as possible; still it is of the greatest importance to carry out at first all possible experiments with the new nuclear splitting, but this you will no doubt discuss further with Dr. Frisch. It is a pity that there is so small an influx of physics students who could help with the work, but we must, as I have also written to Dr. Rasmussen, see to it that everything possible is done to provide the necessary manpower for the research in the Institute. With many kind regards to all your family and to everybody in the Institute. Yours sincerely, [Niels Bohr]
FREDERIC AND IRENE JOLIOT-CURIE BOHR TO M. AND Mme JOLIOT-CURIE,
30 April 1932
[Carbon copy] [K~ benhavn,April ] 30th [19]32. Dear Monsieur and Madame Joliot, I thank you very much for your kind letter and your papers as well as for the beautiful photographs. Of course, we take here very great interest in the recent important discoveries in which you have taken so prominent a part. We have therefore studied your photographs very carefully, and I should be thankful to hear your opinion about some points concerning them. From your letter I understand that you think that the electron tracks cannot all be due to Compton recoil, as they are initially too evenly distributed in all directions. I wonder, however, whether one can be sure that the tracks on the photographs constitute the initial part of the path of the electron. One would rather expect that the electrons originate within the substance of the walls of the Wilson chamber or even outside these walls, if they are sufficiently thin. In that case, however, the elec-
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trons may suffer a high degree of scattering within the substance of the walls or even a bending of their path by the magnetic field in the space outside the chamber. In this connection I should also like to ask you whether the proton tracks excited by the neutrons may not for a considerable part originate in the water sheet on the piston and the glass instead of in the water vapour within the chamber. Now this is of course a minor point which is in no way essential for the qualitative interpretation of the effect, but I am especially interested to know what effects do actually take place in the gas itself on account of a theoretical discussion (of which I think that Mr. Solomon has told you) of the effects which may arise from collisions between neutrons and the extranuclear electrons of the atoms to which they penetrate. In contrast to what one might expect on classical mechanics it appears namely from a simple argument of wave mechanics that any such effects would be extremely rare compared with the collision effects with protons; the probabilities being proportional to the square of the mass of the electron and the proton respectively. Of course any electron track due to an elastic collision would be very short and only detectable under very pure conditions, but I should be much obliged if you would kindly tell me whether your experiments have given any definite information regarding this point. With kindest regards, also to Madame Curie, Yours sincerely, [Niels Bohr]
OSKAR KLEIN KLEIN TO BOHR,
2 [December] 1935 4 1
[Handwritten] Morby, 2.[1]2.1935. Kaere Bohr! Vi havde fornylig et rart B e s ~ gaf Kalckar, som fortalte om de morsomme Fremskridt Du har gjort med Kernesprargsmaalet og at Du har skrevet et Brev derom ti1 Nature42. Samtidigt fortalte han ogsaa at de eksperimentelle Arbejder i Instituttet var kommet videre. Det laa n z r for mig, som stadig har den almindeliggjorte Diracligning i Hovedet, at se efter hvordan den forholder sig ti1 dine Resultater. Man kunde da taenke paa om en saadan Ligning kunde bruges ti1 en omtrentlig Beskrivelse af hvad Du, i Fralge Kalckar, kalder et Compound System. En saadan Ligning tager nemlig Sigte paa en Partikel (eller et System), 4'
42
For the correction of the date, see the Introduction, ref. 33. Introduction, ref. 24.
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der har en given Ladning, men hvis Hvilemasse M kan antage forskellige Vmdier, der ved den simplest mulige Almindeliggerrelse af Diracs Ligning er givet ved Formeln M = M O r n 2 , hvor MO og X er to Konstanter, der kendetegner den paagaldende Partikel, og 1 kan antage forskellige Heltalsvardier, enten kun ulige eller kun lige (hvor Nu1 maa undtages) o p ti1 en vis for Partikeln karaktaristisk Maximalvardi n (der er = 1 for Elektronen). Da n angiver Antallet af uafhangige Systemer af Diracske Matricer hvoraf de i Ligningen indgaaende Matricer kan betragtes som sammensat, ligger det n a r at satte n lig med det Antal Partikler, der i Ferlge Paulis Neutrinohypotese bestemmer Kernens Statistik, nemlig A + 2 2 , hvor A er Atomvzgtens hele Tal og Z Atomnummeret (En saadan Antagelse har Destouches prervet at gerre for Protonen i et i ervrigt vidstnok urigtigt Forserg at opstille en Slags Diracligning for en Kernes Tyngdepunktbevzgelse). Dette giver n - 400 i Slutningen af det periodiske System. Hvis vi nu prerver paa at identificere den maximale Energiforskel mellem to Tilstande af vor Partikel med den sterrste y-Straalekvant Ey, der kan udsendes af tilsvarende Compound System, har vi saaledes Ey + M d 2 . Hvis paa den anden Side n er nogenlunde stort, saa er den mindste Energiforskel mellem to af Partikelns Tilstande AE 2MoX2/n3og altsaa aE 4Ey/n3. I slutningen af det periodiske System giver dette hE $Ey. Da de haardeste y-Straaler vel svarer ti1 nogle Millioner Volt bliver dette altsaa mindre end en Volt i Overensstemmelse med dine Betragtninger over Neutronindfangning. Endnu for Cd har man n 200 og altsaa AE +Ey. hvilket vel er tilstrakkelig lille. Jeg maa understrege at det ikke drejer sig om en fuldstandig Teori der kunde forklare Kernernes Reaktioner, men at det vel herjst kan v z r e Tale om en tilnarmet Beskrivelse af en Atomkerne, saalznge denne kan betragtes som et afsluttet System, og at den valgte Ligning heller ikke er den eneste men kun den simpleste Almindeliggerrelse. I ovrigt vilde jeg kun med dette Brev yderligere fremhzve hvor interesseret jeg er i Dit Kernearbejde, og at jeg vilde v z r e forfmdelig taknemmelig, hvis Du kunde undvare et Eksemplar af Manuskriptet eller Korrekturet. Med mange venlige Hilsner og Onsker om et godt Aar for Eder alle Din Oskar Klein
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P.S. Jeg sender vedlagt Nerglen som jeg ferrst for nogle Dage siden opdagede at jeg desvmre havde glemt at aflevere.
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Translation Morby, 2 [December] 1935 Dear Bohr, We had recently a pleasant visit from Kalckar, who told us about the nice progress you have made with the nuclear problem and that you have written a note to Nature42 about this. At the same time he told us that the experimental work in the Institute has also advanced. This is of concern to me, as I keep thinking about the generalised Dirac equation, to see how this relates to your results. One could imagine that such an equation might be used for an approximate description of what, according to Kalckar, you call the compound system. Indeed such an equation envisages a particle (or a system) with a given charge, but whose rest mass M can take different values, which, with the simplest generalisation of the Dirac equation are given by the formula
M
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M o m 2 ,
where MOand X are constants which characterise the relevant particle, and I can take various integral values, either only odd or only even (excluding zero) up to a certain maximum value n which is characteristic for the particle (n = 1 for the electron). Since n gives the number of independent systems of Dirac matrices of which the matrices occurring in the equation can be taken to be made up, it is plausible to set n equal to the number of particles which according to Pauli’s neutrino hypothesis determine the statistics of the nucleus, i.e., A + 2 2 where A is the mass number and 2 the atomic number. (Destouches has tried to get such an Ansatz for the proton in an otherwise presumably wrong attempt to obtain a kind of Dirac equation for the centre-of-mass motion of the nucleus.) This gives n 400 near the end of the periodic system. If we now try to identify the maximum energy difference between two states of our particle with the greatest existing y-ray quantum EY which can be emitted by the relevant compound system, we have then EY +MoX2. If on the other hand n is rather large, the smallest energy difference between two states of the particle is AE 2MoX2/n3 and therefore A E - 4EY/n3.Near the end of the periodic system this gives A E I16EY . Since the hardest y-rays correspond to a few million volts, this therefore comes to less than one volt, in agreement with your considerations about neutron capture. Even for Cd one has n 200, and AE iEY.10-6 which is probably sufficiently small. I should stress that this is not a matter of a complete theory which could explain nuclear reactions, but it can at most be a question of an approximate description of a nucleus as long as this can be regarded as a closed system, and that the equation I have chosen is not the only, but only the simplest, generalisation. Besides, I wanted in this letter only to stress
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strongly how greatly I am interested in your nuclear work, and I would be most grateful if you could spare a copy of the manuscript or of the proof. With many kind regards and best wishes to you all for the New Year, Yours, Oskar Klein
P.S. I am sending the enclosed key, which only a few days ago I discovered that I had forgotten to return.
BOHR TO KLEIN,
9 January 1936
[Carbon copy] [Krabenhavn,] 9. Januar [19]36. K a r e Klein, Tak for Dit rare Brev med de interessante Oplysninger om det Massespektrum, som man efter Dine Betragtninger kan vente for et System, der tilfredsstiller en almindeliggjort Diracligning. Selv om dette Spektrum for tunge Kerner giver en Minimum Massedifferens paa ca. 1 Volt, synes Spektret alligevel ikke at have den samme Type som Energiniveauerne for Atomkernerne. Saa vidt jeg forstaar, giver Dit Spektrum jo kun et enkelt Ophobningspunkt for Niveauerne, medens Kernereaktionerne kraver en t z t Niveaufordeling over et udstrakt Energiomraade. Disse Fordelinger strider jo ikke imod hinanden, men synes at vise at Niveauspektret i Kernerne dog vzsentlig bestemmes af deres indre Svingningstilstande. Jeg har endnu ikke sendt Dig den lovede Note, fordi jeg i disse Dage med Kalckars H j a l p har prravet at forbedre saavel Indholdet som Formen. Det synes virkelig, som om Betragtningerne har meget almindelig Gyldighed, og Kalckar og jeg har i Sinde, saa mart Noten er fardig, at tage fat paa en grundig Gennemgang af hele Materialet vedrrarende Kernereaktioner, hvoraf vi haaber at kunne l a r e adskilligt. Jeg haaber, som sagt, at sende Dig den nye Udgave af min Note om faa Dage og sender indtil da blot de venligste Hilsener ti1 Jer alle, Din [Niels Bohr]
Translation [Copenhagen,] 9 January 1936 Dear Klein, Thanks for your good letter with the interesting information about the mass
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spectrum which one can expect on the basis of your considerations, for a system that satisfies a generalised Dirac equation. Even though that spectrum for heavy nuclei gives a minimum mass difference of about 1 volt, the spectrum does not seem to have the same type of energy levels as the atomic nuclei. As far as I understand, your spectrum gives only one point of accumulation for the levels, whereas the nuclear reactions require a dense level distribution over an extended energy region. These distributions do not contradict each other, but seem to show that the level spectrum of nuclei is essentially determined by their internal vibrational states. I have not yet sent you the promised note, because I have tried lately, with Kalckar’s help, to improve both the content and the form. It really seems as if the considerations have very general validity, and as soon as the note is complete, Kalckar and I have in mind to get down to a thorough review of the whole material about nuclear reactions, and we hope to be able to learn a great deal from this. I hope, as I said, to send you the new edition of my note in a few days, and until then send merely the kindest regards to all of you. Yours, [Niels Bohr] HENDRIK A. KRAMERS KRAMERS TO BOHR,
11 March 1936
[Handwritten] KAMERLINGH ONNES LABORATORIUM DER RIJKS-UNIVERSITEIT TE LEIDEN AFDEELING VOOR THEORETISCHE NATUURKUNDE (LANGEBRUG 1 11) LEIDEN, 11 Mrt. 1936 K z r e Bohr, Det var morsomt at lEse i Nature om dine Kern-betragtninger42a: de gav netop Klarhed i det Spmgsmaal, som blev d r ~ f t e tsaa indgaaende paa sidste Solvay Kongres. Jeg har to Ting, som jeg vilde spmge dig i den Anledning. 1) Situationen med de mange, lige tunge, Partikler i Kernen minder i flere Henseender om Situationen af de fri Elektroner i et Metal. Denne sidste kan nu med stor Sukces beskrives paa den Bloch’ske Maade43, selv om denne stader paa berygtede Vanskeligheder naar man s ~ g e nmmere r at bestemme Approximationens Godhed. Vil der alligevel ikke bestaa en lignende Behandlingsmaade for 42a
43
Introduction, ref. 24. Introduction, ref. 44a.
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Kernen; d.v.s. man [suplponerer et Fermi Lov for Protoner og et for Neutroner (eller et for begge t o ad Gangen): selv om dette giver Fejl hvis man benytter det ti1 at beskrive Totalenergien, saa kunde det v z r e rigtigt for at bestemme den omtrentlige Fordeling af Kernens hrajere stationaere Tilstande. 2) Burde man ikke vente, at et hurtigt Elektron, som styrter ind i en tung Kerne, kunde “anslaa” denne (evt. under Udsendelse af et Neutrino, eller hvad der svarer ti1 disse taenkte Neutrinoprocesser i Virkeligheden). De Naturvidenskabelige Studenter fra Utrecht b e s ~ g e rKrabenhavn i Dagene lige efter Paaske. Maaske har du allerede hrart om det, fordi den fysisk-kemiske Del vilde gerne se Instituttet paa Blegdamsvej. Studenterne har spurgt om jeg vilde gaa med som en Slags Leder. I denne Anledning vilde det v z r e vigtigt for mig at vide, om der afholdes et lille Fysikermrade i Paasketiden; og - hvis dette er saaledes - i hvilken Uge det skal vzre. Hvis der er noget bestemt i denne Retning, kunde saa Frk. Schultz ikke lige skrive mig et Kort om det? Jeg h ~ r t eat Solvay-Kongressen i Aar sandsynligvis vil dreje sig om Kosmisk Straaling. Hvis dette har sin Rigtighed vilde jeg blot grare opmzrksom paa - hvis dette overhovedet taget er n~dvendigt- at Prof. Clay i Amsterdam vilde v m e en meget sympatisk Fysiker at have med i Diskussionen. Hans Iver, Flid og Begejstring for Kosm. Str. er uden lige, og jeg synes, at de vigtigste Bidrag ti1 Bredde- og Lzngde-Variationen af Intensiteter netop stammer frarst og fremmest fra ham, og at hans Arbejder netop paa dette Omraade har vzret meget nrajagtigere og mere tilforladelige end de amerikanske. I aften taler vi paa Ehrenfest-Kolloquiet om dine Kerner: med Casimir og Uhlenbeck som sagkyndige. Hjertelig Hilsen fra Hjem ti1 Hjem Din Kramers
Translation Leiden, 11 March 1936 Dear Bohr, which are just It was interesting to read in Nature about your nuclear the answer to the question which was discussed so thoroughly at the last Solvay Conference. I have two questions to ask you in this connection. 1. The situation of the many equally heavy particles in the nucleus is reminiscent in many respects of the situation of the free electrons in a metal. Now the latter can be described very successfully by Bloch’s method43, even though this meets with notorious difficulties if one tries to determine the validity of the ap-
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proximation. Will there not nevertheless exist a similar treatment for the nucleus; i.e., one would assume a Fermi law for the protons and one for the neutrons (or one for both together); even if this gives an error if one uses it to describe the total energy, it could still be right for determining the approximate distribution of the higher energy levels of the nucleus. 2. Should one not expect that a fast electron which falls into a heavy nucleus could “excite” this (possibly with the emission of a neutrino, or whatever corresponds to these imaginary neutrino processes in reality). The natural science students from Utrecht will visit Copenhagen immediately after Easter. Perhaps you have already heard about this, because the physics and chemistry section would like to see the Institute on Blegdamsvej. The students have asked whether I would go with them as a kind of leader. In this connection it would be important for me to know whether there will be a small meeting of physicists at Easter time, and, if so, in which week this will take place. If something has been settled about this, could Miss Schultz drop me a line about it? I heard that the Solvay Congress this year will most likely deal with cosmic radiation. If this is true I would just point out - if this is indeed necessary - that Professor Clay in Amsterdam is a very congenial physicist to have participate in the discussion. His zeal, energy and enthusiasm for cosmic rays is without equal, and I believe that the most important contributions on the latitude and longitude dependence of the intensity come just mainly from him, and that his papers on that subject were much more accurate and more reliable than the American ones. Tonight we will talk in the Ehrenfest Colloquium about your nuclei, with Casimir and Uhlenbeck as experts. Affectionate greetings from house to house, Yours, Kramers BOHR TO KRAMERS,
14 March 1936
[Typewritten] UNIVERSITETETS INSTITUT FOR
15, K0BENHAVN 14. Marts 1936.
BLEGDAMSVEJ
DEN
0.
TEORETISK FYSIK
K z r e Kramers, Mange Tak for Dit rare Brev, som fik mig ti1 at lznges endnu mere efter at se Dig snart igen. Det vilde j o v z r e forfserdelig morsomt, om Du kom herop sammen med de hollandske Studenter, som jeg for nogen Tid siden har lovet at
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vise Instituttet og holde et orienterende Foredrag for. Men jeg skynder mig at skrive, at vi af forskellige Grunde stadig har maattet udskyde vor aarlige Konferens, og at den nu i disse Dage er blevet endelig fastsat ti1 10. Juni, ti1 hvilken Tid den nye store Udvidelse af Instituttet, der er blevet noget forsinket ved den kedelige Lockout, vil v a r e helt fardig. Denne Gang tanker vi foruden Kerneproblemerne ogsaa at komme ind paa forkellige biologiske Anvendelser af Atomfysikken, hvori j o navnlig Hevesy er saa dybt interesseret. Vi haaber ogsaa paa et stort Beserg af de gamle Medarbejdere ved Instituttet og ferrst og fremmest paa, at Du selv kommer med. For Midler, der staar ti1 Instituttets Raadighed ti1 Afholdelse af Konferensen kan vi bestride Dine Rejseudgifter. Iervrigt vil der i umiddelbar Fortsattelse af Konferensen, d.v.s. ca. 20. Juni i Kerbenhavn afholdes den anden internationale Kongres for “Videnskabens Enhed”, hvor Diskussionsemnet skal vzere Kausalitetsproblemet i Fysik og Biologi. Der ventes betydelig Deltagelse ikke alene af Fagfilosoffer, men ogsaa af Biologer, og man har bedt mig indtrade i Organisationskomiteen og holde et indledende Foredrag. Jeg haaber, at saa mange som muligt af Deltagerne i Konferensen, og i s a r Du selv, kan blive ogsaa ti1 denne Kongres, hvor jeg tror, at der vil v a r e en enestaaende Lejlighed ti1 at bibringe alle virkelig interesserede et Indtryk af, at det fra Fysikernes Side ikke drejer sig om Mystik, men om nergterne Bestrabelser for at fremme Forstaaelsen af Granserne for selv de mest elementare Begrebers Anvendelighed. Det er naturligvis en praktisk Vanskelighed, at saa mange af de Fysikere, der har bidraget saa vasentligt ti1 Fremskridtet paa dette Omraade, pludselig synes at vzere forskrzekkede for Konsekvenserne af deres egen Indsats. Men, uforbederlig Optimist som jeg stadig er, tror jeg, at netop denne Krise vil bringe den endelige Afklaring af Situationen. I denne Forbindelse vil jeg alligevel gerne sige, at jeg slet ikke er glad for Diracs sidste Artikel i idet jeg er yderst skeptisk med Hensyn ti1 Rigtigheden af de nye Forserg i Chicago. Alt hvad Dirac gerr ligger jo dog i en harjere Plan af Saglighed end de fleste andres, og jeg var meget rerrt over, under mit sidste Beserg i England at herre om, med hvor stor Grundighed og Forstaaelse af vore Bestrabelser han igen havde studeret vor gamle Afhandling sammen med Slater45.Denne Afhandling har imidlertid, tror jeg, allerede gjort sin Nytte og maaske ikke mindst hjulpet til, at vi nu befinder 0s i et herjere Stadium, hvor en mere naturlig Generalisation af de klassiske Idealer kan komme ti1 sin Ret. Med Hensyn ti1 Dine Sperrgsmaal vedrarrende Kerneproblemerne ved jeg ikke helt, hvad jeg skal sige. Navnlig er Analogien mellem Partiklernes Bevagelser i P . A . M . Dirac, Does Conservation of Energy Hold in Atomic Processes?, Nature 137 (1936) 298-299. ‘’ N . Bohr, H . A . Kramers and J.C. Slater, The Quantum Theory of Radiation, Phil. Mag. 47 (1924) 785-802. Reproduced in Vol. 5, p . [99]. 44
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Kernen og Elektronbevzgelsen i et Metal mig ikke tilstrzkkelig klar. Hvis jeg i denne Forbindelse skulde vove et Paradox, vil jeg hellere sige, at Utilstrzkkeligheden af Gamows og Heisenbergs Synspunkter for at gerre Rede for Kernernes Reaktioner snarere minder om de Blochske Metoders Svigten overfor Problemet om Supraledningsevnen. Heller ikke synes jeg, at der er nogen simpel Analogi mellem Metallernes Forhold ved hrajere Temperaturer og Kernernes h ~ j ant slaaede Tilstande. I det mindste forekommer det mig, at det mulige Fremskridt i de nye Betragtninger over Kernerne ferrst og fremmest turde ligge i Erkendelsen af, at vi selv ved de meget hraje Energiniveauer for det sammensatte Kernesystem, som vi har at gerre med ved de szdvanlige Kernereaktioner, paa ingen Maade kan tale om nogen selvstzndigt kvantiseret Bevzgelse af de enkelte Kernepartikler. Jeg haaber imidlertid, at det ikke skal vare lznge, f0r vi faar Lejlighed ti1 at tale nzrmere sammen om alle disse Sperrgsmaal, og i s z r skal jeg, saa mart den mere udferrlige Afhandling, som Kalckar og jeg arbejder paa, er fzrdig, sende Dig et Eksemplar af Manuskriptet. Jeg behraver ikke at gentage, hvor glade vi alle vil v z r e for at se Dig heroppe snarest muligt, og heller ikke at betone at Hensigten med at fortzlle saa udferrligt om Konferensen ikke er at fraraade et tidligere Beserg, naar blot dette ikke skal betyde, at vi derfor maa savne Dig ved Konferensen. Med de hjerteligste Hilsener fra Hjem ti1 Hjem, Din Niels Bohr
Translation Copenhagen, 14 March 1936 Dear Kramers, Many thanks for your good letter which made me long even more to see you again soon. It would indeed be extremely nice if you could just come together with the Dutch students whom I have already promised some time ago to show over the Institute and to give an introductory talk. But I hasten to write that for various reasons we had still to postpone our yearly conference and that this has recently been definitely fixed for 10 June, by which time the new big extension of the Institute, which was somewhat delayed by the tiresome lockout, will be finished. This time we intend to include, besides the nuclear problems, also various biological applications of atomic physics, in which Hevesy in particular is so deeply interested. We also hope for a large attendance of old collaborators of the Institute, and above all that you will come yourself. From the means at the disposal of the Institute for the organisation of this conference we can cover your travel expenses. In addition there will be immediately after the conference,
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i.e., about 20 June, the second international congress for the “Unity of Science”, where the subject for discussion will be the causality problem in physics and biology. We expect substantial participation not only from professional philosophers, but also from biologists, and I have been asked to join the organising committee and deliver an introductory lecture. I hope that as many of the participants of the conference as possible, particularly you yourself, can also stay on for this congress where I believe there will be a unique opportunity to convey to all those really interested the idea that for the physicists this is not a matter of mysticism, but a sober attempt to advance the understanding of the limits of applicability of even the most elementary concepts. It is of course a practical difficulty that so many of the physicists who have contributed so essentially to progress in this area, suddenly appear to be frightened by the consequences of their own efforts. But as the incorrigible optimist I still am, I believe that just this crisis will bring the final clarification of the situation. In this connection I would however like to say that I am not at all pleased with Dirac’s latest paper in since I am extremely sceptical about the correctness of the new experiments in Chicago. All that Dirac does, however, lies in a higher plane of objectivity than most others’, and I was deeply moved to hear, on my last visit to England, with what great thoroughness and understanding of our efforts he again had studied our old paper with Slater45.That paper has however, I believe, already served its purpose, not least perhaps by helping us reach a higher level where a more natural generalisation of the classical ideals can come into its own. About your questions on the nuclear problems I don’t quite know what to say. In particular the analogy between the motion of the particles in the nucleus and that of the electrons in a metal is not sufficiently clear to me. If I might venture a paradox in this connection I would sooner say that the inadequacy of Gamow’s and Heisenberg’s point of view in explaining nuclear reactions reminds us rather of the failure of Bloch’s method for the problem of superconductivity. Nor do I think that there is any simple analogy between the behaviour of metals at higher temperatures and the highly excited states of nuclei. It appears to me at least that the possible progress in the new considerations about nuclei should lie primarily in the recognition that even at the very high energy levels of the compound system with which we have to do in the usual nuclear reactions we cannot talk in any way of the independently quantised motion of single nuclear particles. I hope however that before long we shall have an opportunity to talk together further about all these questions, and in particular I shall send you a copy of the manuscript of the more detailed paper on which Kalckar and I are working, as soon as it is ready. I need not repeat how pleased we shall all be to see you here as early as possi-
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ble, nor to stress that in writing in such detail about the conference it was not the intention to prejudice an earlier visit, provided this does not mean that we would miss you at the conference. With cordial greetings from house to house, Yours, Niels Bohr
KRAMERS TO BOHR,
20 March 1936
[Handwritten] Leiden, 20 Marts 1936 Kzere Bohr, Jeg blev uhyre glad for dit sidste udferrlige Brev. Ferrst og fremmest vil jeg gaa lidt ind paa Sperrgsmaalet, om jeg kan komme ti1 K ~ b e n h a v ni Aar. Da jeg herrte, at Konferencen ikke skal finde Sted ferr Juni, har jeg sagt ti1 Utrechter Studenterne, at jeg ikke rejste med ti1 Kerbenhavn i Paaske. Det bliver for meget; jeg skal bruge mine Ferier ti1 at blive fzrdig med anden Del af min Bog om Kvanteteorien (som snart truer ti1 at gaa mig paa Nerverne). Det er meget rerrende, at du endda har lovet selv at fortzlle Utrechter Studenterne noget om dine og Instituttets Bestrzbelser, og de vil sikkert szette herj Pris paa det. Kun en Del af Dem er Fysikere, foruden Kemikere er der endnu Biologer og Farmaceuter, men det er vistnok Meningen, at de sidste to Grupper beserger Krogh, medens de eksakte kommer hos dig (vistnok enten Lerrdag 18 April om Formiddagen eller Tirsdag 21 April; jeg havde saadan halvt tzenkt mig at du skulde vzere bortrejst ti1 den Tid). Et stort Sperrgsmaal er imidlertid om jeg kan gerre mig fri i Juni. Det er j o netop den Maaned, hvor Halvdelen af Hollzndere eksaminerer anden Halvdel, og Universitetet er naturligvis med i denne Sport. Endvidere er der international Kerle-Kongres i Scheveningen, med videnskabelig Sektion i Leiden, omtrent 16 Juni. Men du skriver saaledes, at jeg skal gerre hvad jeg kan for at gerre rnig fri. Vi har undret 0s ogsaa meget i Leiden over Dirac’s Villighed ti1 at opgive saa meget af Kvantemekanikken. Jeg tror man maa sige, at han mangler - overfor Eksperimerenterne - den Uafhzengighed hvormed f . Eks. Heisenberg ser paa Tingene. I hvert Fald haaber jeg, at der mart kommer en som f. Eks. Bothe, som gentager Shanklands Forserg. Hvad angaar mine Bemzerkninger om den eventuelle Mulighed at beskrive Kernens Tilstand paa Bloch’s Maade, saa maa Du vistnok have troet, at jeg netop har misforstaaet et af de vzesentligste Punkter i din Opfattelse. Sagen er imidlertid, at jeg fornylig kom ind paa det gamle Spsrgsmaal, hvorfor Bloch’s
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Teori for Metalelektronerne overhovedet taget er saa nogenlunde rigtig; og dette tror jeg er der ingen som rigtig ved. Bloch faar jo en Mulighed for Strermbzerende Tilstande i et Metalkrystal, ved at antage at to* Elektroner praktisk talt uafhangigt af hinanden kan bevinde sig ved samme Atomkerne, og dog skal de forskellige “Energi-baand” (i hvert Fald det laveste eller de to eller tre laveste) mere eller mindre imitere det fri Metalatoms laveste Energitilstand(e). Min Ide var derfor, at Bloch’s Behandlingsmaade derfor alligevel ikke turde v a r e helt uegnet ti1 at beskrive dine Kerne-tilstande. Husk paa, at naar der overferres Energi ti1 Metalelektronerne (Sml. f . Eks. Weizsacker’s (rigtignok lidt grov) Teori for Bremsning af a-Straaler i et det heller ikke altid er netop en bestemt Elektron-tilstand, som zndres. (I den szedvanlige Foto-effekt Teori ser det rigtignok ud, som om et bestemt Elektron i Fermisaen slynges v a k , men jeg kunde godt t a n k e mig, at denne Teori er ravgal, eller i hvert Fald paa samme Maade gal som Gamow’s Teori for Geiger-Nuttall Kurven er det.) Et Sperrgsmaal endnu (som du ikke behaver at beware, ligesaa lidt som alt andet): paa hvilken Maade bringer du de store Afstande mellem Niveau-erne i Niveau-skemaet for RaC Kernen i Overensstemmelse med den store Niveautzthed, som du har Brug for? Jeg kan tzenke mig forskellige Svar, men der er ingen som tilfredsstiller mig. Det viste sig idag at vor lille San havde faaet Difteritis. Han er ret urolig, og jeg er oppe i Nat for afvekslende at skrive Breve og at trerste ham, medens min Kone, som har Influenza, og praktisk talt ikke sov sidste Nat, faar lidt Hvile. Du skal ikke beklage mig, fordi Drengen er uendelig serd: bare haabe, at de andre Barn bliver fri for Sygdommen. Tusind Hilsner fra 0s alle, ogsaa ti1 din Kone din Kramers * Naar der er 1 frit Elektron pro Atom.
Translation Leiden, 20 March 1936 Dear Bohr, I was enormously pleased by your last detailed letter. First of all I should discuss the question whether I can come to Copenhagen this year. When I heard that the conference will not be held until June, I told the students in Utrecht that I would not go with them to Copenhagen at Easter. That would be too much; 46
Introduction, ref. 45.
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I shall need my vacations to finish the second part of my book on quantum theory (which threatens soon to get on my nerves). It is very touching that you have even promised to tell the students from Utrecht something yourself about the endeavours of the Institute and of you yourself, and they will certainly appreciate this greatly. Only some of them are physicists; besides chemists there are also biologists and pharmacologists, but it is probably the intention that the last two groups should visit Krogh, while the exact scientists come to you (probably either during the morning of Saturday 18 April, or Tuesday 21 April; I had thought that you might be out of town at that time). It is however a big question whether I can get away in June. That is just the month when half the Dutch examine the other half, and the university naturally takes part in this pastime. Furthermore there is an international refrigeration conference in Scheveningen, with a scientific section in Leiden, about 16 June. But you write in such a way that I shall do what I can to get away. Here in Leiden we have also been surprised at Dirac’s readiness to give up so much of quantum mechanics. I think one must say that he lacks the independence towards the experimentalists with which for example Heisenberg looks at things. In any case I hope that someone like for example Bothe will soon repeat Shankland’s experiment. As regards my remarks about the possibility of describing the state of a nucleus by Bloch’s method, you may have thought that I completely misunderstood the most essential points of your view. However, the fact is that I have lately become involved with the old question why Bloch’s theory for electrons in metals, taken as a whole, is so tolerably correct, and I believe nobody really knows this. After all Bloch gets the possibility of current-carrying states in a metal crystal, with the assumption that two* electrons can, practically speaking independently of each other, be located near the same nucleus, yet the various “energy bands” (in any case the lowest, or the two or three lowest ones) should resemble more or less the lowest level(s) of the free metal atom. My idea was therefore that Bloch’s method might nevertheless not be wholly unsuitable for describing your nuclear states. Bear in mind that when energy is transmitted to the metal electrons (compare for example Weizsacker’s theory of the stopping of a-particles in metals46 (admittedly a little crude)) there is by no means always a definite electron state which changes. (In the usual theory of the photo-effect it looks indeed as if a definite electron from the Fermi sea escaped, but I can well imagine that this theory is absurd, or at least absurd in the same way as Gamow’s theory of the Geiger-Nuttall curve.) One more question (which you need answer as little as everything else): By * If
there is one free electron per atom
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what method do you reconcile the large distances between the levels in the level scheme of RaC nuclei with the high level density which you need? I can think of several answers, but I do not find any of them satisfactory. It turned out today that our little son has diphtheria. He is very restless, and I am up during the night, alternately writing letters and comforting him, while my wife, who herself has influenza, and hardly slept last night, gets a little rest. You need not feel sorry for me, as the boy is very sweet. I only hope that the other children will escape the disease. A thousand greetings from all of us, also t o your wife, Yours, Kramers
JOHANN KUDAR BOHR TO KUDAR,
28 January 1930
[Carbon copy] UNIVERSITETETS INSTITUT
15, K0BENHAVN 28. Januar 1930.
BLEGDAMSVEJ
FOR
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0.
TEORETISK FYSIK
Sehr geehrter Dr. Kudar, Ich habe mit Interesse die mir freundlichst zugesandten Korrekturen Ihrer Arbeiten uber /3-Strah1spektren4’ gelesen. Wir sind j a hier seit langerer Zeit in dem Problem der kontinuierlichen 6-Spektren sehr interessiert. Wie Gamow in seinem in der physikalischen Zeitschrift referierten Vortrag in Charkow erwahnt hat, bin ich darauf gefasst, dass wir mit einem Effekt zu tun haben, deren Erklarung sich der bisherigen Fassung der Quantenmechanik entzieht und sogar auf eine beschrankte Gultigkeit der Energieerhaltung hindeutet. Wie Sie aus der einliegenden Note48 sehen werden, war mein Gedanke dabei, dass in der bisherigen Fassung der Quantentheorie nicht behorige Rucksicht auf die Individualitat der Elementarteilchen genommen ist, und dass daher die Theorie versagt bei Problemen, wo es sich um Dimensionen handelt von derselben Grossenordnung wie der klassisch geschatzte Diameter des Elektrons. Die Note ist eine Kopie eines Aufsatzes, der im Fruhjahr geschrieben aber anderer Arbeit wegen zur Seite gelegt wurde. In den letzten Monaten habe ich mich wieder mit diesen Fragen beschaftigt, besonders in Verbindung mit den tiefliegenden Schwierigkeiten der relativistischen 17 4X
Introduction, ref. 5a. Probably the manuscript cited in the Introduction, ref. 1 .
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Quantenmechanik, die in Diracs Theorie zu Tage treten, und ich hoffe in nachster Zukunft eine Darstellung meines Standpunktes zu geben. Wie gesagt habe ich die Betrachtungen in Ihren Abhandlungen rnit Interesse gelesen, aber ich muss gestehen, dass ich nicht recht verstehe, auf welcher Grundlage Sie sich stellen. Ihre Berechnung des Radius des Kerninneren beruht ja auf der Auffassung des Elektrons als Punktladung in der ublichen quantenmechanischen Umdeutung, und wenn dieser Radius kleiner ausfallt als der ‘ ‘Elektronenradius”, so bedeutet dies eben, dass das Problem ausserhalb der Reichweite dieser Theorie liegt. Der nahere Vergleich der Rechnungsresultate rnit den Versuchsergebnissen scheint mir deshalb schwer zu verteidigen. Besonders sehe ich nicht ein, wie Sie die kontinuierlichen Spektren rnit der wohldefinierten Lebensdauer der Atome versohnen konnen. Wenn die Elektronen, wie es nach Ihrer Auffassung der Fall sein sollte, einfach im Kerninnern komprimiert waren, versteht man meiner Ansicht nach nicht, warum man einen kontinuierlichen Spektrum bekommt, und ins besondere nicht warum man die untere Grenze dieses Spektrums mit Hilfe der gewohnlichen Ruhemassen berechnen kann. Ubrigens erscheint dem Wert des Elektronradius rnit dessen Hilfe Sie Ubereinstimmung rnit den Messungsergebnissen erzielt haben, eine gewisse Willkur anzuhaften. Es kann sich ja hier nur um eine Schatzung der Grossenordnung handeln, aber die gewohnlich angegebenen aus einfachen klassischen Modellen berechneten Werte sind nur etwa die Halfte des Wertes, den Sie benutzen. Mit freundlichem Gruss, Ihr ergebener [Niels Bohr]
WOLFGANG PAUL1 PAULI TO BOHR,
11 February 1938
[Handwritten] Physikalisches Institut der Eidg. Technischen Hochschule Zurich
7, 11.11.38 Gloriastrarje 35
ZURICH
Lieber Bohr, Bloch gab mir Deinen Brief und die Note uber den K e r n p h ~ t o e f f e k zu t ~ ~lesen und ich will gerne Deiner Aufforderung nachkommen, daruber kurz meine Mei4y
Introduction, ref. 79.
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nung zu sagen. Die Hauptsache scheint mir in dem Satz S. 1 unten zu liegen, der mit “this apparent contradiction . . . ” beginnt und mit “singular radiation properties” (S. 2 oben) endet. Es scheint mir nun, dafi dieser Satz zwar lang, aber doch zu kurz ist! Denn fur das modellmafiige Verstandnis scheint es mir ganz wesentlich zu sein, dafi der Begriff “special vibratory motions” erstens genauer prazisiert und zweitens mehr detailliert aus einem Model1 deduziert wird. Was aus einem Flussigkeits- oder Tropfchenmodell folgt, kann ich z.B. uberhaupt nicht ubersehen. Fur den festen Korper und seine Schwingungen ist es allerdings wahr, darj weitgehende Analogieen zu dem von Dir geforderten Mechanismus bei der Absorption ultraroten Lichtes tatsachlich vorhanden sind. Ich erinnerte mich namlich gleich alter Zeiten, wo ich noch jung, ein kompetenter Gelehrter und sehr boshaft gewesen bin und eine Formel fur die Dampfung der sogenannten Reststrahlen infolge der Anharmonizitat der Schwingungen abgeleitet habe.” Diese Dampfung entspricht genau Deiner Conversion-probability Fc, wahrend auch dort die naturliche Strahlungsdampfung r R vollig gegen Fc vernachlassigt werden kann. Der Mechanismus ist der, dafi z.B. im NaCl nur diejenigen speziellen Schwingungen Licht absorbieren, bei denen die Na-Atome alle untereinander synchron schwingen und ebenso die C1-Atome untereinander .** (Beim Kern allerdings wird man neben den Dipolmomenten, auch die Quadrupolmomente in Betracht ziehen mussen!) - Die Theorie ist dann sehr ausfuhrlich von Born u. Blackman ( Z S . f . Phys. 82, 551, 1933) u. Blackman (ZS. f. Phys. 86, 421, 1933) entwickelt worden. (Das Hauptresultat war, darj in der Formel fur D (S. 2 unten) in diesem Fall Fc stark frequenzabhangig wird.) Beim Kern ist aber naturlich alles vie1 verwickelter als beim festen Korper, wo der Platzwechsel der Atome vernachlassigt werden kann. Daher mein Bedurfnis nach genauerer modellmafiiger Erlauterung. Auch mu13 ich die Beurteilung der Gute der Experimente und der Sicherheit der aus ihren ableitbaren Schlusse den kompetenten Fachleuten uberlassen. Ich danke auch noch sehr fur die Mitteilungen uber Houtermans u. habe grofies Interesse wieder etwas uber ihn zu horen, sobald sich etwas Neues ereignet. Es ist ja wirklich ruhrend von Dir, wie sehr Du Dich seines Falles angenommen hast! Viele herzliche Grurje, auch von Haus zu Haus Stets Dein W. Pauli * Verh. d. deutsch. phys. Ges. 6, 10, 1925 *- Die Anharrnonizitat der Oszillatoren bewirkt d a m , dal3 die Energie allrnahlich von der auf Licht reagierenden Schwingung auf die anderen Schwingungen ubergeht.
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Translation Zurich, 11 February 1938 Dear Bohr, Bloch let me read your letter and the note about the nuclear ph~to-effect~’, and I shall gladly respond to your invitation to indicate my opinion briefly. The essence seems to me to lie in the sentence at the bottom of p. 1, starting “This apparent contradiction . . . ” and ending “singular radiation properties” (top of p. 2). It seems to me here that this sentence is long, but still too short! For in order to understand the treatment in terms of a model it seems to me absolutely essential that the concept “special vibratory motions’’ in the first place be made more precise, and secondly be derived in more detail from a model. What follows from a liquid or droplet model, for example, I cannot see at all. For the solid body and its vibrations it is indeed true that there are in fact farreaching analogies of the absorption of infra-red light to the mechanism you postulate. I at once remembered the old days, when I was still young, a competent scholar and very malicious, and when I derived a formula for the damping of the so-called Reststrahlen because of the anharmonicity of the vibrations*, This damping corresponds exactly to your conversion probability I‘c, while there, too, the natural radiation width r R is completely negligible compared to r c . The mechanism is that, for example in NaC1, only those special vibrations absorb light in which all the Na atoms vibrate in phase with each other, and similarly the C1 atoms**. (In the nucleus one will however have to consider, besides the dipole moments, also the quadrupole moments.) The theory was then developed in great detail by Born and Blackman ( Z . Phys. 82, 551, 1933) and Blackman (Z. Phys. 86, 421, 1933). (The main result was that in the formula for u (bottom of p. 2) in that case r c becomes strongly dependent on frequency.) In the nucleus everything is of course much more complicated than in the solid, where the exchange of atoms between sites can be neglected. Hence my desire for a more accurate model explanation. In addition I must leave the jugdment on the quality of the experiments, and the certainty of the conclusions that can be drawn from them, to the competent experts. I thank you also very much for the news of Houtermans, and shall be very interested to hear more about him if anything further happens. It is really very touching that you have concerned yourself so much with his case. Many cordial greetings, also from house to house, Yours ever, W. Pauli
*
Verh. d. deutsch. phys. Ges. 6 , 10, 1925
** The anharmonicity of the vibrations then has the consequence that the energy will gradually be transferred from the optically active vibration t o the other vibrations.
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RUDOLF PEIERLS BOHR TO PEIERLS,
9 September 1936
[Typewritten]
15, K0BENHAVN 9. September 1936.
UNIVERSITETETS INSTITUT
BLEGDAMSVEJ
FOR
DEN
0.
TEORETISK FYSIK
Lieber Peierls, Ich bedaure, dass ich Ihrem freundlichen und interessanten Brief nicht fruher beantworten konnte, weil Kalckar und ich erst vor kurzem von einer skandinavischen Naturforschertagung in Finland zuruckkamen. Inzwischen haben Sie sicherlich die Artikel von Bethe in Physical Review” gesehen, von der wir schon vor einigen Monaten durch Placzek horten, aber erst jetzt haben naher kennen gelernt. Bethes Uberlegungen sind wohl im Prinzip ahnlich wie die, Sie angestellt haben, und die mit seinen Rechnungen weniger eng verknupfte Diskussion der empirischen Daten uber gerade und ungerade Kernen U.S.W. scheint uns durchaus vernunftig. Die Abschatzung, die Bethe und Sie unter Annahmen der unabhangigen Bewegung der Kernteilchen gemacht haben, ist ja sehr interessant, aber die Begrundung, die Bethe fur die Ubereinstimmung mit den empirischen Befunden gegeben hat, scheint uns wenig durchsichtig zu sein. Ich war daher interessiert zu sehen, dass Sie meine Uberzeugung zu teilen scheinen, dass eine mehr tiefgehende Analyse des Niveauschemas nur durch ein naheres Studium der in meiner Nature Artikel als kollective bezeichnete Bewegungsart der Kernsubstanz moglich sein diirfte. Mit einem einfachen Vergleich der Schwingungen eines festen Korpers muss man aber schon deshalb vorsichtig sein, weil, wie ich bei der Konferenz betonte, die Amplituden der Kernbewegungen schon in den niedrigsten Niveauen von derselben Grossenordnung wie die Kerndimensionen sind. Auch haben wir die Konsequenz dieser Auffassung fur die y-Strahl-Erscheinungen naher untersucht und haben nicht nur in qualitativer Hinsicht (Quadrupolstrahlung), sondern auch in quantitativer Weise eine befriedigende Ubereinstimmung mit der durch Neutroneneinfang erhaltenen Abschatzung erreicht. Mit Ihrer Kritik der Bemerkungen von Bloch und Gamow” sind wir insbesonderen ganz einig; sie durfte, wie wir
” ”
Introduction, ref. 44. Introduction, ref. 59.
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auch hier im Institut diskutiert haben, auf einer ganz unzulassigen Deutung der Formalismus der Austauschkrafte beruhen. Wir werden uns bestreben, unsere Abhandlungs2 in kurzer Zeit fertig zu bringen und sollen Ihnen moglichst bald eine Kopie des Manuskriptes zugehen lassen. Falls Sie vorher beabsichtigen, einige von Ihren Uberlegungen zu publizieren, sol1 ich dankbar sein, wenn Sie uns freundlichst naheres daruber mitteilen wollen. Mit herzlichen Grussen von uns allen. Ihr Niels Bohr
BOHR TO PEIERLS,
17 October 1936
[Typewritten] 15, K0BENHAVN 17. Oktober 1936.
UNIVERSITETETS INSTITUT
BLEGDAMSVEJ
FOR
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0.
TEORETISK FYSIK
Lieber Peierls, ich war sehr interessiert in Ihrem freundlichen Brief vom 1 lten Okt. und glaube, dass unsere Ansichten uber den Kernzustand weitgehend ubereinstimmen. Ich hoffe aber im Laufe von etwa einer Woche Ihnen einen kleinen Aufsatz schicken zu konnen, den ich seit langerer Zeit in Vorbereitung gehabt habe, und in welchem ich meine allgemeinen Ansichten uber die Kernprobleme naher prazisiere. Wenn Sie ihn bekommen haben, wurde ich sehr froh sein Ihre Meinung daruber zu horen; und vielleicht ware es auch zweckmassig mit der Stellungnahme zu der Frage der Veroffentlichung Ihrer Ausfuhrungen bis dahin zu warten. Ubrigens haben Kalckar und ich eben einen kleinen Artikel uber die Zertrummerung des A l u m i n i u r n ~geschrieben, ~~ worin wir verschiedene, fur die Kernreaktionen charakteristische Zuge naher diskutieren, und von dem ich eine Kopie gleichzeitig mit dem erwahnten Aufsatz nach Cambridge schicken werde. Mit vielen herzlichen Grussen von uns allen Ihr Niels Bohr
’*Introduction, ref. 46. 53
Introduction, ref. 61.
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PEIERLS TO BOHR,
1949)
8 February 1938
[Typewritten] THE UNIVERSITY, EDGBASTON, BIRMINGHAM,
15.
d. 8.11.38. Lieber Herr Bohr, Vielen Dank fur Ihren Brief und fur die Kopie Ihrer Note54, die ich sehr uberzeugend fand. Wenn ich Sie richtig verstehe, so kommt jetzt also die Selektivitat des Photoeffekts in derselben Weise zustande, wie etwa die Absorptionsbanden eines festen Korpers, der ja auch in weiten Gebieten transparent sein kann, obwohl er in diesen Gebieten zweifellos Energieniveaus besitzt, die eben nur nicht mit dem Grundzustand kombinieren. Was die absoluten Grossenordnungen betrifft, so ist es zweifellos, dass Ihr Argument die alte Schwierigkeit uber die grossen Wirkungsquerschnitte beseitigt. Ich habe versucht, eine formale Ableitung der Formel zu geben, die Sie angeben, insbesondere um mich davon zu uberzeugen, dass fur verschwindende Neutronenbreite der (langlebigen) Kernzustande der Photoeffekt auch wirklich verschwindet (was er offenbar tun muss) und um zu sehen in welcher Weise er fur hinreichende Neutronenbreite in Ihre Formel ubergeht. Das ist mir bisher noch nicht ganz gelungen, aber ich mochte mir das gern weiter uberlegen, insbesondere rnit Hilfe einer formalen Methode zur Behandlung der langlebigen Zustande, von der Ihnen Placzek vielleicht erzahlt hat. Soweit ich die Frage bis jetzt ubersehen kann, erscheint es mir wahrscheinlich, dass die Form der Absorptionslinie nicht genau die einer naturlichen Linienbreite ist. Diese Form folgt nur dann wenn die Wahrscheinlichkeit der Umwandlung der Anregungsenergie aus dem speziellen rnit dem Grundzustand kombinierenden Wellenpaket in langlebige Zustande davon unabhangig ist, wie weit die Umwandlung bereits vorgeschritten ist (denn nur dann zerfallt der spezielle Zustand exponentiell mit der Zeit). Soweit ich bisher sehen konnte, gibt es keinen Grund, warum das in diesem Fall zutreffen sollte, und wenn man an die Analogie rnit einem festen Korper denkt, so hat man j a dort auch Absorptionsbanden deren Form komplizierter ist. Naturlich sind Ihre Resultate bis auf numerische Faktoren \ion der Form der Linie unabhangig. Es war mir auch nicht ganz leicht zu sehen woraus Sie schliessen, dass die Breite der Linie ungefahr gleich der Breite der y-Strahlen ist, aber offenbar haben Sie da noch experimentelles Material benutzt, das mir nicht bekannt ist. Es wurde mich sehr interessieren, o b Sie rnit meiner Bemerkung uber die Li54
Introduction, ref. 79.
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nienform einverstanden sind. Sie hat naturlich keine Bedeutung fur praktische Resultate, kann aber fur die Auswahl einer geeigneten Methode fur die mathematische Behandlung von Interesse sein. Mit nochmals vielem Dank und vielen Grussen, auch von meiner Frau und auch an Frau Bohr, Ihr R. Peierls
BOHR TO PEIERLS,
6 June 1939
[Typewritten] UNIVERSITETETS INSTITUT FOR
15, KQBENHAVN June 6th 1939.
BLEGDAMSVEJ
DEN
0.
TEORETISK FYSIK
Dear Peierls, I thank you for your kind letter and need not say how happy I am to know - as I first heard from Cockcroft a few days ago - that Landau is now back in Kapitza’s Institute and has taken up work again. I look forward very much to come to Birmingham again and it shall certainly be a great pleasure to me to accept the kind invitation of Mrs. Peierls and you t o stay in your home, where I spent so delightful days on my last visit. I have been very thankful for your kind interest then in my little article on the human cultures and I hope that you were fairly satisfied with the final form of the article when it appeared in “Nature””. On my next visit I should be very happy if we could work in [for] a few days together on a brief note to “Nature”56 about the main results of our common work on the nuclear dispersion theory and, if it would suit you, I shall be glad to come to Birmingham about the 28th of June. Due to the unquiet times and my unavoidable occupation with the fission problem I regret that I have not yet found opportunity to finish our article with Placzek but, as Placzek suggested, it would be nice if a short account of the results could appear in “Nature” in a near future, and I shall bring with me a draft Placzek and I have written. When we meet I hope also that we can arrange to work together some later quiet time to finish the greater article to appear in the Proceedings of the Danish Academy. Perhaps you could come to Denmark N.Bohr, NaturalPhilosophy and Human Cultures, Nature 143 (1939) 268-212. Reproduced (from the Congress Report) in Vol. 10. 5 6 Introduction, ref. 8 2 . 55
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for this purpose some time in August or September, but about that we can best speak when we meet in Birmingham. With kindest regards and best wishes to Mrs. Peierls and yourself from my wife and Yours, Niels Bohr
2 November 1947 [Typewritten with handwritten postscript]
PEIERLS TO BOHR,
DEPARTMENT OF MATHEMATICAL PHYSICS, THE UNIVERSITY, EDGBASTON,
15. 2nd November, 1947.
BIRMINGHAM,
Dear Uncle Nick5’, Here is, at last, the promised re-draft of the paper58. I was very disappointed that it took me so long to get it ready, but I struck a number of minor formal difficulties in the presentation. It also has increased somewhat in length, but I think it would be hard to say the same things in a substantially shorter paper. I am particularly sorry about the delay since, owing to difficulties with transportation, I have to leave for the United States already on 5th November, so that there is no hope of getting your comments before I leave. Your comments would reach me if they were sent c/o British Supply Office, P.O. Box 680, Benjamin Franklin Station, Washington D.C. to get there by 15th November, or c/o Bethe at Cornell, by the 18th. This applies in particular if there are any questions which you would like me to discuss with Placzek. Otherwise it would, of course, be quite all right for you to make any changes you wish and send the paper off. I hope to be back here on the 21st November. It may help if I add a few notes on my reasons for changes which I have made. (“Old draft” here refers to the typescript dated 9.10.47. which you sent me58a): Section 1. This is meant as a rough sketch, and you may like to change the wording of this. Section 2. This is substantially the old section 1, but with the discussion of the Breit-Wigner formula omitted, as we agreed. I have left in the discussion of the phenomena at very high energies, which, I believe, helps to complete the picture.
’-
“Uncle Nick” was a form of address started by Oppenheimer at Los Alamos where Niels Bohr had to use the pseudonym Nicholas Baker. 5 8 Introduction, ref. 89. ”“ Introduction, ref. 88.
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You were doubtful whether this should not be omitted. If that still is your view it can easily be taken out without breaking the continuity of the rest. I have added on p. 3, the point that the “potential scattering” need not be exclusively elastic. Section 3. This is the new section which gives an elementary derivation of the Breit-Wigner formula. I gave a misleading picture of this in Copenhagen by stating that four principles are involved. Actually the conservation theorem is not necessary for this purpose. Section 4. It seems more logical to discuss detailed balancing before the conservation theorem, and this required some slight changes in this section, which otherwise is just the old section 3. I have shortened somewhat the discussion of the precautions necessary in applying detailed balancing to quantum problems. It seems a satisfactory point of view that, in all cases in which the states of the compound nucleus can be described as definite states in the sense of the quantum mechanic formalism, the formalism automatically implies the law of detailed balancing, and it is therefore not necessary to construct an actual circular process which would violate the Second Law of thermodynamics if detailed balancing did not hold. (It must, of course, always be possible to construct such a process.) Section 5 . This is based on the old section 2. I have altered the mathematics slightly by retaining the complex scattering amplitude S I rather than splitting it at once into modulus and phase. This seems to make it a little easier to see how the potential scattering term enters in (32). On the potential scattering term itself, it seems to me unnecessary to regard the application of (32) to the potential scattering alone as approximate (old p. 14, bottom) since the potential scattering by itself should be defined as the solution of a definite wave equation. The interference between potential and “true” scattering would present no difficulty at all if the potential scattering were purely elastic. This was true in the very first draft of this part, in which the potential scattering was defined in a formal way based on the Peierls-Kapur equations. In the view now taken, which I regard as more satisfactory from a physical point of view, this is no longer true, but this leaves a certain amount of conjecture as regards the interference between inelastic potential and “true” scattering. A more precise answer could, however, come only from a much more quantitative study, including a definite model for the potential scattering, and I feel we ought not to attempt this at the present stage. I have also put back the generalization to particles with spin to a later point, so as to avoid introducing the quantity which in the old draft is called ~ A J The . reason is that in the case of spin one must consider, instead of one incident wave, a number of incident waves with different spin directions, which are incoherent,
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and which, in general, will have different phases. The cross section is then obtained by averaging. I believe therefore that an equation like (26) of the old draft could not be justified in the case of particles with spin, though, of course the inequality (35) with J in place of 1 must still hold. I have omitted the analogy with the scattering of light by a system of oscillators in a box. It seems to me that most readers would not be sufficiently familiar with the theory of this model to accept statements about its properties as obvious, and one would hardly want to present an extensive mathematical study of the model. I have also omitted the statement on the bottom of p. 12 of the old draft that in the continuous level region the phase is always that corresponding to full resonance. It seems hard to justify this in a convincing manner. In the pre-war draft of the paper, this statement was justified from the Peierls-Kapur formalism, but it depended again on a very formal, and probably inconvenient, definition of the potential scattering. Since the statement is not needed for the conclusion it seemed wiser to omit it. Section 6 is very short, and you may prefer to treat it as part of section 5. This can be done by just omitting the heading. With best wishes, Yours sincerely, R. Peierls Apologies for the typing, which is my own.
PEIERLS TO BOHR,
6 February 1948
[Typewritten] DEPARTMENT OF MATHEMATICAL PHYSICS, THE UNIVERSITY, EDGBASTON, BIRMINGHAM,
15.
6 February 1948. Dear Uncle Nick, I should probably have written before to say that I had a brief opportunity while I was in America to discuss the draft of our paper with Placzek. Placzek raised a number of small points that might want amending, but it seemed to us that as all these could be taken care of by alterations of a few words, they could well wait until we knew your reaction to the main outline. It has occurred to me that one of these points might be causing you difficulty and that it might save you trouble to draw your attention to it. It concerns the derivation of the Breit-Wigner formula. The derivation which I have sketched is valid only for
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that part of the resonance curve for which the kinetic energy of the emerging neutron (or other particle) differs only by a small fraction from its value at resonance. It does not cover either cases in which the width of the resonance level is comparable to the kinetic energy of the neutron at resonance or the crosssection for thermal neutrons ( l / u law). We tried to see whether it was easy to generalise the derivation so as to cover these cases as well, but we felt that this was not possible without spoiling the transparency of the argument, but that it was preferable, therefore, to leave the derivation as it stands and merely to make clear to what category of problems it is applicable. Since the purpose of the paper is mainly to deal with high energies, it would be quite reasonable to use an argument which is not appropriate for very low velocities. I am afraid that local arrangements made it necessary to take a decision on our plans for the summer about which I wrote to you before, and we have decided to go ahead with a conference here in the week starting 20th September. This will be a joint affair of the Physics and Mathematical Physics Departments. I very much hope that in doing so we are not clashing too badly with any plans you have in mind. With very best wishes to all friends in Copenhagen, Yours sincerely, R . Peierls BOHR TO PEIERLS,
22 August 1949
[Typewritten] 15, KQBENHAVN August 22nd, 1949
UNIVERSITETETS INSTITU’I
BLEGDAMSVEJ
FOR
DEN
0.
TEORETISK FYSIK
Dear Peierls, It has been a pleasure to me that it is now arranged that Lindhard will be with you next year. I am sure that it will be a great experience to him and I also hope that it will mean a still closer cooperation between our groups. As a small beginning I reckon that Lindhard’s stay with you will be helpful in completing our old work with Placzek. In the last weeks I have gone through the old manuscripts with Lindhard and discussed with him the latest progress as regards nuclear constitution and in particular the success of the method of considering the binding of the nucleons separately in the nuclear field. I realize that one sometimes has taken the drop model too literally and, to clear my thoughts, I have written down a few tentative comments5’ of which I shall be very glad to hear your opinion. 59
Introduction, ref. 147.
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They do not contain much new, but I feel that the development gives a simple basis for the treatment of the problems of nuclear reactions and removes doubts as regards the conclusions to be drawn from dispersion theory and detailed balancing. As soon as I get time, I will try to incorporate such views in our old manuscript and will, if not before, give it to Lindhard when he leaves. This summer I have been busy with the preparation of a series of lectures on general topics, which I shall deliver in Edinburgh in the autumn and have also worked with Rosenfeld o n the completion of our work on the measurability of field and charge quantities6'. It has come out that the situation is just as required by Schwinger's formalism and that it is simpler than assumed by Heisenberg in that respect that charge fluctuations are well defined in sharply limited space-time extensions, just like field fluctuations. Also this work I hope to complete in the autumn months. As you may understand, it will be quite a busy time for me and, if it is not too inconvenient to you, I should be glad if Lindhard could stay here until I leave for Edinburgh in the middle of October or in any case till the end of September. With kindest regards and best wishes to your family and yourself from us all, Yours,
xed d2. 26 August 1949 [Typewritten with handwritten addition]
PEIERLS TO BOHR,
DEPARTMENT OF MATHEMATICAL PHYSICS, THE UNIVERSITY, EDGBASTON, BIRMINGHAM,
15.
26th August 1949. Dear Uncle Nick, Thank you for your letter. It will be quite all right for Lindhard to come here in the middle of October. I gather from Born that your lectures in Edinburgh will have longish intervals between them and this makes me wonder whether there might be a chance of your spending a little while in Birmingham while you are in this country. It would, of course, give us the greatest pleasure if that were possible and we would be able to look after the expenses arising from such a visit. However, you need not decide this now. I have read your note with great interest, but I am afraid I do not agree with N . Bohr and L. Rosenfeld, Field and Charge Measurements in Quantum Electrodynamics, Phys. Rev. 78 (1950) 794-798. Reproduced in Vol. 7.
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some of the points. If I understand correctly the argument on the second page, you deduce from the large indeterminacy of position that it is possible to describe the motion of each particle as if it were moving in a smooth field of force. I do not believe that this conclusion is correct. At least if one assumes the forces between the nucleons t o be of the type usually assumed (i.e. two-body forces, partly of exchange character, and compatible with the properties of light nuclei) then the attempt to find the best potential to represent the motion has been carried out by Euler6’ for a nuclear force obeying a Gaussian law and by Huby6* for the “meson potential”. Both have calculated the higher approximations which take into account the correlations between individual nucleons and find that these higher terms are by no means small and severely alter the magnitude of the total binding energy. This tends to prove that, while the potential energy of a particle does not depend much on its position relative to the centre of the whole nucleus, it does depend decisively on its position relative to the neighbouring nucleons. It is in the nature of exchange forces that this kind of correlation becomes particularly strong since each nucleon tends to be coupled strongly with only three others. Now in the last few months we have seen evidence that properties of nuclei could be described very well by means of a “shell model” which would seem to contradict the conclusion about the importance of correlations. Supposing that this evidence is really conclusive it would mean either that the nuclear forces are not of the kind which are now generally accepted, or that there exists some other way of describing the motion in which the correlations are not neglected and in which, nevertheless, the energy values can be put in correspondence with the shell model. I think it is important to face this difficulty and to recognize that with at least the usual assumptions about nuclear forces the uncertainty in the position is not sufficient to make the shell model a good approximation. For the same reason I am not very happy about the view you take at the end of the second page, in which the capture of a particle into the nucleus proceeds first by way of a stationary state in a smooth potential. In a formal way one can, of course, always consider such states with limited life-time due to the possibility of exchange of energy between the nucleons. I should expect, however, that in the energy region corresponding to the capture of a neutron of few MeV, the lifetime of such a state would be so short that it would not be very helpful in describing nuclear processes. However, at much higher excitation energies it may well H. Euler, Uber die Art der Wechselwirkung in den schweren Atomkernen, Z. Phys. 105 (1937)’ 553-575. 62 R . Huby, Investigations on the Binding Energy of Heavy Nuclei, Proc. Phys. SOC. London A62 ( 1 949) 62-7 1.
6‘
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be that such states would help to understand the maxima and minima in the excitation curves found, for example, by Pollard and his collaborators at Yale. Kindest regards, from all of us and also to Mrs. Bohr, Yours sincerely, R.E. Peierls 7 December 1949 [Typewritten with handwritten postscript]
PEIERLS TO BOHR,
DEPARTMENT OF MATHEMATICAL PHYSICS, THE UNIVERSITY, EDGBASTON,
15. 7th December 1949.
BIRMINGHAM,
Dear Uncle Nick, I have made provisional arrangements to fly to Copenhagen on the morning of 2nd January (there is no suitable plane on the 1st) and if this arrangement is still convenient to you I shall arrive in Copenhagen about 3.30 p.m. I shall be needed again in Birmingham on 9th January and so will probably have to leave on the 8th. It may help if I put down a few points that I did not have time to explain adequately either here or at Edinburgh. It seems to me that the contents of the paper as at present drafted are largely, if not entirely, independent of the model one makes of the nucleus, though the values one would tend to guess for the various constants occurring in the equations do, of course, depend very much on the model. In the past there has been a tendency to confuse the two matters, i.e. to identify the model that you first proposed of a nucleus, with the mathematical formalism developed to investigate this model, which, however, is far more general. For this reason I entirely agree that it would be desirable in the introduction to explain this and to say also that one should now have an open mind about the model and that the experimental facts about “magic numbers” and the success of the theory of J e n ~ e nand ~~ Goeppert-Mayera are vital pieces of evidence. However, the question of what exactly one must conclude from these things is, to my mind, essentially unsolved. In earlier correspondence I insisted that it was not correct to regard each particle as moving in the average field of the others, if our present views about the forces were anything like correct. This, however, does not prove that one cannot get a shell structure out of the present h3 (J
Introduction, ref. 146. Introduction, ref. 145.
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forces. It might be possible, at least in the case of one single nucleon outside a closed shell, to find a picture describing it as a particle moving in a suitable field of force which would, however, not be the average potential of the others. The situation is reminiscent of that in field theory, where one gets large errors (and indeed infinities) if one regards the disturbance caused by the electron in the field as small. We are now learning how to take into account the disturbance which inevitably accompanies an electron and in some sense this is the meaning of “renormalization”. One might hope in the nucleus equally to think of the motion of a nucleon in an otherwise saturated nuclear fluid, taking into account the disturbance it will locally cause in it, and this might lead to a reasonable onebody picture. I am, therefore, not sure that there is enough evidence on which to say we must abandon our present picture of the forces, but equally it is not certain that we can retain this picture and, while I am most anxious to discuss these problems with you and see what progress one can make, I feel that for the present paper it would be wiser to admit the existence of unsolved problems rather than to attempt a complete answer in this context. Yours very sincerely, R.E. Peierls We greatly enjoyed your brief visit. I am looking forward to the days in Copenhagen, but please say quite frankly whether this is still convenient. If you would rather leave it until you pass through this country, this would be very nice for me, too.
BOHR TO PEIERLS,
17 December 1949
[Typewritten] UNIVERSITETETS INSTITUT FOR
15, K0BENHAVN 17th December 1949.
BLEGDAMSVEJ DEN
0.
TEORETISK FYSIK
Dear Peierls, Thank you very much for your kind letter. I was most interested in your remarks about the nuclear problem and I look forward very much to discuss the whole situation thoroughly with you. I have, however, not been quite well since my return and had to be in bed for some days with a bad cold and have not been able to get as far with my obligations as I had reckoned. Now it has all come so that Rosenfeld has had to postpone his visit to Copenhagen to revise the proof
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of our paper65till New Year’s time and on your question I may therefore say that it might be best to postpone our work a little further till I come back to England. About the arrangement I will speak to Lindhard whom we expect back for X’mas and with whom we all are looking forward to talk about all your work in Birmingham. When he has arrived and I know a little more of my plans I shall write again. With kindest regards and best wishes for X’mas and the New Year to you and your family from us all, Yours, Uncle Nick
EBBE RASMUSSEN66 BOHR TO RASMUSSEN,
14 February 1939
[Typewritten] THE INSTITUTE FOR ADVANCED STUDY SCHOOL OF MATHEMATICS FINE HALL PRINCETON, N E W JERSEY
14 Februar, 1939 Kzre Dr. Rasmussen, Tak for Deres rare Brev af 21 Januar. Jeg ferlger jo alt paa Instituttet med st~lrsteSpznding, og i s z r den sidste Udvikling vedrerrende de nye Kernesprzng“ S e e ref. 60.
‘‘ Ebbe Kjeld Rasmussen (12 April
1901 - 9 October 1959). Danish experimental physicist. Graduated (cand. mag.) from the University of Copenhagen in 1926 and worked from 1926 to 1928 as a research assistant at Denmark’s Technical University, partly with problems related to medical applications. In 1928 Bohr offered him a post as research assistant at his institute where Rasmussen uorked until 1942, when he was appointed professor at the Royal Danish School of Veterinary Sciences and Agriculture. He obtained his doctorate (dr. Phil.) in 1932 for a thesis on the spectra of the noble gases. In 1956 he was appointed professor at the University of Copenhagen. He was elected to fellowship of the Royal Danish Academy in 1951 and was elected secretary of the Academy in 1959, shortly before his death. Rasmussen’s research interests lay above all within the area of spectroscopy and most of his papers deal with experimental studies of the fine structure and hyperfine structure in the spectra of a wide range of elements and isotopes. Obituaries by N. Bohr, V. Middelboe, J . M . Lyshede (all in Fys. Tidsskr. 58 (1960) 1-9), by J. Koch (Akademiet for de tekniske Videnskabers Arsskrift, 1960), and by J.K. Bmggild (Overs. Dan. Vidensk. Selsk. Virks. Juni 1959 - Maj 1960, pp. 117-123).
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ninger. Som De sikkert har forstaaet af mine mange Telegrammer blev jeg bragt i temmelig stor Forlegenhed ved i saa mange Uger intet at herre om Frisch’s vigtige Forserg. Straks efter at Hahn’s Opdagelse6’ og Frk. Meitner’s og Frisch’s Forklaring blev bekendt herovre, blev der naturligvis ivarksat lignende Undersergelser i omtrent alle amerikanske Laboratorier, og jeg maatte selv ved Konferencen i Washington den 28 Januar overvare de ferrste Forserg med Kernesprangninger, uden at ane, at Frisch allerede den 12 Januar havde gennemferrt langt mere overbevisende og fuldstandigere Undersergelser og endda den 16 Januar sendt et Brev ti1 Nature68derom. Ferrst den 30 Jan. fik jeg gennem en tilfaldig Bemarkning i et Brev fra Hans ti1 Erik6’ at vide om Forsergene, og jeg har siden hver Dag maattet t a n k e paa, hvor meget bedre alt vilde have varet kommet, hvis man fra Instituttet blot som aftalt straks havde telegraferet om alt vigtigt, eller blot endda, som jeg saa udtrykkeligt bad om, altid straks vilde sende mig Eksemplarer af alle Manuskripter ti1 Offentliggerrelse fra Instituttet. Som Forholdene ligger nu, har man ikke alene med Rette kunnet hzevde, at Forsergene herovre har vzeret foretaget ganske uafhangigt, men man er endda, efter min Mening ganske med Urette, fra forskellig Side gaaet saa vidt at paastaa, at selve Forklaringen af Hahn’s Forsag for enhver Fysiker maatte v a r e en fuldstandig Selvferlgelighed. I mine Bestrabelser paa at sikre at Frk. Meitner og Frisch faar den fortjente Anerkendelse for deres afgerrende Bidrag ti1 den nye vidunderlige Udvikling, har jeg paa det sidste Punkt maattet kzempe imod manglende Forstaaelse hos flere frernragende Fysikere, som Ferlge af den for dem ganske ubegribelige Situation, at jeg saa lange stod helt uden Underretning om de vigtige Opdagelser i Kerbenhavn. Her var jo saadant ganske utznkeligt, og som De vist har herrt indeholdt alle de store amerikanske Aviser allerede den 30 Jan. yderst begejstrede, ja fantastiske Beretninger om Forsergene herovre. Ikke alene for mit eget Arbejde her, men ferrst og fremmest for Instituttets Skyld er det aldeles afgerrende at jeg holdes fuldstzendigt a jour med alt vigtigt der foregaar i Kerbenhavn, saavel hvad Forsergsresultater, som hvad Arbejdsplaner paa alle Omraader angaar, og jeg maa sige at baade Rosenfeld og jeg med stor Skuffelse fra Dag ti1 Dag har ventet paa nye Telegrammer, som Svar paa mit lange Telegram af 4 Februar. Dersom De og Fru Schultz mener at Omkostningerne ved saadanne Telegrammer - - - jeg vil gerne have mindst et night-letter om Ugen - - er vanskelige at opferre paa Maanedsregnskabet skal jeg nok ordne det selv paa anden Maade naar jeg kommer hjem. Jeg beherver j o ikke i denne Forbindelse at sige, hvor taknemmelig jeg er for den store Indsats alle paa Instituttet og i s a r 67
69
Introduction, ref. 96. Introduction, ref. 98. Bohr’s sons.
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Frisch har gjort i de sidste Tider, jeg er ogsaa fuldstandig forberedt paa, at alle Laboratoriets Midler indenfor rimelige Grznser anvendes paa at drive de nye Undersergelser baade med Neutroner, Deuteroner og Photoner med sterrst mulig Kraft og jeg vil v z r e meget taknemmelig for, om De talte indgaaende med Frisch om, hvordan dette bedst lader sig gare. Naturligvis vil i s z r Prof. Hevesy’s Raad her v z r e af sterrste Betydning, og jeg er spz ndt paa, hvad han mener, der kan gerres paa Instituttet med Hensyn ti1 de kemiske Problemer, der rejser sig i denne Henseende. Det var ogsaa paa hans Indsigt og Deltagelse i Undersergelserne at min Bemzrkning i Telegrammet om (anskeligheden af at benytte Bly af forskellig Isotopsammensztning sigtede. Som det fremgaar af min lille Note ti1 Phys. Rev.”, som jeg sendte Frisch for nogle Dage siden, er der nemlig Mulighed for, at man vil finde en stor Forskel hos Isotoper med lige og ulige Neutrontal. Jeg skal nok fra min Side gerre alt for at holde Dem underrettet paa Instituttet om den teoretiske Udvikling, men i 0jeblikket maa naturligvis Hovedvagten lagges paa at gerre Forserg under de mest varierede Betingelser. Baade Rosenfeld og Erik, der som De kan t a n k e nyder alle Oplevelserne herovre, sender sammen med mig de venligste Hilsner ti1 Dem selv og Deres Familie og alle paa Instituttet. Deres hengivne Niels Bohr P.S. Med Hensyn ti1 Anerkendelsen af Frk. Meitner’s og Frisch’s store Indsats er jeg sikker paa at alt, trods midlertidige Vanskeligheder, vil ende paa bedste Maade og jeg haaber i sz r at mine smaa Noter i Nature’l og Phys. Rev. vil bidrage ti1 at give den videnskabelige Offentlighed den rette Opfattelse af Forholdene.
Translation Princeton, 14 February 1939 Dear Dr. Rasmussen, Thank you for your good letter of 21 January. I do follow everything in the Institute with the greatest interest, and particularly the latest development concerning the new splitting of nuclei. As you have no doubt gathered from my many telegrams I found myself in rather great embarrassment through not having heard anything for so many weeks about Frisch’s important experiments. As soon as Hahn’s discovery6’ and its explanation by Miss Meitner and Frisch -11
Introduction, ref. 115
-’ Introduction, ref. 99.
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became known here, similar investigations were naturally undertaken in almost all American laboratories, and I was myself in the position to see at the conference in Washington the first experiments on nuclear fragments without knowing that already on 12 January Frisch had carried out a far more convincing and complete investigation, and had even sent a letter to Nature6’ about it on 16 January. The first I knew of these experiments was on 30 January, from a casual remark in a letter from Hans to Erik6’, and I had to think since then every day how much better everything would have come out if one had only cabled me immediately from the Institute about anything important, as we agreed, or even only sent me directly copies of all manuscripts for publication from the Institute, as I explicitly requested. As things stand now, one has not only been able to claim, rightly, that the experiments over here were done independently, but one has even gone so far, from various sides, as to claim, in my view wrongly, that the very interpretation of Hahn’s experiment was necessarily self-evident for every physicist. In my endeavours to ensure that Miss Meitner and Frisch are given the deserved recognition for their decisive contribution to the new wonderful development, I had to fight, on this latter point, with a lack of understanding on the part of many outstanding physicists, as a result of the situation, which was for them quite incomprehensible, that I was for so long entirely without information about the important discoveries in Copenhagen. Here this would be unthinkable, and as you surely have heard, already on 30 January all the major American papers had highly enthusiastic, and even fantastic, reports on the experiments done over here. Not only for my own work here, but above all for the sake of the Institute, it is quite vital that I be kept completely up to date about everything important that happens in Copenhagen, both about experimental results and about the plans for the work in all fields, and I must say that both Rosenfeld and I have waited with disappointment from day to day for further telegrams in reply to my long telegram of 4 February. In case you and Mrs. Schultz think that the expense of such telegrams will be difficult to include in the monthly account - I would like to have at least one night letter a week - I can arrange that myself in some other way when I get back. I need not say in this connection how grateful I am for the great contributions everybody in the Institute, and particularly Frisch, have made lately; I am also quite prepared to have all resources of the laboratory within reasonable limits used for pushing the new investigations, both with neutrons, deuterons and photons, ahead as strongly as possible, and I would be very grateful if you could discuss with Frisch in detail how best to d o this. Here, of course, Prof. Hevesy’s advice will be of the greatest significance, and I wonder what he thinks can be done in the Institute about the chemical problems arising in this connection. It was also his insight and participation that I had in mind in the remark in my telegram about the desira-
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bility of using lead with various isotopic compositions. As is clear from my little note to the Phys. Revs7' which I sent to Frisch a few days ago, there is a possibilit y that one will find a large difference between isotopes with even and odd neutron numbers. From my side I shall do everything to keep you in the Institute informed about theoretical developments, but for the moment the main emphasis must naturally be on doing experiments under the most varied circumstances. Both Rosenfeld and Erik, who, as you can imagine, enjoys all the experiences over here, join me in sending the kindest regards to yourself and your family and everybody in the Institute. Yours sincerely, Niels Bohr P.S. As regards the recognition of the great contribution by Miss Meitner and Frisch, I am sure that, in spite of temporary difficulties, all will end in the best way, and I hope, in particular, that my little notes in Nature7' and in Phys. Rev. will contribute to giving the scientific public the right view of the position.
20 February 1939 [Typewritten with handwritten addition]
RASMUSSEN TO BOHR,
15 , KQBENHAVN 0 . 20. Februar 1939.
UNIVERSITETETS INSTITUT
BLEGDAMSVEJ
FOR
DEN
TEORETISK FYSIK
Kaere Professor Bohr, Selv om vi ikke har holdt Merde i de sidste Par Uger, dels paa Grund af Professor Hevesys Bortrejse og dels paa Grund af den store Travlhed paa Instituttet med Uranspaltningen, vil jeg dog supplere de telegrafiske Efterretninger med et ganske almindeligt Brev. Det har jo vaeret en spaendende Tid ogsaa her paa Instituttet, og vi har alle i h0j Grad f0lt Savnet af vor Chef ti1 at lede Arbejdet ind i de rette Baner og ti1 at fremskynde Publikationerne. Frisch's Note er ferrst kommet i NATURE i Dag, hvilket jo er over en Maaned efter Indsendelsen, men det er der jo ikke noget at g ~ r eved. Om Arbejdets Fremadskriden, siden Frisch afsluttede sine Forsag, er der det at berette, som allerede telegraferet, at Frisch sammen med H~jspandingsfolkene har gentaget Uran- og Thoriumspaltningen med Neutroner fra en Lithiumtarget bestraalet med Deuteroner ved 700 000 Volt, hvilket gik glat. Derimod viste Stofferne fra Pt ti1 Bi ingen Effekt. Dernast gik de over ti1 Protoner for
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at se, om ogsaa 17 Mill. Volts y-Straaler kunde frembringe Effekten. Paa Grund af Neutronerne fra Resterne af Deuterium var det nadvendigt at optage en Udbyttekurve ved voksende Spzndinger, da y-Straaling jo satter skarpt ind ved 450 000 Volt. Hvis Effekten overhovedet findes, er den imidlertid uhyre svag. Efter Professorens Telegram forsager de nu at arbejde efter de deri angivne Retningslinier og udskyder derfor Afgarelsen af y-Straale-Effekten ti1 senere. Ogsaa Cyclotronen har vzret nzsten uafbrudt i Gang i mange Dage, idet Jacobsen har lavet Uranspaltninger med 4,5 Mev Deuteroner (ca. 1 Microampere), hvilket tilsyneladende ogsaa gik fint. Han bestraalede en Pille af Uranoxyd og opsamlede Recoil-Stumperne paa en Blyplade anbragt t z t ved og genfandt ogsaa de af Hahn fundne Perioder. Derved kom Jacobsen ganske uafvidende ti1 at lave et Forserg, som Frisch og Frk. Meitner egentlig havde aftalt at ville foretage her paa Instituttet i den kommende Uge. Imidlertid har de sidste Par Dages intensive Arbejde ogsaa vist Effekt for mange andre Stoffer, saa han i 0jeblikket ikke er sikker paa, at det virkelig har varet Recoil-Atomer, men maaske en eller anden Forureningseffekt. Det vil vel nok blive afklaret i Labet af den kommende Uge. Frisch er i Stockholm i disse Dage for at modtage sine Forzldre, men skulde komme igen i Morgen. Hvis Frk. Meitner kommer med, skulde de jo nok ved forenede Krzfter kunne klare Problemerne. Der har endnu ikke vzret det mindste i de danske Aviser om Uranspaltningen. Derimod er vi blevet ringet op af Magister Rosenkjzr og Ing. Bergsae, der har faaet Nys om Sagen og derfor gerne vil have en Radioudsendelse derom i en n z r Fremtid. Den skulde nzsrmest forme sig som en Samtale mellem Bergsere og nogle af Medarbejderne (Frisch, Jacobsen), og hvis det bliver ti1 noget, skal vi nok gare alt for, at det skal blive saa sagligt som muligt. Af praktiske Sager maa jeg n m n e , at Statspolitiet nu er gaaet over ti1 kun at give Opholdstilladelse for Emigranter for 3 Maaneder ad Gangen. Selv Frisch, der j o altid hidtil fik sin Opholdstilladelse fornyet hvert halve Aar, har denne Gang kun faaet for 3 Maaneder, d.v.s. ti1 i Begyndelsen af Maj, og dette opnaaedes endda farst efter, at Statspolitiet ringede Fru Schultz o p og meddelte, at Justitsministeriet havde sendt Frisch’s Ansagning tilbage med Forespargsel om, hvorvidt der var foretaget Skridt ti1 Frisch’s videre Udvandring. Fru Schultz opnaaede imidlertid ved Henvisning ti1 Professorens Fravzrelse at faa Sagen udsat indtil Professorens Hjemkomst i Begyndelsen af Maj. (Frisch selv ved ikke noget om denne Samtale.) Endvidere maa jeg fortzlle, at Werners atter har v m e t her i Byen, og at han betroede mig, at han nu havde sagt sin Afsked ved Lareanstalten, samt at hans Professorat formentlig vilde blive besat nu i Labet af Foraaret. Det bliver spandende, hvem der sager, og navnlig hvem der faar det. Professoren har vel hart om Prof. S.P.L. Sarensens Dad. Der maa altsaa ti1
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Efteraaret indvzelges et nyt Medlem i Direktionen for Selskabet for Naturlzrens Udbredelse (Prof. Bjerrum?). Ellers tror jeg ikke, at her er mere af Betydning at berette fra Instituttet. Mit eget Arbejde med Hafnium skrider stadig godt fremad, og jeg glzder mig unzegtelig ogsaa ti1 snart at faa en Afslutning paa det. Og endelig kan jeg navne den mindre betydningsfulde, men for Merller og mig dog glzdelige Ting, at vi nu har Kontrakt med et hollandsk Forlag om vor Bog, der forervrigt her er udkommet i 2 . Oplag, og at der ogsaa foreligger Foresp~rgslerfra Tyskland og England. Hermed vil jeg slutte for denne Gang med mange Hilsener fra alle paa Instituttet ti1 Dem, Prof. Rosenfeld og Erik. Deres hengivne Ebbe Rasmussen. Ogsaa mange venlige Hilsener fra mig. Betty Schultz.
Translation Copenhagen, 20 February 1939 Dear Professor Bohr, Although we have not held any meetings during the last couple of weeks, partly because of Professor Hevesy’s absence, and partly because the Institute was so busy with the uranium splitting, I shall still supplement the telegraphic reports with a quite general letter. This has really been an exciting time, also here in the Institute, and we have all felt very strongly the absence of our boss to lead the work in the right directions and to accelerate the publications. Frisch’s note appeared in Nature only today, which is actually over a month after its submission, but there is nothing to be done about that. About the progress of the work since Frisch concluded his experiments, it can be reported, as already mentioned in a telegram, that Frisch, together with the high-tension people, repeated the splitting of uranium and thorium with neutrons from a lithium target irradiated with 700 000 volt deuterons, which worked smoothly. Substances from Pt to Bi, on the other hand, showed no effect. Next they went over to protons to see whether 17 MeV y-rays could also produce the effect. Because of the neutrons left over from the deuterium it was necessary to take a yield curve with increasing voltage, since the y-rays set in suddenly at 450 000 volts. If the effect exists at all it is however extremely weak. After your telegram they are now trying to work according to the guidelines given there and have therefore postponed the conclusion of the y-ray experiments till later.
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The cyclotron, too, has been working almost incessantly for many days, as Jacobsen has done the uranium splitting with 4.5 MeV deuterons (about 1 microamp), which apparently also went well. He irradiated a pellet of uranium oxide and collected the recoil fragments on a lead plate placed nearby, and also recovered the periods found by Hahn. Thus Jacobsen happened quite unwittingly to do an experiment which Frisch and Miss Meitner had really planned to carry out here in the Institute next week. However, the intensive work of the last few days has also shown the effect for many other substances, so that at the moment he is not sure whether these were really recoil atoms, or perhaps some kind of impurity effect. This will no doubt be cleared up in the course of next week. Frisch is in Stockholm at the moment to meet his parents, but should be back tomorrow. If Miss Meitner comes with him they could no doubt clarify these problems with a combined effort. There has not yet been the slightest mention of the splitting of uranium in the Danish papers. However, we had a call from Magister Rosenkjcer and Engineer Bergscae, who have heard about the matter, and would therefore like to have a radio programme about it in the near future. This should preferably take the form of an interview between Bergscae and some of the collaborators (Frisch, Jacobsen) and if something comes of this we shall do everything to make this as objective as possible. About practical matters I should mention that the state police have now started to give residence permits for emigrants only for 3 months at a time. Even Frisch, who up to now always had his residence permit renewed every six months, has this time been given it only for three months, i.e., until the beginning of May, and even this was achieved only after the state police phoned Mrs. Schultz and informed her that the Ministry of Justice had sent Frisch’s application back with the query whether any steps had been taken for Frisch’s further emigration. Mrs. Schultz referred, however, to your absence and succeeded in getting the matter postponed until your return in the beginning of May. (Frisch himself knows nothing of this conversation.) I should also report that the Werners have again been here in town, and that he confided to me that he has now submitted his resignation from the Technical University, and that his professorship will presumably be filled in the course of the spring, It will be exciting to see who will apply, and particularly who will get it. You will presumably have heard of the death of Professor S.P.L. Scarensen. There should then be in the autumn an election of a new member of the Board of Directors of the Society for the Dissemination of Natural Science (Professor Bjerrum?). Otherwise I do not think that there is anything else of importance to report
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from the Institute. My own work with hafnium is still making good progress, and I cannot deny that I will be glad to see the end of it. Finally I can mention the less important, but for Msller and myself pleasing news, that we now have a contract with a Dutch publisher for our book, which incidentally has appeared here in a second edition, and that there are also enquiries from Germany and England. With this I shall close for this time with many greetings from everybody in the Institute to you, Professor Rosenfeld and Erik. Yours sincerely, Ebbe Rasmussen Also many kind regards from me. Betty Schultz.
RASMUSSEN TO BOHR,
24 February 1939
[Typewritten] Kbhvn. 24. Feb. 1939. K a r e Professor Bohr, Mange Tak for Deres Brev af 14. ds., som jeg har modtaget i Dag. Jeg forstaar fuldstandig de Vanskeligheder, De har haft paa Grund af Frischs Forsammelighed med at holde Dem underrettet om sine vigtige Forssg, men vi stolede alle paa, at han selv havde sendt Besked, som han havde lovet 0s. Men efter denne kedelige Sag har jeg gjort, hvad jeg kunde, for at faa sendt Telegrammer, saa mart der forelaa Resultater, idet jeg daglig interviewer begge Arbejdsgrupper, selv om det maaske derved bliver opfattet, som om jeg stikker min N a s e i Sager, der ikke kommer mig ved. Jacobsen har haft et Uheld med Cyclotronen, som maatte skilles ad og renses, men nu virker den igen. Deuteron-Effekten er bekraftet for Uran, men endnu ikke forssgt for Thorium, hvilket dog vist er n m t e Punkt paa Programmet. Derimod kniber det vist stadig med at blive sikker paa Recoil-Fanomenet for Uran. Og i Dag har Frisch og Frk. Meitner, som lige telegraferet, lavet RecoilForssgct saa at de alligevel synes at komme f s r Jacobsen dermed. Da Bjerge” har lovet ogsaa at skrive i Aften, behsver jeg vist ikke at omtale Forsergene i Hsjspandingshallen. Torkild Bjerge (8 March 1902 - 7 February 1974). Danish experimental physicist. Graduated in 1926 as chemical engineer from Denmark’s Technical University where he worked as a research assistant at the physical laboratory from 1928. He received his masters degree (mag. scient.) in physics in i2
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Det har nu vist sig at v a r e rigtigt, at Professoratet paa Lareanstalten skal besattes nu, idet Ans~gningsfristenu d l ~ b e rd. 11 Marts. Det vides endnu ikke, om Jacobsen vil serge, hvorimod Bjerge og R.E.H. Rasmussen naturligvis s ~ g e r , da de vel maa anses for Favoritter. Hvis jeg indgiver en Ans~ gning,haaber jeg, at De vil forstaa, at det ikke er ensbetydende med, at jeg er ked af at v a r e ved Institutet. Hvis jeg ikke var Familieforserger, vilde jeg naturligvis aldrig serge bort herfra, hvor jeg har haft saa storartede Arbejdsvilkaar. Men der er nu ingen Fare for at jeg faar det. Af de Sager, vi har d r ~ f t e paa t vort ugentlige M ~ d ie Dag, vil jeg lige navne, at vi har talt om Indsamling ti1 en Gave ti1 O l ~ e n der ~ ~fylder , 50 i en n a r Fremtid, nemlig d. 6. April. Jeg skriver dette i saa god Tid, fordi jeg tror, at det vilde g la de Olsen allermest, hvis Professoren sendte ham en egenhandig Lyk~ nskning paa Dagen. Der blev ogsaa d r ~ f t e tMuligheden for at skaffe Olsen Dannebrogsordenen, selv om det vist egentlig er Skik ferrst at uddele denne efter 25 Aars lang og tro Tjeneste. Dette Forslag stammede markvardigvis fra J e n ~ e n ’ ~ , hvilket maaske forklares derved, at Jensen kun er et Par Aar yngre end Olsen, men har betydelig kortere Tjenestealder. Jeg skal nok skrive snart igen samt g ~ r emit bedste ti1 en effektiv Telegrafering. Mange venlige Hilsener ti1 Dem, Erik og Prof. Rosenfeld. Deres hengivne Ebbe Rasmussen
Translation Copenhagen, 24 February 1939 Dear Professor Bohr, Many thanks for your letter of the 14th, which I received today. I fully understand the difficulties which you had because Frisch neglected to keep you inform1931. Bjerge studied in Rutherford’s laboratory in Cambridge in 1934-1935 and in 1937 he was appointed research assistant at Bohr’s institute. He obtained his doctorate (dr. p h i [ . ) in 1938 for a thesis on artificial radioisotopes with short half-lives. He also participated in the building of the high tension equipment at the Institute. In 1939 he was appointed professor at Denmark’s Technical University, in 1955 he became a member of the Danish Atomic Energy Commission, and in 1956 he was appointed director of the Commission’s research plant at R i s ~ He . retired in 1970. Bjerge’s research interests lay within the areas of neutron physics (including fission) and induced radioactivity. Obituary by H . Hajgaard Jensen and F. Juul (Fys. Tidsskr. 72 (1974) 177-180). 7 3 Holger Olsen, laboratory master, had already started working at Bohr’s institute in 1920, before its official opening. 74 August Jensen had been appointed non-scientific assistant at Bohr’s institute in 1924.
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ed about his important experiments, but we were all confident that he had sent a message, as he promised us. But after this tiresome business I have done what I could to get telegrams sent as soon as there are results; I interview both working groups daily, even if this could be understood as if I was poking my nose into things which do not concern me. Jacobsen had a mishap with the cyclotron, which had to be dismantled and cleaned, but it is now working again. The deuteron effect is confirmed for uranium, but has not yet been tried for thorium, which I suppose is the next item on the programme. On the other hand there seem to be continuous difficulties in confirming the recoil phenomenon in uranium. And today, as has been cabled, Frisch and Miss Meitner have set up the recoil experiment, so that it seems they will nevertheless get there before Jacobsen. As Bjerge72 has promised t o write tonight, I think I need not describe the experiments in the high tension laboratory. It has now proved correct that the chair in the Technical University will be filled now, since the applications close on 11 March. It is not yet known whether Jacobsen will apply, whereas Bjerge and R.E.H. Rasmussen naturally will apply, since they may well be considered leading candidates. If I put in an application I hope you will understand that this does not mean that I am tired of being at the Institute. If I had no family responsibilities I would of course never try to leave from here, where I have had such outstanding working conditions. But there is no risk of my getting it. Of the matters discussed at our weekly meeting today I should also mention that we have talked about a collection for a gift to O l ~ e n ’ ~who , will be 50 in the near future, viz. on 6 April. I am writing about this so early because I believe that it would give Olsen the greatest pleasure if you could send him a personal note of good wishes in honour of the occasion. The possibility was also discussed of getting for Olsen the Dannebrog Order, although it probably is really the custom to award this first after 25 years’ faithful service. This proposal curiously enough came from J e n ~ e n which ~ ~ , is perhaps explained by the fact that Jensen is only a few years younger than Olsen, but has a substantially shorter length of service. I shall soon write again and shall do my best to achieve an effective despatch of telegrams. With friendly greetings to you, Erik and Professor Rosenfeld, Yours sincerely, Ebbe Rasmussen
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RASMUSSEN TO
(1929-1949)
BOHR,3 March 1939
[Typewritten] UNIVERSITETETS INSTITUT FOR
BLEGDAMSVEJ DEN
15,
KQBENHAVN 0.
3. Marts 1939.
TEORETISK FYSIK
K a r e Professor Bohr. Hermed sender vi en Afskrift af den som vi paa Professorens Forslag er begyndt at fore fra i Mandags, idet hver af de tre Arbejdsgrupper: Frisch-Meitner, H~j spa ndi ngsfolkog Cyclotronfolk hver Dag skriver et Par Linier om Arbejdet. Endvidere vil der stadig, saa mart der foreligger Resultater, blive sendt Telegrammer. Gennem Fru Bohr herrte jeg desuden, at Professoren tankte paa at give Frisch en Gageforhojelse, hvilket selvfolgelig er i h0j Grad fortjent. Men jeg synes dog, at der var rimeligt at vente, ti1 Professoren kommer hjem, i s a r da vi for Tiden er ved at skrabe Bunden af Kassen. Vi har heller ikke engageret yderligere Medh j a l p ti1 det videnskabelige Arbejde, hvilket imidlertid lige saa meget skyldes Manglen paa ledig kvalificeret Arbejdskraft. Hvis Professoren kunde medbringe et Par unge flinke Amerikanere, vilde det jo viere storartet. Med Hensyn ti1 det okonomiske maa vi maaske, hvis det bliver nodvendigt, foresperrge hos Insulinfondet eller eventuelt forsoge at faa et Carlsbergkvartal udbetalt fOr Tiden? Med venlige Hilsener ti1 Dem, Prof. Rosenfeld og Erik, Deres hengivne Ebbe Rasmussen
Translation Copenhagen, 3 March 1939 Dear Professor Bohr, We enclose a transcript of the journal7*which we started to keep last Monday at your suggestion, so that each of the three working groups: Frisch-Meitner, the high-tension people, and the cyclotron people, write daily a few lines about their work. In addition, telegrams will continue to be sent as soon as there are results. I also heard from Mrs. Bohr that you are thinking of giving Frisch a salary increase, which he of course amply deserves. It seems to me however that it would be reasonable to wait until your return, since at present we are about to scrape the bottom of the barrel. We have also not engaged any additional research assistants, though this is also largely due to the lack of available 75
These pages have not been included here.
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qualified personnel. If you could bring along a few young able Americans, this would be great. As regards the finances, may we perhaps, if necessary, apply to the Insulin Foundation, or perhaps try to get the quarterly Carlsberg money paid early? With best wishes to you, Professor Rosenfeld and Erik, Yours sincerely, Ebbe Rasmussen
10 March 1939 [Typewritten with a few handwritten additions]
BOHR TO RASMUSSEN,
THE INSTITUTE FOR ADVANCED STUDY SCHOOL OF MATHEMATICS FINE HALL PRINCETON, N E W JERSEY
10 Marts, 1939 Ksere Dr. Rasmussen, De kan tro at jeg var glad for i Morges at faa saa mange rare Breve fra Instituttet, baade fra Dem selv, Fru Schultz, Dr. Bjerge og Hevesy. Ogsaa fra In g e n i ~ rBergsere fik jeg et Brev med hele Radiointerviewet, som gik udmzerket igennem, og som det var mig en stor Glzede at hsre herovre. Jeg er jo mer end lykkelig paa Instituttets Vegne over det store Arbejde som Frisch og alle de andre har gjort, og jeg haaber at De alle har forstaaet Grunden ti1 den Utaalmodighed, som mine Breve og Telegrammer maaske har givet Dem Indtryk af; men det var jo kritiske Dage for mig i mine Bestrzebelser for at sikre Frk. Meitner og Frisch en rimelig Andel i &en for den store Opdagelse, og for at hjselpe ti1 at man fra Instituttets Side kunde gerre en Indsats paa det nye Omraade, der i nogen Grad svarede ti1 de udmzerkede Krzefter, der er knyttede dertil, og de store Hjzelpemidler, som vi paa Grund af den megen Stertte raader over. Naturligvis er det ikke efter min Mening at der paa nogen Maade skal jages med Unders~gelserne, og man skal jo heller ikke tage bogstaveligt hvad jeg har skrevet om daglige Optegnelser og stadige Telegrammer, men blot gaa frem efter den bedst mulige Plan, og holde mig underrettet gennem Telegrammer og Breve om alt af szerlig Interesse for mig selv og de mange Fysikere som jeg staar i saa nser Forbindelse med herovre. Navnlig tzenkte jeg j o paa at det maaske var svzert for Dem hjemme at danne sig den rette Forestilling om de nzesten ubegrzensede Hjzelpemidler, som de nzesten utallige Fysikere herovre arbejder med, og den Begejstring, hvormed de nye Fzenomener overalt er taget op ti1 Undersagelse, samt den Iver, hvormed disses Forklaring diskuteres imellem Teoretikere
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herovre. Netop den Tvivl, som i hvert Tilfalde ti1 at begynde med fremsattes af Fermi angaaende de Retningslinier, der foresloges i Frk. Meitners og Frischs Note og paa hvis Videreferrelse jeg selv har gjort et stort Arbejde, medferrte at visse Oplysninger fik szrlig Vardi for Problemernes Opklaring. I den Henseende har Arbejdet paa Instituttet virkelig allerede kommet ti1 at spille en stor Rolle for Diskussionerne herovre, og jeg har i disse Dage i s a r vzret glad for Frischs og Frk. Meitners sidste Telegram om deres direkte Paavisning af at de oprindelig ti1 Transuraner tilskrevne Perioder - i Modsztning ti1 den Opfattelse som Hahn har givet Udtryk for i sin sidste Artikel i Naturwis~enschaften’~~ - maa tilskrives de ved Uran-Fissionen dannede nye Stoffer. I et I n d l ~ g ’i ~et Brev ti1 min Kone, der var afsendt nogle Dage ferr, har jeg sergt at give et Overblik over Problemerne, som de i 0jeblikket syntes at ligge for mig; ogsaa med Hensyn ti1 de 0nsker om videre Forserg der er udtalt deri, skal man jo ikke, naturligvis, gerre andet end, hvad der passer rimeligt ind i Arbejdsplanerne paa Instituttet. I Hevesys Brev, som jeg fik i Dag, beskriver han Muligheden af at man maaske i Stedet for Mesothorium kan gerre Forserg med Radium selv, hvad der naturligvis vilde v a r e storartet, men hvad jeg slet ikke selv havde turdet haabe. Et af de vigtigste Sperrgsmaal for den teoretiske Diskussion er nemlig stadig Omfanget af de Stoffer, der kan bringes ti1 at undergaa Fission; og netop i denne Henseende er det interessant at vi, hvis min Opfattelse er rigtig, allerede har tre saadanne Stoffer, nemlig foruden Uran 238 og Thorium 232 ogsaa Uran 235, der paa Grund af den forskellige Proton-Neutron Sammensztning skulde vise saa forskellige Egenskaber. Foruden Fission-Problemerne er jeg naturligvis uhyre interesseret i alt andet paa Instituttet, og ikke mindst i Deres eget Arbejde med Hafnium Finstrukturen. Om hele Sperrgsmaalet om de tunge Kerners Momenter har Rosenfeld og jeg i0vrigt haft mange interesssante Diskussioner herovre, i s m med Rabi. Rosenfeld beder ogsaa om at takke Merller for hans lange og interessante Breve, med hvis Indhold han (bortset fra Sp~rgsmaaletom Muligheden af Meson-Udsendelse under Fission*) er enig, og som han haaber at kunne besvare udferrligt med naste Post. * Hverken Rosenfeld eller jeg mener, at der er nogen-som-helst Sandsynlighed for at der kan udsendes Mesoner ved Kernefissionen, fordi den Energi, der her er Tale o m , j o slet ikke er ti1 Raadighed for nogen Kerneomdannelse paa et givet Tidspunkt, men farst frigmes gradvis under den gensidige elektrostatiske F r a s t ~ d n i n gaf Kernefragmenterne under deres Bev2egelse bort fra hinanden.
0. Hahn and F. Strassmann, Nachweis der Entstehung aktiver Bariumisotope aus Uran und Thorium durch Neutronenbestrahlung; Nachweis weiterer aktiver Bruchstucke bei der Uranspaltung, Naturwiss. 27 (1939) 89-95. 7 6 Introduction, ref. 116.
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Jeg skal ogsaa v a r e meget glad for stadigt at blive underrettet om Fortsattelsen af Hevesys Undersergelser, hvori alle Biologer her tager den sterrste Interesse. Hvordan gaar det egentlig med de planlagte Undersergelser over Neutronens magnetiske Moment? Jeg er naturligvis klar over at de rimeligvis har maattet v a r e lagt forelerbig ti1 Side paa Grund af det meget andet Arbejde. Lignende Unders~gelser er imidlertid ogsaa under Forberedelse herovre paa Columbia Universitetet, og hvis man er saa vidt i Kerbenhavn, at man hurtigt kunde faa et afgerrende Resultat vilde det derfor v z r e meget ernskeligt; men ogsaa i denne Henseende kan jo kun De paa Stedet bedermme, hvad der er det rimeligste at gerre. Lignende gzlder naturligvis de planlagte Unders~gelser over Kernefotoeffekter, i hvilket Sperrgsmaal jeg stadig er overordentlig interesseret. Med mange venlige Hilsner ti1 Dem alle og en Tak ti1 hver i s z r for Brevene, som jeg ikke med denne Post kan naa at ware enkeltvis paa, Deres hengivne Niels Bohr
P.S. Lige nu fik jeg ogsaa et meget interessant Brev fra Dr. Jacobsen. Vil De takke ham og sige hvor glad jeg er for at det gaar saa godt med CyclotronArbejdet. Jeg tror dog ikke som ovenfor n a v n t at der kan komme noget ud af at serge efter Mesoner. Iervrigt maa vi gerre det yderste for at skaffe H j z l p nok ti1 alle Undersergelserne, men jeg ved jo at ingen bedre end De selv ferlger de studerende og tanker paa hvilke Muligheder de i saa Henseende byder. Hele det pekuniare Sperrgsmaal rummer j o heldigvis for 0jeblikket ikke nogen Vanskelighed, og vil forhaabentlig heller ikke senere gerre det. Det bliver ogsaa en stor H j a l p at Tom Lauritsen kommer over ti1 Sommer for at arbejde et Aar i Instituttet, og at ogsaa Prof. Lauritsen selv synes sikkert at komme ti1 Kerbenhavn hele nzste Foraar. NB.
Translation Princeton, 10 March 1939 Dear Dr. Rasmussen, You can believe that I was pleased to get this morning so many good letters from the Institute, both from yourself, and from Mrs. Schultz, Dr. Bjerge, and Hevesy. I also had a letter from Engineer Bergsere with the text of the radio interview, which came over excellently, and to which I listened with great pleasure over here. I am really more than happy on behalf of the Institute with the great
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work that Frisch and all the others have done, and I hope that you have all understood the reason for the impression of impatience which my letters and telegrams have perhaps given; but these were really critical days for me and my endeavours to ensure for Miss Meitner and Frisch a reasonable share in the credit for the great discovery, and t o allow the Institute to make a contribution to the new field, which would in some measure correspond to the excellent staff attached t o it, and the great equipment at our disposal because of the strong support we have had. Of course it is not my idea that you should rush with the investigations in any way, and one should also not take too literally what I have written about daily reports or continuous telegrams, but only work according to the best possible plan and keep me informed by telegrams and letters about everything of particular interest for me and for the many physicists with whom I have such close contacts over here. I have thought in particular that it may be difficult for you people at home to imagine correctly the almost unlimited means with which the almost innumerable physicists over here are working, and the enthusiasm with which the new phenomena are taken up for study and the eagerness with which their explanation is discussed by the theoreticians over here. Precisely the doubts, raised at least to begin with by Fermi, about the lines of reasoning proposed in the Note by Miss Meitner and Frisch, and on whose extension I have myself done a substantial piece of work, made certain pieces of information of particular value for the clarification of the problem. In this respect the work of the Institute has really already come to play a major part in the discussions over here, and in the last few days I have been especially glad to have the telegram from Frisch and Miss Meitner about their direct demonstration that the periods ascribed earlier to transuranic elements can be attributed to the new elements produced in uranium fission - contrary to the interpretation expressed by Hahn in his latest article in N a t u r w i s ~ e n s c h a f t e n ~ ~ ~ . In an enclosure76 to a letter sent to my wife a few days ago, I have tried to give a review of the problems as they appear to me at this moment; also as regards the requests made there for further experiments, one should of course do only what fits reasonably into the working programme of the Institute. In Hevesy’s letter, which I received today, he describes the possibility that instead of mesothorium one could perhaps do the experiment with radium itself, which would of course be great, but which I had hardly dared hope for. Namely one of the most important questions for the theoretical discussion is always the range of substances which can be made to undergo fission; and just in this respect it is interesting that, if my interpretation is right, we already have three such substances, namely besides uranium 238 and thorium 2 3 2 , also uranium 2 3 5 , which, because of the different neutron-proton ratio, should show different properties.
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Besides the fission problems I am naturally enormously interested in everything else in the Institute, not least in your work on the hafnium fine structure. About the whole question of the moments of heavy nuclei, incidentally, Rosenfeld and I have had many interesting discussions here, particularly with Rabi. Rosenfeld also sends his thanks to M ~ l l e for r his long and interesting letters, and he agrees with their contents (apart from the question of the possibility of meson emission in fission*) and he hopes to be able to reply at length by the next post. I should also be glad to be kept informed continuously about the progress of Hevesy's investigations, in which all biologists here are taking the greatest interest. How is the planned work on the magnetic moment of the neutron getting on? It is of course clear to me that you probably had to put this aside for the time being because of the amount of other work. However, similar investigations are also in preparation over here at Columbia University, and if one were far enough in Copenhagen to get a final result quickly this would be very desirable; but in this respect also you can only judge on the spot what it is reasonable to do. The same applies of course to the planned studies of the nuclear photo-effect, a question in which I am still greatly interested. With many kind regards to all of you, and thanks to everybody for the letters to which I cannot manage to reply individually by this post. Yours sincerely, Niels Bohr P.S. I have now also received a very interesting letter from Dr. Jacobsen. Please thank him and say how pleased I am that it is going so well with the cyclotron work. But I do not think, as mentioned above, that anything can come out of searching for mesons. Incidentally, we must do all we can to provide enough help for all experiments; but I know that nobody is in a better position than you to follow the students and to decide what possibility they offer in this respect. The whole financial question fortunately presents for the moment no difficulty, and I hope it will not do so later either. It will also be a great help that Tom Lauritsen is coming over in the summer to work in the Institute for a year, and that also Professor Lauritsen himself seems sure to come to Copenhagen for the whole of next spring. NB.
* Neither Rosenfeld nor 1 believe that there is any probability at all that mesons could be emitted in the nuclear fission, because the energy with which one is concerned here is hardly available for a nuclear reaction at any given time, but is released gradually under the mutual electrostatic repulsion of the nuclear fragments during their motion away from each other.
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RASMUSSEN TO BOHR,
(1929- 1949)
24 March 1939
[Typewritten] UNIVERSITETETS INSTITUT FOR
15, KQBENHAVN 24. Marts 1939.
BLEGDAMSVEJ DEN
0.
TEORETISK FYSIK
K m e Professor Bohr, Mange Tak for Deres venlige Brev af 10. Marts med de mange “Tips” for Arbejdet. Vi har endvidere modtaget den Oversigt over Problemerne, som var sendt ti1 Fru Bohr, og vi har skrevet den af i flere Eksemplarer og omdelt dem ti1 alle interesserede. Om Arbejdet er der kun det at meddele, at Frk. Meitner nu har gentaget Rekylforsoget med Thorium, hvilket der telegraferes om i Dag. H un sender en Note ti1 “Nature”77 derom, og vil derefter afslutte sit Ophold her, idet hun mener at rejse paa Sondag. Frk. M. har vzret meget glad for sit Ophold her, og det har j o ogsaa i h0j Grad vzret nyttigt for Instituttet. Forovrigt er der en stErk Tilstromning ti1 Prof. Hevesys Afdeling. Hahn er kommet tilbage igen (han er endnu ikke helt annekteret af Tyskland, da han er fra Slovakiet), og i Gaar kom der en ung svensk Mediciner, Dr. 0hnell fra Stockholm, og i Dag en Farmakolog Dr. Bayard fra Liege for ved H j z l p af medbragte Stipendier at studere hos Prof. Hevesy. Paa teoretisk Afdeling er kommet Dr. Steensholt fra Norge, og i kzlderen arbejder stadig Dr. Simons, hvis Manuskript Professoren vel allerede har faaet. Om Cyclotronen kan jeg fortzelle, at Jacobsen i den sidste Tid nzsten daglig har leveret aktive Natrium- og Kaliumprzeparater ti1 Prof. Hevesy, samt at han flittigt fortsztter med Uran-Deuteron-Forsogene. Endvidere er Vzerkstedet nu i Gang med at lave et SEt nye Duanter ti1 Cyclotronen, hvortil vi ude i Byen har faaet presset Kobberpladerne i den bedst mulige Form. Jacobsen mener dermed at kunne foroge Intensiteten af beam. Hojspzendingsgruppen har stadig bestraalet Uran og Thorium for Frk. M., men med de ovrige Forsog gaar det vist ikke saa hurtigt, som man onsker. Bjerge ligger nu i Sengen paa anden Uge, og K o ~ har h ~i denne ~ Tid travlt med Eksamen paa Soofficersskolen.
”
L. Meitner, New Products of the Fission of the Thorium Nucleus, Nature 143 (1939) 637. - 19 September 1971). Danish experimental physicist. After studies in
’’ Jmgen Koch (6 April 1909
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Vi skal nu ogsaa ti1 at t z n k e paa Eksamensopgaver for de Studerende. Blandt de tre, der skal op ti1 Eksamen nu ti1 Sommer, vil sikkert en, nemlig HyllingChristensen, vzere brugbar som fremtidig Medhjxlp. Det forlyder nu, at Lmeanstalten har nedsat et Udvalg ti1 Bed~mmelseaf Ansergerne ti1 Professoratet i Fysik. Det kan jo ikke nzegtes, at det ser noget mzerkeligt ud, at der beszttes et Professorat i Fysik i Danmark, uden at Professor Bohr bliver spurgt. Hermed mange Hilsener ti1 Dem, Erik og Prof. Rosenfeld fra alle paa Instituttet. Deres hengivne Ebbe Rasmussen
Translation Copenhagen, 24 March 1939 Dear Professor Bohr, Many thanks for your kind letter of 10 March with the many “tips” for our work. We have also received the review of the problems which you sent to Mrs. Bohr, and we have made several copies of this and distributed them to all those interested. About the work the only thing to report is that Miss Meitner repeated the recoil experiment with thorium, about which I cabled today. She is sending a note about this to “Nature”77, and after that will end her stay here as she intends to leave on Sunday. Miss Meitner has been very pleased with her stay here, which has also been of very great benefit t o the Institute.
Danzig and Berlin, Koch graduated in engineering (Diplomingenior) in 1933 from the Technical University in Berlin where he obtained his doctorate (Dr. Ing.) in 1936. The same year he was appointed research assistant at Bohr’s institute where he worked until 1957. In 1942 he obtained a doctorate in physics (dr. phil.) for a thesis o n mass-spectrographic separation of isotopes. In 1957 Koch was appointed professor at the University of Copenhagen and director of the biophysical laboratory of the University which under his directorship was transformed into a more general type of physical laboratory, Physical Laboratory 11. From 1952 he also worked as a consultant to the Danish health authorities on questions related to radioactivity and radiation hazards. Koch’s research interests lay within the areas of neutron physics (including fission), isotope separation, and production and application of fast ions, as well as with medical and other applications of physics. Obituaries by K.G. Hansen, E. Juel Henningsen and H . H ~ j g a a r dJensen, and by N.O. Lassen (Fys. Tidsskr. 70 (1972) 97-120).
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Otherwise there has been a great influx into Professor Hevesy’s group. Hahn has come back again (he has not yet been annexed completely by Germany, since he comes from Slovakia), and yesterday a young Swedish medical man, Dr. Qhnell came from Stockholm, and today a pharmacologist, Dr. Bayard from Libge to work with the help of their own scholarships under Professor Hevesy. In the theoretical department Dr. Steensholt has arrived from Norway, and in the basement Dr. Simons is still at work; you should already have received his manuscript. About the cyclotron I can report that Jacobsen has lately delivered almost daily active sodium and potassium samples to Professor Hevesy, and he also continues assiduously with the uranium-deuteron experiments. In addition the workshop is now engaged in making a new set of dees for the cyclotron, and for this we have had copper plates pressed in the best possible shape. With this Jacobsen expects to be able to increase the beam intensity. The high-tension group has continued irradiating uranium and thorium for Miss Meitner, but with the other experiments things are not going as fast as one might wish. Bjerge was now been in bed for the second week, and Koch” has lately been busy with the examination for the Naval Academy. Now we shall have to think also of test problems for the students. Amongst the three who will take the exam by the summer there is surely one, namely Hylling-Christensen, who will be suitable as a future helper. It is now reported that the Technical University has set up a committee to judge the applicants for the professorship in physics. It cannot be denied that it looks very peculiar if a physics chair in Denmark is filled without Professor Bohr being consulted. With best regards to you, Erik and Professor Rosenfeld from everybody in the Institute. Yours sincerely, Ebbe Rasmussen
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1949)
LEON ROSENFELD BOHR TO ROSENFELD,
8 January 1936
[Typewritten] UNIVERSITETETS INSTITUT FOR
15, K0BENHAVN 8. Januar 1936.
BLEGDAMSVEJ
DEN
0.
TEORETISK FYSIK
K a r e Rosenfeld, Jeg er meget ked af, at Du saa lange ikke har hart fra mig, men jeg svarede ikke straks paa Dit Brev i November om vort Arbejde og Dine Bemarkninger om Verlaines Studier, fordi jeg dengang regnede med at se Dig meget mart her i Kabenhavn. Jeg fik imidlertid saa travlt med mange forskellige Ting, at jeg dog maatte udskyde Fortsattelsen af vort Samarbejde, hvad jeg j o ogsaa havde Indtryk af passede Dig selv bedst paa Grund af Undervisningen i Likge. Straks efter at jeg kom tilbage ti1 Kabenhavn fra en lille Juleferie i Norge, hvor min Kone fik Dit Brev, har jeg imidlertid set paa det hele igen. Hvad Dine Bemarkninger om Verlaines Undersagelser angaar, tror jeg, at jeg fuldstandig forstaar, hvad Du mener, og at jeg er ganske enig deri. Det er mig imidlertid lidt w a r t at komme helt ti1 Klarhed over alle Enkeltheder, fordi jeg ikke er tilstrzekkelig kendt med den Tydning, Verlaine selv giver sine Resultater, og den Maade hvorpaa Perceptionsproblemet er behandlet i den saakaldte Gestalt-Psychologie. Af Litteraturen kender jeg kun William James’ klassiske Kritik af den sadvanlige psykologiske Analyse, som for mig har vzret en rig Kilde ti1 Inspiration ved min Indlevelse i de psykologiske Komplementaritetsforhold. Jeg synes ubetinget, at Du snarest skulde tale med Verlaine og se, hvorledes han reagerer paa Dine Betragtninger. Vi kunde da altid tale narmere om det hele, far Du giver Dine Bemarkninger den endelige Form. Det vil ogsaa v a r e en stor Belzring for mig, da jeg er indbudt af Warburg Society i London ti1 i Februar at holde et Foredrag med Titel: “Some humanistic aspects of atomic theory”, ved hvilken Lejlighed jeg har i Sinde saavidt muligt at pracisere min almindelige Indstilling ti1 erkendelsesteoretiske, psykologiske og biologiske Problemer. I London skal jeg ogsaa i Physical and Chemical Society tale om “space and time in atomic theory”, med hvilke Spargsmaal jeg i Efteraaret igen har arbejdet en Del, og hvorom jeg haaber at benytte Lejligheden ti1 at gare min gamle Afhandling helt fardig. Ogsaa der vil det jo v a r e en meget stor H j a l p for mig at kunne tale indgaaende med Dig forinden, og jeg vil derfor gerne sparge Dig, om Du, som vi allerede talte om i Bryssel, kunde komme her paa et saa tidligt
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Tidspunkt som muligt for saa senere, naar jeg rejser ti1 London ca. den 8. Februar, at tage tilbage ti1 Liege for at g ~ r Din e Undervisning fzrdig. Det vil j o ogsaa v z r e forfzrdelig rart, om vi, inden jeg rejste, kunde gme vort Arbejde om Tzthedsmaalingerne helt fzrdigt, saa jeg eventuelt kunde forelzgge det i Royal Society under mit Besag i England, der vil vare ca. 14 Dage. I den sidste Tid har jeg iervrigt vzret meget optaget af et helt andet Sp~rgsmaal,nemlig NeutronIndfangning af Atomkerner. Jeg har her genoptaget en gammel Tanke, som slog mig allerede under Diskussionerne med Bethe ved sidste Konferens i K~benhavn, nemlig at Bevzgelsen af en Neutron, som traenger ind i Kernen, ingenlunde kan beskrives som et eenlegemet Problem i et fast Kraftfelt, men at tvzrtimod Neutronen saa at sige ojeblikkelig vil dele sin Energi med de andre Kernepartikler og danne et intermediate system med Levetid tilstrzkkelig lang, for at der bliver en stor Sandsynlighed for Straalingsovergang, fOr en Neutron eller en anden Partikel forlader Systemet som F d g e af en Udskillelsesproces, der ikke staar i nogen direkte Forbindelse med Intrzngningsprocessen. Dette Synspunkt synes ikke alene at forklare Neutronindfangningen, men ogsaa at 10se et stort Antal af de andre Vanskeligheder, hvormed Gamow har ksempet paa Grund af sin skematiserede Atomkernemodel. I det hele taget f ~ r e rBetragtningerne ti1 en vzsentlig anden Opfattelse af Kernernes Bygning end den szdvanlige, hvorved man har ikke gjort n z r Forskel nok mellem de ssedvanlige Atomproblemer og Kerneproblemet, medens disse efter min Opfattelse maa betragtes som ekstreme Tilfaelde af svag og s t z r k Kobling mellem Enkeltpartiklernes Bevzgelse, der kraver helt forskellige Angrebslinier. Jeg er netop i Begreb med at afslutte en lille Artikel derom ti1 N a t ~ r e ’ ~som , jeg skal sende Dig, saa snart den er faerdig, hvis Du da ikke allerede forinden skulde v z r e kommet her tilbage, hvortil jeg glzder mig meget. Med mange venlige Hilsener fra 0s alle og de bedste 0nsker om et glzdeligt Nytaar for Dig og Din hele Familie, Din Niels Bohr
Translation Copenhagen, 8 January 1936 Dear Rosenfeld, I am very sorry that you have not heard from me for so long, but I did not immediately answer your letter in November about our paper and your remarks about Verlaine’s studies, because I then counted on seeing you here in 79
Introduction, ref. 24.
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Copenhagen very soon. I was however so busy with many different matters that I had to postpone our collaboration, and I have the impression that this also suited you because of your teaching in Liege. However, on my return to Copenhagen from a little Christmas vacation in Norway, where my wife received your letter, I have again attended to the whole matter. As regards your remarks about Verlaine’s investigations, I believe I understand completely what you mean, and I entirely agree with it. However, it is a little difficult for me to see clearly all the details because I am not sufficiently familiar with the interpretation which Verlaine himself gives to his results, and with the way the problem of perception is treated in the so-called Gestalt Psychology. Of the literature I know only William James’ classical critique of the ordinary psychological analysis, which for me has been a rich source of inspiration for my insight into the psychological complementarity conditions. I think you really should talk as soon as possible with Verlaine and see how he reacts to your comments. We can still always talk further about all this, before you put your remarks into their final form. That will also be very instructive for me, since I have been invited by the Warburg Society in London to give a lecture in February with the title “Some humanistic aspects of atomic theory”, and for this occasion I have in mind to elaborate as far as possible on my general attitude to the epistemological, psychological and biological problems. In London I shall also talk to the Physical and Chemical Society on “space and time in atomic theory”; this is a problem on which I have again worked a good deal in the autumn, and on which I hope to use this opportunity to complete my old paper. Also here it would be a very great help for me to be able to talk fully with you in advance, and I would like to ask you whether you could come here as early as possible, as we already discussed in Brussels, and then later, when I go to London about 8 February, return to Liege to finish your teaching. It would also be very nice if before my departure we could complete our paper about the density measurements, so that I could present this to the Royal Society during my visit to England, where I shall stay about a fortnight. By the way, I have lately been very busy with quite a different question, namely the capture of neutrons by nuclei. I have taken up an old idea again, which already occurred to me in the discussions with Bethe during the last conference in Copenhagen, namely that the motion of a neutron which penetrates into the nucleus can in no way be described as a one-body problem in a static potential, but on the contrary the neutron will so-to-speak instantaneously share its energy with the other nuclear particles, and create an intermediate system with a sufficiently long lifetime so that there remains a large probability of a radiative transition, before a neutron or another particle leaves the system as a result of an escape process which has no direct connection with the capture process. This point of view
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seems not only to explain the neutron capture, but also to solve a large number of other difficulties, with which Gamow has struggled on the basis of his schematic model of the nucleus. On the whole these considerations lead one to an essentially different concept of nuclear structure from the ordinary, which does not make nearly enough distinction between the usual atomic problems and nuclear problems, since these in my opinion should be regarded as extreme cases of weak and strong coupling between the motion of individual particles, requiring quite different lines of approach. I am just about to finish a little article for Nature79 about this, which I shall send you as soon as it is ready, unless you return here already before then, which would please me very much. With many kind regards from all of us and with best wishes for a happy New Year to you and all your family. Yours, Niels Bohr
BOHR TO ROSENFELD,
16 August 194979a
[Typewritten] UNIVERSITETETS INSTITUT FOR
15, KQBENHAVN 16. August 1949.
BLEGDAMSVEJ DEN
0.
TEORETISK FYSIK
p.t. Tisvilde K z r e Rosenfeld. Hjemkommen ti1 Tisvilde sender jeg den kopi af udkastet ti1 vores manuskript" som jeg havde glemt at tage med ti1 Kerbenhavn d a jeg afsendte brevet ti1 dig i gaar. Jeg haaber at du var tilfreds med brevet ti1 Pauli, og jeg er spzndt paa at herre din kritik af mine rent orienterende bemzrkninger om kerneproblemerneS1.Som du sikkert forstaar er grunden ti1 min optagethed med dette emne, at jeg ser nye muligheder for en afrunding af behandlingen af de gamle problemer jeg discuterede med Peierls og Placzek, og hvormed du hjalp mig saa godt f O r du We are grateful to Mrs. Y. Rosenfeld for lending us this letter. N. Bohr and L. Rosenfeld, Field and Charge Measurements in Quantum Electrodynamics, Phys. Rev. 78 (1950) 794-798. Reproduced in Vol. 7 . Introduction. ref. 147.
79a
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under krigen maatte rejse fra K~be nha vn.Ogsaa her foreligger en gammel sag som gerne snart skulle bringes ti1 en rimelig afslutning. Det betyder imidlertid ingenlunde at jeg er mindre optaget af de ting vi arbejder sammen paa, og jeg ved slet ikke om jeg i mit brev rigtigt fik sagt hvor lykkelig jeg er over arbejdets udvikling og de fremskridt du har gjort dermed. F ~ r s t og fremmest drejer det sig dog om hvad baggrund der paa saadan maade kan skabes for videre fremskridt, og herom glzder jeg mig ogsaa saa meget ti1 at tale med dig, naar du igen kommer ti1 K~be nha vn. Med endnu mange venlige hilsner og gode onsker for dig og din familie din Niels Bohr
Translation Tisvilde, 16 August 1949 Dear Rosenfeld, On my return to Tisvilde I am sending you the copy of the draft for our manuscript", which I had forgotten t o take with me to Copenhagen when I sent a letter to you yesterday. I hope you are satisfied with my letter to Pauli, and I am looking forward to your appraisal of my purely exploratory remarks about the nuclear problems". As you no doubt appreciate, the reason for my preoccupation with that subject is that I see new possibilities for rounding off the treatment of the old problems which I discussed with Peierls and Placzek, and with which you helped me so much before you had to leave Copenhagen during the War. Here, too, there is an old matter which I would like to bring to a reasonable conclusion before long. However, this does not mean in any way that I am less concerned with the matters on which we are working together, and I do not know at all whether I managed to say in my letter how happy I am with the way the paper is developing and with the progress you have made with it. In the first place, the point is after all what background can be created in this way for further progress, and about this also I look forward very much to talking with you when you come again to Copenhagen. Again many kind regards and good wishes for you and your family, Yours, Niels Bohr
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E
ROSENFELD TO BOHR,
(1929- 1949)
19 August 1949
[Handwritten] UNIVERSITY OF MANCHESTER MANCHESTER
I3
19. August 1949 K a r e Bohr, Mange tak for Dine venlige breve fra den 15. og 16. med de forskellige indlag. Brevet ti1 Pauli synes jeg er aldeles udmarket. Jeg var valdig interesseret i Dine bemzerkninger om den “kvasi-atomiske” kzernemodel: det er j o et emne, som jeg i mit foredrag i Base1 skal behandle. Jeg vil derfor gerne straks meddele Dig mit syn paa dette spargsmaal; hvis Du i det falgende skulde bemarke nogen starre fejltagelse, var jeg meget taknemmelig hvis Du vilde skrive mig et par korte antydninger om den, saa at jeg kunde rette den inden den for foredraget planlagte dag (den 8. September). Farst og fremmest er jeg lidt bange for, at Du har faaet et altfor optimistisk indtryk af modellens raekkevidde. Saadanne almindelige og skematiske betragtninger som Feenbergsg2 og NordheimsS3er jeg ikke tilbajelig ti1 at tilskrive mere end kvalitativ og orienterende vardi. Saa snart man praver paa at uddybe den i kvantitativ retning, svigter modellen fuldstandig. Man kan ikke redde sig ved at sige, at denne svigten ligger i, at man negligerer de ikke-centrale koblinger: det er f.eks. umuligt udfra nogensomhelst perturbationsregning at forklare vardien 3 for loB karnens impulsmoment i grundtilstanden. Dette iagttagelsesresultat viser, at man i hvert fald maa betragte de ikke-centrale krafter som en ganske vasentlig bestanddel af vekselvirkningsenergien, og ikke blot som perturbation. Men situationen er i virkeligheden endnu varre: det viser sig nemlig, at man slet ikke kan gare rede for tritonens (3H) bindingsenergi, selv om man saa strengt som muligt tager hensyn ti1 de ikke-centrale krafter mellem par af nucleoner. Dette tyder paa, at man desuden skulde regne med betydelige krafter mellem flere nucleoner paa en gang (many-body forces). Dette betyder nu, at nucleonernes vekselvirkninger har en ikke-additiv karakter, som synes mig uforenelig med tanken om, at der kunde defineres et udjavnet karnefelt som vilde paavirke hvert sarskilt nucleon, som er et vasentligt t r a k ved den kvasi-atomiske model. Ligeledes synes mzetningsegenskaberne hos kaernekrafterne ikke at fare ti1 en jaevn fordeling af nucleonerne indenfor kzernen, men tvzertimod ti1 en tendens ti1 grupperinger af nucleoner, f.eks., i a-partikler (rettere sagt: “a-clusters” som naturligvis ikke bevarer deres 82
Introduction, ref. 148. Introduction, ref. 149.
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identitet, men oplmes og dannes stadig paany). Man kan ligefrem udfra selve den kvasi-atomiske model udlede, at denne tendens ti1 “a-clustering” bestaar som f ~ l g af e de simpleste t r a k hos kzrnekrafterne, som er nerdvendige ti1 at forklare deuteronens egenskaber og a-partiklens sarlige stabilitet. Jeg tror derfor ikke, at tanken om et udjzvnet karnefelt har nogen konsekvent basis, og heller ikke at den dertil svarende kvasi-atomiske model egner sig som udgangspunkt for en kvantitativ behandling af kerneegenskaberne. Jeg er spandt paa at h ~ r e hvad , Du synes om disse mine tvivl. Med de hjerteligste hilsner fra hjem ti1 hjem Din L. Rosenfeld
Translation Manchester, 19 August 1949 Dear Bohr, Many thanks for your kind letters of the 15th and 16th with the various enclosures. The letter to Pauli is, I think, quite excellent. I was most interested in your remarks on the “quasi-atomic” nuclear model: this is just the topic I shall deal with in my lecture in Basle. I shall therefore tell you immediately about my thoughts on this question; if you see in what follows any major error I would be very grateful if you could write to me a few short hints about this so that I could correct it by the date of the lecture (8 September). Above all I am a little worried that you have got an altogether too optimistic impression of the generality of the model. I am not prepared to attach to such general and schematic considerations as Feenberg’ss2 and Nordheim’ss3 more than a qualitative and tentative value. As soon as one tries to explore the model in a quantitative sense, it fails completely. One cannot save oneself by saying that this failure is due to the neglect of non-central interactions: it is for example impossible to explain the spin value of 3 for the ground state of loB by any perturbation calculation whatsoever. This experimental result shows that one must consider the non-central forces in every case as a quite essential part of the interaction energy, and not merely as a perturbation. But the situation is really even worse: it actually turns out that one cannot explain the binding energy of the triton (3H) even if one allows as much as possible for the non-central nucleon-nucleon forces. This suggests that one should in addition reckon with significant forces acting between several nucleons at a time (many-body forces). Now this means that the interactions between nucleons have a non-additive character, which seems to me incompatible with the thought that it could be
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possible to define a smoothed-out field of force acting on individual nucleons, which is an essential feature of the quasi-atomic model. Similarly it seems that the saturation properties of the nuclear forces will not lead to a smooth distribution of nucleons inside nuclei, but on the contrary to a tendency to clustering of nucleons, for example in a-particles (more correctly in “a-clusters”, which of course do not retain their identity, but dissolve and re-form all the time). One can even from the quasi-atomic model itself deduce that this tendency towards “a-clustering” exists as the result of the simplest features of the nuclear force, which are required to explain the properties of the deuteron and the special stability of the a-particle. I therefore do not believe that the idea of a smoothedout nuclear field can have any consistent basis, nor that the corresponding quasiatomic model is a suitable starting-point for a quantitative treatment of nuclear properties. I look forward to hearing your reaction to these doubts of mine. With cordial greetings from house to house. Yours, L. Rosenfeld BOHR TO ROSENFELD,
29 August 1949
[Carbon copy] [Kabenhavn,] 29. august [19]49. K z r e Rosenfeld, Jeg var meget taknemmelig for, at Du svarede mig s i hurtigt p i mit spargsmil om Dit syn p i kerneproblemerne. Selvfdgelig har Du sA meget s t ~ r r ekendskab ti1 mange sider af disse problemer, og det var netop derfor, at jeg gerne ville sparge Dig ti1 rids. Jeg er imidlertid ikke helt sikker p i , at jeg tydelig nok havde forklaret, hvad der for mig er pointen i bemzrkningerne. Naturligvis har Du ret i, at Feenbergs og Nordheims betragtninger er af meget kvalitativ og orienterende art; men grunden ti1 at deres resultater gjorde stort indtryk p i mig er, at det drejer sig om en mulig forklaring af lovmzssigheder af en art, som ikke en gang kvalitativt har vzret angribelig ud fra andre synspunkter om kernernes konstitution. Mine simple bemzrkninger tog iavrigt kun direkte sigte p i tunge kerner med mange protoner og neutroner, og for at gme det lidt tydeligere, sender jeg i dette brev en p i nogle s m i punkter rettet udgave af bemzrkningerne. For lette kerner ligger sagen j o vasentlig anderledes. Her har man j o altid angrebet problemet i s t ~ r r elighed med atomerne og med a1 forskel p i karakteren af de kraftfelter, det drejer sig om, er det interessant at t a n k e p i , at man for eksempel ved deuteronen har at g ~ r emed banedimensioner, der er store i forhold ti1 krafternes rzkkevidde, og derfor med et ejendommeligt, for den klassiske beskrivelse gan-
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ske fremmed t r z k af berlgemekanikken. G i r man imidlertid over ti1 tunge kerner, er hovedsperrgsmilet, hvorvidt kernestoffet er uigennemtraxgeligt for nukleonerne, eller rettere: i hvor h0j grad de enkelte kernedele perturberer de berlgefunktioner, som ville ware ti1 en bevzgelse i et fzelles kernefelt. Hvis nemlig disse perturbationer ikke ganske zndrer problemet, synes jeg virkelig, at man i stedet for at starte betragtningerne med en mere klassisk dribemodel, m i g i ud fra den hypotetiske idealiserede kernemodel som en ferrste tilnzrmelse. Jeg har i disse dage ogsi talt med RamseyS4, der gjorde opmzrksom p i beregningerne i Din bogs5 om viskositeten i en Fermi gas, og sorn giver en uendelig gnidningskoefficient for temperaturen T = 0. Man kan dog efter min mening ikke heraf drage den slutning, at kernestoffet har vzedskekarakter, da det j o netop drejer sig om en luftart med stor fri vejlzngde og derfor viskositetsproblemerne kun tager direkte sigte p i overferrelse af impuls inden for store dimensioner. N i r man ved formel anvendelse af Pauliprincippet betragter den fri vejlzngde for nukleonerne i kernerne som uendelig stor, kommer man jo netop ti1 det synspunkt, at bindingerne af de enkelte nukleoner i kernen i farste tilnzrmelse kan betragtes hver for sig. Hvor velfunderede sidanne betragtninger er, er jo en ganske anden sag, og det som jeg synes m i vaere hovedpunktet, er at finde ud af den betydning, som exchange effekterne vil have og at underserge, hvorvidt exchange perioderne er lange eller korte i sammenligning med de ti1 billedet svarende “orbital” perioder. I det sidste tilfzlde vil j o angrebspunktet v z r e irrelevant, men i det ferrste tilfzelde vil man virkelig, s i vidt jeg kan se, have at gerre med en rationel approksimationsmetode. Jeg skal imidlertid v z r e meget glad for at herre, om Du synes at sidanne bemzrkninger i nogen grad imerdekommer Din kritik. Det vil iervrigt interessere Dig at se den indlagte kopi af et brev, som jeg modtog fra Pauli for nogle dage siden, og hvori han tvivler p i rigtigheden af vore bemzrkninger om ladningsfluktuationerne. Jeg svarede ham straks - og indlzgger en kopi af mit brev - at jeg ikke troede, at han havde ret, og sendte ham Dine optegnelser om fluktuationerne i de forskellige mulige tilfzlde. Jeg gjorde det s i godt jeg kunne huske, men har siden ikke vzret helt sikker p i , om Du gav mig optegnelserne i London i fjor eller om Du bragte dem med Dig i sommer. Det skal v z r e meget interessant, hvad der kommer ud af diskussionerne mellem Dig og Pauli, og jeg er spzndt p i at herre narmere, n i r Du har talt med ham om det altsammen.
’‘ ’’
William Henderson Ramsey got his P h D under Rosenfeld in Manchester and spent most of 1949 at Bohr’s institute. L. Rosenfeld, Nuclear Forces I - I I , North-Holland Publ. Co., Amsterdam 194811949.
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Jeg sender dette brev af sted i hast i hibet om, at det vil n i Dig I Tyrol, men ellers hiber jeg, at det bliver eftersendt ti1 Basel. Med mange venlige hilsner fra 0s alle ti1 Dig og hele Din familie, Din [Niels Bohr]
Translation [Copenhagen,] 29 .August 1949 Dear Rosenfeld, I am very grateful for your quick answer to my question about your view of the nuclear problems. Of course you have a so much greater knowledge of many aspects of these problems, and it was just for that reason that I wanted to ask for your advice. However, I am not quite sure that I have explained sufficiently clearly what was for me the point of the remarks. You are of course right that Feenberg’s and Nordheim’s considerations are very qualitative and tentative, but the reason that their results made a great impression on me was that this concerns a possible explanation of regularities of a kind which could not be approached even qualitatively on the basis of any other views of the nuclear constitution. Besides, my simple remarks were intended directly only for heavy nuclei with many protons and neutrons, and in order to make this a little clearer, I am enclosing with this letter a formulation of my remarks which has been corrected in some small points. For light nuclei the matter is after all essentially different. Here one has always tackled the problem in close analogy with atoms, and, with all the differences in the nature of the force fields involved, it is interesting to think that, for example, in the deuteron the dimensions of the orbit are large compared to the range of the force and one is therefore dealing with a peculiar feature of wave mechanics, which is quite foreign to the classical description. However, if one turns to the heavy nuclei, the main question is how far the nuclear matter is impermeable for nucleons, or better: to what extent the individual nuclear particles perturb the wave functions which correspond to motion in a common field of force. For unless these perturbations alter the problem completely I really think that one should start from the hypothetical idealised nuclear model as a first approximation instead of from a purely classical drop model. A few days ago I also talked with Ramseyg4, who pointed out the calculations in your bookg5of the viscosity of a Fermi gas, which give an infinite coefficient of friction at temperature T = 0. But in my opinion one cannot conclude from this that nuclear matter has the character of a liquid, since one is just dealing with a gas of a large mean free path, and the viscosity problem therefore takes into
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direct account only the momentum transfer over long distances. If one concludes from the formal application of the Pauli principle that the mean free path of nucleons in the nucleus is infinite, one is led to the point of view that the binding of each nucleon in the nucleus can in first approximation be treated independently. How valid such considerations are is quite another matter, and I think the main point must be to find out the significance of exchange effects and to investigate whether the exchange periods are long or short compared to the “orbital” periods appropriate to the picture. In the latter case the approach is irrelevant, but in the former case one is, as far as I can see, dealing with a rational method of approximation. I shall however be very glad to hear whether you think that these remarks meet your criticism to some degree. You will also be interested to see the enclosed copy of a letter which I received from Pauli a few days ago, and in which he expresses doubts about the correctness of our remarks on charge fluctuations. I replied at once - a copy of my letter is enclosed - that I did not think he was right, and I sent him your notes about fluctuations in the various possible cases. I did this as well as I could remember, but afterwards I was not quite sure whether you gave me these notes last year in London, or brought them with you this summer. The outcome of your discussions with Pauli will be very interesting, and I look forward to hearing more details when you have talked with him about all this. I am sending this off in haste, in the hope that it will still reach you in Tyrol, but otherwise I hope it will be sent on to you in Basle. With all best wishes from all of us to you and all your family. Yours, [Niels Bohr]
ERNEST RUTHERFORD BOHR TO RUTHERFORD,
30 June 193486
[Typewritten] UNIVERSITETETS INSTITUT FOR
BLEGDAMSVEJ DEN
15, K0BENHAVN 0.
June 30th 1934.
TEORETISK FYSIK
Dear Rutherford, As you have perhaps heard from Gamow, we have recently here made a x6
We are grateful to Cambridge University Library for providing us with a copy of this letter.
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number of experiments on induced radioactivity by neutron impact. Although so far we have mainly been able to confirm the results found by Fermi and others8’, it has given us occasion of much discussion about the nuclear disintegrations. Especially we are very doubtful as regards Fermi’s idea, that neutrons are in certain cases directly attached to nuclei under emission of radiation, and it appears to me more probable that in such cases, where isotopic radioactive elements are formed, the collision resulted in the expulsion of two neutrons from the nucleus instead of the attachment of one. This would give rise to the subsequent emission of a positron instead of an electron and might perhaps explain some observations of Joliotg8 regarding unexpected appearance of positrons. Another fact, however, which might perhaps be explained by the emission of several neutrons as result of a nuclear collision is the remarkable difference in the life time of the active nitrogen formed on one hand by bombarding Boron with a-particles and on the other hand by bombarding Carbon with protons or diplonsS9.It seems to me probable that in the first place two neutrons are emitted with the resulting formation of a nitrogen of atomic weight 12, while in the second case a nitrogen of atomic weight 13 is formed according to the usual scheme. Likely this idea is not new to you, but from a discussion we had here the other day in connection with a very pleasant visit of Leipunski it appeared to us, that it would explain all the known facts, and I should therefore be very glad to know, whether you have objections to it. I became mainly interested in the question, because it struck me that from general mechanical arguments the most likely course of the disintegration processes, by which neutrons are emitted will in contrast to what is the case with the expulsion of charged particles be that in which the greatest number of particles consistent with energy balance are expelled. A few days ago I received an invitation from Millikan to attend the congress in London in October which will surely be most interesting. It was also a great pleasure to me the other day to hear from Mr. Bjerge”, how happy he is for his work in Cambridge and for all the kindness shown him by you and your collaborators. Margrethe and I had a very interesting journey in Russia about which I look forward very much to tell you, when we meet again. We both send you and Mary our kindest regards and best wishes, yours, Niels Bohr
*’
E. Fermi, Radioattivifa indotta (provocata) da bombardamenro di neutroni, Ric. Scient. 1 (1934) 283, and subsequent publications under this title. ** 1. Curie, F. Joliot and P. Preiswerk, Radioelements Crees par bombardement de neutrons.’ Nouveau type de radioactivite, Compt. Rend. 198 (1934) 2089-2091. “Diplon” was the name used at the time instead of “deuteron”. 9” For a biographical note on Torkild Bjerge, see p. [629].
’’
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B J 0 R N TRUMPY9' TRUMPY TO BOHR,
12 February 1943
[Typewritten] PROFESSOR D R . B. TRUMPY DET GEOFYSISKE INSTITUTT
Bergen 12-2 1943. K j m e professor Bohr, Som De vet har vi her i Bergen bygget et hayspenningsanlegg for 1,8-1,9 mill. volt. Det negative raret - rantgenrerret - har v m t ferdig i noen tid og vi har med meget godt resultat behandlet kreftpasienter ved anlegget. Det positive raret er imidlertid enni ikke ferdig, vesentlig p i grunn av materialmangel, og vire planlagte undersakelser med dette raret er derfor e n n i ikke begyndt. Det var n i min tanke at rantgenrerret i ventetiden kunne anvendes ti1 visse underserkelser over kjerneproblemer, idet det kanskje var mulig i framstille kjerneisomere ved bestriling med den meget energirike rerntgenstriling. Vi kan som nevnt n i 1,8-1,9 mill. volt, og ved 1,6 mill. volt oppnir vi en rarstram p i 1 mA. Det gir en strilingsintensitet p i ca 250 r/min. i 70 cm's avstand fra antikatoden og i nmheten av denne er den tilsvarende starre. For A ake falsomheten har jeg laget tellerar av forskjellige materialer og har bestrilt selve tellererret. Forelapig har jeg undersakt Ag, Cu, Ni, Zn, Pb, Al, Sn og Fe, og forsakene ga i samtlige tilfeller et positivt resultat9*. Rarene ble aktivert ved behandling med 1,5 mill. volt rerntgenstriling, og levetiden ble milt. Ag, Cu og Zn ga alle bare en halvtid p i henholdsvis 40 sek. 28 sek. og 1,5 min. De andre elementene ga flere forskjellige halvtider som varierer fra noen sekunder ti1 mange minutter. Fe f.eks. gir ca 15 sek og 2,6 min, og Pb 1,4 min og 22 min. Jeg vil nadig p i det nivzrende tidspunkt gi niermere opplysninger om de milte halvtider da milingene e n n i er i gang og neryaktig-
B j m n Trumpy (1900-1975). Norwegian physicist. Graduated in 1922 as a chemical engineer from Norway's Technical University where he obtained his doctorate in 1927. Trumpy worked as scientific assistant and later as lecturer at Norway's Technical University from 1922 to 1935, when he was appointed professor at the Geophysical Institute in Bergen. H e studied with Born and Bohr during the years 1928-1929. When the University of Bergen was established in 1948, Trumpy became its first rektor. In 1960 he was appointed permanent Norwegian member of the Council of the European Centre for Nuclear Research (CERN). Trumpy published papers, mainly experimental, within the areas of atomic and molecular physics, cosmic radiation, earth magnetism and nuclear physics. y 2 Cf. B. Trumpy, Isomeric Nuclei, Bergens museums i r b o k , 1943, Naturvitenskapelig rekke, no. 10. "
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heten e n n i ikke kan garanteres. Tidligere kjendt er sividt jeg kan se bare en isomer for '%Ag (40 sek) og en for P b (1,4-1,6 min). *Al, med bare en stabil grunntilstand, synes i ha hele tre halvtider. Her er jeg imidlertid e n n i ikke sikker, men det er i allfall to. Jeg holder n i p i med en noyaktigere underscakelse av halvtidene og forsaker i fastlegge den kritiske spenning ved hvilken aktiveringen inntrer. Disse mange nye aktiveringsmuligheter har forbauset meg noksi meget. Feilkilder som helt kan forfalske resultatene kan jeg ikke se. Og det er tilfretsstillende i iaktta at de t o tidligere kjendte isomere med stabil grunntilstand, Ag (40 sek) og P b (1,4-1,6 sek), gjennfinnes. Det er meg ikke klart hvorledes den nivzsrende teori for de metastabile tilstander (isomere) skal kunne forenes med mine resultater. For A1 f.eks. ma de to forskjellige tilstander ifolge teorien ha en meget stor spin-differens, for at de relativt store halvtider p i ca 30 sek og 10 min skal kunne forklares. Den eneste stabile grunntilstand for A1 har spin 5/2 og mulighetene synes derfor ringe. Ei heller synes det enkelt i forklare tilstedevaxelsen av flere halvtider. Jeg vil meget gjerne komme ti1 Kjobenhavn n i r forsokene er avsluttet for A tale om mine resultater, men forelopig er det vanskelig med reisen. Det ville imidlertid glede meg meget allerede p i det nivarende tidspunkt 8 hore Deres mening om saken. Med de hjerteligste hilsener o g s i ti1 Deres frue. Deres B. Trumpy * Aluminium
Translation Bergen, 12 February 1943 Dear Professor Bohr, As you know we have built here in Bergen a high-voltage installation for 1.8-1.9 MV. The negative tube - the X-ray tube - has been ready for some time and we have treated cancer patients with very good results. Meanwhile the positive tube is not yet finished, mainly because of shortage of materials, so that the research we planned to d o with this tube has not yet started. I then got the idea that during this waiting period the X-ray tube could be used for certain studies of nuclear problems, since it seemed quite possible to produce nuclear isomers by very energetic X-rays. As I mentioned we can reach 1.8-1.9 MV, and at 1.6 MV we reach a tube current of 1 mA. This gives a radiation inten-
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sity of about 250 r/min at 70 cm distance from the anticathode, and closer to it correspondingly more. For greater sensitivity I coated counters with various materials and exposed the counters to the radiation. So far I have studied Ag, Cu, Ni, Zn, P b , Al, Sn, and Fe, and in all cases the experiments gave a positive result92. The counters were activated by treatment with 1.5 MV X-rays, and the lifetime was measured. Ag, Cu and Zn each gave only one half-life of 40 sec, 28 sec, and 1.5 min, respectively. The other elements each gave different half-lives varying from a few seconds to many minutes. For example Fe gives about 15 sec and 2.6 min, and Pb 1.4 min and 22 min. I am reluctant to give at this moment further information about measured half-lives, because the measurements are still in progress and their accuracy cannot yet be guaranteed. The only previously known isomers are one of 'S:Ag (40 sec) and one for P b (1.4-1.6 min). Al*, with only a stable ground state, seems to have as many as three half-lives. Here, however, I am not yet sure, but there are two in any case. I plan to make a more accurate determination of the half-lives and will try to determine the critical voltage at which each activation appears. These many new possibilities of activation have surprised me greatly. I cannot see any sources of error which could entirely falsify these results. It is also satisfactory to find that the two previously known isomers with a stable ground state, Ag (40 sec) and Pb (1.4-1.6 sec) are observed again. It is not clear to me how the existing theory of metastable states (isomers) can be reconciled with my results. For Al, for example, the theory would require the two different states to have a very large spin difference, to explain the relatively long half-lives of 30 sec and 10 min. The only stable ground state for A1 has a spin of 5/2, and the possibilities therefore seem few. It also does not seem easy to explain the existence of many half-lives. I shall be glad to come to Copenhagen when the experiments are finished and talk about my results, but at present travel is difficult. Meanwhile I would be very pleased to hear already now your views on the matter. With kindest regards, also to your wife, Yours, B. Trumpy
Plluminium
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BOHR TO TRUMPY,
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16 February 1943
[Carbon copy] [Kerbenhavn,] 16. Februar [19]43. K a r e Professor Trumpy, Tak for Deres venlige Brev. Det glzedede mig meget at herre om Deres interessante Forserg. Jeg synes, at det er en valdig god Ide at bestraale selve TAlerrerret, naar det gzelder om at underserge svage Effekter, og det ser jo ud, som om De har fundet en ny og virksom Metode ti1 at efterspore Kerneisomerer. Forklaringen paa, at Atomerne kan bringes i saadanne Tilstande, turde vzere, at Kernerne ved Straalingen, der j o har kontinuert Frekvensomraade, kan bringes o p ti1 en eller anden af de stationme Tilstande med Anslagsenergi omkring 1.5 MeV, og at de derfra, foruden at falde tilbage ti1 Normaltilstanden, har Mulighed for at gaa over ti1 andre Tilstande med lavere Energi og med et fra Grundtilstanden forskelligt Spin. Fra den velkendte Formel for Energien i de forskellige Rotationstilstande falger det jo, at der selv for lette Kerner som A1 maa v a r e Energiniveauer med forskelligt Spin under 100.000 eV. Sandsynligheden for en Overferrelse fra den ferrst anslaaede Tilstand ti1 en af disse metastabile Tilstande vil afhange af Niveaufordelingen, idet der for at opnaa sterrre Spinforskelle maa krzves et ikke altfor ringe Antal Overgangsmuligheder. Som De skriver, vil det derfor v a r e meget interessant at underserge, hvorledes Fremkomsten af aktive Isomerer og deres Antal vil afhange af Rerntgenstraalernes maksimale Energi. Jeg skal v a r e overordentlig interesseret i at herre om Fortsmtelsen af Forsergene, og i s a r glEder vi 0s alle over Muligheden for snart at se Dem her i Kerbenhavn igen. Med de hjerteligste Hilsener og bedste 0nsker Deres hengivne [Niels Bohr]
Translation [Copenhagen,] 16 February 1943 Dear Professor Trumpy, Thank you for your kind letter. I was very pleased to hear of your interesting experiments. I think it is a very good idea to irradiate the counters themselves when one is examining very weak effects, and it does look as if you have found a new and effective method for tracing nuclear isomers. The explanation how the atoms can be brought to such a state is presumably that the radiation, which after all has a continuous frequency spectrum, can excite the nuclei to one or other
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stationary state with an excitation energy of about 1.5 MeV, and from there, besides dropping back to the ground state, there is the possibility of a transition to other states of lower energy and with a spin differing from that of the ground state. From the well-known formula for the energy in the various states of rotation it follows that even for such light nuclei as A1 there should be energy levels with various spin values below 100 000 eV. The probability of a transition from the initially excited state to one of these metastable states will depend on the level distribution, in that a large spin difference may be reached through a not too small number of possible transitions. As you say, it will therefore be very interesting to investigate how the appearance of active isomers and their number depend on the maximum energy of the X-rays. I shall be extremely interested to hear of the continuation of the experiments, and all of us are especially pleased at the possibility of seeing you soon again here in Copenhagen. With kindest regards and best wishes, Yours sincerely, [Niels Bohr]
JOHN A. WHEELER BOHR TO WHEELER,
20 July 1939
[Carbon copy] UNIVERSITETETS INSTITUT FOR
BLEGDAMSVEJ DEN
15,
K0BENHAVN 0.
20-7 1939
TEORETISK FYSIK
p.t. Tisvilde Dear Wheeler, I hope you have received my telegram explaining the delay in answering your kind letter containing the manuscript of our paperg3. I received it and your telegram when I a few days ago returned from a small journey to Sweden, planned when I expected the manuscript at a somewhat earlier date. I read through it with great pleasure and admiration for all the work you have done with it and it was of course very tempting to wire that it could be published in the present state. Still I felt that a few smaller alterations were advisable and y3
Introduction, ref. 121
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I hope that the delay of publication caused by this letter will only be small. The first point concerns the considerations on the last pages of Section 11. I must confess that I am not clear of the exact interpretation and generality of equation (28). I suppose that Vmeans the difference between the total energy and the potential at a given point in configuration space, but what is to be understood exactly with &;Ida is not quite clear to me. In particular however I do not understand why you have left out the usual factor 2 in the exponent, which refers to the square of the wave amplitude determining the quantum-mechanical intensities. It appears to me that the inclusion of this factor in equation (28) as well as in equation (30) changes the situation entirely and brings at once the life time of a nucleus in the ground-state up to a far more reasonable value. In connection with the estimate of this life time I do not also quite understand the difference between the values obtained by equation (28) and (30) and it appears even to me that quite apart from the factor 2 already mentioned, it is rather an underestimate to take the width of the barrier equal to the nuclear radius rather than the nuclear diameter. At the same time I do not quite understand the point in your last sentences. Of course the question of the proper treatment of the tunnel effect for fission is a very intricate one, but the only simple estimate seems to me to be obtainable just on the lines indicated by equation (30), and it would therefore raise a very serious paradox suggesting a doubt of the value to be taken for the barrier height if actually this estimate led to so short a life time as given in the paper, and which is much smaller than the estimate we, as far as I remember, came to in our discussions in Princeton. I would therefore propose that the last pages in section 11, beginning perhaps with the 3rd line from bottom of page 17, was changed somewhat in the following way: “An accurate estimate for the stability against fission of a heavy nucleus in the ground-state will of course involve a very complicated mathematical problem. Still applying the well-known theory for the wray decay a determination of the order of magnitude of the life time due to fission can be obtained by comparing the nucleus with a simple system consisting of two approximately equal masses held together by a force exhibiting a potential barrier of a height comparable with the critical fission energy and a width comparable with the nuclear diameter.” (Here I do not know what and how many formulae you would think it reasonable to introduce, but I am sure it would be easy, for instance by explaining the reduced masses to be applied to keep the same numbers of the formulae as in the present text. Incidentally also the reference at page 21 to the present equation (28) must perhaps be changed.) “It will be seen that the life time thus estimated is not only enormously large compared with the time interval of the order sec. involved in the actual fission processes initiated by neutron impacts, but that this is even large compared with the life time for uranium and
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thorium for a-ray decay. This remarkable stability of heavy nuclei against fission is as seen due to the large masses involved, a point which was already indicated in the quoted article of Meitner and F r i s ~ h where ~ ~ , just the essential character of the fission effect was stressed.” Of course it will be easy for you, if you agree in the main argument to find the proper form for the indicated alterations. I may only mention that a reference to the work of Meitner and Frisch at this place appears to me to be especially appropriate since they took a very clear and correct attitude to this fundamental point. I f , however, by closer consideration of the whole estimate and in particular of the odious factor 2 you find that I have made a fool of myself you shall of course just write what you think defensible and sufficiently cautious. The other places where I should like to propose alterations are much smaller and only a question of form. As you will see from the enclosed pages 26, 27 and 56, I have in ink introduced proposals of alterations as regards the reference to the paper of Peierls, Placzek and me, the intentions of which are to bring the text in the manuscript to harmonize as much as possible with the little note which I enclose for your information and which will appear in Nature” in one of the next issues if it has not already appeared when you get this letter. In this connection I should also like to draw your attention to the spin factors which appear in the formula (42) and which are omitted in (37) although strictly such factors follow from the statistical deduction of this and several other formulae in Section 111. It is in no way my intention to insist on further complications in the text of this paragraph but only t o ask you to consider the question of consistency of representation. Actually the specification of the spin problem is somewhat more complicated than most of the formulae in the paper indicate since we shall expect a dependence of all the r’s on J , but for our purpose such finesses are of course of small importance and you may perhaps just once more consider the question of reasonable consistency in this respect. (If you for such purposes compare any formula with those in the Nature-note, I would just like to say that while equation (1) and (2) are of course quite general, it is in ( 3 ) and therefore also in (4) for brevity tacitly assumed that s = 0 and i = 0.) As a still smaller point I should also like to draw your attention to a few of the references to the literature. First of all I found that it would perhaps not appear reasonable to cite Abelsong6 on page 1 quite parallel with Hahn and
Introduction, ref. 98. Introduction, ref. 82. ‘)‘ Abelson published a number of papers in Phys. Rev. in 1939, identifying various fission products by their X-ray emission.
y4
9
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Strassmann. If you think a reference to Abelson is necessary at this place I would at any rate propose that the words “See also” was introduced before his name. On page 2 I missed a reference to the work of the Columbia group in reference (3), but this is of course only of very small importance since the work of this group is cited in reference (4). On page 21 I thought that it would be correct at the end of reference (10) to add “ A short abstract of this paper has since appeared in Phys. Rev. 5 5 , 987 (1 939). ” As regards Frenkel’s paper I have not yet seen the full publication announced, but I suppose that you have studied his manuscript, which I believe was left in your hands, sufficiently closely, that we can defend not to enter more detailed in his work, which as far as I gathered from the first perusal of his manuscript and from the abstract in Phys. Rev.” has not got hold of any of the more essential points discussed in our paper. If you have Frenkel’s manuscript with you I should be glad if you at opportunity would kindly send it to me as I want to write t o him about it. As a last very smallest point I would like still to ask you to introduce after my name in the title the words: “University of Copenhagen, p o t . The Institute for Advanced Study, Princeton”, as I am afraid that the present title might give rise to the misunderstanding that I was now permanently in Princeton. In concluding this letter which I hope will not give you too much trouble I wish once more most strongly to give expression for the very great pleasure our collaboration has given me and the hope that we shall be able to continue such collaboration in a near future. I wish also on behalf of Erik and me to thank your wife and yourself for all the kindness you showed us during our stay in Princeton which was a so delightful and interesting time to both of us. Yours ever [Niels Bohr]
BOHR TO WHEELER,
4 October 1939 (1)
[Draft telegram] See p. [ 7 2 ] .
’’ J . Frenkel, On the Splitting of Heavy Nuclei by Slow Neutrons, Phys. Rev. 55 (1939) 987.
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E (1929-
BOHR TO WHEELER,
1949)
4 October 1939 ( 2 )
[Carbon copy] [K~benhavn,]October 4, 1939. Dear Wheeler, It was a great pleasure to me yesterday to receive your kind letter with the proposal of a joint note on the protactinium fission’’, about the discovery of which I had no previous knowledge, since no copies of the “Physical Review” of August 15, have as yet arrived in Copenhagen. A few days ago, however, I had received the issue of September 1, with our long paper, which I was very happy to see in print. I have also managed now to see the issue of August 15, which on telephone inquiry was kindly lent me by the Physical Institute in Lund. While I, of course, was in complete agreement with the content of the new note and with the desirability of a comment from our side on the subject, I found, however, that it might perhaps be more advisable t o give it a somewhat different form. As you will see from the enclosed proposal of a new redaction, I thought it better to start with the mention of the new discovery and to give a comparative survey of all cases of fission hitherto known, based on our theoretical estimates. Above all, this permits us, as I thought, better to emphasize the qualitative character of our estimates and to draw attention to the way in which new useful information could be obtained by the continuation of the experiments. Of course you are perfectly free to make any change in the form and content which you may think desirable. As regards our long paper, I admired, when reading it again perhaps still more all the work you have put into it and the many most instructive diagrams you have composed. In connection with the estimate of Ef,Fig. 4 is certainly most adequate but, of course, I need not emphasize that the shape and curvature of the curve in the important region are not so well fixed that small alterations in the estimates should be quite excluded. Just for this reason a threshold estimate for P a by use of the argument illustrated by Fig. 6 would of course be most welcome. Our collaboration has given me the greatest pleasure indeed and I have therefore most heartily appreciated its continuation in our new note. As well Rosenfeld as Erik and I speak very often of the happy times we in spite of all anxieties spent in Princeton where we all so much enjoyed the truly human and scientific spirit of the whole little community. In Europe life is surely most upset at present, but in this small neutral country we try notwithstanding the increasing difficulties to go on with the work and at the moment the experiments in the
‘)’Introduction,
ref. 125.
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laboratory go quite well and I have also myself made some progress with the various investigations which I have so long time had in my mind and which I hope to [be] able to publish soon. Also all the boys are occupied with their school and university work. All the time, however, we are aware that a catastrophy might come any day and I need not say how thankful my wife and I are for your and Mrs. Wheelers kind thought of offering to have one of the boys with you for a time. This would of course under circumstances be extremely helpful for us and at the same time a source of the greatest pleasure to any of the boys. By hearing about it Erik was indeed more than ready to return to America at once. Even if we do not think it would be wise to make any such decisions at the moment we are naturally most thankful to you both for the possibility of taking it into serious consideration if any great change for the worse should take place. With our kindest regards and best wishes Yours [Niels Bohr]
BOHR TO WHEELER,
16 December 1939
[Carbon copy] [K~benhavn,]December 16, [19]39. Dear Wheeler, Recently we have here, especially in connection with the study by Meitner and Frisch of the various radioactive products of uranium and thorium fission99, been very interested in the statistical distribution of the fission fragments. You will remember that we discussed this problem last spring in connection with the Columbia experiments, but that we did not then arrive at any final conclusion as regards the explanation. In the last weeks, however, I have been reconsidering the matter and find, if I am not wrong, that it is not only possible by means of the calculations in our paper to obtain a simple interpretation of the observed asymmetry in the nuclear fissions, but that even our estimate of the fission probability and its variation with neutron energy strictly speaking involves the assumption that the mode of division of the nucleus in two parts is practically confined to a very small number of possibilities. I have, therefore, written a short note'" which I am enclosing and which I should propose, if you agree, that we
''
L. Meitner and O.R. Frisch, Products of the Fission of the Uranium Nucleus, Nature 143 (1939) 411-412; On the Products of the Fission of Uranium and Thorium under Neutron Bombardment, Mat.-Fys. Medd. Dan. Vidensk. Selsk. 17, no. 5 (1939). See also ref. 7 7 . l o o Introduction, ref. 128.
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send jointly to the Physical Review as an addendum to our paper. As you will see, I have not done anything else than to use the calculations of Sections I and I1 for an estimate of the critical energy for different divisions based on a comparison between the total energy released and the potential energy of the fragments at contact. I am of course aware that such a comparison cannot give any quantitative estimate, but I am primarily thinking of such general conclusions as can be immediately derived by looking at the beautiful diagram illustrating the fission mechanism which you prepared for the Washington Meeting and which I regretted for a moment that you omitted from the many other beautiful figures printed in our paper. In the note I have therefore proposed to include a few figures to illustrate the argument. As regards the derivation of the fission probability given in Section I11 of our paper, I had already this summer, when I received the manuscript, some doubt as to the permissibility of estimating the statistical weight of the transition state only by the additional possibilities of excitation of the system. I do not only think of the more formal difficulty in counting stationary states for the short-lived transition state but, primarily, of the question of how to discriminate between the different modes of dividing the particles of the compound nucleus into two separate nuclei. At that time I thought, however, that this problem could be simply solved by the introduction in formula (32) of a factor taking account of the relative statistical weights of these various modes of division and that the estimate of the total output would, therefore, not be seriously changed even if we had to do with a considerable latitude of division modes. In connection with the completion of the work on the paper with Peierls and Placzek"', of which I hope soon to send you a proof, I have, however, studied the general consequences of statistical arguments to nuclear problems more closely and have come to the conclusion that, in a case like ours, the argument presupposes a given mode of division which, of course, may have a certain latitude on account of the irreversible rupture and accompanying neutron emission. I believe in fact that, if the probability of fission was nearly the same over a considerable range of division possibilities, the total output of si [Si ?] [in] fission should be much larger than that found experimentally and, if I am right, this argument therefore constitutes an independent support of the selectivity of the fission process revealed by the study of the energy distribution of the fragments and of the chemical properties of the fission products. I hope that you will find this conclusion correct and that you will check most critically my estimates of the energy balance. Of course you are entirely free, if you think it desirable, to introduce a few mathematical formulae and some more Ill/
Introduction, ref. 86.
P A R T I!:
SELECTED CORRESPONDENCE
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detailed numerical calculations or any other wanted additions and corrections in the note. From my conversations with Tate I got the impression that a note like this would be more suitable as a short article in “Physical Review” than as a “Letter to the Editor”, and that it would not mean any greater delay in the publication. Also as regards this point I shall of course leave the matter entirely to your judgment. If you do not wish to introduce substantial changes, it will hardly be necessary for me to see the proof. But I should be glad to hear from you at your earliest convenience as regards your attitude to the argument and also to receive a copy of the manuscript in its final form. If required I shall then at once telegraph to you as regards any point about which you want my opinion. With many grateful thoughts at our collaboration in this year which has nearly passed and which has been so full of joyful and tragic events, and with kindest regards and best wishes for the New Year from us all to Mrs. Wheeler and yourself, Yours, [Niels Bohr]
P.S. Your kind letter of December 8, with the original drawings of our paper in Physical Review, has just arrived. I was very interested in learning about your own work and the experimental work in the laboratory, and I send the kindest regards and best wishes to all common friends in Princeton.
WHEELER TO BOHR,
19 January 1940
[Telegram] See p. [73]
WHEELER TO BOHR,
[Telegram] See p. [73].
12 February 1940
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E
BOHR TO WHEELER,
(1929-1949)
4 July 1949
[Carbon copy] [K~benhavn,]July 4th, 1949. Dear Wheeler, It was a great pleasure to learn that you and Mrs. Wheeler and the children will be in Europe next year and my wife and I look forward very much to see you both here and not least would I enjoy if we could take up some work together like in old days. The manuscript you sent me''' came as a great surprise but, realizing that it more represents an account of the discussions we through the years have had about the theme rather than some original contribution of which I feel innocent, I do not only agree with the plan, but welcome it as a token of the continuation of our co-operation. Since I received it just before leaving Copenhagen for the country, I should like to think a few days whether I might suggest some smaller alterations or additions and shall then write t o you again. With kindest regards and best wishes from us all, Yours, [Niels Bohr]
BOHR TO WHEELER,
13 July 1949
[Carbon copy] UNIVERSITETETS INSTITUT
BLEGDAMSVEJ
15
FOR
COPENHAGEN, DENMARK
TEORETISK FYSIK
p.t. Tisvildeleje, 13.7. [ 19149.
Dear Wheeler, I hope you have received my answer of your kind letter which I sent you just before leaving Copenhagen. In the meantime I have been able to study the paper more carefully and although on the whole I agree with the content I have thought that in some points alterations in the exposition might be helpful. As regards the main point of a dynamical explanation of asymmetrical fission, I entirely agree with the trend of the arguments, but I wondered whether these ought not to be developed a little more explicitly. In this connection I also felt that the phenomenon of a-ray release in fission might be treated somewhat more in detail by very simple considerations I0 2
Introduction. ref. 131
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As regards principles the major question is, of course, the extent to which classical mechanical considerations can be applied to the fission process. While, as argued in our old paper, we have in the initial deformations t o do with high quantum states where zero-point effects may be neglected for the purpose, the equilibrium problems in the transitory stages are more delicate and arguments may be given for the importance of quantum effects in determining the probability of the final issue. The inadequacy of Frenkel’s attempt to explain the asymmetry by typical tunnel effects is certainly very strikingly illustrated by the impossible consequences as regards the variation of the cross-section with activation energy, but I thought that it might also be stressed that the absolute values of the lifetimes (or partial widths) of the various radiation and disintegration processes obtained by the familiar considerations are throughout in approximate agreement with experience. More jokingly, I may confess that I do not quite understand the sentence that the “helpful consultation with Dr. Havas failed to disclose the source of the discrepancy” - Quite apart from the very illustrative comparison of the nuclear masses given in the figures the main point is here to me the irrelevance of such comparison as regards conclusions about the transitory states of the fission process. A minor point are the incidental remarks in the note (8) on p. 5. Of course, the presence of the individual nucleons sets a limit to the liquid drop model but as far as this model is taken literally, i.e. the thickness of the surface layer is considered vanishingly small compared with the dimensions of the drop, a drawing out of the liquid to a fine thread will demand a very great expenditure of energy. It is true that the potential energy of the electrification will tend to vanish, but the surface energy will increase in a measure of the same order as the ratio between the radius of the drop and the radius of the cross-section of the thread. In this connection I am also not sure that I quite understand the speaking of equilibrium states. Surely, the thread itself will, quite apart from its instability to accidental disturbances, immediately start t o contract by the ends if left to itself. Moreover, if a finite part of the electrified matter is found in two spheres at the ends of the thread the tension of the latter which is proportional to its circumference will not be able to resist the repulsion of the spheres. These remarks are, of course, quite trivial, but I have wondered whether the note as it stands could not give rise to confusion in the mind of readers. It would be very tempting to me to help in an effort to bring the little but, I am sure, to many welcome article in a shape in which the arguments were still more accessible. Just now I am very occupied with pressing duties, and in a few days I am expecting a visit by Rosenfeld to complete our old paper about field
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and charge measurements, but if you and Hill have no objections to a little delay in the publication of the note it would be wonderful if you could visit us here and work with me on it for a week’s time either in August in Tisvilde or in September in Copenhagen. I need not say that it should be a very great pleasure to my wife and me if Mrs. Wheeler could join you. With kindest regards and best wishes Yours, [Niels Bohr] P.S. From Hill’s letterlo3 accompanying the manuscript I understood that he would send me an appendix one of the next days, but I have not heard from him since and I have also so far not written to him. Still, I suppose that you are yourself keeping in touch with Hill.
WHEELER TO BOHR,
3 September 1949
[Typewritten] Les Goelands St Jean-de-Luz, B.P. France September 3, 1949 Dear Professor Bohr, Thank you for your recent letter and for your considerations on the relation between the liquid drop model and the independent particle model of the nucleus. I am especially anxious to learn from you your feeling about the quantitative side of this question - how far for example, a nucleon of typical energy can travel through the nucleus without large exchange of energy with the other nucleons. I enclose the text of an appendix on neutron emission just received from Hill, together with captions for figures 1, 2, 3 and 4 and preliminary drawings for figures 1 and 4. John Toll who is here with me and I have just been looking into the problem of propagation of light in vacuo when electric and magnetic fields are present. The double refraction of space which occurs shows some very interesting properties. In particular this refraction connects up with an interesting type of absorption which we have never seen discussed previously, in which a gamma ray of for lo’
Hill to Bohr, 15 J u n e 1 9 4 9 . BSC, microfilm no. 33
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example 10’’ electron volts can travel only a few centimeters in vacuo, subject t o a magnetic field of 20,000 gauss, without creating a pair. It is interesting that the cross section for this process is proportional to the first instead of the second power of the magnetic field strength. I hope to talk with you about the reconciliation between some results obtained from the Dirac theory of the electron and Mdler’s theorem about proportionality of space extension of a dynamical system and angular momentum of that system’04. In the case of the Dirac electron it turns out that the higher the angular momentum the smaller the size of the region within which it can be localized. The other subject with which I have been concerned during these past weeks is the description of nature in terms where the notions of space and time do not enter, the analogue for gravitation of the action at a distance description of electrodynamics. Obviously the notion of dimensionality does not enter into this description. Consequently it is interesting to ask what conditions must be imposed on the description in order that it should reduce in the case of very many particles to the usual three plus one dimensions of space time. It will be a pleasure t o discuss these and other questions with you in Copenhagen. Sincerely, John Wheeler
WHEELER TO BOHR,
12 December 1949
[Typewritten] Pension Domecq 70 rue d’Assas Paris 6 , France December 12, 1949 Dear Professor Bohr, Thank you for your recent letter and the interesting news about your Edinburgh lectures and the progress of your work with Rosenfeld and with Peierls. Since my return from Copenhagen I have spent the majority of my time working on the paper on which we made so much progress in Copenhagen. The principal points which have taken the most time are the question of quadrupole moments and the question of justifying the liquid drop model from Cf.C. Maller, On the Definition of the Centre of Gravity of an Arbitrary Closed System in the Theory ofRelativity, Comm. Dublin Inst. Adv. Study, Series A, no. 5 (1949). See also C. Maller, The Theory of Relativity (2nd ed.), Oxford Univ. Press, 1972, sect. 6.3. lo4
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1949)
the point of view of the individual particle picture by standard quantum mechanical methods, in addition to the clear - and of course to us convincing - reasoning of the paper as it stood when we separated. It has turned out to be possible to show very clearly that the quadrupole moment created by deformation of the nucleus by a single particle in an otherwise empty shell exceeds by a factor of approximately five the quadrupole moment directly due to the charged distribution of that particle itself. This result explains the paradox pointed out in the last Physical Review by Foldy, which has up to now presented great difficulties for the explanation of nuclear quadrupole moments. It also turns out that the deformation of the nucleus caused by one unbalanced particle greatly affects the energy level spacing for the next particle. Consequently there is a coupling effectively brought into play between one particle and another which must greatly influence the order of filling of incomplete shells. The other point which has presented more difficulty is to find a type of wave function which will bring into evidence the capillary oscillations of the liquid drop model starting from the individual particle picture. Obviously standard perturbation theory is not at all in order in this case, since the correlations between the motions of the several particles which are called for would require one in that type of perturbation treatment to use mixtures of states in which many particles are simultaneously excited. Instead of this what I have done is to represent the wave function of the system as a super-position of determinants built out of individual particle wave functions all calculated for a particular deformation of the nucleus. The determinant in question is multiplied by a function of the deformation and is summed over all values of the deformation. The expectation value of the energy is then expressed in terms of the single unknown function of the deformation. It turns out that this expectation energy consists of two parts, of which one describes the potential energy of the deformation, and the other describes the kinetic energy of deformation (i.e., contains derivatives of the function in question). The difficulty at the moment is about the dependence of this kinetic energy term upon the number of particles in the system. I had expected a coefficient inversely proportional to the first power of the number of particles but find a coefficient inversely proportional to the three halves power of the number of particles. It is difficult for me to believe that literal acceptance of the single particle picture should cause such a great discrepancy and I am trying to find the source of this trouble. If you think it would be better not to attempt to do this before publishing the paper I should be glad to have your advice what would be best to do. I do, however, feel that it will add much to the convincing power of what we have to say to be able to give a mathematical demonstration. I enclose four or five small photographs sent o n by Hill. They amply justify the view that the asymmetry can be largely explained by the magnification of
PART 11: SELECTED CORRESPONDEKCE
(1929- 1949)
small original asymmetries during the course of the division process, as you will note. Hill mentioned in his letter that he had carried the computations further than the time intervals indicated in the diagram but he has as yet not sent on curves based on these later moments, nor the more extensive details of his work. I will report to you when I hear from him. I have been planning to visit Manchester about January 25th in order to see the cosmic ray work in progress there and talk with several of the people. You mention in your letter the possibility of my coming to Copenhagen to talk with you. This would be the greatest pleasure for me because there are so many problems of common interest to discuss. I would be very glad to hear from you if it would be convenient to come to Copenhagen either the week before my visit to Manchester (January 14-21) or the week just after (January 27 - February 3). Please remember me to Mrs. Bohr and thank her for her patience in letting me take so much of your time when I was last in Copenhagen. Janette joins me in sending best Christmas and New Year’s wishes. Sincerely, John Wheeler
WHEELER, 24 December 1949 [Carbon copy]
BOHR TO
[K~benhavn,]December 24, [19]49 Dear Wheeler, Thank you for your letter in which I was of course very interested, and I have in these days discussed its content with Lindhard who works this year with Peierls in Birmingham and is at the moment here on Christmas vacation. What you tell about your considerations of the quadrupole moment of a nucleus with one particle in an otherwise empty shell seems to us very beautiful and convincing and, as we understand, the point is that the deformation of the nucleus arising from the presence of this particle will imply a comparatively large additional quadrupole moment of the particles in the closed shells. As regards the problem of the treatment of the oscillations of an excited nucleus, starting from an individual particle picture, we are, however, not certain that we fully understand your considerations. The attack is surely of a very direct kind, but it seems not beforehand quit,e clear to me how one can analyse the effect of the nuclear deformations and their time derivatives so generally. It would seem that the actual physical problem is rather to examine the semiadiabatic changes of the individual particle binding accompanying the oscillatory
P A R T 11: S E L E C T E D C O R R E S P O N D E N C E ( 1 9 2 9 -
1949)
deformations of the whole nucleus, and that the justification for the customary treatment of the problem should be the appearance of additional terms in the whole nuclear energy of a type corresponding to those of capillary oscillations of a liquid drop. It might perhaps not be justified to expect such results and it would surely be most interesting if the additional energy was of another type, but, as said, I am quite prepared that we have not understood your considerations properly and I shall be very glad indeed if you could explain your calculations and results in somewhat more detail. Your question whether any more exhaustive treatment of the problem should be attempted before the publication of the paper is a matter on which I find it difficult to give any advice before understanding it better, although, of course, it would be most desirable if the problem could be cleared up. Just for such and for many other reasons I am happy that you will be able to visit us in Copenhagen in the near future. As you know, Rosenfeld will come here in the two first weeks of January to revise our paper on the problem of measurements in quantum electrodynamics and it might therefore be the very best if you could come in the week from January 14th to 21st. If, however, unforeseen disturbances should occur, it would also be very convenient if you came in the week from January 27th to February 3rd on your return from Manchester. As soon as I hear from you how it stands with the work and I can survey my plans it will perhaps be easier for us to judge what is the most practical time for your visit to which everybody here is looking forward very much. Hoping that you and your family are enjoying a happy Christmas, my wife and I send you all our kindest greetings and warmest wishes for the New Year. Yours, [Niels Bohr]
INTRODUCTION
The folders listed below form part of the collection of Bohr Manuscripts in the Niels Bohr Archive. All except one are microfilmed under the designation “Bohr MSS”, and the corresponding microfilm number is given for each folder (abbreviation, mf.). The titles of the folders have been assigned by the cataloguers, as have all dates in square brackets. Unbracketed dates are taken from the manuscripts. During the work on the present volume some dates have been confirmed, while others have been corrected, as indicated in footnotes. Numbers in the margin facing an item indicate the pages on which the item is reproduced; they are followed by the letter E if only excerpts are given. Items for which English translations are given are indicated by the letter T.
INVENTORY OF MANUSCRIPTS IN THE NIELS BOHR ARCHIVE
I851-[891
1 ,&Ray Spectra and Energy Conservation 1929 Carbon copy, handwritten [O. Klein], 5 pp., English, mf. 12. Unpublished manuscript.
2 Faraday Lecture 1930 Typewritten with carbon copy (12 + 11 pp.) and one handwritten page [H.B.G. Casimir], 24 pp., English and Danish, mf. 12. Probably typescript of shorthand report of the Faraday Lecture, given on 8 May 1930. The handwritten sheet is dated 3 October 1930. [ I I ~ J - [ I I ~EI
3 Properties of the Neutron 1932 Typewritten and carbon copy with handwritten corrections [N. Bohr, 0. Klein and L. Rosenfeld], 10 pp., English, mf. 13. Unpublished manuscripts, dated between 18 and 25 April 1932.
[1231-[1271E
4 Electron and Proton [1933-19341 Typewritten, carbon copy and handwritten [Betty Schultz], 10 pp., English, mf. 13. Unpublished manuscripts.
[1431-[1471E
5 Neutron Capture and Nuclear Constitution [ 1935-19361 Typewritten, carbon copy and handwritten [F. Kalckar and L. Rosenfeld], 11 pp., English, mf. 14. Manuscripts and outline. Titles: “The Nuclear Constitution and Neutron Captures” and “Nuclear Constitution and Quantum Mechanics”.
6 Neutroners Indfangning [ 1937?] Typewritten and carbon copy with handwritten corrections [F. Kalckar], 14 pp., Danish, mf. 14. Unpublished Danish version of “Neutron Capture and Nuclear Constitution”, Nature 137 (1936) 344-348.
7 Transmutation of Atomic Nuclei [1936-19371 Typewritten, carbon copy and handwritten [N. Bohr and F. Kalckar], 54 pp., English and Danish, mf. 14. Drafts for the Bohr-Kalckar paper.
’ Catalogued as of
[1932]. Catalogued as of [1936].
INVENTORY OF MANUSCRIPTS IN THE NIELS BOHR ARCHIVE
[I7Y]-[IRI]
8 Selective Capture of Slow Neutrons [1936] Typewritten and carbon copy with handwritten corrections [N. Bohr and F. Kalckar], 3 pp., English, mf. 14. Incomplete draft of unpublished paper.
I1831-[189J
9 Disintegration of Atomic Nuclei [IIJ [1936] Carbon copy with handwritten corrections [F. Kalckar], 8 pp., English, mf. 14. Unpublished manuscript. entitled “On the Disintegration of Aluminium by a-rays”.
I I I ) I J - I IEY ~ J
10 Excitation and Radiation [1936] Typewritten, carbon copy and handwritten [F. Kalckar, L. Rosenfeld and N. Bohr], 15 pp., English and Danish, mf. 14. Incomplete draft, entitled “Excitation and Radiation of Atomic Nuclei”.
11 Disintegration of Atomic Nuclei [IJ [1936-19371 Typewritten and carbon copy with handwritten corrections [N.Bohr, F. Kalckar and unidentified], 8 pp., English, mf. 14. Incomplete draft, entitled “On the Disintegration of Atomic Nuclei by Impact of Charged Particles”. IIYSI-II~XI E
12 Spin Exchange in Atomic Nuclei [1936] Typewritten, carbon copy and handwritten [F. Kalckar, L. Rosenfeld, N. Bohr, P.A.M. Dirac and unidentified], 18 pp., English and Danish, mf. 14. Incomplete drafts, entitled “Spin Exchange in Atomic Nuclei” and “Spin Exchange between Nuclear Particles”. One page is dated 7 April 1936.
IIYYI-[ZO~I E
13 Transmutations of Lithium by Proton Impacts 119361 Carbon copy and handwritten [F. Kalckar and N. Bohr], 9 pp., English, mf. 14. Draft of unpublished paper.
14 Moscow Lecture 1937 Typewritten, 24 pp., English, mf. 14. Typescript of shorthand report of lecture on the properties of atoms and nuclei, given to the U.S.S.R. Academy of Sciences in Moscow on 19 June 1937. Catalogued as of [1937].
INVENTORY OF MANUSCRIPTS I N THE NIELS BOHR ARCHIVE
[ ~ ~ I I - I ~ SEZ I
15 Nuclear Mechanics 1937 Typewritten, carbon copy and handwritten [L. Rosenfeld, J.C. Jacobsen, F. Kalckar, N. Bohr and unidentified], 79 pp., English, Danish and French, mf. 14. Drafts related t o Bohr’s addresses to the International Congress of Physics, Chemistry and Biology in Paris, 30 September - 7 October 1937. Many pages are dated, all except one carrying dates between 3 October and 3 December 1937.
[2831-[2851 E
16 Various Notes [z] [1937-1938?] Carbon copy and handwritten [F. Kalckar, L. Rosenfeld and N. Bohr (?)I, 11 pp., English, mf. 14. Notes and calculations, i.a. concerning nuclear vibrations and rotations. One page has the title: “Interaction between Neutrons and Nuclei”.
12911-I2961 T
17 Nuclear Excitations and Isomeries 1937 Typewritten, carbon copy and handwritten [G. Placzek and L. Rosenfeld (?)I, 5 pp., English and Danish, mf. 14. Unpublished manuscript, dated 7 December 1937.
18 Nuclear Photo-effects [1937-19381 Typewritten, carbon copy and handwritten [F. Kalckar, N. Bohr and L. Rosenfeld], 10 pp., English and Danish, mf. 15. Material for paper: Nature 141 (1938) 326-327. Most pages are dated, carrying dates between 20 December [I9371 and 31 January 1938.
19 Various Notes [IIZ] 1938 Carbon copy and handwritten [unidentified], 2 pp., English and Danish, mf. 15. Address to the British Association for the Advancement of Science, given o n 18 August 1938. Preface to popular Danish book on atomic physics.
20 Nuclear Reactions in Continuous Energy Region 1938-1940 Typewritten, carbon copy and handwritten [N. Bohr, R. Peierls, L. Rosenfeld and unidentified], 323 pp., English and Danish, mf. 15. Material for Bohr-Peierls-Placzek paper. More than half the pages are dated, carrying dates between 1938 and 1940. Catalogued as of [1935-19371. Catalogued as of [1938].
INVENTORY OF MANUSCRIPTS IN THE NIELS BOHR ARCHIVE
13471.13~31T
21 Summary on Fission 1939 Carbon copy with handwritten corrections [L. Rosenfeld], 5 pp., Danish, not microfilmed. Probably review sent to Rasmussen 10 March 1939.
135~1.13571 E
22 Notes from Bohr’s Stay in Princeton 1939 Handwritten [Erik Bohr, N. Bohr and L. Rosenfeld], 15 pp., English and Danish, mf. 16. Manuscripts entitled “Residual Excitation of Heavy Nuclei after (3-ray Emission” and “Spin Dependence of Nuclear Forces”. Lecture notes, dated 20 March and 27 March 1939.
[!951-[3YR]
23 Chain Reactions of Nuclear Fission 1939 Typewritten and carbon copy, 3 pp., English, mf. 16. Unpublished manuscript, dated 5 August 1939.
[3Y9]-[402]
24 Fission of Protactinium 1939 Carbon copy, 2 pp., English, mf. 16. Unpublished manuscript. Handwritten note by Bohr: “Wheeler’s first proposal”.
[402]-[4081 T
25 Teori for Atomkerners Fission Typewritten, 1 p., Danish, mf. 16.
1939
Outline of address to the Royal Danish Academy, given on 3 November 1939. 14h71-14731 E
26 Statistical Distribution of Fission Fragments [ 1939?] Typewritten and carbon copy with handwritten corrections [L. Rosenfeld], 10 pp., English, mf. 16. Drafts of unpublished paper.
lJxil-1slill E
27 Mechanism of Transmutations of Atomic Nuclei 1947 Carbon copies and handwritten [G. Placzek], 46 pp., English, mf. 17. Drafts of the unpublished Bohr-Peierls-Placzek paper. One further copy, in the possession of Jens Lindhard (photocopy in the Niels Bohr Archive; not microfilmed), has some amendments in Bohr’s handwriting.
‘Catalogued as of [1939-19401
I N V E N T O R Y O F M A N U S C R I P T S I N T H E NIELS B O H R A R C H I V E
15211-15251E
28 Comments on Atomic and Nuclear Constitution 1949 Typewritten and carbon copy with handwritten corrections [L. Rosenfeld], 20 pp., English, mf. 19. Drafts of unpublished note. One draft is dated 15 August 1949.
29 Work on Fission by Bohr, Hill and Wheeler 1949-1950 Typewritten, carbon copy and handwritten [A. Bohr, S . Rozental and J.A. Wheeler], 50 pp., English and Danish, mf. 19. Drafts. Most of the material is dated between 6 July 1949 and 9 February 1950.
INDEX
Subjects which appear throughout the volume, such as compound nucleus, level distribution, neutron capture and quantum mechanics, are not listed (but, e.g., level density and wave mechanics are). Parentheses have been used to indicate a cursory reference to a subject which is otherwise treated more extensively. The word used in the index is not always identical with the one in the text; it is hoped that the many cross references will help the reader identify such subjects. A dash between page numbers is used to indicate that the subject constitutes the topic of those pages, whereas f. and f f . after a page number indicates that the subject appears on one or more of the pages immediately following. An italicised page number indicates a biographical note or a reference to a biographical note in another volume. A person in a group photograph has only been included when helshe is mentioned in the text as well.
INDEX
Abelson, P . 365, 566, 659 f . activation energy for fission (see also critical deformation energy) 70, 433, 459, 666 Ageno, M . 74, 478 a-ray emission 29 f., 87, 95 ff., 113, 131, 146, 152 f., 155 f . , 186, 189, 201, 204, 210, 215 f . , 218, 220, 230, 248, 249-252, 255 ff., 263 f., 277, 281, 308 f., 322, 337, 344, 361, 367, 374, 376, (415), 426, (444), 453, 658 f., 665 scattering, see scattering of a-rays Alvarez, L.W. 365 Amaldi, E. 156, 478 American Physical Society N e w York meeting, February 1939 61, 64, 553 Princeton meeting, June 1939 383 Washington meeting, April 1939 68-69, 359-361, 386, 663 Anderson, C.D. 126 f., 166, 174, 216, 219 Anderson, H.L. 61, 365, 379 f . , 384, 386 angular momentum, including orbital moment (see also spin) 1 1 , 13, 30, 38, 42, (79), 80, 94, 106, 113, 135 f., 138, 197 f., 202, 236-237, (239), 255, 261, 317, 329, 337, 376 ff., 380 f., 392, 491, 493 ff., 498, 500 f., 51 1 ff., 515 ff., 524, 578 f., 615, 634, 637, 668 Ann Arbor, see Michigan, University of annihilation 126, 415, 444 antiproton 12 Aoki, H . 239 Arnold, W.A. 559 Aston, F.W. 94, 100, 154, 165, 174, 201, 285, 306, 320 asymmetrical fission, see fission, symmetrical/ asymmetrical asymmetry, see symmetry atomic energy, see nuclear energy number 67, 135, 155, 193, 197, 231, 236, 274, 280, 306 f., 311, 317, 320 f., 324, 329, 344 f., 350 ff., 357, 365, 367 f., 371 f., 380, 415, 417, 428, 431, 440, 445 f., 455, 457, 465, 478, 553, 593 f. weight (see also mass number) 15, 94, 155, 158, 164 ff., 168, 170, 172 ff., 177 f., 189,
215, 218, 262, 365, 367 f., 376, 379, 385, 417, 446, 470, 473, 593 f., 652 Auger, P . 263 Bainbridge, K.T. 201 band spectrum 80, 231, (299), 316, 328, 611 barrier penetration 110, 155-156, 165, 174, 185 ff., 203, 210, 249-257, (264), 281, 308, (310), 314 f., 322, (324), 326 ff., 374 f., 426, 430, 453, 456, (551), 586 f., 658, 666 Barschall, H . H . 382, 385, 397, 404 Bayard, P. 638, 640 Beck, G. 9, 10, 100, 137-138, 140, 202 Bergwe, P . 626, 628, 633, 635 Berkeley 39, 350, 353 P-ray emission 5-11, 13 f., 55, 57, (68), 85-89, 96-97, 103, 113, 117, 125, 131 f., 136, 137-140, 152 f., 166, 174 f., 215 f . , 218 ff., 274 f., 280, 295 f., 306-307, 309, 321, 323, 344 f., 350, 353, 355-357, 365 ff., 378, 384 ff., 415, 417, 420, 431, 435, 444 ff., 448, 457, 461, 547 f., 555, 557, 567, 605-606, 676, 679 Bethe, H.A. 16 f., 19, 24, 29 f., 31, 32, 38 f . , 146, 181, 194, 209, 227, 248, 250, 259 f., 264, 312, 325, 370, 377 f., 385, 387 f . , 484, 491 f., 507, 534, 539-540, 609, 613, 642 f. billiard-ball model of nucleus 158, 167-168, 176, 207-208 binding energy 12, 15, 22, 29, 34, 72, 76 f . , 93, 112-113, 145, 153, 169, 177, 188 f., 193, 208, 210, 234, 258, 277, 285, 311, 313, 324, 326, 342, 345, 357, 361, 367, 369 f., 375 f., 381, 383, 385 ff., 404, 407 f., 419 ff., 423 f., 426,428 ff., 432,434,438, 440, 448 f., 451 ff., 455 f., 458, 460, 463, 465, 470, 478, 484, 490, 507, 523-524, 560, 575 f., 618, 646 f. biology 167, 175, 216, 220, 599 ff., 641, 643 Birmingham 49 f., 612 f., (615), 617,619, 621, 670 Bjerge, T. 28, 263, 560, 629-630, 631, 633, 635, 638, 640, 652 Bjerrum, N. 576 f., 627 f. black-body radiation (see also Planck’s law) 45, 108, 262, 293 f., 298, 303, 313, 315 f . ,
INDEX
318, 326 f f . , 335, 419, 423, 426-428, 448, 451, 454, 501, 585, 587 Blackett, P.M.S. 134, 135 f., 166, 174, 216, 219 Blackman, M. 607 f. Blau, M. 425, 453, 586 f. Bloch, F. 10, 14,25 f., 31, 32, 38, 44, 194, 534, 540-544, 596 f., 600 ff., 606, 608 f . Bocciarelli, D. 478 Baggild, J.K. 28, 413, 443, 621 Bohr, Aage V I , 81, 680 Bohr, Erik 58, 356, 560, 622 ff., 627, 629 ff., 660 f., 679 Bohr, Hans 58, 60, 64, 550, 564, 579 ff., 622, 624 Bohr, Margrethe 60, 68, (556), 564, 632, 634, 636, 638 f . , 652, 667, 670 Bohr-Kalckar papers 18 f f . , 25, 27-34, 39, 49, 156, (183-189), (211), 223-264, 299, (306), (320), (3691, (4131, (443), (489), (505), 539, 572 f., 580 ff., 595 f., 600 f., 610, 676 f. Bohr-Peierls-Placzek papers (47), 48-52, (go), 332, 340, (377), 391-393, 487-519, 612621, (644 f.), 659, 663, 678 f. Bohr-Wheeler papers (67), 68-74, 81-83, 345, 359-389, (398), 399-404, (413), (443), (467-473) (484), 551, 561 f., 657-671, 679 f . Bologna meeting, 1937 44 Bonner, T.W. 478 Booth, E.T. 61, 365, 380, 385, 401, 404, 441, 465, 469 Born, M. 21, 23, 28, 305, 319, 607 f., 617, 653 Bose-Einstein statistics 94 f., 117 Bothe, W. 13, 43 f., 50, 100, 134, 262, 298 f., 314 f., 327 f., 336 f., 389, 393, 542 f . , 602, 604 Breit, G. 29, 31, 32, 47, 189, 209, 246, 312, 325, 377, 491, 507 f., 510, 539 Breit-Wigner formula 29, 32, 48, 246 f . , 312, 325, 377, (379), 380, 388,491, 507 f., 510, 539, 613 ff. Brickwedde, F.G. 56 British Association for the Advancement of Science 47, 333-337, 678 Broch, E.K. 412 Broglie, L. de 134, 305, 319 Bromberg, J. VI, 21
Brostram, K . J . 28, 413, 443 Brubaker. W . 478 California, University of, see Berkeley Cambridge 6, 19, 21, 32, 47, (53), (63), 216, 220, 333, 550, 555, 567, 578 ff., 610, 630, (651), 652 capillarity (see also surface tensiodenergy) 36, 70, 82, 259, 261, 373, 567, 669, 671 Carlsberg Foundation VII, 217, 221, 632 f . Casimir, H.B.G. 28, 597 f., 676 causality 97, 114, 305, 320, 583, 585, 599, 601 Cavendish Laboratory 95, (216), (220), 336, (630) Chadwick, J . 117, 126, 134, 152, 156, 165, 174, 185, 216, 219, 307, 321 chain reaction 67, 72, 75, 395-398, 437, 441 f., 462, 465 f., 679 charge number, see atomic number charge ratio in fission, see fission, symmetricaVasymmetrical Chemical Society (London) 7, 91, (117) Clay, J . 597 f. cloud-chamber tracks (201), 350, 353, 413, 431, 443, 457 f., 591-592 Cockcroft, J.D. 134, 135, 165, 173, 201, 216, 220, 612 Cohen, R.S. 55 coherence 12, 492 f., 497, 501 f., 515, 574 f., 577, 614 collective motion 32, 38, 80, 153 f., 168, 177, 186 f., 193, 197 f . , 211, 233, 237, 255, 278, 293, 314, 327, 332, 498, 529, 539,609 Columbia University 57, 61, 71 f., 81, 349 f . , 352 f., 380, 550, 552 f . , 635,637,660,662 commutation relations 104 complementarity 87, 104 f., 108, 11 1, 305, 320, 641, 643 Compton effect 13, 109 recoil 591 wavelength 12 f., 109 f., 126, 131 f . Condon, E.U. 87, 95, 230, 281, 308, 322 conduction electrons 25 f., 596 f., 600 f., 603 f . configuration space 70, 373 f., 386 f., 658 conservation laws 6, 88, 105, 207, (230), 276, (309), (322), 492 f., 499, 510, 512 f., 555, 614
INDEX
conservation of angular momentum ( l l ) , 135 f., 275, 493-494, 513 of charge 8, 112, 132, 136, 570 f. of energy 4-14, 85-89,96 f . , 103 ff., 107 f f . , I l l ff., 118, 132, 136 ff., (145), (152), 201, 275, 280, 307, (310), 321, (324), 417 f . , 446, 513, 547 f., 568 f f . , 605, 676 Constable, J.E.R. 185 Copenhagen conference 1932 10, 1 1 , 115-118, 570 f . 1933 570 f f . 1934 19 f . , 572 f., 642 f . 1936 27, 28, 38, 582 ff., 599 ff., 609 1947 50 1952 83, 527-529 on “Unity of Knowledge”, 1936 583, 585, 599, 601 “Copenhagen spirit” 544 Copenhagen University (207), (217), (221), (431), (457), 621, 639, 660 correspondence with classical physics (8), 9, 87, 93, 96, 104, 107-108, 109, 113, 125, 129-132, 260-261, 264, 304 f., 309, 319, 322, 375, 523, 548 cosmic rays 13, 109, 126-127, 166, 174, 425, 453, 578 f., 597 f., (653), 670 coupling between modes 43, 46, 239, 262, 298, 316, 328-329, 332, 336, 372, 392, 421, 449, 563 between particles 34, 38, 82, 186, 189, 198, 209, 229 ff., 236 f., 246, 253 f., 259, 261, 267, 269, 276, 278, 282, 293, 308 f., 312, 314, 322 f., 325, 327, 477, 489, 498, 505, 508, 618, 642, 644, 646 f., 669 of angular momenta 30, (198), (237), 261 covalent bond 274, (305), (319) Crane, H.R. 31, 201 ff. critical deformation energy 70, 361, 365 f., 369-374, 375, 377, 381 ff., 386 ff., 401, 404, 407 f., 432 ff., 438 ff., 458 f f . , 463 f f . , 470 ff., 477 f., 484,658,661, 663, 666 cross section for fission, see fission cross section Crowther, B.M. 201 Curie, 1. 125, 134, 135, 152, 166, 174, 185,
216, 219, 309, 323, 344, 365, 407 f . , 536, 591-592, 652 Curie, M. 100, 134, 592 cyclotron 2, 3, 217, 221, 560, 590 f., 626, 628 f., 631 f . , 635, 637 f., 640 Davis, W. 60 de Broglie wavelength, see wavelength, de Broglie Dee, P.1. 336 delayed neutrons 68, 350 f., 353, 357, 369, 383-386, 407 f., (566) Delbruck, M. 10, 22-24, 28, 141, 533 f., 537, 544-547, 570 f . Delsasso, L.A. 201, 203 Dempster, A . J . 367, 370 density of energy levels, see level density Destouches, J . 593 f. detailed balancing 47 f., 392, 492 f., 499 f . , 508 f . , 510-512, 614, 617 deuteron 14, 75, 135, 156, 201, 230, 257 f., 337, 349 ff., 353, 367, 377, 387-388, 477 f f . , 483-484, 552, 560, 588 ff., 623 ff., 631, 638, 640, 647 f . , 650, 652 dimensional analysis 234, 371 dipole moment 45, 95, 194, 237 f., 262, 278, 315, 327, 544, 607 f. radiation 32, 44, 194, 237 f., 278, 315, 327, 336, 544 transition 38, 262, 278, 327 Dirac, P.A.M. 6 f., 10, 11 f., 107, 110, 125 f., 132, 134, 135 ff., 166, 174, 196, 305, 319, 534, 547-550, 570 f., 599, 601 f., 604, 606, 677 Dirac equation (see also electron theory, relativistic and quantum mechanics, relativistic) 12, 18, 107, 125, (135 f.), 549, 592 ff. dispersion nuclear (see also Breit-Wigner formula) 49, 332, 344, 377, 388, 392, 491 ff., 497, 507, 508-510, 612, 617 optical 247, 249, 268 f., 278, 312, 325 Dodson, R.W. 56, 365 doorway state 43 Doppler effect 298, 378 f. Droste, G. v. 387
INDEX
Duke University 39 Duncanson, W.E. 185, 188 Dunning, J.R.28, 57,61 ff., 71, 365, 380,385, 401, 404, 407 f., 441, 465, 469, 553 ff. Eddington, A S . 6, 555 Edinburgh Lectures, Bohr’s, 1949 617, 668 Ehrenberg, W. 156 Ehrenfest, P. 8, 10, 36, 100, 567 ff., 597 f. Einstein, A. 8, 93, 95, 108, 165, 174, 304 f., 308, 318 f., 322, 570 f. Eisenbud, L. 508 elastic scattering, see scattering, elastic electron diameter 5, 8, 12, 93, 104 f., 108 ff., 117, 126, 131 f . , (548), 605 f. scattering, see scattering of electrons spin, see spin of electron theory, relativistic (see also Dirac equation and quantum mechanics, relativistic) 4, (8), 13, 125 f., 132, (135 f.), 166, 174, 305, 319, (540-541), 547, 549, 578 f., 668 elementary particle 87 f., 103, 105, 107 f., 110, 117, 125 f., 140 f., 166, 174, 186, 207, 216, 219, 230, 258, 274, 279, 374, 376, 415, 445, 490, 506-507, 605 Ellis, C.D. 100, 134, 137 f . Elsasser, W.M. 156 entropy 259 equipartition of energy 54, 422, 450 Euler, H. 28, 582 ff., 618 evaporation 27, 29 f., 39, 209 f., 216, 220, 241 ff., 252, 255, 262, 268 f., 276 f., 298, 313 f., 326 f., 335 f., 342, 344, 349, 350, 353, 378, 382, 384, 386, 388, 419, 423-428, 432 f., 448, 451-454, 458 f., 586 f . even/odd nuclei 36, 38, 65, 94, 117, 197, 231, 236, 274, 280, 307, 321, 345, 367 f., 380 f., 384, 387, 440, 465, 478, 583 f . , 609, 623, 625 exchange forces (see also spin exchange) 34, 36, (38), 79, 193, 197, 236, 524, 549, 582 ff., 610, 618, 649, 651 exclusion principle 20, 27, 34, 81, 94, 106, 1 1 1 f . , 117, 193, 197 f., 231, 236, 274, 279 f., 304, 307, 319, 321, 523, 549, 580 ff., 584, 649, 651
Fahlenbrach, H. 185, 188 Faraday Lecture, Bohr’s 7, 13, 91-97, 103, 117, 156, 306, 320, 676
Feather, N. 384 Feenberg, E. 70, 79 ff., 369 f., 372, 646 ff., 650
Fermi, E . 13 f., 17, 20, 56, 60-63, 66 f., 100, 134, 145, 152, 154 ff., 166 f., 170, 175, 178, 275, 280, 307, 309, 321, 323, 344, 365, 379, 384, 386, 407 f., 428, 455, 534, 540 f . , 550-555, 572 f., 580 f., 634, 636, 652
Fermi distribution 34, 385 f., 582 ff., 597 f. gas 30, 259, 539, 649 f. sea 27, 603 f. Fermi-Dirac statistics 25, 94 f., 117 Feshbach, H. 508 Fierz, M. 78, 542 f. fine structure 110, 197,236-237,281, 309,322, 621, 634, 637
fine-structure constant 106 ff., 113, 130 f., 578 f. fission barrier 66 f., 70-71, 370 ff., 375 ff., 380, 382 f., 386 ff., 658 cross section 58, 65, 71, 74 f., 342, 344 f., 349, 351 f., 365 f., 377 ff., 388 f., 397 f., 477 ff., 484, 559, 589 deuteron-induced 75, 349, 351, (367), 387-388, 477, 479, 483-484, 552, 588 ff., (623 f.), 626, 628 f., 631, 638, 640 fragments 53, 55 f., 66, 70, 72 f., 344, 350 ff., 357, 361, 365 f., 371, 373, 378 f., 384 ff., 389, 407 f., 413, 431 f., 436, 441, 443, 457 f., 461, 465, 467-473, 550 f . , 553, 557 ff., 564, 566, 626, 628, 634, 637, 662 f., 679 probability 71, 73, 344 f., 349 ff., 361, 366, 370, 373 ff., 380 ff., 387 f., 398, 433 f . , 437 ff., 459 f., 462 ff., 469, 472, 477 f., 484, 553, 561 ff., 662 f., 666 symmetrical/asymmetrical (see also statistical distribution of fission fragments) 72-74, 82, 387, 467-473, 669-670
559, 662-663, 665,’
threshold, see critical deformation energy track 413, 431 f., 443, 457 f.
INDEX
width 375 ff., 380 ff., (659) yield 54, (74), 345, 349, 351, 375, 377, 379, 384, 386 f., 401, 404, 438 f., 441, 463 ff., 469, 472 f., 479, 484, 626 f. fluctuations 108, 342, 367, 418, 433, 435, 447, 459, 461, 477, 556, 558, 563, 617, 649, 65 1 Flugge, S. 387 Foldy, L.L. 82, 669 Fowler, R.D. 56, 365 Fowler, R.H. 6, 10, 534, 555-556 Fowler, W.A. 201, 203 Franck, J . 28, 31, 304, 318, 578 f. Franck-Hertz experiment 304, 318 Frenkel, J . 27, 29, 70, 209, 241-242, 313, 326, 369, 660, 666 Frisch, O.R. 16 f., 20, 28, 52-54, 55 ff., 62 ff., 66 ff., 156, 209, 248, 342, 344 f., 361, 365, 369, 374, 407 f., 431 f., 457 f., 469, 473, 535, 550 ff., 556-566, 588 ff., 622 ff., 636, 659, 662 fusion 419-420, 448
Gale, A.J.V. 557 f. y-ray ernission/spectrum 6, (14 f.), (19), 32, 36, 38, (54), 80, 95, 97, 113, 131, 137, 146, 152 ff., 167 f., 175, 177, 201 ff., 208 f., 237, 262, 276, 278, 281, 298, 310 f., 315, 323 f., 327, 336 f., 384, 388, (423), 427, (451), 454, 549, 555, 567, 593 f., 609, 626 f . , (677) scattering, see scattering of y-rays Gamow, G. 6, 8, 13, 19 f., 25, 27, 29, 31, 32, 36 ff., 87, 95, 127, 134, 137, 141, 147, 153, 165, 173, 186 f., 189, 230, 250, 254, 256, 281, 308 f., 322, 367, (374), 384, (388), 535, 540, 547 f., 555, 567-573, 578 f., (586 f.), 600 f., 603 ff., 609, 642, 644, 651 Gant, D.H.T. 479 Geiger, H . 127 Geiger-Nuttall relation 27, 95, 141, 308, 322, 603 f. Gentner, W. 43 f., 50, 262, 298 f., 315, 328, 389, 393, 543 giant dipole 50
Gifford Lectures, Bohr’s, see Edinburgh Lectures, Bohr’s, 1949
Gilbert, C.W. 337 Glasoe, G.N. 61, 365, 380 Goeppert-Mayer, M., see Mayer, M.G. Goldhaber, M. 204, 256 Goodeve, C.F. 19 Goudsmit, S.A. 100, 304, 319 Graaff, R. van de 216, 220 gravitation 8, 132, 568 ff., 668 Green, G.K. 365 Grosse, A. v. 401, 404, 441, 465 Gurney, R.W. 87, 95, 185, 230, 281, 308, 322 Hafstad, L.R. 31, 56, 256, 365, 384, 389 Hahn, L. 638, 640 Hahn, 0. 28, 42, 52, 56, 59 f., 62 f., 66 f., 285, 317, 329, 342, 344 f., 360, 365 f., 378 f., 382, 407 f., 431, 438, 457, 462, 469, 552 ff., 563 ff., 622 ff., 626, 628, 634, 636, 659
Halban, H . von 384, 386, 397 Hammach, K.C. 79 Hansen, K.G. 639 Hanstein, H.B. 384, 386 Hardy, G.H. 258 Harkins, W.D. 253, 280, 307, 321 harmonic oscillator 276, 498, 501 f., 574 f., 615
Harris, W.T. 385 Harvard University 39, 539, 572 f., 583, 585 Havas, P. 666 Haxel, 0. 78, 185 f., 253 heat radiation, see black-body radiation Heisenberg, W. 10, 12 f., 17, 19, 21, 25, 28, 34, 35, 36, 45, 76, 87, 100, 104, 125, 127, 134, 138 ff., 156, 165-166, 174, 193, 197, 231, 274 f., 280, 305, 307, 319 ff., 490, 507, 528, 533, 535, 570 f., 573-587, 600 ff., 604, 617 Hellrnann, S. 364, 564 Helsinki conference, 1936 39, 159-178, 609 Hertz, G . 304, 318 Hevesy, G. de 3, 4, 28, 53, 140, 156, 216, 220, 589, 599 f . , 623 ff., 627, 633 ff., 640 Heydenburg, N.P. 31, 256 Heyn, F. 244 Hill, D.L. 74, 82 f., 667, 669 f., 680 Hajgaard Jensen, H . 630, 639 hole theory (see also positron) 549
INDEX
Houtermans, F.G. 542, 607 f . Hoyle, F. 385 Huby, R . 618 Husimi, K. 239 Hylleraas, E.A. 10, 412 Hylling-Christensen, V. 639 f. hyperfine structure 94, 231, 621 identical nuclei 96 f., 11 1 , 11 3 f . independent-particle model (see also shell model) 25,27, 34, 38,76,79 ff., 186, 193, 231, 246, 275, 278, 281, 308 f . , 322 f., 336, 428, 455, 523-524, 582, 584, 609, 649, 651, 667, 669 f. indeterminacy principle, see uncertainty principle indicator, radioactive, see tracer individuality of particles 88, 94, 118, 605 inelastic scattering, see scattering, inelastic interaction between object and measuring instrument 104-105, 139, 164, 173, 305, 320 internal conversion 95, 194,237,239,315, 327, 607 f. intra-nuclear electrons 11 f., 88 f . , 93 f., 96, 111-114, 166, 174, 307, 321, 414-415, 444 isomeric nuclei 13, 42, 67, 127, 239, 291-296, 317, 329, 653-657, 678 isotope separation (72), 398, 441, 465
Kalckar, F. 10, 18, 19 f., 22, 25, 27, 28, 29 f., 31, 32, 33, 34, 39, 48 f., 144, 156, 180. 184, 192, 196, 200, 21 1, 223-264, 272 f . , 284, 299, 306, 320, 369, 413, 443, 489, 493, 499, 505, 510, 539 f . , 542, 544, 572 f., 580 ff., 592, 594 ff., 600 f., 609 f., 676 ff. Kanner, M.H. 382, 385, 397, 404 Kapitza, P . 548, 612 Kapur, P.L. 28, 49, 493, 508 Kapur-Peierls method 49, (493). (508), 614 f. Kikuchi, S. 239 Kinsey, B.B. 201 Kirchhoff, G.R. 303, 318 Klein, 0. 18 f., 86, 88, 110, 536, 547, 592-596, 676 Klein-Nishina formula 109 Klein’s paradox 4, 110 Knudsen, M . 423 f., 451 Koch, J . 28, 621, 638-639, 640 Kofoed-Hansen, 0. 528 Kohn, W. 529 Kowarski, L. 384, 386, 397 Kramers, H.A. 7, 10, 13, 25-27, 28, 134, 305, 319, 536, 596-605 Kristensen, P . 528 Krogh, S.A.S. 602, 604 Kronig, R. de L. 10, 94 Kudar, J . 7, 536, 605-606
Jacobsen, J.C.G. 2, 13, 28, 62, 68, 140, 272, 479, 484, 536, 552, 560, 574 f., 588, 590-591, 626, 628 f f . , 635, 637 f., 640, 678 James, W. 641, 643 Japan Lectures, Bohr’s, 1937 41 Jensen, A. 630, 631 Jensen, J . H . D . 28, 77-78, 79 f . , 619 Jentschke, W. 365 Johns Hopkins University 39, 57 Joliot-Curie, F. 1 1 f . , 14, 67, 125, 134, 135 ff., 152, 166, 174, 185, 216, 219, 309, 323, 365, 384, 386, 397, 407 f., 536, 591-592, 652 Joliot-Curie, I . , see Curie, I . Jordan, P . 28, 305, 319, 557 Juel Henningsen, E. 639 Juul, F . 630
Ladenburg, R. 382 f., 397, 404 Landau, L. 8, 30, 33, 132, 260, 262, 264, 314, 326, 499, 510, 568 ff., 612 Langevin, P . 134, 583, 585 Lassen, N.O. 479, 484, 639 latent heat of evaporation 210, 252, 277, 313 f., 326 f., 426, 453 Lauritsen, C . C . 201 ff., 635, 637 Lauritsen, T. 413, 443, 635, 637 Lawrence, E.O. 134, 135, 217, 221, 590 f. Leiden 36, 567, (596 f.), 602, (603), 604 Leipunski, A.I. 652 letters from and to Niels Bohr 534-538 level density 15, 21 f . , 24, 27, 30, 38, 41 f., 158, 169, 177, 208, 258-259, 260, 264, 268 f . , 312, 325, (337), 345, 351, 353, 357, 361, 375, 384 f . , 389, 392,401, 595 f., 603, 605
INDEX
width 15, 21, 32, 43, 47 f., 154 f., 170, 178, 187, 209, 211, 249, 255, 298, 337, 345, 375 f f . , 392 f . , 398, 421, 449, 490-491, 492, 501, 507 f . , 512, 519, 616, 666 Levi, H . 28, 46 Lindhard, J . 51, 79, 616 f., 621, 670, 679 line shape 45, 61 1-612 width 45, 108, 298, 611 liquid-drop model 16 f . , 27, 29 f., 32, 34, 36-37, 40, 44 f., 47, 56,67, 69-70, 74, 76, 79, 81 f . , 141, 193-194, 216, 220, 241, (261), (312), (325), 326, 336, 342, 344, 365 f., 369-374, 386, 389, 401, 407 f., 416, 419, 421, 423-427, 432 f., 445, 448 ff., 451-454, 458 f., 523 f., 544, 559, 567, 582-583, 584, 607 f., 616, (620). 666 ff., 671 liquid helium 34, 423, 450, 582-583, 584 Livingston, M.S. 248 London lecture, Bohr’s 1936 19, 21 f., 157-158, 641, 643 1939 360 Los Alamos 50 Lyshede, J . M . 621
Meitner, L. 6, 9, 10, 28, 42, 52 ff., 55, 56 ff., 62 f . , 66 f., 69, 100, 134, 285, 317, 329, 342, 344 f., 361, 365 f . , 369, 374, 378 f., 382, 407 f . , 432, 438, 458, 462, 469, 473, 550ff., 574f., 589,622ff., 628f., 631ff., 636, 638 ff., 659, 662 meson 77, 618, 634 f., 637 mesothorium 350, 353, 589, 634, 636 Meyer, R.C. 31, 56, 357, 365, 383 f . , 389 Michigan, University of 39, (577) microcanonical ensemble 375 f., 392 Middelboe, V. 621 Miller, H . 185, 188 Millikan, R.A. 100, 126 f., 652 Mitchell, Miss 553 Msller, C . 17, 28, 528, 627, 629, 634, 637, 668 monomolecular reaction 375-378, 434, 459 Morse, M. 70 Moscow lecture, Bohr’s, 1937 41, 677 Mott, N.F. 51, 100, 134, 137 f . , 186, 254, 494, 513 Mottelson, B. 529 multiple-mode excitation 293 f. multipole radiation (see also quadrupole) 194, 278, 315, 327
magic numbers 77 f., 80, 619 magnetic moment 13, 94, 105-106, 112, 125 f., 131, 560, 635, 637 magneton 13, 106, 126, 131 Maier-Leibnitz, H . 13 massdefect 12, 34, 52, 67, 93 f . , 112-113, 153, 208, 231, 234 ff., 307, 321, 367 ff., 372, 470, 576, 582, 584 mass number (see also atomic weight) 42, 66, 193, 197, 274, 280, 306 f., 311, 313, 317, 321, 324 ff., 329, 344 f., 350 ff., 357, 367 f., 371 f., 380, 384, 414 f . , 417, 428, 431, 438, 440-441, 444 ff., 455, 457, 463 f f . , 478, 523, 553 mass ratio in fission, see fission, symmetrical/ asymmetrical Massey, H.S.W. 51, 494, 513 Matthee, H . 545 Maxwell distribution 210, 243, 277, 313, 326 Mayer, M.G. 77 ff., 619 McKay, H.A.C. 28, 156 mean free path 17, 81, 423, 451, 649, 651
negative-energy states 6 f . , 107, 109, 549 neutrino 8-9, 13-14, 132, 275, 280, 307, 321, 540 f . , 593 f., 597 f. neutron diameter 11 f., 131 properties of (12), 115-121, (415), (445), 676 scattering, see scattering of neutrons New York meeting, 1939, see American Physical Society Nier, A.O. 71, 378, 441, 465 Nishina, Y. 76, 540 f. Nordheim, L.W. 79 ff., 384, 646 f f . , 650 Nordic Electrical Engineers’ Meeting, 1937 41, 213-221 Nordic Scientists’ Meeting, 1936, see Helsinki conference, 1936 Norwegian Society of Engineers, see Oslo lecture, Bohr’s, 1940 nuclear density (see also packing of particles in nuclei) 167, 175, 216, 220, 232 f., 416, 420, 424, 445, 448, 452, 523
INDEX
energy (60), 75 f . , 437, 441-442, 462, 465-466 model (see also independent-particle model, liquid-drop model and shell model) 19, 27, 29, 44, 51, 67, 76-83, 95, 141, 145, 147, 153 ff., 181, 186, 194, 236, 239, 246, 259, 274 f., 280 f., 307, 321, 336, 507 f., 539, 607 f., 614 f . , 619, 642, 644, 646 f f . spin, see spin of nucleus temperature, see temperature of nucleus nucleon spin, see spin of nucleon Ohnell 638, 640 Oliphant, M.L. 28, 201 Olsen, H. 630, 631 Oppenheimer, J . R . 30, 48, 211, 257, 261, 263, 387 f., 484, 493, 499, 510 optical spectrum, see spectrum, optical theorem 51, 492-493, 496, 499, 508, 512-513, 614 orbit 80, 108, 112 f., 145 f., 197,217, 221, 31 1, 325, 429, 456, 648 ff. orbital moment, see angular momentum Oslo lecture, Bohr’s, 1940 41 1-466 packing fraction, see mass defect packing of particles in nuclei (see also nuclear density) 152, 164, 173, 186, 193, 197, 211, 215, 219, 229, 239, (274), (279 f.), 282, 289, 293, 335 f., 414, 444, 489, 505, 523 pair creation 5, 11, 305, 319, 668 Paris lecture, Bohr’s January 1937 39 October 1937 41, 229, 265-282, 678 Pauli, W. 5-6, 8, 9, 13, 17, 28, 36, 37, 44 f., 46, 78, 79, 132, 134, 135-136, 138 f., 275, 280, 307, 321, 533, 536, 541 ff., 570 f., 606-608, 644 ff., 649, 651 Pauli principle, see exclusion principle Peaslee, D.C. 508 Pegram, G.B. 61, 550 f f . Peierls, R.E. 28, 32, 38, 45, 46, 47, 48, 49 ff., 76, 80 f., 134, 261, 332, 340, 377, 385, 391-393, 487-519, 537, 539, 570 f., 609-621,644 f., 659,663,668, 670, 678 f. Peierls-Kapur method, see Kapur-Peierls method
periodic system of elements (113), (156), 164, 173, 267, 269, 279, 304, 319, 407 f., 417, 446, 593 f. Perrin, F. 100, 134, 156 perturbation theory 108 f., 275, 646 f., 669 phase 49, 374, 377, 379, 392 f., 492, 494, 496 ff., 501, 514 ff., 614 f . Phillips, M. 257, 387 f., 484 photo-effect, nuclear 30, 42, 43-52, 261-262, 263, 297-299, 306, 316, 320, 328, 331-332, 384, 393, 493, 519, 542 f., 574 f., 585 ff., 606-608, 61 1 , 635, 637, 678 photoelectric effect 27, 304, 315, 318, 327, 603 f. photo-fission 388-389 Placzek, G. 28, 29, 47, 48, 49 f f . , 53, 62, 63-64, 66 f., 71, 80, 156, 209, 248, 292, 312, 325, 332, 340, 377 f., 391-393, 398, 487-519, 539 f., 544, 554, 609, 611 ff., 615 f., 644 f., 659, 663, 678 f. Planck, M. 42, 111, 215, 218, 303, 317 f., 329 Planck Festschrift, 1938 42, 46, 301-329 Planck’s law (see also black-body radiation) 241, 276, 303, 308, 316, 318, 322, 427, 454 plutonium 71 Pollard, E.C. 619 Pose, H. 185 f. positron 11 f., 14, 125 f., 135 ff., 140, 166, 174 f., 185, 188, 216, 219, 274 f., 280, 305 f., 319, 321, 415, 420, 444, 448, 652 potential scattering 50, 392, 490 ff., 496 ff., 501 f., 506, 508, 512, 515 ff., 614 f. Potter, R.D. 60 Prankl, F. 365 Preiswerk, P . 652 Princeton 39, 51, 56 ff., 63 f . , 68 ff., (72 f.), 74, (345), 355 f., (361), 383, (402), (404), (550), (552), 554, 556. (557), 558, 564, (588 f.), 590, (591), (621), (633), (635), 658, 660 f., 664, 679 protactinium 72, 372, 399-404, 407 f., 469, 473, 479, 484, 661, 679 proton negative 12-13, 126 f., 578 f. structure of 11, (13), (87), (103), 125, 131, (41% (445)
INDEX
quadrupole 27, 44, 82, 194, 238 f . , 315, 327, 544, 607 ff., 668 ff. quantum electrodynamics 110, 570 f., (617), (621), (644), 671 mechanics, relativistic (see also Dirac equation and electron theory, relativistic) 6 f., 88, 106-111, 112, 126, 547, 555, 605-606 number 79, 138, 145, 153, 176, 193, 279, 304, 317, 319, 376 f., 420, 449, 524 postulates (87), 281, 304, 309, 318, 323 quenching 332 Rabi, 1.1. 31, 544, 634, 637 radiation damping 107 f., 502, 607 f. Ramanujan, S. 258 Ramsey, W.H. 649, 650 Rasmussen, E.K. 28, 58, 68, 537, 590 f., 62I-640 Rasmussen, R.E.H. 28, 630 f . Rayleigh, Lord 70 Rechenberg, H. 578 Reddemann, H. 22, 24, 544, 546 reduced mass 73 f . , 376, 658 reflection of wave 154, 245, 497 ff. relativistic electron theory, see electron theory, relativistic quantum mechanics, see quantum mechanics, relativistic relativity, general 8, 132, 568 f f . residual excitation (68), 242-243, 276 f., 337, 351, 353, 355-357, 375 ff., 382, 388, 393, 424, 452, 477 f., 484, 679 resonance, sharpness of, see sharpness of resonance Roberts, R.B. 31, 56, 357, 365, 383 f., 389 Rochester, University of 39 Rockefeller Foundation 217, 221, 540 f. Rome conference, 1931 8, 99-114 Rosenfeld, L. 10, 19, 22, 24, 28, 50, 54 ff., 60, 64-65, 68, 80 f., 116, 130, 134, 144, 192, 196, 272 f., 284, 292, 348, 356, 468, 529, 533 f . , 537, 544, 545-547, 557 f., 564, 570 f . , 617, 620 ff., 627, 629 ff., 637, 641-651, 661, 666, 668, 671, 676 ff. Rosenkjzr 626, 628 Rosseland, S. 95
rotational state of nucleus 27, 30, 38, 80, 236, 294, 312, 325, 522, 524, 656 f. Royal Danish Academy VII,(XIIIf.), X V I I I , 12, 15, 17, 39, 41, 47, 49, 75, 119-121, 149-150, 151-156, (211), (223), 287-289, 299, (306), (320), 332, 339-340, (393), 405-408, 409-410, (413), (443), (469), 481-482, (484), 485-486, (505), 539, 612, 621, (662), 679 Royal Society (London) 39, 539, 642 f. Rozental, S. 52, 680 Rutherford, E. 11, 3, 6, 14, 20 f., 95, 117, 134, 152, 163, 165, 172 f., 185, 201, 215 f., 218 ff., 279, 303, 308, 310, 317 f., 322, 324, 329, 407 f . , 413, 443, 537, 555 f., 572 f . , 576 f., 580 f . , 630, 651-652 Sargent curve 385 f. Savitch, P. 344, 365, 407 f . scattering (see also potential scattering) coherent 12, 492-493, 497, 501, 515-516, 574 f., 577 elastic 14, 50, 336, 490, 494 ff., 506, 510, 513 ff., 614 inelastic 14, 349, 351, 382, 397, 506, 515 ff., 614 of a-rays 93, 95, 188, 256 of electrons 11, 109-110, 529 of fission fragments 432, 458 of y-rays 12, 573-577 of neutrons 14 f., 29, 146, 152, 154, 181, 245 f f . , 249, 312, 325, 336, 349, 351, 382, 397, 560, 566 of radiation 108-109, 615 Scharff, M. 528 Schiff, L . I . 83 Schrodinger, E. 9, 134, 305, 319 Schultz, B. 57 ff., 124, 557 f., 564, 567, 588, 597 f., 622, 624, 626 ff., 633, 635, 676 Schwinger, J . 617 Segre, E. 55, (100) selection rule 261, 317, 329, 493, 513 selectivity 15, 32, 45, 47, 50, 154 ff., 158, 179-181, 189, 209, 211, 244, 256, 278, 294, 298 f., 311, 316, 324 f . , 328, 332, 335, 428-430, 438, 440, 454-457, 463 f., 470, 472, 585, 587, 611, 663, 677 Serber, R. 30, 48, 211, 261, 263, 493, 499, 510
INDEX
Shankland, R.S. 13, 602, 604 sharpness of resonance (see also level width) 152, 154 f., 169 f . , 177 f., 187, 209, 246, 255 f., 299, 311, 315, 324, 327, 337 shell model 74, 76-83, 145, 529, 618 ff., 669 f. Shire, E.S. 201 Simons, L . 560, 566, 638, 640 single-mode excitation 293 f. Sitte, K. 9 Slack, F.G. 61, 365, 380, 385, 469 Slater, J.C. 599, 601 Society for the Dissemination of Natural Science (Danish) 75, 41 1, 443, 627 f. Society for the Protection of Science and Learning (London) 542 f. Soddy, F. 308, 322 Solomon, J . 10, 592 Solvay Conference, 7th, 1933 8-10, 12, 37, 129-141, 596 f. Sommerfeld, A. 100, 110, 304, 319 Serrensen, S.P.L. 626, 628 space-time coordinates/description 87, 93, 104 f., 110 f . specific heat 209, 233, 293, 313, 326, 422, 450 spectrum, optical (see also band spectrum) 94 f., 108f., 111, 113, 127, 164, 172, 197, 204, (209), 231, 304 ff., 309, 318 f., 321 f., 621 spin of electron 36, 94, 105 ff., 125, 275, 304, 319, 523, 583, 585 of neutrino 275 of nucleon 30, 36, 197, 202, 204, 237, 261, 274, 280, 307, 321, 376, 583, 585, (679) of nucleus (see also angular momentum) 5, 7, 29 f., 36, 38, 42, (79), 80, 153, 187, 195-198, 202 ff., 211, 231, 236 f., 248, 256, 261, 274, 280, 294, 306, 321, (356), 376, 378, 381, 392, 491-492, 494, 496, 500, 507, 509, 511, 513, 518 f., 524, 583 f., 614 f . , 646 f., 654 ff., (679) of positron ( l l ) , 135 f . spin exchange (see also exchange forces) 195-198, 204, 677 spin-orbit coupling 30, 78 f. Squire, C.F. 56 Stachel, J.J. 55 Stanford University 540 f . , 544
statistical distribution of fission fragments (see also fission, symmetrical/asymmetrical) 66, 72-74, 344, 350, 352-353, 361, 366, 386-387, 467-413, 553, 662-663, 679 equilibrium 54, 392, (477), 492, 499 ff., 510 f f . mechanics (see also Maxwell distribution and microcanonical ensemble) 209, 259, 262, 314, 326, 344, 366, 373, 386, (433), (459), 499, 511, (555) weight 392, 500, 509, 511, 663 statistics of nuclei 5, 7, 94, 96, 11 1, 113, 117, 593 f . Steensholt, G. 638, 640 Stern, 0. 28, 100, 126, 131 stopping of charged particles 26, 75, 431 f., 451 f., 524, 559, 603 f. Strassmann, F. 52, 56, 63, 67, 342, 344 f., 365 f., 378 f . , 382, 407 f., 431, 457, 469, 553, 555, 557 f., 565, 660 Stuewer, R.H. VI, 16 successive disintegrations 55, 74, 210, 244, 277, 295 f., 351, 353, 368 f., 384, 425, 431,431,452-453,451,462,475-479,484 Suess, H.E. 78 superconductivity 25, 600 f . superposition 48, 108, 386, 392, 492, 494, 514, 669 surface tensiodenergy (see also capillarity) 34, 47, 52 f., 56, 194, 234, 336, 365, 369 ff., 421, 432, 436, 449, 458, 461, 561 f., 582, 584, (666) symmetry 12 f., 125,202,211,274,280, 306 f., 315, 321, 328, 336, 392, 549, 578 f. Szilard, L. 384, 386 Tate, J.T. 73, 664 Teller, E. 28, 31, 56 temperature of nucleus 27, 29, 209 ff., (233), 241 ff., 252, 259 f., 262 f., 268 f., 276 f., 293, 298, 312 ff., 325 f f . , 336, 342, 380, 419-423, 424 ff., 434, 448-450, 452 ff., 459 f . , (477) thermal energy 209 f . , 259 f., 277, 313, 316, 326, 328, 335, 342, 344, 366, 404, 419 ff., 424 ff., 432 ff., 441, 448 ff., 452 ff., 458 f., 461 f., 465, (586 f.)
INDEX
thermal radiation, see black-body radiation Thomas B. Thrige Foundation 217, 221 Thomson, G.P. 5, 87 Thomson, J.J. 109 thorium (56), 57 f., 64 ff., 75, 343 ff., 349 ff., 353, (357), 361, 366 f., 370, 372, 374, 377, 381, 383 f., 388 f., 401, 404, 407 f., 431, 433, 437, 439 ff., 457, 459, 462, 464 f., 469, 473, 478, 484, 551 ff., 559 f., 566, 588 f., 625, 627, 629, 631, 634, 636, 638 f., 659, 662 Toll, J . 667 Toronto, University of 39 Toyoda, T. 76 Trabacchi, G.C. 100, 478 tracer 167, 175, 216, 220 transition state for fission 375 f., 382 f., 387, 470, 663, (666) “transuranic elements” 52, 58, 64, 67, 559, 561 f., 565, 634, 636 Trumpy, B. 42, 537, 653-657 tunnel effect, see barrier penetration Turner, L.A. 71, 385 Tuve, M . A . 31, 56, 60 f., 64, 256, 350, 353, 383, 550 ff. Uhlenbeck, G.E. 304, 319, 597 f. uncertainty principle 4 f., 9, 15, 87, 104 f., 1 1 1 , 139, 305, 320, 518, 523, 548, 618 University College, London 19, 157-158, (643) uranium 42, 52 f . , 56, 58, 60 ff., 71 f., 74 f., 285,295 f., 317, 329, 343 ff., 349 ff., 357, 361, 365 ff., 370, 372 ff., 377 ff., 382 ff., 388 f., 397 f., 401 f., 404, 407 f., 413, 431 ff., 437 ff., 443, 457 ff., 462 ff., 469 f., 472 f., 478, 484, 551 f f . , 558 ff., 565 f . , 588 f., 625 ff., 631, 634, 636, 638, 640, 658, 662
Washington conference February 1937 30, 31, 227, 264, 540 January 1939 56, 59, (63), 64, 66, 550 f., (555), 564, 622, 624 April 1939 68-69, 359-361, 386, 663 wave equation 492, 614 equation, relativistic, see Dirac equation function (5), 81, 146, (246), 494 ff., 501, 509, 513 ff., 518 f., 549, 649 f., 658, 669 mechanics ( 9 , (7), 11, 15, 87, 95, 181, 392, 407 f., 508, 510, 592, 649 f. packet 45 f., 87, 373, 524, 611 wavelength, de Broglie 154, 181, 187, 240, 244 f . , 247 f f . , 253, 255, 277, 311, 325, 376 ff., 381, 388, 392, 429, 456, 491, 500, 509, 511, 517 Weekes, D.F. 248 Weisskopf, V.F. 26, 27, 28, 30, 80, 209, 260, 262, 314, 326, 375, 383, 385, 499, 508, 510, 544 Weizsacker, C.F. von 10, 26, 28, 42, 70, 235, 239, 294, 317, 329, 369, 582 ff., 603 f. Wentzel, G. 543 Werner, S. 626, 628 Wheeler, J.A. 16-17, 20, 31, 39, 56, 67 f., 69-74, 81-83, 345, 359-389, 398, 399-404, 413, 443, 469, 484, 538, 551, 561 f., 657-671, 679 f. width of energy level, see level width of spectral line, see line width Wightman, A. 528 Wigner, E. (see also Breit-Wigner formula) 29, 31, 32, 47, 189, 209, 312, 325, 375, 377, 491, 507 f., 510, 539 Williams, E.J. 13, 127, 578 f. Wilson, R . 528 f. Winther, A. 528
Verlaine 641 f f . Voorhis, C.C. van 382, 397, 404
Yamanouchi, T . 76-77 Yost, F.L. 384 Yukawa, H. 586 f .
Walton, E.T.S. 134, 165, 173, 201, 216, 220 Wambacher, H . 425, 453, 586 f. Wang, P . 357, 383 f .
zero-point motion 34, 74, 316, 329, 342, 372-373, 374, 376, 583 f., 666 Zinn, W.H. 384, 386
