Nishina Memorial Lectures: Creators of Modern Physics

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Lecture Notes in Physics Editorial Board R. Beig, Wien, Austria W. Beiglböck, Heidelberg, Germany W. Domcke, Garching, Germany B.-G. Englert, Singapore U. Frisch, Nice, France P. Hänggi, Augsburg, Germany G. Hasinger, Garching, Germany K. Hepp, Zürich, Switzerland W. Hillebrandt, Garching, Germany D. Imboden, Zürich, Switzerland R. L. Jaffe, Cambridge, MA, USA R. Lipowsky, Potsdam, Germany H. v. Löhneysen, Karlsruhe, Germany I. Ojima, Kyoto, Japan D. Sornette, Nice, France, and Zürich, Switzerland S. Theisen, Potsdam, Germany W. Weise, Garching, Germany J. Wess, München, Germany J. Zittartz, Köln, Germany

The Lecture Notes in Physics The series Lecture Notes in Physics (LNP), founded in 1969, reports new developments in physics research and teaching – quickly and informally, but with a high quality and the explicit aim to summarize and communicate current knowledge in an accessible way. Books published in this series are conceived as bridging material between advanced graduate textbooks and the forefront of research and to serve three purposes: • to be a compact and modern up-to-date source of reference on a well-defined topic • to serve as an accessible introduction to the field to postgraduate students and nonspecialist researchers from related areas • to be a source of advanced teaching material for specialized seminars, courses and schools Both monographs and multi-author volumes will be considered for publication. Edited volumes should, however, consist of a very limited number of contributions only. Proceedings will not be considered for LNP. Volumes published in LNP are disseminated both in print and in electronic formats, the electronic archive being available at springerlink.com. The series content is indexed, abstracted and referenced by many abstracting and information services, bibliographic networks, subscription agencies, library networks, and consortia. Proposals should be send to a member of the Editorial Board, or directly to the managing editor at Springer: Dr Christian Caron Springer Heidelberg Physics Editorial Department I Tiergartenstrasse 17 69121 Heidelberg / Germany [email protected]

Nishina Memorial Foundation (Ed.)

Nishina Memorial Lectures Creators of Modern Physics

Editor Nishina Memorial Foundation 2-28-45 Honkomagome Bunkyo-Ku, Tokyo, Japan [email protected]

Nishina Memorial Foundation (Ed.), Nishina Memorial Lectures, Lect. Notes Phys. 746 (Nishina Memorial Foundation, 2008), DOI 10.1007/ 978-4-431-77056-5

Library of Congress Control Number: 2007940477 ISSN 0075-8450 ISBN 978-4-431-77055-8 Nishina Memorial Foundation Japan This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilm or in any other way, and storage in data banks. Duplication of this publication or parts thereof is permitted only under the provisions of the German Copyright Law of September 9, 1965, in its current version, and permission for use must always be obtained from Springer. Violations are liable for prosecution under the German Copyright Law. Springer is a part of Springer Science+Business Media springer.com c Nishina Memorial Foundation 2008 The use of general descriptive names, registered names, trademarks, etc. in this publication does not imply, even in the absence of a specific statement, that such names are exempt from the relevant protective laws and regulations and therefore free for general use. Typesetting: by the authors and Integra using a Springer LATEX macro package Cover design: eStudio Calamar S.L., F. Steinen-Broo, Pau/Girona, Spain Printed on acid-free paper

SPIN: 12184644

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Yoshio Nishina (1890 – 1951)

Chronology of Yoshio Nishina December 6, 1890 July, 1918 August, 1920 April, 1921 1921 – 1922 1923 – 1928 1928 December, 1928 1937 1937 1940 1944 February, 1946 November, 1946 August, 1948 January 10, 1951 December, 1955

Born in Satosho, Okayama Prefecture, Japan Graduated from the Imperial University of Tokyo (Electrical Engineering Department) Entered the Institute of Physical and Chemical Research (RIKEN) in Tokyo Left Tokyo for Europe Research under E. Rutherford at the Cavendish Laboratory; attended lectures at G¨ottingen Universiy Research under Niels Bohr in Copenhagen Derivation of the Klein-Nishina formula Returned to RIKEN Discovery of a new particle Constructed a small cyclotron Discovery of 237 U and symmetric fission Costructed a large cyclotron Awarded the Order of Cultural Merit, Japan President of RIKEN Elected a member of the Japan Academy Died in Tokyo Nishina Memorial Foundation was established

Preface

Yoshio Nishina, referred to in Japan as the Father of Modern Physics, is well known for his theoretical work on the Klein–Nishina formula, which was done with Oskar Klein in the 6 years he spent in Copenhagen under Niels Bohr during the great era of the development of quantum physics. As described by Professor Ryogo Kubo in Chap. 2 of this volume, Nishina returned to Tokyo in 1929, and started to build up experimental and theoretical groups at RIKEN. His achievements there were many and great: (1) Encouraging Hideki Yukawa and Sin-itiro Tomonaga to tackle a new frontier of physics, leading eventually to their making breakthroughs in fundamental theoretical physics that won them Nobel prizes; (2) the discovery of “mesotrons” (the name for Yukawa particles at that time, now called muons) in 1937, which was published in Phys. Rev., parallel to two American groups; (3) construction of small and large cyclotrons and subsequent discoveries of an important radioisotope 237 U and of symmetric fission phenomena by fast neutron irradiation of uranium (1939 – 40), published in Phys. Rev. and Nature; and (4) creation of a new style of research institute, open to external reseachers, an idea inherited from Copenhagen. During World-War-II his laboratory was severely damaged, and also his cyclotrons were destroyed and thrown into Tokyo Bay right after the end of the war. Nishina devoted all his strength to re-establishing his scientific activities from scratch, but passed away in 1951 with many unfinished attempts left behind. We can say that what Japan is now owes a great deal to Nishina’s major contributions to science and the scientific community. Shortly after his death, in 1955, the Nishina Memorial Foundation (NMF) was established to commemorate the great contributions of Yoshio Nishina and to stimulate scientific development in the field of modern quantum physics. This was made possible by all the eﬀorts of his successors, collaborators, friends, and influential people even outside science, who respected and loved Yoshio Nishina. These included Nishina’s best friend, Ernest O. Lawrence, a Nobel Laureate in 1933, who wrote the following to Sin-itiro Tomonaga as early as 1952:

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Preface Dear Dr. Tomonaga, I am glad to hear that you are establishing a research fund in memory of Dr. Nishina. He was truly a great man of science for not only did he himself make fundamental contributions to knowledge, but also he was an inspiring and generous leader whose beneficent influence was felt the world over. Therefore, the establishment of a fund for scientific research would constitute a particularly fitting memorial and I would count it a privilege and an honor to be associated with this worthy undertaking, Cordially yours, Ernest O. Lawrence

Fig. 1 Letter of E. O. Lawrence to Sin-itiro Tomonaga in 1952

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It is to be noted that a substantial amount of the initial funding was donated by 44 distinguished scientists from foreign countries, including E. Amaldi, P.W. Anderson, J. Bardeen, C. Bloch, N. Bloembergen, N. Bohr, R.M. Bozorth, A.H. Compton, F.C. Frank, H. Froehlich, M. Levy, R.E. Marshak, H.W. Massey, M.G. Mayer, N.F. Mott, R.S. Mulliken, L.E.F. Neel, L. Onsager, A. Pais, R.E. Peierls, I.I. Rabi, L.I. Schiﬀ, F. Seitz, J.C. Slater, C.H. Townes, J.H. Van Vleck, I. Waller, G. Wentzel, J.A. Wheeler, and C.N. Yang. This list bears witness to the admiration felt throughout the world for Yoshio Nishina and the appreciation of his warm and noble character. Among the missions of the Nishina Memorial Foundation is (i) to award the Nishina Memorial Prize to promising young scientists. Already 154 scientists have received the prize. Many of them have gone on to win further prestigious prizes, both national and international, the most notable being the two Nobel Prizes awarded to Leo Esaki and Masatoshi Koshiba. The other missions are (ii) to send young scientists to foreign countries, (iii) to invite distinguished scientists from foreign countries, (iv) to give young scientists from developing countiries the chance to engage in research work in Japan, (v) to explore and record uncovered historical events and documents related to Nishina’s life and work, and, last but not least, (vi) to deliver a series of public lectures. Sin-itiro Tomonaga, the second president of the Foundation, emphasized this last aspect, and promoted a series of public lectures, the Nishina Memorial Lectures (NML), by inviting distinguished scientists from abroad as well as from Japan. During the first 50 years the number of the NML has exceeded 100 and about 30% of them were delivered by foreign guests. A list of NML is given in the appendix. Many of the NML have been documented, albeit irregularly, in individual booklets, but these are not easily accessible to the public. Thus, on the occasion of the 50th anniversary of the Foundation, we decided to publish the collected lecture documents which have been accumulated over the past five decades. The entire documentation of the NML in Japanese has recently been published by Springer Japan in three volumes, bearing the subtitle of ’Creation of Contemporary Physics’. The present volume, part of the Springer Lecture Notes in Physics, reproduces the documented lectures given in English in their original print versions. I would like to thank Prof. Masatoshi Namiki for the valuable editorial work. We hope that this volume will help young readers to grasp and enjoy the progress of modern physics, as described in these first-hand records of lectures given by its creators.

September 2007

Toshimitsu Yamazaki President of the Nishina Memorial Foundation

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Fig. 2 Photograph of a Wilson chamber track of a new cosmic-ray particle with a mass of 1/7 to 1/10 of the proton mass, reported by Nishina, Takeuchi and Ichimiya in Phys. Rev. 52 (1937) 1198, taken from Kagaku 7 (1937) 408

Fig. 3 Papers on experiments using fast neutrons, reporting the discovery of symmetric fission of uranium, Nature 146 (1940) 24, and the discovery of 237 U, Phys. Rev. 57 (1940) 1182

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Fig. 4 A happy reunion of Yoshio Nishina with his friend, Isidol Rabi (a Nobel Laureate in 1944)

Contents

Chronology of Yoshio Nishina . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi Preface . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii Toshimitsu Yamazaki 1

Abstraction in Modern Science . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Werner Karl Heisenberg

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Yoshio Nishina, the Pioneer of Modern Physics in Japan . . . . . . . . . . . . 17 Ryogo Kubo

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Tomonaga Sin-Itiro : A Memorial – Two Shakers of Physics . . . . . . . . . 27 Julian Schwinger

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The Discovery of the Parity Violation in Weak Interactions and Its Recent Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43 Chien-Shiung Wu

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Origins of Life . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 Freeman J. Dyson

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The Computing Machines in the Future . . . . . . . . . . . . . . . . . . . . . . . . . . 99 Richard P. Feynman

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Niels Bohr and the Development of Concepts in Nuclear Physics . . . . 115 Ben R. Mottelson

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From X-Ray to Electron Spectroscopy . . . . . . . . . . . . . . . . . . . . . . . . . . . . 137 Kai Siegbahn

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Theoretical Paradigms for the Sciences of Complexity . . . . . . . . . . . . . . 229 Philip W. Anderson

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Contents

10 Some Ideas on the Aesthetics of Science . . . . . . . . . . . . . . . . . . . . . . . . . . 235 Philip W. Anderson 11 Particle Physics and Cosmology: New Aspects of an Old Relationship . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 245 Leon Van Hove 12 The Experimental Discovery of CP Violation . . . . . . . . . . . . . . . . . . . . . 261 James W. Cronin 13 The Nanometer Age: Challenge and Change . . . . . . . . . . . . . . . . . . . . . . 281 Heinrich Rohrer 14 From Rice to Snow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297 Pierre-Gilles de Gennes 15 SCIENCE — A Round Peg in a Square World . . . . . . . . . . . . . . . . . . . . 319 Harold Kroto 16 Are We Really Made of Quarks? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 349 Jerome I. Friedman 17 Very Elementary Particle Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 371 Martinus J.G. Veltman 18 The Klein-Nishina Formula & Quantum Electrodynamics . . . . . . . . . . 393 Chen Ning Yang A

List of Nishina Memorial Lectures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 399

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Abstraction in Modern Science Werner Karl Heisenberg

Abstract This lecture was presented by Werner Karl Heisenbergr as the Nishina Memorial Lecture at Asahi Lecture Hall (Tokyo) on April 26, 1967.

May I – before I start my lecture – express my deep gratitude for the invitation to this country, to those who have made this invitation possible, for the greatest hospitality which my wife and I enjoy in this beautiful country. And also I would like to thank Professor Tomonaga for his very kind words and to Dr. Yanase for all the labor he has taken to translate this lecture.

Development of Natural Sciences and Tendency toward Abstraction

Werner Karl Heisenberg c NMF

So the lecture will be on abstraction in modern science. When the present state of natural sciences is compared with that of an earlier period, it is often asserted that the sciences have become more and more abstract in the course of their development and that they have reached at present in many areas a downright strange character of abstractness, which is only partially compensated as a huge practical success which the physical sciences have exhibited in their technological applications. I do not wish to enter here into the value question, which is often raised at this point. We shall not discuss, therefore, whether the physical sciences of an earlier period Werner Karl Heisenberg (1901 – 1976). Nobel Laureate in Physics (1932) W. K. Heisenberg: Abstraction in Modern Science, Lect. Notes Phys. 746, 1–15 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 1

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were more gratifying in the sense that they through their devoted thoroughness to the details of the natural phenomena had given a living picture of the relationships which we find in nature, or whether on the contrary the enormous expansion of the technical possibilities which is based upon modern research has irrefutably proven the superiority of our present conception of the natural sciences. This question of value will for now be completely bypassed. Instead, the attempt will be made to examine more closely the process of abstraction in the development of sciences. We shall examine insofar as this is possible in such a short lecture what really happens when the sciences obviously following and in a necessity rise from one level of abstraction to the next higher one for the sake of what goals of knowledge does this laborious ascent generally proceed? In so doing, it will become apparent that very similar processes are going through in the diﬀerent branches of the scientific field, which through their very comparison become more comprehensible. When, for instance, a biologist traces specks of metabolism and propagation of living organisms to chemical reactions; when the chemist replaces the detailed description of the properties of a substance with a more or less complicated chemical formula; finally, when the physicist expresses the laws of physical nature in mathematical equations, there is always eﬀected here a development whose basic type is perhaps most clearly recognizable in the development of mathematics, and whose necessity must be investigated.

Case of Mathematics We can begin with the question what is abstraction and what role does it play in conceptional thinking. The answer could be formulated perhaps so. Abstraction denotes the possibility of considering one object or a group of objects from just one viewpoint while disregarding all other properties of the object. The isolating of one characteristic, which in a particular relationship is looked upon as especially important in contrast to all other properties, that constitutes an essence of abstraction. As it is easily comprehended, all concept formation is based upon this process of abstraction. For the formation of a concept piece of process that one can recognize similarity, homogeneity. But since total equality practically never occurs in the phenomenal world, the homogeneity arises out of similarity only through the process of abstraction, so the isolating of one characteristic while omitting all others. In order to form, let us say, the concept tree, one must perceive that there are certain common characteristic about birch trees and fir trees, which one through abstraction can isolate and thereby grasp. The filtering out of common features can under circumstances be an act of knowledge of a greater significance. It must have been recognized very early in the history of mankind that there is for example inter-comparison of let us say three cows and three apples, the common feature, which is expressed by the word ”three.” The formation of the concept of number is already a decisive step from the sphere of the immediately given sensible word into the framework of rationally graspable thought

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structures. The sentence that two nuts and two nuts yield together four nuts remains also correct when one replaces the word nut with bread or with reference to any other object. We could therefore generalize this and close it in the abstract form two and two make four. That was the most important discovery. The peculiar ordering power of this concept of number was probably recognized already very early and contributed to the fact that the individual numbers then were taken or interpreted to be important symbols. From the standpoint of present day mathematics, the individual number is however less important to be sure than the basic operation of counting. It is the latter operation, which enables the procession, depositing of the series of natural numbers and produces implicitly with it all the eﬀects, which are studied for instance in the mathematical theory of numbers. With counting, a decisive step is obviously taken in abstraction through which the entrance way opened into mathematics and into the mathematically formulated physical sciences. At this point we can now already study one phenomenon with which we shall meet time and again in the various levels of abstraction in mathematics or in the modern sciences and which for the development of abstract thinking and science can be referred to almost as a kind of fundamental phenomenon. This is a term used by the German poet and scientist Goethe, although Goethe would not have used this expression, Urph¨anomen or fundamental phenomenon, in this special connection. One can define it perhaps as the unfolding of the abstract structures. The notions, which are first formed through abstraction from individual eﬀects or from manifold experiences, gain their own independent existence. They show themselves to be much richer and much more fruitful than they look when they were first considered. They manifested their lethal development and independent power of ordering insofar as they give rise to the formation of new forms and notions, negate the comprehension of the relation to one another, and somehow they prove themselves successful in their attempt to understand the world of phenomena. From the notion of counting and its related simple arithmetic operations was developed later for example, partly in ancient and partly in modern times, a complicated arithmetic and theory of numbers, which really only uncovered that, which was presented from the very beginning in the number concept. Further number and the theory of number relations, which developed from it, oﬀered the possibility of comparing lines by measuring. From here, a scientific geometry could be developed, which already extends conceptually beyond number theory. In the attempt to establish geometry or number theory this way, the Pythagoreans, early Greek philosophers, ran up against the diﬃculties of the irrational ratios between the lengths of lines and they were forced to enlarge their class of numbers. They had to invent so to speak the notion of irrational number. Preceding a step further from here, the Greek mathematicians arrived at the notion of the continuum and the well known paradoxes, which Xeno, the philosopher studied. But on this point, we shall not enter into these diﬃculties in the development of mathematics but only point out the abundance of forms, which implicitly already contained the notion of number and which can be as I said unfolded from it.

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The following then can be said to resolve the process of abstraction. The notion, which has formed the process gains its own existence and enables an unexpected abundance of forms or all the structures to be derived from it, which forms can later prove their value in some way or other in understanding the phenomena surrounding us.

Mathematical Truth is Valid on Other Planets It is well known from this basic phenomenon that heated discussion arose as to what the object of mathematics really is. The mathematics is concerned with genuine knowledge that can hardly be doubted, but knowledge of what? In mathematics, are we describing something objectively real, which exists in some sense independently for us or is mathematics only a capacity of human thinking? Are the laws, which we derive in mathematics only statements concerning the structure of human thinking? I do not really wish here to unravel this diﬃcult problematic but only to make one remark, which underlines the objective character of mathematics. It is not improbable that there is there also something similar to life on other planets. Let us say in Mars but in any case in other solar systems probably. And the possibility must be reckoned with throughout that there are on some other heavenly body living beings in whom the ability for abstract thinking is so far developed that they have found the concept of number. If this is so and if these living beings have followed up their concept of number with a scientific mathematics, they would arrive at exactly the same statements on number theory as we human beings have. Arithmetic and number theory could not appear basically any diﬀerent to them as it does to us and their results would have to agree with ours. If mathematics is to hold true statements about human thinking, then it would hold true in any case not only for human thinking but for thinking as such. No matter how many types thinking beings there are, mathematics must be the same in all cases. This statement could be compared with other scientific statements. No doubt exactly the same laws of nature hold true on other planets or on other heavenly bodies lying still much farther distance as we find here on the earth. This is now not only a theoretical supposition, rather we can look through our telescopes and observe that there are the same chemical elements on the stars as here on the earth and that they enter into the same chemical compounds and emit light from the same spectral bands. But whether this scientific statement, which is based on observation, has anything to do with the statements made earlier about mathematics and further what it has to do with it shall not be investigated at this point. Let us for a moment turn back to mathematics before we look at the development of the physical sciences. In the course of its history, mathematics has again and again formed new and more comprehensive notions and has thus risen to continually higher levels of abstraction. The class of numbers was extended through to the irrational numbers and to the complex numbers. The concept of function gave access to the realms of higher analysis and diﬀerential and integral calculus. The no-

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tion of group proved itself equally applicable in algebra, geometry, in the theory of functions, and suggested the idea that it should be possible on the higher level of abstraction and to comprehend entire mathematics with its many diﬀerent disciplines and the one unifying point of view. Group theory was developed as such an abstract foundation of entire mathematics. The diﬃculties encountered in group theory finally necessitated the step from mathematics to mathematical logic, which was aﬀected in 20s, especially by David Hilbert and his associates in G¨ottingen. Each time, the step from one level of abstraction to the next higher one had to be taken because problems could not be solved and not really be understood in the narrow sphere in which they first were posed. The connection with other problems in wider fields first provided the possibility for new mode of understanding and provided the inducement for concept formation or further more comprehensive concepts. For instance when it was realized that the action of parallels in Euclidean geometry could not be demonstrated, the nonEuclidean geometry was developed but the true understanding was first reached when much more general question was posed – within a particular action system, can it be proven that there are no inherent contradictions involved? When the question was so posed, then the core of the problem had been reached. At the end of this development, mathematics exist at present in such a form that its foundation can only be discussed in exceptionally abstract terms whose relation to anything in our experience seems to have totally disappeared. The following statement is said to have been expressed by the mathematician and philosopher Bertrand Russell. “Mathematics is concerned with objects about which nothing is known as to what they are and it consists of statements about which it is not known whether they are true or false”. As a commenter into the second part of this statement, it is known namely only that they are formally correct but not whether they are object in reality to which they can be related. But the history of mathematics should serve you only as an example in which the necessity and the development to abstraction and to unification can be recognized.

In Physical Sciences? - Development of Biology The question shall now be raised whether something similar took place in the physical sciences. In so doing I wish to begin with a science, which according to object is closest to life and therefore perhaps least abstract, namely biology. In its former classification into zoology and botany, it was to a large extent a description of many forms of life, which we meet here on our earth. The science compared these forms with an aim of bringing some sort of order into that first almost incalculable multiplicity of living phenomena and seeking further consistency of natural law in the field of living beings. In so doing the question arose of itself according to what aspects could the various living beings be compared? What, therefore, let’s say, were the common characteristics, which could serve as a basis of comparison? Already the investigations of the German poet and scientist, Goethe, into the metamorphosis

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of plants were for example already directed towards such a goal. At this point, the first step towards abstraction had to follow. Individual living beings were no longer primarily investigated but rather the biological functions as such, such as growth, metabolism, propagation, breathing, circulation, and so on, which characterized life. These functions provided the points of view according to which very diﬀerent living beings could be well compared. They prove themselves like the mathematical concepts of which I spoke as unexpectedly fruitful. They developed to a certain extent their own power of ordering very broad areas of biology. Thus they arose out of the study of the processes of heredity, the Darwinian Theory of Evolution, which for the first time promised to explain the abundance of various forms of organic life on earth within one extensive unified viewpoint. The research into breathing and metabolism on the other hand led oﬀ itself to the question of the chemical processes in living organisms. It gave rise to the comparison of these processes with the chemical processes, which takes place in the laboratory and with this the bridge was laid between biology and chemistry. At the same time, the question was raised whether the chemical process in living organism and those in inanimate meta proceed according to the same natural laws. Thus by itself the question shifted from the biological functions to the further question as to how these biological functions where materialized in nature. As long as the sites were kept on the biological functions themselves, the point of view still fits entirely into the intellectual world of say the poet Goethe and his friend and philosopher Carlos who referred to the close connection between the biological functions of organs and to unconscious cyclical processes. But with the question of material actualization of the functions, the sphere of biology in its proper sense was forced out for it now became evident that one could only then really understand the biological processes when one also had scientifically analyzed and explained the corresponding chemical and physical processes. On this next level of abstraction then, all biological relationships are at first disregarded and the only question is what physical and chemical processes as correlates to biological process actually take place in the organism. Proceeding along this line, we have arrived at present at the knowledge of very general relationships, which appear to define all living processes on earth as an essential unity and which can be most easily expressed in terms of atomic physics. As a special example, we can name the hereditary factors whose continuity from organism to organism is regulated by the well known Mendel laws. These hereditary factors are apparently given materially through the arrangement of a larger quantity of four characteristic molecule fragments in the two chains of chain molecule, which is called deoxyribonucleic acid and which plays a decisive role in the foundation of cell nucleus. The extension of biology into chemistry and atomic physics allows therefore the unified interpretation of basic biological phenomena for the entire realm of living objects on earth. Whether existing life on say other planets would be based on the same atomic and chemical structures cannot be decided at the moment but it is possible that we will know the answer to this question in a not too distant future.

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In the Domain of Chemistry A development similar to that in biology then took place in chemistry and I wish to select from the history of chemistry only one episode, which is characteristic of the phenomenon abstraction and unification, namely, the development of concept of valency. Chemistry has to do with the properties of substances and investigates a question how substances with certain given properties can be transformed into those with other properties. How substances can be combined, separated, altered? When one began to quantitatively analyze the compounds of substances and to ask how much of the diﬀerent chemical elements is present in the compound in question, then integer number ratios were discovered. Now the atomic representation had already been previously employed as a suitable illustration by which the compound of elements could be considered. In so doing, one proceeded always from the following known comparison or picture. If one mixes, let us say white sand and red sand, the resulting sand whose red color is lighter or darker depending on the ratio of the mixture. The chemical compound of two elements was also thus envisaged. Instead of the grains of the sand, one thought of atoms. Since the chemical compound is more varied in its properties from the elements of which it is formed that the sand mixture from both types of sand, the picture had to be improved. Assuming that the diﬀerent atoms first arrange themselves together into atomic groups, which then as molecules applied basic units of the compound. The integer number ratios of the basic matter could then be interpreted and could be the reason for the rational ratios of the number of atoms in the molecule. The experiments of various kinds supported such intuitive interpretation and allowed more of a further assigning of the so-called valence number to the individual atom, which symbolizes the possibility of combining it with other atoms. In so doing, it remained that at any rate, and this is point with which we are concerned here, completely unclear at first whether one should visualize the valency as a directional force or as a geometric quality of the atom or as something else. Whether the atoms are themselves real material structure or only helpful geometrical pictures suitable for the mathematical representation of their chemical event? That had to remain undecided for a rather long time. A mathematical representation is here understood that assembles in the rules for combination. Therefore here for example, the valency and rules for valency are isomorphic with the phenomena in the same sense in which, let us say, if it were expressed in the mathematical language of group theory, the linear transformations of a vector are isomorphic to the rotation in three-dimensional space. Returning now to practical problems and omitting the language of mathematics, this means the following. One can use the valence representation in order to predict, which chemical compounds are possible between the elements in question but whether the valency is more of something real in the same sense in which say a force or geometrical form can be said to be real, this question could remain unanswered for a long time. Its decision was for chemistry not especially important. While the attention was focused on the complicated process of the chemical reaction and especially on the quantitative mixture ratio and all other aspect were disregarded, that’s

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to say through the process of abstraction, the notion was gained, which allowed for the unified interpretation and partial comprehension of the various chemical reactions. It was only much later in modern atomic physics, namely that it was first learned what type of reality stands behind the valency concept. Indeed we cannot even now correctly say whether valency is really a force or an electronic orbit or a change in the electric charge density of an atom or only the possibility of something of such kind. But today’s physics that means after Bohr’s theory of atom and after quantum mechanics, this uncertainty is no longer related to the thing itself but only to its formulation in language whose imperfection we cannot basically improve or remove. It is only a short way from the valency concept to the formal abstract language of today’s chemistry, which enables a chemist to understand the contents and results of his work in all areas of his science.

History of Physics The stream of information, which the observing biologist or chemist gather, flows therefore through the gradient of questions aiming at unified comprehension and thereby leading to abstract contents finally of itself into the broad field of atomic physics. It appears accordingly as though atomic physics with central procession must already be comprehensive enough in order to supply the basic structure for all natural phenomena, a structure to which all phenomena can be related and according to which all phenomena can be ordered. But even in the case of physics, which appears here as a common basis for biology and chemistry, this is in no way self evident since there are so many diﬀerent physical phenomena whose interrelationship is at first unrecognizable. Therefore the development of physics is also still to be dealt with and we want indeed to cast the glance first at its earliest beginnings. At the beginning of the ancient Greek science, there existed as it’s well known, the theory of Pythagoreans that as we know from Aristotle things are numbers. Now if one tries to interpret in a modern sense the description of this Pythagorean theory according to Aristotle, the meaning is probably the following that the phenomena can be so ordered and understood as they are related through mathematical forms and only so they can be ordered. But this relationship is not thought of as an arbitrary act of our known faculty of our mind but rather as something objective. It is said for instance that the numbers are the substantial essence of things or the entire heavens is harmony and number. But this at first probably meant simply the order of the world. For the ancient philosophers, the world was a cosmos with ordered thing and not chaos. The understanding thus gained appears not yet all too abstract. For instance, the astronomical observations are interpreted according to the notion of orbit. The stars move in circles, the circle is the course of its high degree of symmetry and especially perfect figure, so orbital motion is therefore evident as such. For the more complicated mo-

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tion of planets, however, several orbital motions, cycles, and epicycles had to be combined in order to represent the observations correctly, but this was complete enough for then attainable degree of exactitude. The sun and the moon’s eclipse could be a rather well predicted using Ptolemy astronomy. The modern period beginning with Newton’s physics opposed now this classical concept with a question, has not the motion of the moon about the earth something in common with the motion of a falling stone or with a motion of the stone that is thrown. The discovery that there is something common present here upon which one can concentrate while disregarding all other multiplying diﬀerences belongs to the most momentous events in the history of natural sciences. The common element was uncovered through the formation of the concept of force, which caused the variations in the quantity of motion of a body. Here especially that of gravity. Although this concept of falls originates from sensible experience, let’s say from the sensation of lifting a heavy weight, yet the notion is already defined abstractly in Newton’s axioms, mainly through the variation of the quantity of motion and without reference to the sensation. With the few simple notions like mass, velocity, quantity of motion, or as we now say momentum and force, a close system of axioms was formulated by Newton, which while disregarding all other properties of the bodies, was now suﬃcient to handle all the mechanical processes of motion. As it is well known, this axiomatic system, similar to the concept of number in the history of mathematics, proved itself exceptionally fruitful during the following period. For over 200 years mathematicians and physicist have derived new and interesting conclusions from Newtonian starting point, which we learnt in school in the simple form mass times acceleration is equal to force. The theory of planetary motion was begun by Newton himself and developed and refined by the later astronomy. The motion of the spinning top was studied and explained. Fluid mechanics, elastic bodies were developed. The analogy between mechanics and optics was worked out mathematically. All the time two aspects had to be especially emphasized in this process. First, when one asks only about the pragmatic side of science, let’s say when one compares Newtonian mechanics and its performance of astronomical predictions with that of classical astronomy, then what Newtonian physics in its beginnings in this case hardly be distinguished from classical astronomy. Basically the motion of the planets could be represented as exactly as is desirable through a superimposition of cycles and epicycles. The convincing power of Newtonian physics then did not primarily originate from its practical applicability, but it is rather based on its ability of synthesizing, its unifying explanation of very diﬀerent phenomena on the power of systematizing, which proceeds from Newtonian starting point. From this basis new fields of mechanics, astronomy physics, were opened up in the following centuries, if there still was a need for significant scientific accomplishments of series of researchers; however, the result already rests even if it was not first recognizable on Newton starting point, exactly as a concept of number already contains implicitly the entire number theory. Also if beings are dealt with reason, other planets were to make the Newtonian basis the starting point for their own scientific considerations, they could obtain only the same answer to the same

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questions. In this respect the development of the Newtonian physics is an excellent example for that unfolding of abstract concepts, which had been discussed already at the beginning of this talk. First in the 19th century it appeared then nevertheless that the Newtonian starting point was not rich enough to produce the corresponding mathematical formulation of all observable phenomena. The electrical phenomena for example, which especially since the discoveries of Galvani, Volta, and Faraday held the main center of interest for the physicists, did not fit correctly into the picture of the concept of mechanics. Faraday therefore leaning on the theory of elastic bodies invented the notion of field of force whose time changes were investigated and explained independent of the motion of the bodies. From such a starting point, the Maxwell theory of electromagnetic phenomena later developed out of which came Einstein’s theory of relativity and finally his general field theory, which Einstein hoped could be developed into the foundation for the entire field of physics. We shall not enter into the details of this development. What is important here for our concentration is only the fact that even at the beginning of the present century, physics was, as a consequence of such development, still in no way uniform. The material bodies whose motion was studied in mechanics were acted upon by something distinctly diﬀerent, namely the forces, which caused their motion and which as fields of force represented their own reality according to their own laws of nature. The diﬀerent fields of force stood unrelated next to one another. To the electromagnetic forces and to those of gravity, which had already been known for a long time and to the chemical valency forces were added in recent decades the forces in the atomic nucleus and in the actions responsible for radioactive decay. As a result of this various coexisting intuitive descriptions and separate types of force, a question was posed, which science could not avoid. I did convince the nature ultimately is uniformly ordered, that all phenomena proceed finally from the same uniform laws of nature. Therefore it must be possible in the end to uncover the underlying structure common to all the diﬀerent areas of physics.

Unification by the Concept of “Potential Reality” Modern atomic physics has approached this goal through the means of abstraction and through the formation of more comprehensive concepts. The seemingly contradictory description by waves and particles, which arose in the interpretation of atomic research, led first to the formation of the concept of possibility of a near potential reality as a nucleus of the theoretical interpretation. With this the antithesis was dissolved between the material particles of Newtonian physics on the one hand and the field of the force of Faraday-Maxwell physics. Both are possible forms of appearance of the same physical reality. The contrast between force and matter has lost its prime significance, although the very abstract notion of a mere potential reality proved itself as exceptionally fruitful. So the atomic interpretation of biological and chemical phenomena first became possible. But the search after connections

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between the various types of field of forces arose in recent decades simply out of new experiment. To each type of field of force, there corresponds, in the sense of the aforementioned potential reality, a definite type of elementary particle. So light quantum or photon corresponds to the electromagnetic field, the electrons correspond to certain extent to valency force in chemistry. The mesons correspond to the nuclear force that has been first pointed out by Yukawa. In recent experiments with elementary particle, it became apparent that new such particles may be created in collision of very high speed elementary particles and it seems indeed that if there is availability of suﬃcient impact energy for the formation of the new particles, then elementary particles of every desired type can be generated. The diﬀerent elementary particles are therefore so to say all made out of the same substance, and we call these substances as simply energy or matter, they can all be converted into one another. With this the fields of force can also be transformed into each other. The inner relationship is directly recognizable through experimentation. There stills remains for the physicist, a task of formulating the natural laws according to which the transformation of elementary particles takes place. These laws should represent or describe in a precise and therefore necessarily abstract mathematical language what can be seen in the experiments. The completion of this task should not be too diﬃcult considering the growing amount of information, which experimental physics working with the greatest technical means furnishes us. Next to the concept of a potential reality related to space and time, the requirement of relativistic causality, namely that eﬀect cannot be transmitted more quickly than the speed of light, this seems to play a special role. For the mathematical formulation, there is a left over finally a group theoretical structure, a totality of symmetry requirements, which can be represented through rather simple mathematical statements. Whether this structure is finally suﬃcient for the complete representation of experiment can again first become apparent through the process of unfolding, which has been repeatedly spoken oﬀ, but the details are not important for the considerations here. One can say the relation of the various fields of physics seems to be already explored through the experiments during the recent decades. Therefore we believe that the uniform physical structure of nature is already now recognizable in its contours. At this point the limits of arriving at an understanding of nature found in the very essence of abstraction itself must be referred to. If at first many important details are disregarded in favor of the one characteristic by which the ordering succeeds, then one limits oneself necessarily to the working out of a structure only a type of skeleton, which could first become a true representation through the addition of a great number of further details. The relationship between the phenomena and the basic structure is in general so intricate that it can hardly be followed everywhere in the details. Only in physics has the relation between the concepts with which we directly describe the phenomena and those which occur as the formulation of the natural laws really been worked out. In chemistry, this has only succeeded to a considerably more limited extent and biology is first beginning in a few places to understand how the notions, which originate from our immediate knowledge of life and which retain unrestrictedly their values can fit together with that basic struc-

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ture. Still in spite of this, the understanding gained through abstraction mediates to a certain extent a natural coordinate system through which the phenomena can be related and according to which they can be ordered. The understanding of the universe gained in this manner is related to the basically hoped for and continually striven after knowledge like say the recognizable plan of a landscape scene from a very high flying airplane is to the picture which one can gain by wandering and living in such a landscape.

Don’t be Afraid of the Limitlessness Let us now return to the question, which I posted at the beginning. The tendency towards abstraction in the science rests therefore ultimately on the necessity of continually questioning after uniform understanding. The German poet and scientist Goethe deplores this once in relation to his notion of Urph¨anomen – primary phenomenon, which he invented. He writes in his theory of color when that fundamental phenomenon is found still the problem would remain that it would not be recognized as such. That we would search for something further over and beyond it when we should here confess the limits of immediate experience. Goethe felt clearly that to step to abstraction could not be avoided if one continues to question. What he means to say with the words is beyond it that is precisely the next higher level of abstraction. Goethe wants to avoid it. We should acknowledge limits of experience and not try to pass beyond them because beyond these limits, immediate experience is impossible and the realm of constructive thinking detached from sensible experience begins. This realm remained almost strange and sinister for Goethe, most of all because the limitlessness of this realm probably frightened him. Only thinkers of an entirely diﬀerent mentality than Goethe could be attracted to the limitless expanse, which is here conspicuous. It was for instance a German philosopher Nietzsche who stated that abstract is many a hardship, for me on a good day a feast and an ecstasy. But human being so reflective upon nature, do question further because they grasp the world as unity and they want to comprehend its uniform structure. They formed for this purpose, more and more comprehensive notions whose relationship with direct sensible experience is only diﬃcult to recognize but the existence of such a relationship is the unconditional piece of precision that abstraction mediates at all the understanding of the world.

In Fine Arts and Religion After one has been able to survey this process in the area of today’s natural sciences over such a wide extent, one can add the conclusion of such a consideration only with diﬃculty-resisted temptation of casting a view on other areas of human thought

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and life on art and religion and asking whether similar processes have taken place or still take place there. In field of fine arts for instance, a certain similarity is conspicuous between that which occurs in the case of the development of an art style from simple basic forms and that which was here named as unfolding of abstract structures. As in the sciences, one has the impression that with the basic forms, for example in Romanic architecture, the architecture of early medieval times in Europe, the semicircle and the square, the possibilities for shaping them into assuming for the richer forms of later period, they are already extensively co-determined. We see that the development of the style is concerned therefore more with unfolding than with newly creating. A very important common characteristic consist also in the fact that we cannot invent such basic forms but only discover them. The basic forms possess a genuine objectivity. In the physical sciences, they must represent reality. In art one has to express the spirit of life in the period in question. One can discover under favorable circumstances that there are forms which can perform this task but one cannot simply construct them. More diﬃcult to judge is the occasionally expressed opinion that the abstractness of modern art has causes similar to those of the abstractness of modern science, that is somehow related to the latter contents. If the comparison on this point should be justified, it means that modern art has gained the possibility of representing and making visible further comprehensive relationships not expressible by earlier periods of art by renouncing the direct connection with sensible experience. Modern art, this would then be the statement, can reproduce the unity of the world better than classical arts. But whether this interpretation is correct or not, I am not able to decide. Often the development of modern art is also diﬀerently interpreted. The disintegration of old orders, for example of religious bonds, is reflected in our time but is dissolving of the traditional forms and art of which then only a few abstract elements remain. If the latter is the correct interpretation, then there exists no relationship with abstractness of modern science. For in the case of abstractness of science, actually new understanding is gained into more far reaching relationships. Perhaps here it is permissible to mention one more comparison from the field of history that abstractness arises out of the continuous questioning and out of striving for unity that can be clearly recognized from one of the most significant events in the history of the Christian religion. The notion of god in the Jewish religion represents the higher level of abstraction compared to the concept of the many diﬀerent cases of nature whose operation in the world can be directly experienced. Only on this higher level of abstraction is the unity of divine activity recognizable. The struggle of the representatives of the Jewish religion against Christ was, if we may here follow Martin Buber, a struggle centered around the maintaining of the purity of abstraction around the assertion of the higher level already once gained. Contrary to this, Christ had to insist upon the requirement that abstraction may not detach itself from life. The human being must directly experience the activity of the god in the world even when there is no more intelligible representation of the god. The use of comparison that the main diﬃculty of all abstraction is here as characterized that is only too familiar to us also in the history of sciences. Every natural

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science would be worthless whose assertions could not be observationally verified in nature and every art would be worthless, which was no longer able to move to aﬀect human being, no longer able to enlighten for them the meaning of existence. But it would not be reasonable at this point to allow our view to go too far distance, where we have only concerned ourselves towards making more understandable the development of abstraction in modern science. We have to limit ourselves then here to the statement that modern science integrates itself in a natural way into a very wide system of understandable connections, a system which arises with eﬀect that man is continuously questioning and that this continual questioning is a form in which man responds to the world surrounding him in order to recognize its intrinsic relationships and to enable himself to live there.

Fig. 1.1 Professor and Mrs. Heisenberg on their visit to the Nishina Memorial Foundation (1967)

1 Abstraction in Modern Science

Fig. 1.2 Professor Heisenberg (center) and Professor Yanase (interpreter, left) on the stage

Fig. 1.3 An unusual long queue formed in front of Asahi Lecture Hall

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Yoshio Nishina, the Pioneer of Modern Physics in Japan Ryogo Kubo

Abstract This address was presented by Ryogo Kubo as the Nishina Centennial Symposium at the Japan Medical Association(Tokyo), December 5, 1990.

We are gathered here today to celebrate the centennial anniversary of Dr. Yoshio Nishina [1]. He was born one hundred years ago in 1890 in a small village called Satosho near the city of Okayama as the eighth child of a respected family. His grandfather was the local governor of that area. There still remains the old house where he spent his childhood with his parents and family. The house is now restored and is open to the public as a museum to commemorate the great man of whom the village can rightly be proud. I visited the place and was very much impressed by his notebooks, R. Kubo handwritings, and drawings of his schooldays. All are very NMF c beautifully done proving that he was extremely bright and was regarded as a genius. After finishing the local elementary school and the middle school, he entered the sixth national high school at Okayama. The national high school at that time was completely diﬀerent from high school of today. It was an elite school corresponding to junior college for students proceeding to imperial universities. Nishina must have enjoyed his youth there. He liked to study by himself but was also a sportsman. After this, Nishina went to Tokyo to have his undergraduate education in the Engineering School of the Tokyo Imperial University. He elected electrical engineering

Ryogo Kubo (1920 – 1995). Nishina Memorial Foundation (Japan) at the time of this address R. Kubo: Yoshio Nishina, the Pioneer of Modern Physics in Japan, Lect. Notes Phys. 746, 17–26 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 2

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as his major and graduated from the Electrical Engineering Department with honors receiving a silver watch from the Emperor. But Nishina did not want to work in industry as an electrical engineer. He wanted to do something more useful than just engineering and more attractive and worth devoting his unusual talent. He considered electrical engineering as more or less a finished discipline. He thought electrochemistry was more attractive. So he accepted an invitation from Professor Kujirai, who had just started his new laboratory at RIKEN, a newly established research institute for physics and chemistry. This institute was planned taking the Kaiserliche Institut of Germany as a model. So Nishina became a research fellow at RIKEN and concurrently he registered at the graduate school of physics of the the Tokyo Imperial University to study physics under the guidance of Professor Hantaro Nagaoka, who was concurrently a chief researcher at RIKEN holding a laboratory there. Professor Nagaoka was the most influential person in the scientific community of Japan at that time. After three years of studying physics, fortune smiled on him. In the spring of 1921 he was ordered by RIKEN to go to Europe to study physics. This must have been a great encouragement for him. New physics was just being born in Europe. Europe was boiling with expectation of new ideas and new discoveries. This lucky event matched his talent and ambition. Fate made him stay in Europe for seven years, which he himself probably did not originally plan. This transformed him into a first rate physicist, which would not have been really possible if he had remained in Japan. Nishina went first to Cambridge because Nagaoka introduced him to Rutherford. He stayed at the Cavendish Laboratory and performed some experiments on Compton scattering, which were not so successful but gave him valuable experience for his later studies. Nishina eagerly wished to work with Niels Bohr at Copenhagen and asked Bohr if this was possible. Bohr was kind enough to accept him at his Institute. So Nishina was able to move to Copenhagen in 1923. There Nishina started working on the X-ray spectroscopy of atoms under Hevesy’s guidance, and soon was able to publish his first scientific paper [2] on the X-ray absorption spectra in the L-series of the elements La(57) to Hf(72) with the co-authorship of Coster and Werner. He continued the X-ray work after both Hevesy and Coster left Copenhagen and became the leader of the X-ray spectroscopy group. Indeed, Nishina made significant contributions in this field [3]. This was from 1923 to 1926, just the period when new quantum mechanics was rapidly developing. Copenhagen was the center of the revolution. Niels Bohr was the leader at revolution surrounded by its stars. There was great excitement every day. How happy Nishina was to be at the very center of this great revolution and close to the great leader and brilliant young pioneers. This excitement is vividly seen in Nishina’s notes kept in the archives of the Nishina Memorial Foundation. However, Nishina had already stayed in Copenhagen for quite a long time. The grant from RIKEN was already discontinued. His expenses were supported by his relatives at home. Also, Bohr was kind enough to arrange a grant from the Danish Government which lasted for three years. It was about time for Nishina to return home. But he wanted to do something significant in theoretical physics which he could bring back to Japan after staying so many years at the center of theoretical

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physics of the world. Indeed, Nishina had been interested in theoretical physics ever since the time he turned to physics. Before coming to Copenhagen, he attended in Goettingen the lectures by Born and Hilbert. Now he wished to study theory more seriously. So he went to Hamburg in February of 1928 to study under Pauli and there he worked out a theoretical paper in collaboration with Rabi [4]. Coming back to Copenhagen he decided to take up a new problem. He thus chose the theory of Compton scattering for which he had kept a great interest for many years. The new theory is based on the Dirac theory of relativistic quantum mechanics. The method of calculation had not been so well established at that time, so the calculation was by no means easy. He started working on this problem in cooperation with Oscar Klein from the spring of 1928, and was able to finish the work [5] in the summer. The Klein-Nishina formula thus obtained is really a gem of quantum mechanics to be remembered in history. I do not dwell on this topic any further, because Professor Ekspong will talk on this subject. So Nishina finally left Copenhagen in October, 1928, cherishing the happy memory of the time spent at Copenhagen with Niels Bohr and many physicists who were fated to carry on the further revolution of modern science. He returned home in December of that year after making visits to several places in the United States. Having returned to Japan, he joined Nagaoka’s group at RIKEN. He must have felt like Urashima Taro or like Rip Van Winkle after so many years of absence from his mother country. There tooOokouchi , science had been progressing, but the atmosphere of the society was not yet as mature as in advanced countries. He had to be patient to realize his ambitions. It took a few more years until he was promoted to a chief researcher in RIKEN and in 1931 he started to build his own laboratory.

Fig. 2.1 Nishina at Copenhagen, with his friends. 1925. From left to right : Nishina, Dennison (USA), Kuhn (Switzerland), Kronig (Holland), Ray (India)

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It was very fortunate that in 1929 he was able to invite Heisenberg and Dirac who accepted the invitation to come to Japan on their way back to Europe from America. Their visit gave great excitement to Japanese physicists, particularly to the younger generation. Nishina made a great eﬀort to arrange their visit, to help the audience to understand their lectures. All of this made Nishina’s presence more impressive among his Japanese colleagues. He was invited to the universities at Kyoto and Hokkaido to lecture on the new quantum mechanics. At Kyoto he met two young physics students, who regarded Nishina as their teacher and later became to play the role of his successor and to lead modern physics in Japan. They were Hideki Yukawa and Sin-itiro Tomonaga. In 1931, Nishina started his laboratory. As the subjects of his research program he chose (1) (2) (3) (4)

quantum mechanics, nuclear physics, studies of atoms and molecules by X-ray spectroscopy, use of spectroscopy for chemical analysis and its applications.

The list was revised the following year. The items (3) and (4) were replaced by (5) study of cosmic rays, (6) generation of high energy proton beams. This list shows what Nishina intended to develop in Japan, in order to bring its science from the state of an undeveloped country to that of advanced societies like Europe and America. It was fortunate for Nishina that he was able to build up his laboratory in a relatively short time. This was only possible because RIKEN at that time was a unique institution. It was very young, less than fifteen years old, and was an entirely new system independent of the government and existing universities. Originally it was planned to raise money for research from industry, which naturally turned out to be unsuccessful. Dr. M. Ookouchi, the third president of RIKEN was an eminent administrator. He created a number of companies to use the inventions made by RIKEN researchers. Many of these companies were very successful and brought a considerable amount of research money back into RIKEN laboratories. Dr. M. Ookouchi used to tell his researchers not to worry about money but only about their work. Therefore RIKEN had an extremely active atmosphere and it was called the paradise of researchers. It is said that Nishina’s spending was always much more than his budget. Universities at that time were extremely poor regarding research money. Thus we see Nishina’s projects progressed unusually fast with the strong support of RIKEN. Nishina was able to recruit brilliant young researchers so that his laboratory grew up very fast. The number of researchers at its maximum exceeded one hundred. A laboratory of this size was never possible in a university or in any other institute. Let us now survey briefly how Nishina actually proceeded to achieve his objectives. Apparently he greatly emphasized theoretical physics. Fortunately, he was

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able to invite very able young researchers to his group. They were Sin-Ichiro Tomonaga, Shoichi Sakata, Minoru Kobayashi, Hidehiko Tamaki and others. Yukawa was not in this group for he joined the new science faculty of Osaka University, but he kept up good contact with Nishina’s group. Nishina himself was not able to do theoretical work as much as he probably wished, because his main eﬀorts turned soon to experimental work. But in collaboration with Tomonaga and Sakata he studied pair creation probabilities by photons [6]. As Prof. Kobayashi recollects, Nishina guided the research work in much the same way as that in Copenhagen. Namely, discussions between researchers were regarded as most important. This style of work was new among the Japanese researchers at that time. Like Bohr, Nishina was able to encourage and train younger researchers. Tomonaga writes in one of his recollections, that he often became pessimistic about whether he was talented enough to do theoretical physics and it would be better to quit. But every time, Nishina warmly encouraged him to recover confidence in his ability. Yukawa also recalls Nishina being like his loving father. When Yukawa got the idea of the meson mediating the nuclear forces [7], Nishina was one of the few who immediately recognized its importance and gave the strongest support. Although the theoretical group of Nishina’s laboratory was not so big, it was the most active in Japan and was influential in developing the quantum theory in Japan. Nishina regarded cosmic ray research as the key subject to start new experimental physics. With a few members of the laboratory he was able to improve the counters and cloud chambers and set up observatories at various places like the top of Mt. Fuji, Shimizu Tunnel and so forth. Great excitement occurred with the finding [7] of a track in 1938 a little later than that made by Anderson, and Neddermeyer which was supposed to be the evidence of a Yukawa particle but later was proved to be another kind of new particle now called a muon. Nishina’s group conducted a considerable amount of work in cosmic ray physics and laid the foundation of a strong tradition of cosmic ray research in Japan [8]. However, the greatest eﬀort of Nishina was related to starting up nuclear physics in Japan, and in particular to the construction of cyclotrons. From 1930, the frontier of physics had shifted to nuclear physics with the use of various kinds of accelerators. In 1935, RIKEN decided to start a nuclear physics program with the cooperation of Nishina and Nishikawa Laboratories. A small cyclotron with a 23 ton electromagnet was successfully constructed by the Nishina group in 1937 [9]. Using this, the researchers irradiated all kinds of elements by fast neutrons. This was important work in nuclear physics. Beside this, radio-biological studies were initiated in Nishina’s group by a team of biologists in cooperation with physicists and chemists [10]. This belongs to the earliest work of radio-biology. Thus, Nishina is regarded as one of the pioneers in this field. The small cyclotron was successful, but it did not satisfy Nishina’s ambition. He wanted to build a large cyclotron, about ten times as large as the small one. Through Dr. Sagane, the son of Prof. Nagaoka, a young member of the Nishina laboratory, Nishina learned that Lawrence at Berkeley was considering a project similar to his idea. So cooperation began between Nishina and Lawrence with a deep friendship between two physicists who had never seen each other before. By this cooperation,

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Nishina was able to buy a big electromagnet from an American company, which was the same make as that used by Lawrence. Unfortunately, however, the construction thereafter met great diﬃculties. It took much longer than Nishina expected. The diﬃculties were even bigger, since Japan was in the war by this time. Nishina did not give up the project. After great eﬀort, the beam finally came out of the big cyclotron in February 1944. Although it was behind Lawrence by more than three years, this cyclotron was the second biggest in the world when it started to operate, of which Nishina had a right to be proud. When he left home for Europe in 1923, there was no nuclear physics at all in Japan, which was far behind in modern physics. But now he was happy to have put his country in second place, behind the United States. However, the story of the large cyclotron was a tragedy, to which I shall come back later.

Fig. 2.2 Nishina standing in front of the ”large cyclotron”, 1943

In 1937, Niels Bohr visited Japan with his family in response to Nishina’s longstanding invitation, and gave great encouragement to Japanese scientists. It was almost the last days of the happy time, because Japan was becoming internationally isolated by her militaristic policies, finally rushing into the reckless war. During the wartime, Nishina’s group had to engage in the project to develop the nuclear bomb. The scale of the project was nothing compared to the Manhattan project and the

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researchers concluded that it was impossible to produce a nuclear bomb within fifty years. Japan was already losing the war then, and finally there came the disasters of Hiroshima and Nagasaki. Nishina was sent there to investigate if the bombs were really atomic. His report must have been a decisive factor in the political leaders’ final decision to surrender. When the war came to an end, there was almost nothing left of Nishina’s ten years’ work. His laboratory at RIKEN was bombed and the small cyclotron was burnt. The big cyclotron fortunately escaped the damage. A few months after the surrender, the American occupation army came into Nishina’s laboratory unexpectedly, broke the machine and sank it in the Tokyo Bay. Later the Secretary of War admitted that the destruction was a mistake by the War Department of the US Government. Even if it was an unfortunate accident, it still discouraged Nishina from resuming his scientific activities. However, this was just the beginning of the disaster.

Fig. 2.3 Professor N. Bohr and Mrs. Bohr, visiting Japan, 1937, at a garden party at Takamine’s home

The following year, in 1946, RIKEN itself was ordered by the Occupation Force to dissolve. The RIKEN family of companies supporting RIKEN, namely the RIKEN CONCERN was considered as something similar to zaibatu, undesirable for demilitarization of the Japanese economy. So RIKEN had to seek some way of living by itself. Since Nishina was the most distinguished among the remaining senior researchers, he had to take the full responsibility for reconstructing RIKEN from its fragments. Thus he had to give up science to become an administrator to earn money for the researchers, pay their salaries, and research money. In the postwar economy in complete social disorder, the task was diﬃcult beyond our imagination.

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Ryogo Kubo

After a great struggle and great eﬀorts, he managed to create a company with the name of RIKEN Co. He managed to construct a production line of penicillin within RIKEN, which was fairly successful at supporting financially the research activities at RIKEN. He became the president of the RIKEN company. Thus he saved RIKEN from collapse. If there were no Nishina, RIKEN would not have survived. The great eﬀort of Nishina to reconstruct RIKEN out of disaster was a part of his sacrifice to save his country . He felt very strongly his responsibility as the most influential leader in science. Building up of science and technology was the slogan of the Japanese to reconstruct the country from ashes. So he was obliged to extend his activities beyond RIKEN to the problems of the whole country. When the Science Council of Japan started in 1948, he was elected a member of the Council and then took up the responsibility of Vice-Presidency. In order to restore scientific international cooperation, he was sent by the Science Council to the General Assembly of ICSU which took place in Copenhagen in 1949. Reunion with Niels Bohr and his family was the greatest pleasure after such terrible years. The year of 1950 brought him happy news. Through the good will of American scientists, particularly Dr. Harry C. Kelly, who was a science adviser at the General Head Quarters of the Occupation Army doing his best to encourage Japanese scientists, the import of radioactive isotopes was made possible. Although the cyclotrons were lost by the war, Nishina now was able to start radio-isotope work, to encourage his fellow researchers to start working in many important fields of physics, chemistry, medicine and biology. Unfortunately, his health was already deteriorating through overwork. It was January 10th of 1951 when he closed his 60 years’ life of dedication to science and his beloved country. Dr. Nishina died too early. In the forty years after his death, Japan has changed greatly. If not to our own satisfaction, modern science and technology have made enormous progress in Japan. Even though the number of Nobel laureates is still too small among the Japanese, the basic level of its modern science is ranked highly with the most advanced countries. And Japan’s advanced technology in application to modern industries is very remarkable. What would Nishina say, if he was still alive and saw today’s Japan? Nishina lived a life in a transient era of history that was most drastic and dramatic. It was the time when quantum theory cast oﬀ the older skin of classical physics, and atomic physics shifted to nuclear physics. Older concepts were revolutionized by new concepts. When Nishina started studying physics, Japan was only a developing country in the far east, far apart from the center of western civilization and the center of science revolution. Although Japan’s physics was steadily progressing before Nishina’s homecoming, as is shown by some significant achievements by Japanese physicists in the 1920’s, for instance, in X-ray crystallography, atomic spectroscopy, and electron diﬀraction experiments, the geographic distance and still backward technological level were great barriers hindering its ability to catch up with physics in the advanced West. Nishina was the right person with the destiny to bridge the gap between the older Japan before 1920 and the modern Japan after 1930. His role could

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be compared to that of Rabi and Oppenheimer in the United States. In fact, the growth of Japanese science and technology in the 1930’s was remarkable. Industries were growing. National universities were created. Higher education was leveling up. Nishina was destined to lead modern science in Japan. As he might have foreseen when he chose physics after studying electrical engineering, he was successful in his pursuit of his objectives. If it had not rushed into the reckless war, Japan would have been able to attain a reasonably advanced level of modern sciences by the 1950’s before Nishina’s untimely death. It is useless to talk about a historical if. But I only mentioned this to remember the great man with unusual talent who devoted his whole life to science and to his country. Thank you very much for your attention.

Fig. 2.4 Professor Ryogo Kubo giving an opening address at the Yoshio Nishina Centennial Symposium in Tokyo (1990)

References 1. Special Issue for the Centennial Anniversary of Yoshio Nishina Buturi (Physical Society of Japan) October 1990. 2. D.Coster, Y.Nishina and S.Werner : Z.Phys. 18 (1923) 207.

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3. Y.Nishina : Phil. Mag. 49 (1925) 521. Y.Nishina and B.Ray : Nature 117 (1926) 120. S.Aoyama, K.Kimura and Y.Nishina : Z.Phys. 44 (1927) 810. 4. Y.Nishina and I.I.Rabi : Verhandl.Deutsch.Phys. Gesell. 3. Reihe 9. Jahrg (1928) 6. 5. O.Klein and Y.Nishina : Z.Phys. 52 (1929)853. 6. Y.Nishina and S.Tomonaga : Proc. Phys-Math.Soc. Japan Third Series 15 (1933) 248. Y.Nishina, S.Tomonaga and S.Sakata :Suppl.Sci.Pap. I.P.C.R. 17 (1934) 1. 7. H.Yukawa : Proc.Phys.-Math Soc. Japan 17 (1935) 48. 8. Y.Sekido, in Early History of Cosmic Ray Studies, ed. Y.Sekido and H.Elliot (D.Reidel Dordrecht 1985) p.187. 9. Y.Nishina, T.Yasaki, H.Ezoe, K.Kimura, and M.Ikawa : Nature 146 (1940) 24. Y.Nishina , T.Yasaki, K.Kimura and M.Ikawa : Phys.Rev. 58 (1940) 660 ; ibid 59 (1941) 323, 677 ; Z.Phys. 119 (1942) 195. 10. Y.Nishina and H.Nakayama : Sci.Pap. I.P.C.R. 34 (1938) 1635. Y.Nishina, Y.Sinoto and D.Sato : Cytologia, 10 (1940) 406, 458 ; ibid 11 (1941) 311.

3

Tomonaga Sin-Itiro : A Memorial – Two Shakers of Physics Julian Schwinger

Abstract This address was presented by Julian Schwinger as the Nishina Memorial Lecture at the Maison Franco-Japanese (Tokyo), on July 8, 1980.

Minasama: I am deeply honored to have the privilege of addressing you today. It is natural that I should do so, as the Nobel prize partner whose work on quantum electrodynamics was most akin in spirit to that of Tomonaga Sin-Itiro. But not until I began preparing this memorial did I become completely aware of how much our scientific lives had in common. I shall mention those aspects in due time. More immediately provocative is the curious similarity hidden in our names. The Japanese character —the kanji— shin (振) has, among other meanings those of ‘to wave’, ‘to shake’. The begin- Julian Schwinger ning of my Germanic name, Schwing, means ‘to swing’, ‘to NMF c shake’. Hence my title, “Two Shakers of Physics”. One cannot speak of Tomonaga without reference to Yukawa Hideki and, of course, Nishina Yoshio. It is a remarkable coincidence that both Japanese Nobel prize winners in physics were born in Tokyo, both had their families move to Kyoto, and also both were sons of professors at Kyoto Imperial University, both attended the Third High School in Kyoto, and both attended and graduated from Kyoto Imperial University with degrees in physics. In their third and final year at the university, both learned the new quantum mechanics together (Tomonaga would later remark, Julian Schwinger (1918 – 1994). Nobel Laureate in Physics (1965) University of California, Los Angeles (USA) at the time of this address J. Schwinger: Tomonaga Sin-Itiro : A Memorial – Two Shakers of Physics, Lect. Notes Phys. 746, 27–42 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 3

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Fig. 3.1 Memorial lecture of Professor Julian Schwinger for Professor Sin-itiro Tomonaga (July 8, 1980, Tokyo)

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about this independent study, that he was happy not to be bothered by the professors). Both graduated in 1929 into a world that seemed to have no place for them, (Yukawa later said “The depression made scholars”). Accordingly, both stayed on as unpaid assistants to Professor Tamaki Kajyuro; Yukawa would eventually succeed him. In 1931, to Nishina comes on stage. He gave a series of lectures at Kyoto Imperial University on quantum mechanics. Sakata Shoichi, then a student, later reported that Yukawa and Tomonaga asked the most questions afterward. Nishina was a graduate in electrical engineering of the Tokyo Imperial University. In 1917 he joined the recently founded Institute of Physical and Chemical Research, the Rikagaku Kenkyusho —– RIKEN. A private institution, RIKEN, was supported financially in various ways, including the holding of patents on the manufacture of sake. After several years at RIKEN, Nishina was sent abroad for further study, a pilgrimage that would last for eight years. He stopped at the Cavendish Laboratory in Cambridge, England, at the University of G¨ottingen in Germany, and then, finally, went to Denmark and Niels Bohr in Copenhagen. He would stay there for six years. And out of that period came the famous Klein-Nishina formula. Nishina returned to Japan in December, 1928, to begin building the Nishina Group. It would, among other contributions, establish Japan in the forefront of research on nuclear and cosmic ray physics —– soryushiron. There was a branch of RIKEN at Kyoto in 1931 when Nishina, the embodiment of the ‘Kopenhagener Geist’, came to lecture and to be impressed by Tomonaga. The acceptance of Nishina’s oﬀer of research position brought Tomonaga to Tokyo in 1932. (Three years earlier he had traveled to Tokyo to hear lectures at RIKEN given by Heisenberg and Dirac.) The year 1932 was a traumatic one for physics. The neutron was discovered; the positron was discovered. The first collaborative efforts of Nishina and Tomonaga dealt with the neutron, the problem of nuclear forces. Although there were no formal publications, this work was reported at the 1932 autumn and 1933 spring meetings that were regularly held by the RIKEN staﬀ. Then, in the 1933 autumn meeting the subject becomes the positron. It was the beginning of a joint research program that would see the publication of a number of papers concerned with various aspects of electron-positron pair creation and annihilation. Tomonaga’s contributions to quantum electrodynamics has begun. While these papers were visible evidence of interest in quantum electrodynamics, we are indebted to Tomonaga for telling us, in his Nobel address, of an unseen but more important step — he read the 1932 paper of Dirac that attempted to find a new basis for electrodynamics. Dirac argued that “the role of the field is to provide a means for making observations of a system of particles”, and therefore, “we cannot suppose the field to be a dynamical system on the same footing as the particles and thus something to be observed in the same way as the particles”. The attempt to demote the dynamical status of the electromagnetic field, or, in the more extreme later proposal of Wheeler and Feynman, to eliminate it entirely, is a false trail, contrary to the fundamental quantum duality between particle and wave, or field. Nevertheless, Dirac’s paper was to be very influential. Tomonaga says, “This paper of Dirac’s attracted my interest because of the novelty of its philosophy and the beauty of its form. Nishina also showed a great interest in this paper and suggested that I

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Julian Schwinger investigate the possibility of predicting some new phenomena by this theory. Then I started computations to see whether the Klein-Nishina formula could be derived from this theory or whether any modification of the formula might result. I found out immediately. however, without performing the calculation through to the end, that it would yield the same answer as the previous theory. The new theory of Dirac’s was in fact mathematically equivalent to the older Heisenberg–Pauli theory and I realized during the calculation that one could pass from one to the other by a unitary transformation. The equivalence of these two theories was also discovered by Rosenfeld and Dirac–Fock–Podolsky and was soon published in their papers.”

I graduated from a high school that was named for Townsend Harris, the first American consul in Japan. Soon after, in 1934, I wrote but did not publish my first research paper. It was on quantum electrodynamics. Several years before, the Danish physicist Møller had proposed a relativistic interaction between two electrons, produced through the retarded intervention of the electromagnetic field. It had been known since 1927 that electrons could also be described by a field, one that had no classical, counterpart. And the dynamical description of this field was understood, when the electrons interacted instantaneously. I asked how things would be when the retarded interaction of Møller was introduced. To answer the question I used the Dirac–Fock–Podolsky formulation. But now, since I was dealing entirely with fields, it was natural to introduce for the electron field, as well, the analogue of the unitary transformation that Tomonaga had already recognized as being applied to the electromagnetic field in Dirac’s original version. Here was the first tentative use of what Tomonaga, in 1943, would correctly characterize as “a formal transformation which is almost self-evident” and I, years later, would call the interaction representation. No, neither of us, in the 1930’s, had reached what would eventually be named the Tomonaga–Schwinger equation. But each of us held a piece which, in combination, would lead to that equation: Tomonaga appreciated the relativistic form of the theory, but was thinking in particle language; I used a field theory, but had not understood the need for a fully relativistic form. Had we met then, would history have been diﬀerent? The reports of the spring and autumn 1936 meetings of the RIKEN staﬀ show something new — Tomonaga had resumed his interest in nuclear physics. In 1937 he went to Germany — to Heisenberg’s Institute at Leipzig. He would stay for two years, working on nuclear physics and on the theory of mesons, to use the modern term. Tomonaga had come with a project in mind: treat Bohr’s liquid drop model of the nucleus, and the way an impinging neutron heats it up, by using the macroscopic concepts of heat conduction and viscosity. This work was published in 1938. It was also the major part of the thesis submitted to Tokyo University in 1939 for the degree of Doctor of Science — Rigakuhakushi. Heisenberg’s interest in cosmic rays then turned Tomonaga’s attention to Yukawa’s meson. The not yet understood fact, that the meson of nuclear forces and the cosmic ray meson observed at sea level are not the same particle, was beginning to thoroughly confuse matters at this time. Tomonaga wondered whether the problem of the meson lifetime could be overcome by including an indirect process, in which the meson turns into a pair of nucleons — proton and neutron — that annihilate to produce the final electron and neutrino. The integral over all nucleon pairs, resulting

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from the perturbation calculation, was — infinite. Tomonaga kept a diary of his impressions during this German period. It poignantly records his emotional reactions to the diﬃculties he encountered. Here are some excerpts: “It has been cold and drizzling since morning and I have devoted the whole day to physics in vain. As it got dark I went to the park. The sky was gray with a bit of the yellow of twilight in it. I could see the silhouetted white birch grove glowing vaguely in the dark. My view was partly obscured by my tired eyes: my nose prickled from the cold and upon returning home I had a nosebleed. After supper I took up my physics again, but at last I gave up. III-starred work indeed!”

Then, “Recently I have felt very sad without any reason, so I went to a film. Returning home I read a book on physics. I don’t understand it very well. Meanwhile I comprehensible?”

Again, “As I went on with the calculation, I found the integral diverged — was infinite. After lunch I went for a walk. The air was astringently cold and the pond in Johanna Park was half frozen, with ducks swimming where there was no ice. I could see a flock of other birds. The flower beds were covered with chestnut leaves against the frost. Walking in the park, I was no longer interested in the existence of neutron, neutrino.”

And finally, “I complained in emotional words to Professor Nishina about the slump in my work, whereupon I got his letter in reply this morning. After reading it my eyes were filled with tears. — He says: only fortune decides your progress in achievements. All of us stand on the dividing line from which the future is invisible. We need not be too anxious about the results, even though they may turn out quite diﬀerent from what you expect. By-and-by you may meet a new chance for success.”

Toward the close of Tomonaga’s stay in Leipzig, Heisenberg suggested a possible physical answer to the clear inapplicability of perturbation methods in meson physics. It involved the self-reaction of the strong meson field surrounding a nucleon. Heisenberg did a classical calculation, showing that the scattering of mesons by nucleons might thereby be strongly reduced, which would be more in conformity with the experimental results. About this idea Tomonaga later remarked, “Heisenberg, in this paper published in 1939, emphasized that the field reaction would be crucial in meson-nucleon scattering. Just at that time I was studying at Leipzig, and I still remember vividly how Heisenberg enthusiastically explained this idea to me and handed me galley proofs of his forthcoming paper. Influenced by Heisenberg, I came to believe that the problem of field reactions far from being meaningless was one which required a “frontal attack”. Indeed, Tomonaga wanted to stay on for another year, to work on the quantum mechanical version of Heisenberg’s classical calculation. The growing clouds of war made this inadvisable, however, and Tomonaga returned to Japan by ship. As it happened, Yukawa who had come to Europe to attend a Solvay Congress, which unfortunately was cancelled, sailed on that very ship. When the ship docked at New York, Yukawa disembarked and, beginning at Columbia

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University, where I first met him, made his way across the United States, visiting various universities. But Tomonaga, after day’s sightseeing in New York that included the Japanese Pavilion at the World’s Fair, continued with the ship through the Panama Canal and on to Japan. About this Tomonaga said, “When I was in Germany I had wanted to stay another year in Europe, but once I was aboard a Japanese ship I became eager to arrive in Japan”. He also remarked about his one day excursion in New York that “I found that I was speaking German rather than English, even though I had not spoken fluent German when I was in Germany”. Tomonaga had returned to Japan with some ideas concerning the quantum treatment of Heisenberg’s proposal that attention to strong field reactions was decisive for understanding the meson-nucleon system. But soon after he began work he became aware, through an abstract of a paper published in 1939, that Wentzel was also attacking this problem of strong coupling. Here is where the scientific orbits of Tomonaga and myself again cross. At about the time that Tomonaga returned to Japan I went to California, to work with Oppenheimer. Our first collaboration was a quantum electrodynamic calculation of the electron-positron pair emitted by an excited oxygen nucleus. And then we turned to meson physics. Heisenberg had suggested that meson-nucleon scattering would be strongly suppressed by field reaction eﬀects. There also existed another proposal to the same end — that the nucleon possessed excited states, isobars, which would produce almost cancelling contributions to the meson scattering process. We showed, classically, that the two explanations of suppressed scattering were one and the same: the eﬀect of the strong field reaction, of the strong coupling, was to produce isobars, bound states of the meson about the nucleon. The problem of giving these ideas a correct quantum framework naturally arose. And then, we became aware, through the published paper, of Wentzel’s quantum considerations on a simple model of the strong coupling of meson and nucleon. I took on the quantum challenge myself. Not liking the way Wentzel had handled it, I redid his calculation in my own style, and, in the process, found that Wentzel had made a mistake. In the short note that Oppenheimer and I eventually published, this work of mine is referred to as “to be published soon”. And it was published, 29 years later, in a collection of essays dedicated to Wentzel. Recently, while surveying Tomonaga’s papers, I came upon his delayed publication of what he had done along the same lines. I then scribbled a note: “It is as though I were looking at my own long unpublished paper”. I believe that both Tomonaga and I gained from this episode added experience in using canonical-unitary-transformations to extract the physical consequences of a theory. I must not leave the year 1939 without mentioning a work that would loom large in Tomonaga’s later activities. But, to set the stage, I turn back to 1937. In this year, Block and Nordsieck considered another kind of strong coupling, that between an electric charge and arbitrarily soft — extremely low frequency — light quanta. They recognized that, in a collision, say between an electron and a nucleus, arbitrarily soft quanta will surely be emitted; a perfectly elastic collision cannot occur. Yet, if only soft photons, those of low energy, are considered, the whole scattering process goes on as though the electrodynamic interactions were ineﬀective. Once this was understood, it was clear that the real problem of electrodynamic field reaction begins

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when arbitrarily hard — unlimited high energy — photons are reintroduced. In 1939 Dancoﬀ performed such a relativistic scattering calculation both for electrons, which have spin 1/2, and for charged particles without spin. The spin 0 calculation gave a finite correction to the scattering, but, for spin 1/2, the correction was infinite. This was confusing. And to explain why that was so, we must talk about electromagnetic mass. Already in classical physics the electric field surrounding an electrically charged body carries energy and contributes mass to the system. That mass varies inversely as a characteristic dimension of the body, and therefore is infinite for a point charge. The magnetic field that accompanies a moving charge implies an additional momentum, and additional electromagnetic, mass. It is very hard, at this level to make those two masses coincide, as they must, in a relativistically invariant theory. The introduction of relativistic quantum mechanics, of quantum field theory, changes the situation completely. For the spin 1/2 electron-positron system, obeying Fermi–Dirac statistics, the electromagnetic mass, while still infinite, is only weakly logarithmically, so. In contrast, the electromagnetic mass for a spin 0 particle, which obeys Bose–Einstein statistics, is more singular than the classical one. Thus, Dancoﬀ’s results were in contradiction to the expectation that spin 0 should exhibit more severe electromagnetic corrections. Tomonaga’s name had been absent from the RIKEN reports for the years from 1937 to 1939, when he was in Germany. It reappears for the 1940 spring meeting under the title “On the Absorption and Decay of Slow Mesons”. Here the simple and important point is made that, when cosmic ray mesons are stopped in matter, the repulsion of the nuclear Coulomb field prevents positive mesons from being absorbed by the nucleus, while negative mesons would preferentially be absorbed before decaying. This was published as a Physical Review Letter in 1940. Subsequent experiments showed that no such asymmetry existed: the cosmic ray meson does not interact significantly with nuclear particles. The RIKEN reports from autumn of 1940 to autumn of 1942 trace stages in the development of Tomonaga’s strong and intermediate coupling meson theories. In particular, under the heading “Field Reaction and Multiple Production” there is discussed a coupled set of equations corresponding to various particle numbers, which is the basis of an approximation scheme, now generally called the Tamm–Dancoﬀ approximation. This series of reports on meson theory was presented to the Meson Symposium — Chukanshi Toronkai — that was initiated in September 1943, where also was heard the suggestion of Sakata’s group that the cosmic ray meson is not the meson responsible for nuclear forces. But meanwhile there occurred the last of the RIKEN meetings held during the war, that of spring 1943. Tomonaga provides the following abstract with the title “Relativistically Invariant Formulation of Quantum Field Theory”: “In the present formulation of quantum fields as a generalization of ordinary quantum mechanics such nonrelativistic concepts as probability amplitude, canonical commutation relation and Schr¨odinger equation are used. Namely these concepts are defined referring to a particular Lorentz frame in space-time. This unsatisfactory feature has been pointed out by many people and also Yukawa emphasized it recently. I make a relativistic generalization of these concepts in quantum mechanics such that they do not refer to any particular

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Julian Schwinger coordinate frame and reformulate the quantum theory of fields in a relativistically invariant manner.”

In the previous year Yukawa had commented on the unsatisfactory nature of quantum field theory, pointing both to its lack of an explicit, manifestly covariant form and to the problem of divergences — infinities. He wished to solve both problems at the same time. To that end, he applied Dirac’s decade earlier suggestion of a generalized transformation function by proposing that the quantum field probability amplitude should refer to a closed surface in space-time. From the graphic presentation of such a surface as a circle, the proposal became known as the theory of maru. Tomonaga’s reaction was to take one problem at a time, and he first proceeded to “reformulate the quantum theory of fields in a relativistically invariant manner”. And in doing so he rejected Yukawa’s more radical proposal in favor of retaining the customary concept of causality — the relation between cause and eﬀect. What was Tomonaga’s reformulation? The abstract I have cited was that of a paper published in the Bulletin of the Institute, RIKEN–Iho. But its contents did not become known outside of Japan until it was translated into English to appear in the second issue, that of August–September, 1946, of the new journal, Progress of Theoretical Physics. It would, however, be some time before this issue became generally available in the United States. Incidentally, in this 1946 paper Tomonaga gave his address as Physics Department, Tokyo Bunrika University. While retaining his connection with RIKEN, he had, in 1941, joined the faculty of this university which later, in 1949, became part of the Tokyo University of Education. Tomonaga begins his paper by pointing out that the standard commutation relations of quantum field theory, referring to two points of space at the same time, are not covariantly formulated: in a relatively moving frame of reference the two points will be assigned diﬀerent times. This is equally true of the Schr¨odinger equation for time evolution, which uses a common time variable for diﬀerent spatial points. He then remarks that there is no diﬃculty in exhibiting commutation relations for arbitrary space-time points when a non-interacting field is considered. The unitary transformation to which we have already referred, now applied to all the fields, provides them with the equations of motion of non-interacting fields, while, in the transformed Schr¨odinger equation, only the interaction terms remain. About this Tomonaga says, “... in our formulation, the theory is divided into two sections. One section gives the laws of behavior of the fields when they are left alone, and the other gives the laws determining the deviation from this behavior due to the interactions. This way of separating the theory can be carried out relativistically”. Certainly commutation relations referring to arbitrary space-time points are four-dimensional in character. But what about the transformed Schr¨odinger equation, which still retains its single time variable? It demands generalization. Tomonaga was confident that he had the answer for, as he put it later, “I was recalling Dirac’s many-time theory which had enchanted me ten years before”. In the theory of Dirac, and then of Dirac–Fock–Podolsky, each particle is assigned its own time variable. But, in a field theory, the role of the particles is played by the small volume elements of space. Therefore, assign to each spatial volume element an independent time coordinate. Thus, the “super many-time theory”. Let me be more

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precise about that idea. At a common value of the time, distinct spatial volume elements constitute independent physical system, for no physical influence is instantaneous. But more than that, no physical influence can travel faster than the speed of light. Therefore any two space-time regions that cannot be connected, even by light signals, are physically independent; they are said to be in space-like relationship. A three-dimensional domain such that any pair of points is in space-like relationship constitutes a space-like surface in the four-dimensional world. All of space at a common time is but a particular coordinate description of a plane space-like surface. Therefore the Schr¨odinger equation, in which time advances by a common amount everywhere in space, should be regarded as describing the normal displacement of plane space-like surface. Its immediate generalization is to the change from one arbitrary space-like surface to an infinitesimally neighboring one, which change can be localized in the neighborhood of a given space-time point. Such is the nature of the generalized Schr¨odinger equation that Tomonaga constructed in 1943, and to which I came toward the end of 1947. By this time the dislocation produced by the war became dominant. Much later Tomonaga recalled that “I myself temporarily stopped working on particle physics after 1943 and was involved in electronics research. Nevertheless the research on magnetrons and on ultra-short wave circuits was basically a continuation of quantum mechanics”. Miyazima Tatsuoki remembers that “One day our boss Dr. Nishina took me to see several engineers at the Naval Technical Research Institute. They had been engaged in the research and development of powerful split anode magnetrons, and they seemed to have come to a concrete conclusion about the phenomena taking place in the electron cloud. Since they were engineers their way of thinking was characteristic of engineers and it was quite natural that they spoke in an engineer’s way, but unfortunately it was completely foreign to me at the beginning. Every time I met them, I used to report to Tomonaga how I could not understand them, but he must have understood something, because after a month or so, he showed me his idea of applying the idea of secular perturbation, well-known in celestial mechanics and quantum theory, to the motion of the electrons in the cloud. I remember that the moment he toll me I said ‘This is it’. Further investigation actually showed that the generation of electromagnetic oscillations in split anode magnetrons cannot be essentially understood by applying his idea”. When Tomonaga approached the problem of ultra-shortwave circuits, which is to say, the behavior of microwaves in waveguides and cavity resonators, he found the engineers still using the old language of impedance. He thought this artificial because there no longer are unique definitions of current and voltage. Instead, being a physicist, Tomonaga begins with the electromagnetic field equations of Maxwell. But he quickly recognizes that those equations contain much more information than is needed to describe a microwave circuit. One usually wants to know only a few things about a typical waveguide junction: if a wave of given amplitude moves into a particular arm, what are the amplitudes of the waves coming out of the various arms, including the initial one? The array of all such relations forms a matrix, even then familiar to physicists as the scattering matrix. I mention here the amusing episode of the German submarine that arrived bearing a dispatch stamped Streng Geheim —

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Top Secret. When delivered to Tomonaga it turned out to be — Heisenberg’s paper on the scattering matrix. Copies of this Top Secret document were soon circulating among the physicists. Tomonaga preferred to speak of the scattering matrix as the characteristic matrix, in this waveguide context. He derives properties of that matrix, such its unitary character, and shows how various experimental arrangements can be described in term of the characteristic matrix of the junction. In the paper published after the war he remarks, concerning the utility of this approach, that “The final decision, however, whether or not new concept is more preferable to impedance should of course be given not only by a theoretical physicist but also by general electro-engineers”. But perhaps my experience is not irrelevant here. During the war I also worked on the electromagnetic problems of microwaves and waveguides. I also began with the physicist’s approach, including the use of the scattering matrix. But long before this three year episode was ended, I was speaking the language of the engineers. I should like to think that those years of distraction for Tomonaga and myself were not without their useful lessons. The waveguide investigations showed the utility of organizing a theory to isolate those inner structural aspects that are not probed under the given experimental circumstances. That lesson was soon appllied in the eﬀective range description of nuclear forces. And it is this viewpoint that would lead to the quantum electrodynamics concept of selfconsistent subtraction or renormalization. Tomonaga already understood the importance of describing relativistic situations covariantly — without specialization to any particular coordinate system. At about this time, I began to learn that lesson pragmatically, in the context of solving a physical problem. As the war in Europe approached its end, the American physicists responsible for creating a massive microwave technology began to dream of high energy electron accelerators. One of the practical questions involved is posed by the strong radiation emitted by relativistic electrons swinging in circular orbits. In studying what is now called synchrotron radiation, I used the action of the field created by the electron’s motion. One part of that reaction describes the energy and momentum lost by the electron to the radiation. The other part is an added inertial eﬀect characterized by an electromagnetic mass. I have mentioned the relativistic diﬃculty that electromagnetic mass usually creates. But, in the covariant method I was using, based on action and proper time, a perfectly invariant form emerged. Moral: to end with an invariant result use a covariant method and maintain covariance to the end of the calculation. And, in the appearance of an invariant electromagnetic mass that simply added to the mechanical mass to form the physical mass of the electron, neither piece being separately distinguishable under ordinary physical circumstances, I was seeing again the advantage of isolating unobservable structural aspects of the theory. Looking back at it, the basic ingredients of the coming quantum electrodynamic revolution were now in place. Lacking was an experimental impetus to combine them, and take them seriously. Suddenly, the Pacific War was over. Amid total desolation Tomonaga reestablished his seminar. But meanwhile, something had been brewing in Sakata’s Nagoya group. It goes back to a theory of M}oller and Rosenfeld, who tried to overcome the nuclear force diﬃculties of meson theory by proposing a mixed field theory, with

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both pseudoscalar and vector mesons of equal mass. I like to think that my modification of this theory, in which the vector meson is more massive, was the prediction of the later discovered — meson. Somewhat analogously, Sakata proposed that the massless vector photon is accompanied by a massive scalar meson called the cohesive or C-meson. About this, Tomonaga said, “in 1946, Sakata proposed a promising method of eliminating the divergence of the electron mass by introducing the idea of a field of cohesive force. It was the idea that there exists an unknown field, of the type of the meson field, which interacts with the electron in addition to the electromagnetic field. Sakata named this field the cohesive force field, because the apparent electromagnetic mass due to the interaction of this field and the electron, though infinite, is negative and therefore the existence of this field could stabilize the electron in some sense. Sakata pointed out the possibility that the electromagnetic mass and the negative new mass cancel each other and that the infinity could be eliminated by suitably choosing the coupling constant between this field and the electron. Thus the diﬃculty which had troubled people for a long time seemed to disappear insofar as the mass was concerned”. Let me break in here and remark that this solution of the mass divergence problem is, in fact, illusory. In 1950, Kinoshita showed that the necessary relation between the two coupling constants would no longer cancel the divergences, when the discussion is extended beyond the lowest order of approximation. Nevertheless, the C-meson hypothesis served usefully as one of the catalysis that led to the introduction of the self-consistent subtraction method. How that came about is described in Tomonaga’s next sentence: “Then what concerned me most was whether the infinities appearing in the electron scattering process could also be removed by the idea of a plus-minus cancellation.” I have already referred to the 1939 calculation of Dancoﬀ, on radiative corrections to electron scattering, which gave an infinite result. Tomonaga and his collaborators now proceeded to calculate the additional eﬀect of the cohesive force field. It encouragingly gave divergent results of the opposite sign, but they did not precisely cancel Candoﬀ’s infinite terms. This conclusion was reported in a letter of November 1, 1947, submitted to the Progress of Theoretical Physics, and also presented at a symposium on elementary particles held in Kyoto that same month. But meanwhile parallel calculations of the electromagnetic eﬀect were going on, repeating Dancoﬀ’s calculations, which were not reported in detail. At first they reproduced Dancoﬀ’s result. But then Tomonaga suggested a new and much more eﬃcient method of calculation. It was to use the covariant formulation of quantum electrodynamics, and subject it to a unitary transformation that immediately isolated the electromagnetic mass term. Tomonaga says, “Owing to this new, more lucid method, we noticed that among the various terms appearing in both Dancoﬀ’s and our previous calculation, one term had been overlooked. There was only one missing term, but it was crucial to the final conclusion. Indeed, if we corrected this error, the infinities appearing in the scattering process of an electron due to the electromagnetic and cohesive force fields cancelled completely, except for the divergence of vacuum polarization type.”

A letter of December 30, 1947, corrected the previous erroneous announcement.

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But what is meant by “the divergence of vacuum polarization type”? From the beginning of Dirac’s theory of positrons it had been recognized that, in a sense, the vacuum behaved as a polarizable medium; the presence of an electromagnetic field induced a charge distribution acting to oppose the inducing field. As a consequence the charges of particles would appear to be reduced, although the actual calculation gave a divergent result. Nevertheless, the eﬀect could be absorbed into a redefinition, a renormalization, of the charge. At this stage, then, Tomonaga had achieved a finite correction to the scattering of electrons, by combining two distinct ideas: the renormalization of charge, and the compensation mechanism of the C-meson field. But meanwhile another line of thought had been developing. In this connection let me quote from a paper, published at about this time, by Taketani Mitsuo: “The present state of theoretical physics is confronted with diﬃculties of extremely ambiguous nature. These diﬃculties can be glossed over but no one believes that a definite solution has been attained. The reason for this is that, on one hand, present theoretical physics itself has logical diﬃculties, while, on the other hand, there is no decisive experiment whereby to determine this theory uniquely.”

In June of 1947 those decisive experiments were made known, in the United States. For three days at the beginning of June, some twenty physicists gathered at Shelter Island, located in a bay near the tip of Long Island, New York. There we heard the details of the experiment by which Lamb and Retherford had used the new microwave techniques to confirm the previously suspected upward displacement of the 2S level of hydrogen. Actually, rumors of this had already spread, and on the train to New York, Victor Weisskopf and I had agreed that electrodynamic eﬀects were involved, and that relativistic calculation would give a finite prediction. But there was also a totally unexpected disclosure, by Isador Rabi: the hyperfine structures in hydrogen and deuterium were larger than anticipated by a fraction of a percent. Here was another flaw in the Dirac electron theory, now referring to magnetic rather than electric properties. Weisskopf and I had described at Shelter Island our idea that the relativistic electron-positron theory, then called the hole theory, would produce a finite electrodynamic energy shift. But it was Hans Bethe who quickly appreciated that a first estimate of this eﬀect could be found without entering into the complications of a relativistic calculation. In a Physical Review article received on June 27, he says, “Schwinger and Weisskopf, and Oppenheimer have suggested that a possible explanation might be the shift of energy levels by the interaction of the electron with the radiation field. This shift came out infinite in all existing theories, and has therefore always been ignored. However, it is possible to identify the most strongly (linearly) divergent term in the level shift with an electromagnetic mass eﬀect which must exist for a bound as well as a free electron. This eﬀect should properly be regarded as already included in the observed mass of the electron, and we must therefore subtract from the theoretical expression, the corresponding expression for a free electron of the same average kinetic energy. The result then diverges only logarithmically (instead of linearly) in non-relativistic theory. Accordingly, it may be expected that in the hole theory, in which the main term (self-energy of the electron) diverges only logarithmically, the result will be convergent after subtraction of the free electron expression. This would set an eﬀective upper limit of the order of mc to the frequencies

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of light which eﬀectively contribute to the shift of the level of a bound electron. I have not carried out the relativistic calculations, but I shall assume that such an eﬀective relativistic limit exists.”

The outcome of Bethe’s calculation agreed so well with the then not very accurately measured level shift that there could be no doubt of its electrodynamic nature. Nevertheless, the relativistic problem, of producing a finite and unique theoretical prediction, still remained. The news of the Lamb–Retherford measurement and of Bethe’s non-relativistic calculation reached Japan in an unconventional way. Tomonaga says, “The first information concerning the Lamb shift was obtained not through the Physical Review, but through the popular science column of weekly U.S. magazine. This information about the Lamb shift prompted us to begin a calculation more exact than Bethe’s tentative one.”

He goes on: “In fact, the contact transformation method could be applied to this case, clarifying Bethe’s calculation and justifying his idea. Therefore the method of covariant contact transformations, by which we did Dancoﬀ’s calculation over again, would also be useful for the problem of performing the relativistic calculation for the Lamb shift.”

Incidentally, in speaking of contact transformations Tomonaga is using another name for canonical or unitary transformations. Tomonaga announced his relativistic program at the already mentioned Kyoto Symposium of November 24–25, 1947. He gave it a name, which appears in the title of a letter accompanying the one of December 30 that points out Dancoﬀ’s error. This title is ‘Application of the SelfConsistent Subtraction Method to the Elastic Scattering of an Electron’. And so, at the end of 1947 Tomonaga was in full possession of the concepts of charge and mass renormalization. Meanwhile, immediately following the Shelter Island Conference I found myself with a brand new wife, and for two months we wandered around the United States. Then it was time to go to work again. I also clarified for myself Bethe’s nonrelativistic calculation by applying a unitary transformation that isolated the electromagnetic mass. This was the model for a relativistic calculation, based on the conventional hole theory formulation of quantum electrodynamics. But here I held an unfair advantage over Tomonaga, for, owing to the communication problems of the time, I knew that there were two kinds of experimental eﬀects to be explained: the electric one of Lamb, and the magnetic one of Rabi. Accordingly, I carried out a calculation of the energy shift in a homogeneous magnetic field, which is the prediction of an additional magnetic moment of the electron, and also considered the Coulomb field of a nucleus in applications to the scattering and to the energy shift of bound states. The results were described in a letter to the Physical Review, received on December 30, 1947, the very same date as Tomonaga’s proposal of the self-consistent subtraction method. The predicted additional magnetic moment accounted for the hyperfine structure measurements, and also for later, more accurate, atomic moment measurements. Concerning scattering I said “· · · the finite radiative correction to the

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elastic scattering of electrons by a Coulomb field provides a satisfactory termination to a subject that has been beset with much confusion”. Considering the absence of experimental data, this is perhaps all that needed to be said. But when it came to energy shifts, what I wrote was, “The values yielded by our theory diﬀer only slightly from those conjectured by Bethe on the basis of a non-relativistic calculation, and are, thus, in good accord with experiment.”

Why did I not quote a precise number? The answer to that was given in a lecture before the American Physical Society at the end of January, 1948. Quite simply, something was wrong. The coupling of the electron spin to the electric field was numerically diﬀerent from what the additional magnetic moment would imply; relativistic invariance was violated in this non-covariant calculation. One could, of course, adjust that spin coupling to have the right value and, in fact, the correct energy shift is obtained in this way. But there was no conviction in such a procedure. The need for a covariant formulation could no longer be ignored. At the time of this meeting the covariant theory had already been constructed, and applied to obtain an invariant expression for the electron electromagnetic mass. I mentioned this briefly. After the talk, Oppenheimer told me about Tomonaga’s prior work. A progress report on the covariant calculations, using the technique of invariant parameters, was presented at the Pocono Manor Inn Conference held March 30 — April 1, 1948. At that very time Tomonaga was writing a letter to Oppenheimer which would accompany a collection of manuscripts describing the work of his group. In response, Oppenheimer sent a telegram: “Grateful for your letter and papers. Found most interesting and valuable mostly paralleling much work done here. Strongly suggest you write a summary account of present state and views for prompt publication in Physical Review. Glad to arrange.” On May 28, 1948, Oppenheimer acknowledges the receipt of Tomonaga’s letter entitled “On Infinite Field Reactions in Quantum Field Theory”. He writes, “Your very good letter came two days ago and today your manuscript arrived. I have sent it on at once to the Physical Review with the request that they publish it as promptly as possible· · · I also sent a brief note which may be of some interest to you in the prosecution of higher order calculations. Particularly in the identification of light quantum self energies, it proves important to apply your relativistic methods throughout. We shall try to get an account of Schwinger’s work on this and other subjects to you in the very near future”. He ends the letter expressing the “hope that before long you will spend some time with us at the Institute where we should all welcome you so warmly”. The point of Oppenheimer’s added note is this: In examining the radiative correction to the Klein–Nishina formula, Tomonaga and his collaborators had encountered a divergence additional to those involved in mass and charge renormalization. It could be identified as a photon mass. But unlike the electromagnetic mass of the electron, which can be amalgamated, as Tomonaga put it., into an already existing mass, there is no photon mass in the Maxwell equations. Tomonaga notes the possibility of a compensation cancellation, analogous to the idea of Sakata. In response, Oppenheimer essentially quotes my observation that a gauge invariant relativistic

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theory cannot have a photon mass and further, that a suﬃciently careful treatment would yield the required zero value. But Tomonaga was not convinced. In a paper submitted about this time he speaks of the “somewhat quibbling way” in which it was argued that the photon mass must vanish. And he was right, for the real subtlety underlying the photon mass problem did not surface for another 10 years, in the eventual recognition of what others would call ‘Schwinger terms’. But even the concept of charge renormalization was troubling to some physicists. Abraham Pais, on April 13, 1948, wrote a letter to Tomonaga in which, after commenting on his own work parallel to that of Sakata, he remarks, “it seems one of the most puzzling problems how to ‘renormalize’ the charge of the electron and of the proton in such a way as to make the experimental values for these quantities equal to each other”. Perhaps I was the first to fully appreciate that charge renormalization is a property of the electromagnetic field alone, which results in a renormalization, a fractional reduction of charge, that is the same for all. But while I’m congratulating myself, I must also mention a terrible mistake I made. Of course, I wasn’t entirely alone — Feynman did it too. It occurred in the relativistic calculation of energy values for bound states. The eﬀect of high energy photons was treated covariantly: that of low energy photons in the conventional way. These two parts had to be joined together, and a subtlly involved in relating the respective four- and three-dimensional treatments was overlooked for several months. But sometime around September, 1948, it was straightened out, and, apart from some uncertainty about the inclusion of vacuum polarization eﬀects, all groups, Japanese and American, agreed on the answer. As I have mentioned, it was the result I had reached many months before by correcting the obvious relativistic error of my first non-covariant calculation. In that same month of September, 1948, Yukawa, accepting an invitation of Oppenheimer, went to the Institute for Advanced Study at Princeton, New Jersey. The letters that he wrote back to Japan were circulated in a new informal journal called Elementary Particle Physics Research — Soryushiron Kenkyu. Volume 0 of that journal also contains the communications of Oppenheimer and Pais to which I have referred, and a letter of Heisenberg to Tomonaga, inquiring whether Heisenberg’s paper, sent during the war, had arrived. In writing to Tomonaga on October 15, 1948, Yukawa says, in part, “Yesterday I met Oppenheimer, who came back from the Solvay Conference. He thinks very highly of your work. Here, many people are interested in Schwinger’s and your work and I think that this is the main reason why the demand for the Progress of Theoretical Physics is high. I am very happy about this”. During the period of intense activity in quantum electrodynamics, Tomonaga was also involved in cosmic ray research. The results of a collaboration with Hayakawa Satio were published in 1949 under the title “Cosmic Ray Underground”. By now, the two mesons had been recognized and named: π and μ. This paper discusses the generation of, and the subsequent eﬀects produced by, the deep penetrating meson. Among other activities in that year of 1949, Tomonaga published a book on quantum mechanics that would be quite influential, and he accepted Oppenheimer’s invitation to visit the Institute for Advanced Study. During the year he spent there he turned in a new direction, one that would also interest me a number of years later. It is

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the quantum many-body problem. The resulting publication of 1950 is entitled “Remarks on Bloch’s Method of Sound Waves Applied to Many-Fermion Problems”. Five years later he would generalize this in a study of quantum collective motion. But the years of enormous scientific productivity were coming to a close, owing to the mounting pressures of other obligation. In 1951 Nishina died, and Tomonaga accepted his administrative burdens. Now Tomonaga’s attention turned toward improving the circumstances and facilities available to younger scientists, including the establishment of new Institutes and Laboratories. In 1956 he became President of the Tokyo University of Education, which post he held for six years. Then, for another six years, he was President of Science Council of Japan, and also, in 1964, assumed the Presidency of the Nishina Memorial Foundation. I deeply regretted that he was unable to be with us in Stockholm on December 10, 1965 to accept his Novel Prize. The lecture that I have often quoted today was delivered May 6, 1966. Following his retirement in 1970, he began to write another volume of his book on quantum mechanics which, unfortunately, was not completed. Two other books, one left in an unfinished state, were published, however. To some extent, these books are directed to the general public rather than the professional scientist. And here again Tomonaga and I found a common path. I have recently completed a series of television programs that attempt to explain relativity to the general public. I very much hope that this series, which was expertly produced by the British Broadcasting Corporation, will eventually be shown in Japan. Just a year ago today, our story came to a close. But Tomonaga Sin-Itiro lives on in the minds and hearts of the many people whose lives he touched, and graced.

4

The Discovery of the Parity Violation in Weak Interactions and Its Recent Developments Chien-Shiung Wu

Abstract This address was presented by Chien-Shiung Wu as the Nishina Memorial Lecture at the University of Tokyo, March 31, 1983

It is a great honor and privilege for me to deliver the Nishina Commemorative Lecture. Dr. Yoshio Nishina made not only fundamental and important contributions to various scientific fields; his great leadership, inspiration and dedication to scientific research and higher education in this country is a most moving and inspiring story to commemorate. The topic of my talk today on the Discovery of the Parity Violation in Weak Interactions and Its Recent Developments is already twenty-six years old. On January 16, 1957, the world of Physics was suddenly shocked by the news that Chien-Shiung Wu c parity is not conserved. The Jackson Professor Otto Frisch NMF of Cambridge University described the announcement as “the obscure phrase ‘parity is not conserved’ circled the globe like a new gospel.” Why has the news caused such excitement? What is the real meaning of the law of Conservation of Parity? What are the implications and consequences of the overthrow of the law of parity on Physics? Put in the simplest language, it means that the results of this discovery unequivocally proved that many natural phenomena, and also the objects of the microscopic world, are not necessarily symmetrical with respect to left and right. Now, one must be even more puzzled and want to understand why people should be so shocked by the discovery in which things turned out not necessarily left-right symmetrical. Chien-Shiung Wu (1912 – 1997). Columbia University (USA) at the time of this address C.-S. Wu: The Discovery of the Parity Violation in Weak Interactions and Its Recent Developments, Lect. Notes Phys. 746, 43–69 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 4

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Part I: Symmetry and Is Parity Conserved in Weak Interactions? (1) Symmetry and Bilateral Symmetry: The general concept of symmetry has a much broader meaning and it has occupied a very important position in the history of human civilization. The left–right symmetry is a bilateral symmetry and also a very prominent one. When the well known mathematician Professor Herman Weyl retired from Princeton University only a few years before the question of parity became the focal point in the theory of particle physics; he gave a series of four beautiful lectures to expound on the subject of symmetry and presented their forms, meanings and corresponding in variance elements (‘Symmetry’ [1], Princeton University Press, 1952). In the limited time permitted for this lecture, only a selected few illustrations will be shown which may give you some ideas that symmetry is indeed present everywhere in nature as well as in works of art or architecture. From such popular consensus and conviction, it is not diﬃcult to imagine how one’s ancestors came to appreciate the idea of symmetry, particularly, the simple bilateral symmetry.

(2) A Few Illustrations of Various Forms of Symmetry : (Fig. 4.1–Fig. 4.8) It seems not an unreasonable conjecture that the concept of symmetry has something to do with these beautiful objects and phenomena existing in nature and also in the works of art and architecture developed with time.

(3) Symmetry in Sciences: Since symmetry occupies such an important position in the history of human civilization, philosophers and scientists have naturally attempted to make use of this idea, but the attempts met with little success. For instance, in 1595, Kepler tried to use the symmetry of geometrical structure to explain the ratio of the diameters of planetary orbits (see Fig. 4.9). The six spheres correspond to the six planets, Saturn, Jupiter, Mars, Earth, Venus, Mercury, separated in this order by cube, tetrahedron, dodecahedron, octahedron, icosahedron. This unsuccessful way of seeking harmony in static forms such as in regular solids by Kepler was long before his famous discovery of the three dynamic laws now bearing his name. Later, scientists no longer sought this harmony in static forms but in dynamic laws. By the 19th century, the idea of symmetry had become the central theme in a number of modern scientific disciplines; the obvious ones are

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Fig. 4.1 Snowflakes or little marvels of frozen water are the best known specimens of hexagonal symmetry. They were the delight of old and young

Fig. 4.2 This figure shows cyclic symmetry of 5 of echinoderma from Ernest Haeckel’s ‘Kunstformen der Natur.’ Their larvae are organized according to the principle of bilateral symmetry

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Fig. 4.3 This figure of a Greek sculpture of a noble praying boy can be used to illustrate bilateral symmetry

Chien-Shiung Wu

Fig. 4.4 A bronze statue from Northern Wei dynasty (385–534) in China also represents bilateral symmetry

Fig. 4.5 The Sumerians seem to have been particularly fond of strict bilateral symmetry. Alas! in this picture the two eagle-headed men are nearly but not quite symmetry (look at their arms)

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Fig. 4.6 (left) Bronze wall “Gui,” Shang dynasty Fig. 4.7 (right) The rear view of the Romanesque cathedral in Mainz. Here shows repetition in the round arcs of the friezes, octagonal central symmetry in the small rosette and the three towers, while bilateral symmetry rules the structure as a whole as well as almost every detail

Fig. 4.8 The Palace of the Doges in Venice may stand for translational symmetry in architecture

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crystallography (see Fig. 4.10), then molecular, atomic, nuclear, particle physics, chemistry and so forth. The importance of symmetry principles eventually dictated the types of fundamental interactions among various elementary particles.

(4) Conservation Laws and Symmetry: The first and perhaps the most important concept of symmetry is that space and time are isotropic and homogeneous. All points and all directions in space are equivalent so that there is no real distinction of absolute location in time and space. These are known as symmetry principles or equivalently invariance principles. The basic laws of conservation of momentum and energy are the direct consequences of the invariance of physical laws under space and time displacements. In other words, “Symmetry and Conservation Laws are really one and the same thing.” (See Fig. 4.11)

(5) The Conservation of Parity and Right-Left Symmetry: The symmetry between the left and right was debated at length by philosophers in the past. The laws of physics have always shown complete symmetry between the left and the right, that is, in all physics, nothing has appeared which would indicate intrinsic diﬀerences between left and right. Left and right being a discrete symmetry, therefore the law of right-left symmetry did not play any great important part in classical physics. It came to its eminence with the introduction of quantum mechanics. In fact, the conservation of parity is the direct consequence of the law of left-right symmetry. The Law of Parity Invariance states that for any atomic or nuclear system, no new physical law should result from the construction of a new system diﬀering from the original by being a mirror image. That is, there is no absolute distinction between a real object (or event) and its mirror image. In other words, two worlds, one based upon a right-handed system (say, real object) and one based upon a left-handed system (say, mirror image) obey the same laws of physics. This law has been built into all physical theories from the 1920’s to 1957 and has severely restricted the predicted behavior of elementary particles.

(6) The “Tau” and “Theta” Puzzle: Up to about 1956 all theoretical physicists accepted the validity of parity conservation, and no experimentalists ever thought of devising tests to challenge its validity. Then, the big puzzle in K-meson decay [2] came onto the scene to stun the experts. K-mesons are unstable particles which were discovered in 1952–1953. Some

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Fig. 4.9 Kepler made an attempt to deduce the distances in the planetary system to regular bodies which are alternatingly inscribed and circumscribed to spheres. This figure was published in 1595 in his ‘Mysterium Cosmographicum,’ by which he believed he had penetrated deeply into the secrets of the Creator

Fig. 4.10 Crystal structure is closely related to symmetry and invariance elements. A crystal lattice has a large number of invariance elements such as displacing to the right by one unit, or upwards by one unit, etc

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Fig. 4.11 Symmetry and conservation laws are really one and the same thing. After the introduction of quantum mechanics in discussing the structure of atoms or molecules, we must refer to their quantum numbers, the idea of which has its roots in symmetry principles

K-mesons decay into two π-mesons, others into three π-mesons. The K-mesons yielding two π-mesons are called “Theta”; those yielding three π-mesons are called “Tau.” “Tau” and “Theta” are identical twins of same mass and same lifetime. θ −→ 2π τ −→ 3π The decays into two or three π-mesons are permitted by theory and therefore, it is nothing startling. But the two decay modes cannot be reconciled with the law of conservation of parity. “Tau” decays to an odd number of π-mesons of odd parity; “Theta” to an even number of π-mesons of odd parity. If one of them observes the conservation of parity, the other must violate it. So deeply rooted was this conception of parity that the physicists involved in the K-meson problem were greatly puzzled by this riddle. To recapture the atmosphere of that frustrating period, I might quote Dr. C. N. Yang [3] who said that ‘the physicist at that time was like a man in a dark room groping for a way out. He is aware of the fact that in some direction there must be a door which will lead him out of his predicament. But in which direction?’ After the parity experiment in polarized 60 Co nuclei showed definitely that both parity and charge conjugation in beta decay were violated, Yang telegraphed the news to J. R. Oppenheimer, who was vacationing in the Virgin Islands. He cabled back “Walked through door. . .” referring to Yang’s above comment.

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(7) The Question of Parity Conservation in Weak Interactions: By April of 1956, various participants in the sixth Rochester Conference began to express their doubt of the Universal Validity of parity. Lee and Yang immediately plunged into a systematic investigation of the status of experimental knowledge concerning the parity conservation and were surprised that although parity was conserved in strong interactions, no experiments had ever been designed specifically to test such an invariance in weak interactions. The weak interactions include β-decay, π-meson and μ-meson decay and strange particle interaction. So, the anxiety that began with a single isolated puzzle in “Tau” and “Theta” cases is now applied to a broad and pressing question: “Is Parity Conserved in All Weak Interactions? [4]

Part II: Conservation of Parity Operation in Radioactive Decays To use “Tau” and “Theta” particles themselves in these tests is impractical. However, the beta decays of radioisotopes are perfectly suited for this experimentation. To understand the meaning of the experiment on polarized nuclei, one must first examine the meaning of conservation of parity in radioactive decays.

Fig. 4.12 The mirror reflection of a spinning ball. The image and the real object could not be distinguished because the top right one looks just like the real ball turned upside down. Reflection can be detected if there is a preferred direction

The law of parity dictates that the physics phenomena of atomic or nuclear systems in the original and its mirror twin should be indistinguishable. Fig. 4.12 shows the mirror reflection of a spinning ball. If the ball ejected particles equally in both

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directions along its axis, the image and the real object could not be distinguished because the top right one looks just like the real ball turned upside down. However, if there is a preferred direction for the ejection of particles, then the reflection can be detected. The image at bottom cannot be mistaken for the real thing, as they have reversed handedness. σ · p changes sign under Mathematically, it states that a pseudoscalar term σ space inversion where p is the electron momentum and σ the spin of the nucleus. If the distribution of emitted electrons from polarized nuclei is asymmetrical (see σ · p of the radioactive decay is not identically Fig. 4.13) the pseudoscalar term σ σ · p 0 will change sign under space inverequal to zero. The pseudoscalar term σ sion therefore the parity is not conserved.

Fig. 4.13 σ the spin of the nucleus; p e the electron momentum. σ · p e ≡ 0. If parity conservation is valid; the expectation value of σ σ · p e ) ≡ drr ψ∗ (rr )[σ σ (rr ) · p e (rr )]ψ(rr ) (σ If parity invariance is valid; then P-operation gives Pψ(rr ) = ψ(−rr ) = ±ψ(r r) σ · p e ) = drr ψ∗ (rr ))[σ σ(−rr ) · p e (−rr )]ψ(rr ) then P(σ σ(rr ) · p e (rr )]ψ(rr ) = − drr ψ∗ (rr )[σ σ · p e ) = −(σ σ · p e ) ≡ 0, the expectation value ( ) of pseuIf parity invariance is valid, (σ doscalar quantity must be identically zero

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Part III: Experimental Discovery of Parity Non-Conservation in Weak Interactions During the years 1945 to 1952, I was completely submerged in the experimental studies of beta decay [5]. It was an exciting period, indeed for all who worked in this field. Although from 1952 on my interest was gradually turning away from beta decay, to me, β-decay was still like a dear old friend; there would always be a place in my heart especially reserved for it. This feeling was rekindled when, one day in the early spring of 1956, my colleague T. D. Lee came up to my oﬃce on the thirteenth floor of Pupin Physics Lab. He asked me a series of questions concerning the status of the experimental knowledge of beta decay. Unfortunately, I could not supply him with any information on the pseudoscalar σ · p from experimental results of β-decay. All the previous β-decay exquantity σ periments investigated were essentially “only” scalar quantities, for example, the shape of the β-spectrum and the intensities or half lives, etc. Before T. D. Lee left my oﬃce, I asked him whether anyone had any ideas about doing this test. He said some people had suggested using polarized nuclei produced in nuclear reactions or using a polarized slow neutron beam from a reactor. Somehow I had great misgivings about using either of these two approaches. I suggested that the best bet would be to use a 60 Co β-source polarized by the adiabatic demagnetization method, by which one could attain a polarization as high as 65%. Dr. Lee was very much interested in the possibility of such a strongly polarized 60 Co β-source and asked me to lend him a reference book on the method.

(1) Polarized 60 Co Experiment—Adiabatic Demagnetization: In this Demagnetization Method the principle of polarization is based upon the fact that in certain paramagnetic salts there are large magnetic fields (∼ 105 –106 gauss) at the nuclei of the paramagnetic ions due to unpaired electrons and, at temperatures of the order of 0.01◦K, the nuclear magnetic moments become oriented with respect to these electron magnetic fields. Since the electron magnetism is easily saturated at low temperature, a field of a few hundred gauss suﬃces. Nuclear orientation will automatically follow. Because of my familiarity with the capability and limitations of this technique, it was only natural that the first thought which came to my mind was to use the polarized 60 Co source.

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(2) My Decision to Go Ahead: Following Dr. Lee’s visit, I began to think things through. This was a golden opportunity for a beta ray physicist to perform a crucial test, and how could I let it pass? Even if it turned out that the conservation of parity in beta decay was actually valid, the experimental result would, at least, set a reasonably upper limit on its violation and thus stop further speculation that parity in β-decay is substantially violated.

(3) Two Major Diﬃculties: As an experimentalist, I was also challenged by two techniques which had never been tried before and were diﬃcult. One was to put an electron detector inside a cryostat at a liquid helium temperature and to make it function as a β-spectrometer; the other was to fabricate a β-source located in a very thin surface layer and have it stay polarized for a time period long enough to obtain suﬃcient statistics. That spring, my husband and I had planned to make a lecture tour to Europe and the Far East. Our passages were booked. I suddenly realized that I had to do the experiment immediately, so I asked Chia-Liu to let me stay and told him to go without me. Fortunately, he fully appreciated the importance of the time element and finally agreed to go alone. In order to do the demagnetization method, one needs very complicated ultralow temperature equipment. There were only two or three low temperature labs in the United States which were equipped to do nuclear orientation experiments. Dr. Ernest Ambler, a pioneer in the nuclear orientation field, had moved from Oxford University to the Low Temperature Lab. at The National Bureau of Standards years earlier. I decided to contact him by phone to determine whether he would be interested in a collaboration. Although we had never met before, it was on June 4, 1956 that I called and put the proposition directly to him. He accepted immediately and enthusiastically.

(4) On the Long Road to Planning: As soon as the spring semester ended in the last part of May, 1956, I started to work in earnest in preparation for the experiment. From the beginning of June until the end of July, two solid months were spent on testing our beta particle detectors. What type of scintillator would be best for this purpose? What shape should the head of the light-guide be? How could we bring the long lucite pipe (4ft) with a small diameter (1in) out of the cryostat? Could one leave the scintillator or the photomultiplier inside the helium cryostat? Would the polarizing magnetic field aﬀect the counting rates? The thorough preparation was worth all the eﬀort. The 4ft long, 1 inch diameter lucite light pipe gave the 137 Cs conversion line (624keV) a fine resolution of

4 The Discovery of the Parity Violation

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17%, this excellent resolution was due mostly to the careful selection of a clear lucite rod, the machining of the lucite head to a logarithmic spiral for maximum light collection, above all, Mrs. Marion Biavati’s personal attention to its surface polish played a major role. In the middle of September, I finally went to Washington D. C. for my first meeting with Dr. Ambler. He was exactly as I had imagined from our numerous telephone conversations; soft-spoken, capable, and eﬃcient. He has been the Director of the National Bureau of Standards since the late seventies. He took me to his lab and introduced me to Dr. R. P. Hudson, who was his immediate supervisor at that time. The two of them had been working closely together. Hudson’s subsequent decision to join our exciting experiment was indeed welcome. In the beta particle counting and the gamma ray anisotropy measurements, we required a great deal of electronics. Dr. R. W. Hayward of the National Bureau of Standards had oﬀered us the use of his 10-channel pulse height analyser and other equipment. The eventual joining of Dr. Hayward and his research assistant D. D. Hoppes, greatly strengthened our group, particularly during the exasperating days and nights when we had hardly any sleep. We wished we could have more such able collaborators. By the time of my third trip to Washington, D. C., I had grown two 60 Co specimens. One was made by taking a good single crystal of CMN (cerium magnesium nitrate) and growing on the upper surface only an additional crystalline layer containg 60 Co. The thickness of the radioactive layer used was about 0.002 inches and contained a few micro curies of activity. The others had the 60 Co evenly distributed throughout the CMN crystal for the study of the anisotropy of the 60 Co gamma rays.

(5) Our Fear Confirmed: The polarization of the thick 60 Co γ-ray source was obtained with no diﬃculty. But we had no such luck for the thin surface 60 Co source. The polarization lasted no more than a few seconds, then completely disappeared. What we had feared all along finally happened: the polarization of a thin layer on the surface did not last long enough for actual observation. The reason for this disappearance of nuclear polarization on the surface was probably due to its sudden rise in temperature caused by heat that reached the surface of the specimen by means of radiation conduction or condensation of the He-exchange gas. The only remedy was to shield the thin CMN crystal in a cooled CMN housing. But where could one obtain many large single CMN crystals in a hurry? I decided to return to Pupin Laboratory at Columbia University and try to find ways to grow some CMN crystals.

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Chien-Shiung Wu

(6) Beautiful Sight of Those Large Single CMN Crystals: I consulted some professional crystallographic experts and, unfortunately, they confirmed my fear that professional care would be needed to grow large-size CMN crystals (1 inch diameter). Both elaborate equipment and plenty of patience were required and we had neither the funds nor the time. Purely relying on ingenuity determination and luck. three of us: an enthusiastic chemist (Herman Fleishman), a dedicated student (Marion Biavati), and I worked together uninterruptedly to grow about ten large, perfect, translucent CMN single crystals at the end of three weeks. The day I carried these precious crystals with me back to Washington, I was the happiest and proudest person in the world. To fabricate a housing out of these CMN crystals, one has to carve a large hole in each of these thin, brittle crystals without causing it to crack. We were so happy when a crystallographer suggested to us that we borrow a dentist’s drill (which is designed in such a way so that it exerts pressure inwardly only). The CMN crystal is known to have a highly anisotropic g-values : g⊥ > g// . In making the housing, one must line up the crystal axis perpendicular to the demagnetization field and glue the CMN pieces together (see Fig. 4.14). Dr. Ambler applied the DuPont cement as it was frequently used in room temperature. This time, we indeed saw an unmistakably asymmetrical eﬀect on the counting rates when the polarization field was turned on. However, the eﬀect was not only eminently clear but also irreversible! The counting rates never returned to their

Fig. 4.14 A schematic diagram showing the demagnetization cryostat used in the measurement of the angular distribution of the electrons from the β-decay of oriented 60 Co nuclei. The 60 Co nuclei were polarized parallel to the axis of the cylindrical cryostat. The electrons were detected by an anthracene scintillation counter. Two NaI γ-ray scintillation counters are also shown

4 The Discovery of the Parity Violation

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original values even when the source was warmed up. The shielding CMN house had caved in. Then the cryostat was warmed up and opened, we saw that was exactly what had happened. As already mentioned, the CMN crystal has a highly anisotropic gvalue. The axis of the crystal had not been set exactly parallel to the magnetic field, a strong torque developed, the ultra-low temperature caused the DuPont cement to completely lose its adhesive property; and the CMN housing under the torque came tumbling down!

(7) Genuine Asymmetry Eﬀect Observed: The second time the housing was put together, fine nylon threads were used to tie the pieces together and, for the first time, we finally saw a genuine asymmetry eﬀect which coincided exactly with the γ-ray anisotropy eﬀect (see Fig. 4.15). That was already in the middle of December, 1956. One half year after the beginning of our planning. I remember the mood then was more cautious and subdued. The discovery would be big if our observation was real, but we cautioned ourselves that more rigorous experimental checks must be carried out before announcing our results to outsiders. Between experimental runs in Washington, I had to dash back to Columbia for teaching and other research activities. One Thursday morning, as I was hurrying to the seminar room (Room 831) at Pupin, I passed Dr. Lee’s oﬃce; the door was open and both Lee and Yang were there. As I stuck my head in to say hello, they inquired about the 60 Co experiment. I casually mentioned that it seemed there was a huge asymmetry eﬀect. Upon hearing this they were excited and pleased. As I passed their room again, after the seminar, they wanted to know more. I told them the eﬀect was large and reproducible, but it must be regarded as preliminary because some systematic checks were not yet completed. I remember on that occasion, Yang also wanted to know whether anyone had calculated the interference term between the G-T and Fermi interaction. I told him that Dr. Masato Morita had carried out these calculations in detail and the interference term might be destructive, depending on the signs between C A and CV . I said I was pleased that the beta transition in 60 Co was a pure G-T transition. We know now that the observed asymmetry parameter A in 60 Co (5 −→ 4) is nearly −1, but it is much reduced in mixed transitions such as in Table 4.1. Table 4.1 β

Ii −→ If Asymmetry Parameter A 60 Co 5 −→ 4 −1 1 n 1/2 −→ 1/2 −0.11 19 Ne 1/2 −→ 1/2 −0.057

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Chien-Shiung Wu

Fig. 4.15 Results of β asymmetry and γ anisotropy from polarized 60 Co experiment. The disappearance of the γ asymmetry coincides exactly with the time of disappearance of γ anisotropy. The measured asymmetry indicates that the emission of electrons is preferred in the direction opposite to that of the nuclear spin

I was thoroughly pleased that I had selected the pure (G-T) transition β-decay in 60 Co for the crucial test of parity.

(8) Rigorous Experimental Checks: One week later, after some modifications on the glass dewar were completed, we began to follow through intense experimental checks on the asymmetry eﬀects observed. First, we had to prove that this asymmetry eﬀect was not due to the strong magnetic field of the CMN crystals produced at extremely low temperatures. We also needed to show that this eﬀect was not due to the remnant magnetization in the sample induced by the strong demagnetization field. The most clear-cut control ex-

4 The Discovery of the Parity Violation

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periment would be one in which a beta activity would be introduced into the CMN crystal, but in which the radioactive nucleus would be known not to be polarized; thus no asymmetry eﬀect should be detected. To carry out all these experiments would take several weeks. On Christmas Eve I returned to New York on the last train as the airport was closed because of heavy snow. I told Dr. Lee that the observed asymmetry was reproducible and huge, but we had not exhausted all experimental checks yet. When I started to make a quick rough estimate of the asymmetry parameter A, I found it was nearly −1. The asymmetry parameter A was estimated as follows: The electron angular distribution is W(θ) = 1 + A

Iz v cos θ I c

“θ” is the angle between the nuclear spin and electron momentum direction. The actually observed asymmetry is ∼ 25% W(0) − W(π) Iz v = −0.25 = A W(0) + W(π) I c I

where Iz = 0.65 calculated from observed γ anisotropy, cv 0.6 from the calibrated pulse height analysis. The back scattering of the electrons from the CMN crystal was found in a magnetic spectrometer to be 30–35. Therefore A −0.25 × (0.65 × 0.60)−1 × 32 −1. The result of A = −1 was the first indication that the interference between parity conserving and parity non-conserving terms in the G-T interaction Hamiltonian was close to maximum or, C A = C A This result is just what one should expect for a two component theory of the neutrino in a pure Gamow-Teller transition. It also implies that, in this case, the charge conjugation is also non invariant. Dr. Lee realized it then and said that this was very good. He told me that during the summer of 1956, when he and Yang worked together, they had not only entertained the idea of the two-component theory of the neutrino, but had also worked out some details of the theory [9]. However, they felt it was too rash to publish it before the violation of the law of parity was experimentally observed. Confronted by the clear evidence of the two-component theory of the neutrino, we discussed possible experiments one could do. One of them was the measurement of electron polarization; the other was the π-μ-e parity experiments. All these possible experiments were soon carried out in various laboratories the world over. The(9 correct interpretation of our very first pioneer experiment on parity non-conservation and charge-conjugation noninvariance played a decisive eﬀect. It also suggested the combined “CP” invariance. This combined operation CP was examined by Landau [9], Wick [10], and Yang [11] even before the parity was overthrown.

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Chien-Shiung Wu

(9) Law of Parity Overthrown: On January 2nd, I went back to the Bureau to continue with our experimental checks. The atmosphere in the period between January 2nd and 8th was probably the most tense in our whole experimental venture. Our cryostat at the NBS was made of glass and the glass joints were put together with low temperature vacuum grease which was concocted by melting together glycerine and Palmolive soap (later on we changed to Ivory soap). The trouble which plagued us repeatedly was the super-fluid leak below the lambda point (T = 2.3K). Each time this happened, it took at least 6 – 8 hours to warm up, regrease and then cool the cryostat down again. To save time, Hopper slept on the ground near the cryostat in a sleeping bag. Whenever the cryostat reached liquid helium temperature he would telephone each of us to go to the lab, no matter what time of the night it was. During the week of January 7th, rumors started to come in fast about the Nevis πμ-e parity experiments. Very much alarmed and excited, the director and the high administration oﬃcials of the NBS came to call on us and wanted to know more about our experiment which was rumored to be as important as the Michelson-Morley one. We were as vigilant as ever. Even after the muon decay had shown the violation of the law of parity, we still did not relax. We, ourselves, had to be totally convinced! After we had finished all the experimental checks which we had set out to do, we finally gathered together around 2 o’clock in the morning of January 9th to celebrate the great event. Dr. Hudson smilingly opened his drawer and pulled out a bottle of wine which turned out to be actually a Chateau Lafite-Rothschild, Vintage 1949. He put it on the table with a few small paper cups. We finally drank to the overthrow of the Law of Parity. I remember vividly several research workers in other sections of the low temperature laboratories stopping by our lab the next morning and being surprised by the silent and relaxed atmosphere. They suddenly turned around to take a look at our waste paper basket and nodded to themselves “All right, the law of parity in beta decay is dead.” I hurried back to the Pupin Laboratories on the night of January 10th and on the morning of the 11th, a Saturday, there was a meeting in Room 831. Lee, Yang, the Nevis group and I were all there. The discussion led by the two theorists was enthralling. Before that meeting our results had already been written up to be submitted to Physical Review [6]. What a great shock to the world of physics! On the afternoon of January 15th, the Department of Physics at Columbia University called a press conference to announce the dramatic overthrow of a basic law of physics, known as the conservation of parity, to the public. The next day, the New York Times carried a front page headline “Basic Concept in Physics Reported Upset in Tests.” The news burst into public view and quickly spread around the world. As Professor O. R. Frisch of Cambridge University described it in a talk at that time, “The obscure phrase ‘parity is not conserved’ circled the globe like a new gospel.” As usual, following an important discovery, we were asked to give symposia, colloquia, and lectures on our experiments. Finally, the American Physical Society held its annual meeting in New York around the end of January. A post-deadline

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paper session was assigned to the topic of the non conservation of parity. Later, Dr. K. K. Darrow recorded the event with his lively and witty pen in the Bulletin of the American Physical Society 2 (1956–57): “On Saturday afternoon to boot—the largest hall normally at our disposal was occupied by so immense a crowd that some of its members did everything but hang from the chandeliers.”

The sudden liberation of our thinking on the basic laws of the physical world was overwhelming. Activities along these lines advanced at an unprecedented pace. First, the non-conservation of parity was also observed in the π± → μ± → e± decays [7] and other weak interactions [8] not restricted to nuclear beta-decays. Thus the parity non-conservation is a fundamental characteristic of the weak interactions and the weak interaction has since manifested into one of the four fundamental interactions in Nature. The (v/c) dependence of the asymmetry parameter A of the beta particles from the polarized 60 Co was also used to examine the validity of the Time Reversal “T” and it was found, in general, sound. If the Time Reversal was still intact; it suggested the Combined CP Invariance based on the CPT Invariance.

Part IV: Recent Improvements on Parity Experiments on Polarized Nucle Refinement in Experimentation: Ever since the pioneer Fparity experiment on polarized 60 Co reported in 1957; practically all the beta-distribution measurements on polarized nuclei were limited to only two directions. One is in parallel and the other, anti-parallel to the nuclear spin axis (i.e. θ = 0◦ and 180◦). It was the goal of our research group in Nuclear Physics at Columbia to improve the cryogenic condition and magnetic field shielding of the parity experiments so that more reliable and precision results could be derived from asymmetry measurements.

a) Utilization of 3 He/4 He Dilution Refrigeration In 1960, London [12] suggested the 3 He/4 He Dilution Refrigeration method to cool the 3 He/4 He mixing. Within a decade, the development of this method already showed remarkable success. We initiated the build-up of the ultra-low temperature Nuclear Physics Lab in Pupin Basement around 1972. The major cryogenic equipment was procured from SHE Co. It could deliver and maintain an ultra-low temperature as low as 11mK at the mixing chamber indefinitely and kept within 1% of fluctuation.

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b) Minimization of the stray magnetic fields surrounding the β source. Furthermore, we developed two intersecting closed magnetic loops which carried the magnetic flux to the permendur source foil (see Fig. 4.16). This design and arrangement greatly minimized the magnetic fields in the region between the source and the β± detector and permitted using a wide range of polarization angle θ.

Fig. 4.16 Detailed drawing of the magnetic loop system and the beta source tail assembly. The detailed double magnetic loop system is shown in the insert to illustrate the three-dimensional arrangement of the two magnetic loops used to rotate the polarization of the 60 Co nuclei. The permendur cross containing the radioactive 60 Co source is clamped to the double magnetic loops in the region when the “open gap” is shown in the insert drawing

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c) Determination of the hyperfine field The magnetic hyperfine field at the Co nucleus in the permendur foil was measured using the NMR/ON technique and found to be 285kG. d) The β-detector The β-particles were detected using a Si(Li) crystal (10mm diameter, 5mm thick) mounted inside the dewar vacuum of the dilution refrigerator.

(2) Experimental Requirements: This experimental arrangement satisfied the following requirements: a) The β-detector was held in a fixed position but the polarization angle θ can be varied continuously over as much of a 0◦ to 360◦ range as possible. b) The β-detector was placed inside the cryostat and operated at 100K and had a good energy resolution and c) The ferromagnetic host of the β-source could be magnetized to near saturation. However, the magnetic field outside the source foil diminishes rapidly away from the surface to reduce any magnetic eﬀects on the β-trajectories.

(3) 60 Co Sources: Two diﬀerent 60 Co sources were prepared. Both source hosts were 25 micron thick permendur foils. a) In one of them, 15μCi of 60 Co were thermally diﬀused into the foil so that 2/3 of the activity lying within 10 microns of the front surface of the foil. b) In the second source, 15μCi of 60 Co were thermally diﬀused so that 2/3 of the activity lying within one micron of the front surface of the foil. Since the angular distribution of β-particles e− from 60 Co → 60 Ni + e− + νe based on the two component theory of the neutrino: Wth (θ) = 1 + AP cv cos θ; where, “P” is the polarizations≡ IIz , “A” the asymmetry coeﬃcient. v velocity of β-particle = c speed of light

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(4) Excellent Agreements Between Experiments and Theory The β-spectrum of 60 Co has an endpoint energy of 315keV and consequently, the region between 100keV and 200keV was chosen for analysis of the data. In the 100 to 200keV region, the data had the predicted energy dependence. v W(θ) − 1 −→ Aexp P cos θ W(θ) − 1 ∼ c v/c The numerical values of Aexp for the two diﬀerent 60 Co sources were obtained by least-square fitting the quantity 1 + PA cos θ to the data shown in Fig. 4.17. For the “thin” source, where internal scattering is small, the experimental results are not only in excellent agreement with the form of the directional distribution, but the experimental asymmetry parameter Aexp = −1.01 ± 0.02 also in splendid agreement with the theoretical value Atheory = −1.

β±

(5) The Allowed but Isospin-Hindered β-Transitions:(I π −→ I π ; T −→ T ± 1, ΔT 0) The β transitions in these nuclei are of particular interest for studies of isospin conservation of nuclear forces and the Time-Reversal Invariance (TRI) tests of the weak interactions. (1) Allowed Fermi transitions require ΔT = O, and consequently, a non-zero value of the Fermi to Gamow-Teller mixing ratio y ≡ CV MF /C A MGT , in ΔT 0 nuclei violates isospin conservation. (2) In TRI tests in nuclear β-decay, the magnitude of T -odd correlations are proportional to y. Consequently, precise measurements of y for these β transitions are of fundamental importance. The mixing ratio, y, can be determined by two rather different methods. One is by measuring the asymmetry of the angular distribution of β particles from oriented nuclei (NO), and the other is the asymmetry of the β-γ circular polarization correlation methods (CP). Both experimental methods are diﬃcult and require extreme care to possible systematic errors. The reported results in the past have been in very poor agreements. Recently, we used our 3 He/4 He ultra-low temperature (T 0.012K) nuclear orientation equipment Fig. 4.16 in determining the value y in isospin-hindered allowed beta transaction. β+ 58 8 Co −→ 31 27 26 Fe32

ΔT 0

β+ 56 56 27 Co29 −→ 26 Fe30

ΔT 0

The directional distribution of beta particles can be written as

4 The Discovery of the Parity Violation

65

Fig. 4.17 Directional distribution of β-particles from polarized 60 Co. The open circles are data taken with the thick source foil and the solid circles are data taken with the “thin” source foil. P is the nuclear polarization obtained from the analysis of the gamma spectra taken with the Ge(Li) detectors. The curves shown for the “thin” source and for the “thick” source are plots of (1 + Aexp P cv cos θβ ) versus θβ

− (vel. of β /the speed of light) Wβ (θ, v) = 1 + Aβ P cv cos θ Y H * H 6 asymmetry the angle between β-particle and parameter nuclear polarization axis. the nuclear polarization

66

Chien-Shiung Wu

The relations between Aβ and y are 56

Co :

58

Co :

0.3333 − 1.6333y 1 + y2 0.2000 − 1.789y Aβ = 1 + y2 Aβ =

From our Aβ (56 Co) = +0.359 ± 0.009 and Aβ (58 Co) = +0.341 ± 0.013 we find 56

Co :

y = −0.091 ± 0.005

58

Co :

y = −0.005 ± 0.008

It is interesting to note that 58 Co has a rather significant mixing y = 0.091 ±0.005. In a previous TRI test, using 56 Co (β-γ correlation on polarized 56 Co), Calaprice et al. [17] found 2|y| sin φ/(1+|y|2) = −0.011±0.022 where y = |y|eCφ . Using our results

Fig. 4.18 Fermi/Gamow-Teller Mixing Ratio Results for the Beta Decay of 56 Co Reading from left to right, the references for experimental points are: (Am 57b), (Da 61), (Ma 62), (Be 67), (Bh 67), (Pi 71), (Ma 82), (Gr 82). Am 57b E. Ambler et al.,: P. R., 108, 503 (1957) Da 61 H. Daniel et al.,: Z. Naturforsch, 160, 118 (1961) Ma 62 L.G. Mann et al.,: P. R., 128, 2134 (1962) Be 67 H. Behrens: Z. Phys., 201, 153 (1967) Bh 67 S. K. Bhattacherjes et al.,: N. P., A96, 81 (1967) Pi 71 O. Pingot: N. P., A174, 627 (1971) Ma 82 J. Markey: Private Comm. Gr 82 J. Groves: P. R. L., 49, 109 (1983) y ≡ CV MF /C A MGT = 0.09l ± 0.005

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Fig. 4.19 Fermi/Gamow-Teller Mixing Ratio Results for the Beta Decay of 58 Co Our results on “y” of 56 Co and 58 Co are compared with previous workers in Fig. 4.18 and Fig. 4.19. For 56 Co, except for those of Ambler et al. (NO) and Pingot (CP), satisfactory agreements were obtained as compared to all other 5 results by CP methods. For 58 Co, the vanishing small value of y is strongly suppressed in the positron decay of 58 Co consistent with isospin selection rules. Solid circles represent nuclear orientation beta-asymmetry method. Open circles represent beta-gamma circular polarization method. The last point represents Columbia’s nuclear polarization result. y ≡ CV MF /C A MGT = −0.005 ± 0.008

for y, we obtain φ = 183 ± 7◦ consistent with non-evidence on T non-conservation. This is indeed a very sensitive method for “TRI” test in weak interaction. So the polarized nuclear experiments gave strong evidences to all Non Parity-Conservation, Non Charge-Conjugation Invariance but still nearly intact Time Reversl Tests. The overthrow of the Parity Law drives home once again the idea that science is not static but ever growing and dynamic. It involves not just the addition of new information but the continuous revision of old knowledge. It is the courage to doubt what has long been established and the incessant search for its verification and proof that pushes the wheel of sciences forward. It is my great pleasure and privilege to be able to share some of my exciting memories with you. These were moments of exaltation and ecstasy. A glimpse of

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this wonder can be the reward of a lifetime. I often wonder, could it be that excitement and ennobling feeling in scientific research has unfailingly kept us scientists dedicating our lives to it contentedly.

Fig. 4.20 Scene of the lecture room of Professor Wu, at University of Tokyo, 1983

References 1. “Symmetry” by Hermann Weyl, Princeton University Press, Princeton, New Jersey (1952) 2. R. H. Dalitz: Phil. Mag., 44, 1068 (1953) 3. C. N. Yang: Selected Papers 1945–1980 with Commentary, Freeman Publishers (1982) 4. T. D. Lee and C. N. Yang: Phys. Rev., 104, 254 (1956) 5. C. S. Wu: Rev. Mod. Phys., 22, 386 (1950) 6. C. S. Wu, E. Ambler, R. W. Hayward, D. D. Hopper and R. F. Hudson: Phys. Rev., 105, 1413 (1957) 7. R. L. Garwin, L. M. Lederman and M. Weinrich: Phys. Rev., 105, 1415 (1957); (in counter experiments) J. I. Friedman and V. L. Telegdi: Phys. Rev., 105, 1681 (1957) (in nuclear emulsions) 8. R. H. Dalitz: Rev. Mod. Phys., 31, 823 (1959); Lecture Notes From Varenna Summer School (1959)

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9.

10. 11. 12. 13. 14. 15. 16. 17.

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J. Steinberger: “Experimental Survey of Strange Particle Decays”, Varenna Summer School (1964) T. D. Lee and C. N. Yang: Phys. Rev., 105, 1671 (1957) L. Landau: Nuclear Physics, 3, 127 (1957) A. Salam: Nuovo Cimento, 5, 299 (1957) It is interesting to recall that in 1929 Weyl (Z. Phys., 56, 330, 1929) proposed the mathematical possibilities of such a two-component massless relativistic particle of spin one-half. It was rejected by Pauli (Handbuch der Physik, Vol. 24, 226– 227) because it violated the law of parity. G. C. Wick, A. S. Wightman and E. P. Wigner: Phys. Rev., 88, 101 (1952) C. N. Yang: Proc. Seattle Congress, Sept. (1956), Rev. Mod. Phys., 29, 231 (1956) H. London: Proc. Int. Conf. on Low Temp Phys. Oxford, p. 157 (1951) H. London, C. R. Clarke and E. Mendoza: Phys. Rev., 128, 1992 (1962) L. M. Chirovsky, W. P. Lee, A. M. Sabbas, J. L. Groves and C. S. Wu: Nuclear Inst. and Methods, will be published soon. L. M. Chirovsky, W. P. Lee, A. M. Sabbas, J. L. Groves and C. S. Wu: Phys. Lett., 948, 127 (1980) J. L. Groves, W. P. Lee, A. M. Sabbas, M. E. Chen, P. S. Kravitz, L. M. Chirovsky and C. S. Wu: Phys. Rev. Lett., 49, 109 (1982) W. P. Lee, A. M. Sabbas, M. E. Chen, P. S. Kravitz, L. M. Chirovsky, J. L. Groves and C. S. Wu: Phys. Rev. C, 28, 345 (1983) F. P. Calaprice, S. J. Freedman, B. Osgood and W. C. Thomlinson: Phys. Rev. C, 15, 381 (1977)

5

Origins of Life Freeman J. Dyson

Abstract This address was presented by Freeman J. Dyson as the Nishina Memorial Lecture at the University of Tokyo, on October 17, 1984, and at Yukawa Institute for Theoretical Physics, on October 23, 1984.

I. Illustrious Predecessors First I would like to express my thanks to the Nishina Memorial Foundation, and to Professor Kubo in particular, for inviting me to give this lecture and making it possible for me to visit Japan. Unfortunately I never met Professor Nishina, and I knew him only by reputation, as the discoverer of the Klein-Nishina formula in quantum electrodynamics. That formula had tremendous importance in the history of physics. It was the first quantitative prediction of quantum electrodynamics in the relativistic domain to be verified experimentally. It gave the physicists of the Freeman J. Dyson c 1930’s and 1940’s confidence that relativistic field theories NMF were not total nonsense. Relativistic field theories described at least one experimental fact correctly. This confidence was the essential foundation on which Professor Tomonaga in Japan and Schwinger and Feynman in America built the structure of quantum electrodynamics as it now exists. All physicists who have taken part in the building of quantum electrodynamics, and later in the building of quantum chromodynamics, not only in Japan but all over the world, owe a great debt of gratitude to Professor Nishina. But I did not come here today to talk about physics. Like other elderly physicists, I stopped some time ago to compete with the young people who are inventing new Freeman J. Dyson (1923 – ). Institute for Advanced Study, Princeton(USA) at the time of this address F. J. Dyson: Origins of Life, Lect. Notes Phys. 746, 71–97 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 5

72

Freeman J. Dyson YOSHIO NISHINA ¨ ERWIN SCHRODINGER MANFRED EIGEN LESLIE ORGEL LYNN MARGULIS MOTOO KIMURA

Fig. 5.1 Illustrious Predecessors

models every day to explain the intricate hierarchy of hadrons and leptons. I admire what the young people are doing, but I prefer to work in a less fashionable area where the pace is slower. I turned my attention to biology and in particular to the problem of the origin of life. This is a problem of chemistry rather than of physics, but a physicist may hope to make a modest contribution to its solution by suggesting ideas which chemical experiments can test. It would be absurd to imagine that the problem of the origin of life can be solved by theoretical speculation alone. Theoretical physicists entering the field of biology must behave with proper humility; our role is not to answer questions but only to ask questions which biologists and chemists may be able to answer. Here (Fig. 5.2) is a short list of references for people who are not expert in biology. The Schr¨odinger book is a wonderful introduction to biology for physicists. I will come back to it presently. The Miller-Orgel book is a good general survey of the state of knowledge about the origin of life, written ten years ago but still useful. The authors are both chemists, and they do particularly well in explaining the details of the chemistry out of which life is supposed to have arisen. The article by Eigen and his collaborators is twice as long as a standard Scientific American article. It contains a full account of the experiments which Eigen and his group have done during the ten years since the Miller-Orgel book was written. These experiments started the “New Wave” in our thinking about the origin of life. The last reference is my own modest contribution to the subject. It contains a mathematically precise account of a model which I shall describe in a less formal fashion in this lecture. S. L. Miller and L. E. Orgel: “The Origins of Life on the Earth” (Prentice-Hall, 1974) M. Eigen, W. Gardiner, P. Schuster and R. Wikler-Oswatitsch: “The Origin of Genetic Information,” Scientific American, 244, 88–118 (April, 1981) F. Dyson: “A Model for the Origin of Life,” J. Molecular Evolution, 18, 344–350 (1982) E. Schr¨odinger: “What is Life? The Physical Aspect of the Living Cell,” (Cambridge University Press, 1944) Fig. 5.2 References

“What is Life?” is a little book, less than a hundred pages long, published by the physicist Erwin Schr¨odinger forty years ago, when he was about as old as I am now. It was extraordinarily influential in guiding the thoughts of the young people who created the new science of molecular biology in the following decade. The book

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is clearly and simply written, with less than ten equations from beginning to end. It is also a fine piece of literature. Although Schr¨odinger was exiled from his native Austria to Ireland after the age of fifty, he wrote English far more beautifully than most of his English and American colleagues. He also knew how to ask the right questions. The basic questions which he asked in his book are the following: What is the physical structure of the molecules which are duplicated when chromosomes divide? How is the process of duplication to be understood? How do these molecules succeed in controlling the metabolisom of cells? How do they create the organization that is visible in the structure and function of higher organisms? He did not answer these questions. But by asking them he set biology moving along the path which led to the epoch-making discoveries of the last forty years, to the double helix, the triplet code, the precise analysis and wholesale synthesis of genes, the quantitative measurement of evolutionary divergence of species. Schr¨odinger showed wisdom not only in the questions which he asked but also in the questions he did not ask. He did not ask any questions about the origin of life. He understood that the time was ripe in 1944 for a fundamental understanding of life’s origin. Until the basic chemistry of living processes was clarified, one could not ask meaningful questions about the possibility of spontaneous generation of these processes in a prebiotic environment. He wisely left the question of origins to a later generation.

Fig. 5.3 Biebricher-Eigen-Luce Experiment. Replication of RNA in a test-tube(1981)

Now, forty years later, the time is ripe to ask the questions which Scho¨odinger avoided. The questions of origin are now becoming experimentally accessible, just as the questions of structure were becoming experimentally accessible in the nineteen-forties. Manfred Eigen is the chief explorer of the new territory. He is, after all, a chemist, and this is a job for chemists. Eigen and his colleagues in Germany have done experiments which show us biological organization originating spontaneously and evolving in a test-tube (Fig. 5.3). More precisely, they have

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demonstrated that a solution of nucletide monomers will under and competes with its progeny for survival. From a certain point of view, one might claim that these experiments already achieved the spontaneous generation of life from non-life. They bring us at least to the point where we can ask and answer questions about the ability of nucleic acids to synthesize and organize themselves. Unfortunately, the conditions in Eigen’s test-tubes are not really pre-biotic. To make his experiments work, Eigen put into the test-tubes a polymerase enzyme, a protein catalyst extracted from a living bacteriophage. The synthesis and replication of the nucleic acid is dependent on the structural guidance provided by the enzyme. We are still far from an experimental demonstration of the appearance of biological order without the help of a biologically-derived precursor. Nevertheless, Eigen has provided the tools with which we may begin to attack the problem of origins. He has brought the origin of life out of the domain of idle speculation and into the domain of experiment. I should also mention at this point three other pioneers who have done the most to clarify my thinking about the origin of life. One is the chemist Leslie Orgel who originally kindled my interest in this subject twenty years ago, one is the biologist Lynn Margulis and one is the geneticist Motoo Kimura here in Japan. Leslie Orgel is, like Manfred Eigen, an experimental chemist. He taught me most of what I know about the chemical antecedents of life. He has done experiments complementary to those of Eigen. Eigen was able to make RNA grow out of nucleotide monomers without having any RNA template for the monomers to copy, but with a polymerase enzyme to tell the monomers what to do. Orgel has done equally important experiments in the opposite direction. Orgel demonstrated that nucleotide monomers will under certain conditions make RNA if they are given an RNA template to copy, without any polymerase enzyme. Orgel found that zinc ions in the solution are a good catalyst for the RNA synthesis. It may not be entirely coincidental that many modern biological enzymes have zinc ions in their active sites. To summarize, Eigen made RNA using an enzyme but no template, and Orgel made RNA using a template but no enzyme. In living cells we make RNA using both templates and enzymes. If we suppose that RNA was the original living molecule, then to understand the origin of life we have to make RNA using neither a template nor an enzyme (Fig. 5.4). Neither Eigen nor Orgel has come close to achieving this goal. Their experiments have given us two solid foundations of knowledge, with a wide river of ignorance running between them. Since we have solid ground on the two sides, it is not hopeless to think of building a bridge over the river. A bridge in science is a theory. When bridges are to be built, theoretical scientists may have a useful role to play. Lynn Margulis is one of the chief bridge-builders in modern biology. She built a bridge between the facts of cellular anatomy and the facts of molecular genetics. Her bridge was the idea that parasitism and symbiosis were the driving forces in the evolution of cellular complexity. She did not invent this idea, but she was its most active promoter and systematizer. She collected the evidence to support her view that the main internal structures of eucaryotic cells did not originate within the cells but are descended from independent living creatures which invaded the cells from outside like carriers of an infectious disease. The invading creatures and their hosts then gradually evolved into a relationship of mutual dependence, so that

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75 1. Biebricher, Eigen and ⎫ Luce (1998) ⎪ Nucleotides ⎪ ⎪ ⎬ Replicase Enzyme ⎪ → RNA ⎪ ⎪ ⎭ No template 2. Lohrmann, Bridson and Orgel (1980) ⎫ Nucleotides ⎪ ⎪ ⎪ ⎪ ⎪ Template RNA ⎬ → RNA ⎪ Zinc (or Magnesium) ⎪ ⎪ ⎪ ⎪ ⎭ No enzyme 3. Biological Replication ⎫ in vivo ⎪ Nucleotides ⎪ ⎪ ⎬ Template RNA → RNA ⎪ ⎪ ⎪ Replicase Enzyme ⎭ 4. Hypothetical ⎫ Pre-biotic Synthesis Nucleotides ⎪ ⎪ ⎪ ⎬ No template ⎪ → RNA ⎪ ⎪ No enzyme ⎭

Fig. 5.4 RNA Experiments

the erstwhile disease organism became by degrees a chronic parasite, a symbiotic partner, and finally an indispensable part of the substance of the host. This Margulis picture of early cellular evolution now has incontrovertible experimental support. The molecular structures of chloroplasts and mitochondria are found to be related more closely to alien bacteria than to the cells in which they have been incorporated for one or two billion years. But there are also general philosophical reasons for believing that the Margulis picture will be valid even in cases where it cannot be experimentally demonstrated. A living cell, in order to survive, must be intensely conservative. It must have a finely tuned molecular organization and it must have eﬃcient mechanisms for destroying promptly any molecules which depart from the overall plan. Any new structure arising within this environment must be an insult to the integrity of the cell. Almost by definition, a new structure will be a disease which the cell will do its best to resist. It is possible to imagine new structures arising internally within the cell and escaping its control, like a cancer growing in a higher organism. But it is much easier to imagine new structures coming in from the outside like infectious bacteria, already prepared by the rigors of independent living to defend themselves against the cell’s eﬀorts to destroy them. The last on my list of illustrious predecessors is the geneticist Motoo Kimura. Kimura developed the mathematical basis for a statistical theory of molecular evolution, and he has been the chief advocate of the neutral theory of evolution. The neutral theory says that, through the history of life from beginning to end, random statistical fluctuations have been more important than Darwinian selection in causing species to evolve. Evolution by random statistical fluctuation is called genetic drift. Kimura maintains that genetic drift drives evolution more powerfully than natural selection. I am indebted to Kimura in two separate ways. First, I use Kimura’s mathematics as a tool for calculating the behavior of molecular populations. The mathematics is correct and useful, whether you believe in the neutral theory of evo-

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lution or not. Second, I find the neutral theory helpful even though I do not accept it as dogma. In my opinion, Kimura has overstated his case, but still his picture of evolution may sometimes be right. Genetic drift and natural selection are both important, and there are times and places where one or the other may be dominant. In particular, I find it reasonable to suppose that genetic drift was dominant in the very earliest phase of biological evolution, before the mechanisms of heredity had become exact. Even if the neutral theory is not true in general, it may be a useful approximation to make in building models of pre-biotic evolution. We know almost nothing about the origin of life. We do not even know whether the origin was gradual or sudden. It might have been a process of slow growth stretched out over millions of years, or it might have been a single molecular event that happened in a fraction of a second. As a rule, natural selection is more important over long periods of time and genetic drift is more important over short periods. If you think of the origin of life as slow, you must think of it as a Darwinian process driven by natural selection. If you think of it as quick, the Kimura picture of evolution by statistical fluctuation without selection is appropriate. In reality the origin of life must have been a complicated process, with incidents of rapid change separated by long periods of slow adaptation. A complete description needs to take into account both drift and selection. In my calculations I have made use of the theorist’s privilege to simplify and idealize a natural process. I have considered the origin of life as an isolated event occurring on a rapid time-scale. In this hypothetical context, it is consistent to examine the consequences of genetic drift acting alone. Darwinian selection will begin its work after the process of genetic drift has given it something to work on.

II. Theories of the Origin of Life There are three main groups of theories about the origin of life. I call them after the names of their most famous advocates, Oparin, Eigen and Cairns-Smith. I have not done the historical research that would be needed to find out who thought of them first (Fig. 5.5). The Oparin theory was described in Oparin’s book “Proiskhozhdenie Zhizni” in 1924, long before anything was known about the structure and chemical nature of genes. Oparin supposed that the order of events in the origin of life was: cells first, enzymes second, genes third. He observed that when a suitably oily liquid is mixed with water it sometimes happens that the two liquids form a stable mixture called a coacervate, with the oily liquid dispersed into small droplets which remain suspended in the water. Coacervate droplets are easily formed by non-biological processes, and they have a certain superficial resemblance to living cells. Oparin proposed that life began by the successive accumulation of more and more complicated molecular populations within the droplets of a coacervate. The physical framework of the cell came first, provided by the naturally occurring droplet. The enzymes came second, organizing the random population of molecules within the droplet into self-sustaining metabolic cycles. The genes came third, since Oparin

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Fig. 5.5 Theories of Origin of Life

had only a vague idea of their function and they appeared to him to belong to a higher level of biological organization than enzymes. The Oparin picture was generally accepted by biologists for half a century. It was popular, not because there was any evidence to support it, but rather because it seemed to be the only alternative to biblical creationism. Then, during the last twenty years, Manfred Eigen provided another alternative by turning the Oparin theory upside-down. The Eigen theory reverses the order of events. It has genes first, enzymes second and cells third. It is now the most fashionable and generally accepted theory. It has become popular for two reasons. First, the experiments of Eigen and of Orgel use RNA as working material and make it plausible that the replication of RNA was the fundamental process around which the rest of biology developed. Second, the discovery of the double helix showed that genes are structurally simpler than enzymes. Once the mystery of the genetic code was understood, it became natural to think of the nucleic acids as primary and of the proteins as secondary structures. Eigen’s theory has self-replicating RNA at the beginning, enzymes appearing soon afterwards to build with the RNA a primitive form of the modern genetic transcription apparatus, and cells appearing later to give the apparatus physical cohesion. The third theory of the origin of life, the theory of Cairns-Smith, is based upon the idea that naturally occurring microscopic crystals of the minerals contained in common clay might have served as the original genetic material before nucleic acids were invented. The microcrystals of clay consist of a regular silicate lattice with a

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regular array of ionic sites, but with an irregular distribution of metals such as magnesium and aluminum occupying the ionic sites. The metal ions can be considered as carriers of information like the nucleotide bases in a molecule of RNA. A microcrystal of clay is usually a flat plate with two plane surfaces exposed to the surrounding medium. Suppose that a microcrystal is contained in a droplet of water with a variety of organic molecules dissolved in the water. The metal ions embedded in the plane surfaces form irregular patterns of electrostatic potential which can adsorb particular molecules to the surfaces and catalyze chemical reactions on the surfaces in ways dependent on the precise arrangement of the ions. In this fashion the information contained in the pattern of ions might be transferred to chemical species dissolved in the water. The crystal might thus perform the same function as RNA in guiding the metabolism of amino-acids and proteins. Moreover, it is conceivable that the clay microcrystal can also replicate the information contained in its ions. When the crystal grows by accreting silicate and metal ions from the surrounding water, the newly accreted layer will tend to carry the same pattern of ionic charges as the layer below it. If the crystal is later cut along the plane separating the old from the new material, we will have a new exposed surface replicating the original pattern. The clay crystal is thus capable in principle of performing both of the essential functions of a genetic material. It can replicate the information which it carries, and it can transfer the information to other molecules. It can do these things in principle. That is to say, it can do them with some undetermined eﬃciency which may be very low. There is no experimental evidence to support the statement that clay can act either as a catalyst or as a replicator with enough specificity to serve as a basis for life. Cairns-Smith asserts that the chemical specificity of clay is adequate for these purposes. The experiments to prove him right or wrong have not been done. The Cairns-Smith theory of the origin of life has clay first, enzymes second, cells third and genes fourth. The beginning of life was a natural clay crystal directing the synthesis of enzyme molecules adsorbed to its surface. Later, the clay and the enzymes learned to make cell membranes and became encapsulated in cells. The original living creatures were cells with clay crystals performing in a crude fashion the functions performed in a modern cell by nucleic acids. This primæval clay-based life may have existed and evolved for many millions of years. Then one day a cell made the discovery that RNA is a better genetic material than clay. As soon as RNA was invented, the cells using RNA had an enormous advantage in metabolic precision over the cells using clay. The clay-based life was eaten or squeezed out of existence and only the RNA-based life survived. At the present time there is no compelling reason to accept or to reject any of the three theories. Any of them, or none of them, could turn out to be right. We do not yet know how to design experiments which might decide between them. I happen to prefer the Oparin theory, not because I think it is necessarily right but because it is unfashionable. In recent years the attention of the experts has been concentrated upon the Eigen theory, and the Oparin theory has been neglected. The Oparin theory deserves a more careful analysis in the light of modern knowledge. For the rest of this lecture I shall be talking mostly about my own attempt to put the Oparin theory into a modern framework using the mathematical methods of Kimura.

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Another reason why I find the Oparin theory attractive is that it fits well into the general picture of evolution portrayed by Lynn Margulis. According to Margulis, most of the big steps in cellular evolution were caused by parasites. I would like to propose the hypothesis that nucleic acids were the oldest and most successful cellular parasites. I am extending the scope of the Margulis picture of evolution to include not only eucaryotic cells but procaryotic cells as well. I propose that the original living creatures were cells with a metabolic apparatus directed by protein enzymes but with no genetic apparatus. Such cells would lack the capacity for exact replication but could grow and divide and reproduce themselves in an approximate statistical fashion. They might have continued to exist for millions of years, gradually diversifying and refining their metabolic pathways. Amongst other things, they discovered how to synthesize ATP, adenosine triphosphate, the magic molecule which serves as the principal energy-carrying intermediate in all modern cells. Cells carrying ATP were able to function more eﬃciently and prevailed in the Darwinian struggle for existence. In time it happened that cells were full of ATP and other related molecules such as AMP, adenosine monophosphate, GMP, guanine monophosphate, and so on.

Fig. 5.6 ATP and AMP

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Now we observe the strange fact that the two molecules ATP and AMP, having almost identical chemical structures, have totally diﬀerent but equally essential functions in modern cells (Fig. 5.6). ATP is the universal energy-carrier. AMP is one of the nucleotides which make up RNA and function as bits of information in the genetic apparatus. GMP is another of the nucleotides in RNA. To get from ATP to AMP, all you have to do is replace a triple phosphate group by a single phosphate radical. I am proposing that the primitive cells had no genetic apparatus but were saturated with molecules like AMP and GMP as a result of the energy-carrying function of ATP. This was a dangerously explosive situation. In one cell which happened to be carrying an unusually rich supply of nucleotides, an accident occurred. The nucleotides began doing the Eigen experiment on RNA synthesis three billion years before it was done by Eigen. Within the cell, with some help from pre-existing enzymes, the nucleotides produced an RNA molecule which then continued to replicate itself. In this way RNA first appeared as a parasitic disease within the cell. The first cells in which the RNA disease occurred probably became sick and died. But then, according to the Margulis scheme, some of the infected cells learned how to survive the infection. The protein-based life learned to tolerate the RNA-based life. The parasite became a symbiont. And then, very slowly over millions of years, the protein-based life learned to make use of the capacity for exact replication which the chemical structure of RNA provided. The primal symbiosis of protein-based life and parasitic RNA grew gradually into a harmonious unity, the modern genetic apparatus. This view of RNA as the oldest and most incurable of our parasitic diseases is only a poetic fancy, not yet a serious scientific theory. Still it is attractive to me for several reasons (Fig. 5.7). First, it is in accordance with our human experience 1. This is extension of Margulis view, proved correct for eucaryotic cells, back into the procaryotic era. 2. Hardware (protein) should come before Software (nucleic acids). 3. Amino-acid synthesis is easier than nucleotide synthesis. 4. Nucleotides might have been by-product of ATP metabolism. 5. The hypothesis may be testable. Fig. 5.7 Arguments Supporting Origin of RNA as Cellular Parasite

that hardware should come before software. The modern cell is like a computercontrolled chemical factory in which the proteins are the hardware and the nucleic acids are the software. In the evolution of machines and computers, we always developed the hardware first before we began to think about software. I find it reasonable that natural evolution should have followed the same pattern. A second argument in favor of the parasite theory of RNA comes from the chemistry of aminoacids and nucleotides. It is easy to synthesize amino-acids, the constituent parts of proteins, out of plausible pre-biotic materials such as water, methane and ammonia. The synthesis of amino-acids from a hypothetical reducing atmosphere was demonstrated in the classic experiment of Miller in 1953. The nucleotides which make up

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nucleic acids are much more diﬃcult to synthesize. Nucleotide bases such as adenine and guanine have been synthesized by Or´o from ammonia and hydrocyanic acid. But to go from a base to a complete nucleotide is a more delicate matter. Furthermore, nucleotides once formed are less stable than amino-acids. Because of the details of the chemistry, it is much easier to imagine a pond on the pre-biotic earth becoming a rich soup of amino-acids than to imagine a pond becoming a rich soup of nucleotides. Nucleotides would have had a better chance to polymerize if they originated in biological processes inside already existing cells. My third reason for liking the parasite theory of RNA is that it may be experimentally testable. If the theory is true, living cells may have existed for a very long time before becoming infected with nucleic acids. There exist microfossils, traces of primitive cells, in rocks which are more than 3 billion years old. It is possible that some of these microfossils might come from cells older than the origin of RNA. It is possible that the microfossils may still carry evidence of the chemical nature of the ancient cells. For example, if the microfossils were found to preserve in their mineral constituents significant quantities of phosphorus, this would be strong evidence that the ancient cells already possessed something resembling a modern genetic apparatus. So far as I know, no such evidence has been found. I do not know whether the processes of fossilization would be likely to leave chemical traces of nucleic acids intact. So long as this possibility exists, we have the opportunity to test the hypothesis of a late origin of RNA by direct observation.

III. The Error Catastrophe The central diﬃculty confronting any theory of the origin of life is the fact that the modern genetic apparatus has to function almost perfectly if it is to function at all. If it does not function perfectly, it will give rise to errors in replicating itself, and the errors will accumulate from generation to generation. The accumulation of errors will result in a progressive deterioration of the system until it is totally disorganized. This deterioration of the replication apparatus is called the “error catastrophe.” Manfred Eigen has given us a simple mathematical statement of the error catastrophe as follows (Fig. 5.8). Suppose that a self-replicating system is specified by N bits of information, and that each time a single bit is copied from parent to daughter the probability of error is ε. Suppose that natural selection operates to penalize errors by a selection factor S . That is to say, a system with no errors has a selective advantage S over a system with one error, and so on. Then Eigen finds the criterion for survival to be Nε < log S (3.1) If the condition (3.1) is satisfied, the selective advantage of the error-free system is great enough to maintain a population with few errors. If the condition (3.1) is not satisfied, the error catastrophe occurs and the replication cannot be sustained. The meaning of (3.1) is easy to interpret in terms of information theory. The left side Nε

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of the inequality is the number of bits of information lost by copying errors in each generation. The right side (log S ) is the number of bits of information supplied by the selective action of the environment. If the information supplied is less than the information lost in each generation, a progressive degeneration is inevitable. In Eigen quasi-species model of RNA replication. Good molecules can survive the multiplication of errors only if Log (Selective advantage) (Error rate) × (Gene length). Error rate must be 10−2 if genes carry useful amount of information. In Eigen-Biebricher experiment average RNA length was 120 nucleotides. This is consistent with error-rate 10−2 in presence of Qβ replicase enzyme. Question: Is error-rate 10−2 possible in pre-biotic soup without enzymes? Fig. 5.8 The Error Catastrophe

The condition (3.1) is very stringent. Since the selective advantage of an errorfree system cannot be astronomically large, the logarithm cannot be much greater than unity. To satisfy (3.1) we must have an error-rate of the order of N −1 at most. This condition is barely satisfied in modern higher organisms which have N of the order of 108 and ε of the order of 10−8 . To achieve an error-rate as low as 10−8 the modern organisms have evolved an extremely elaborate system of double-checking and error-correcting within the replication system. Before any of this delicate apparatus existed, the error-rates must have been much higher. The condition (3.1) thus imposes severe requirements on any theory of the origin of life which, like Eigen’s theory, makes the replication of RNA a central element of life from the beginning. All the experiments which have been done with RNA replication under abiotic conditions give error-rates of the order of 10−2 at best. If we try to satisfy (3.1) without the help of pre- existing organisms, we are limited to a replication-system which can describe itself with less than 100 bits of information. 100 bits of information is far too few to describe any interesting protein chemistry. This does not mean that Eigen’s theory is untenable. It means that Eigen’s theory requires an informationprocessing system which is at the same time extraordinarily simple and extraordinarily free from error. We do not know how to achieve such low error-rates in the initial phases of life’s evolution. I chose to study the Oparin theory because it oﬀers a possible way of escape from the error catastrophe. In the Oparin theory the origin of life is separated from the origin of replication. The first living cells had no system of precise replication and could therefore tolerate high error-rates. The main advantage of the Oparin theory is that it allows early evolution to proceed in spite of high error-rates. It has the first living creatures consisting of populations of molecules with a loose organization and no genetic fine-tuning. There is a high tolerance for errors because the metabolism of the population depends only on the catalytic activity of a majority of the molecules. The system can still function with a substantial minority of ineﬀective or uncooperative molecules. There is no requirement for unanimity. Since the statistical fluctuations in the molecular populations will be large, there is a maximum opportunity for genetic drift to act as driving force of evolution.

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IV. A Toy Model of the Oparin Theory I now stop talking about general principles. Instead I will describe a particular mathematical model which I call a Toy Model of the Oparin Theory. The word Toy means that the model is not intended to be realistic. It leaves out all the complicated details of real organic chemistry. It represents the processes of chemical catalysis by a simple abstract mathematical formula. Its purpose is to provide an idealized picture of molecular evolution which resembles in some qualitative fashion the Oparin picture of the origin of life. After I have described the toy model and deduced its consequences, I will return to the question whether the behavior of the model has any relevance to the evolution of life in the real world. The model is an empty mathematical frame into which we may later try to fit more realistic descriptions of pre-biotic evolution. My analysis of the model is only an elementary exercise in population biology, using equations borrowed from Fisher and Kimura. The equations are the same, whether we are talking about a population of molecules in a droplet or about a population of birds on an island. To define the model, I make a list of ten assumptions (Fig. 5.9). The list begins with general statements, but by the time we get to the end the model will be uniquely defined. This makes it easy to generalize the model by modifying only the more specific assumptions. 1. Cells came first, enzymes second, genes much later (Oparin). 2. A cell is an inert droplet containing a population of monomer units combined into polymer chains. 3. No death of cells. No Darwinian selection. Evolution by genetic drift. 4. Population changes by single substitution mutations. 5. Each of N monomers mutates with equal probability (1/N). 6. Monomers are either active (correct) or inactive (incorrect). 7. Active monomers are in sites where they catalyze correct placement of other monomers. Fig. 5.9 Assumptions of the Toy Model

Assumption 1 (Oparin Theory). Cells came first, enzymes second, genes much later. Assumption 2. A cell is an inert droplet containing a population of polymer molecules which are confined to the cell. The polymers are composed of monomer units which we may imagine to be similar to the amino-acids which make modern proteins. The polymers in the cell contain a fixed number N of monomers. In addition there is an external supply of free monomers which can diﬀuse in and out of the cell, and there is an external supply of energy which causes chemical reactions between polymers and monomers. Assumption 3. Cells do not die and do not interact with one another. There is no Darwinian selection. Evolution of the population of molecules within a cell proceeds by random drift.

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Assumption 4. Changes of population occur by discrete steps, each step consisting of a single substitution mutation. A mutation is a replacement of one monomer by another at one of the sites in a polymer. This assumption is unnecessarily restrictive and is imposed only for the sake of simplicity. At the cost of some complication of the mathematics, we could include a more realistic variety of chemical processes such as splitting and splicing of polymer chains or addition and subtraction of monomers. Assumption 5. At every step, each of the N sites in the polymer population mutates with equal probability (1/N). This assumption is also unrealistic and is made to keep the calculation simple. Assumption 6. In a given population of polymers, the bound monomers can be divided into two classes, active and inactive. This assumption appears to be uncontroversial, but it actually contains the essential simplification which makes the model mathematically tractable. It means that we are replacing the enormous multidimensional space of molecular configurations by a single Boolean variable taking only two values, one for “active” and zero for “inactive.” Assumption 7. The active monomers are in active sites where they contribute to the ability of a polymer to act as an enzyme. To act as an enzyme means to catalyze the mutation of other polymers in a selective manner, so that correct species of monomer is chosen preferentially to move into an active site. Assumption 8 (Fig. 5.10). In a cell with a fraction x of monomers active, the probability that the monomer inserted by a fresh mutation will be active is φ(x). The function φ(x) represents the eﬃciency of the existing population of catalysts in promoting the formation of a new catalyst. The assumption that φ(x) depends on x means that the activity of catalysts is to some extent inherited from the parent population to the newly mutated daughter. The form of φ(x) expresses the law of inheritance from parent to daughter. The numerical value of φ(x) will be determined by the details of the chemistry of the catalysts. Assumption 8 Mean-field approximation. In a cell with a fraction x of units active, the probability of a mutated unit being active is φ(x). This reduces the multi-dimensional random walk of the molecular populations to the one-dimensional random walk of the single parameter x. Assumption 9 Triple-crossing assumption. The curve y = φ(x) is S -shaped, crossing the line y = x at three points x = α, x = β, x = γ, between 0 and 1. Fig. 5.10

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Assumption 8 is a drastic approximation. It replaces the average of the eﬃciencies of a population of catalysts by the eﬃciency of an average catalyst. I call it the “mean field approximation” since it is analogous to the approximation made in the Curie-Weiss mean-field model of a ferromagnet. In physics, we know that the mean-field approximation gives a good qualitative account of the behavior of a ferromagnet. In population biology, similar approximations have been made by Kimura. The eﬀect of the mean-field approximation is to reduce the multidimensional random walk of molecular populations to a one-dimensional random walk of the single parameter x. Both in physics and in population biology, the mean-field approximation may be described as pessimistic. It underestimates the eﬀectiveness of local groupings of molecules in forming an ordered state. The mean-field approximation generally predicts a lower degree of order than is found in an exact theory. Assumption 9 (Fig. 5.11). The curve y = φ(x) is S -shaped, crossing the line

Fig. 5.11 The S -shaped Curve

y = x at three points x = α, β, γ between zero and one. This assumption is again borrowed from the Curie-Weiss model of a ferromagnet. It means that the population of molecules has three possible equilibrium states. An equilibrium state occurs whenever φ(x) = x, since the law of inheritance then gives a daughter population with the same average activity x as the parent population. The equilibrium is stable if the slope of the curve y = φ(x) is less than unity, unstable if the slope is greater than unity. Consider for example the lowest equilibrium state x = α. I call it the disordered state because it has the smallest average activity. Since φ (α) < 1, the equilibrium is stable. If a parent population has average activity x a little above α, the daughter population will tend to slide back down toward α. If the parent popu-

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lation has x a little below α the daughter population will tend to slide up toward α. The same thing happens at the upper equilibrium state x = γ. The upper state is also stable since φ (γ) < 1. I call it the ordered state because it has the largest catalytic activity. A population with activity x close to γ will move closer to γ as it evolves. But the middle equilibrium point x = β is unstable since φ (β) > 1. If a population has x slightly larger than β, it will evolve away from β toward the ordered state x = γ, and if it has x slightly smaller than β it will slide away from β down to the disordered state x = α. The equilibrium at x = β is an unstable saddle-point. We have here a situation analogous to the distinction between life and death in biological systems. I call the ordered state of a cell “alive,” since it has most of the molecules working together in a collaborative fashion to maintain the catalytic cycles which keep them active. I call the disordered state “dead” since it has the molecules uncoordinated and mostly inactive. A population, either in the dead or in the alive state, will generally stay there for a long time, making only small random fluctuations around the stable equilibrium. However, the population of molecules in a cell is finite, and there is always the possibility of a large statistical fluctuation which takes the whole population together over the saddle-point from one stable equilibrium to the other. When a “live” cell makes the big statistical jump over the saddle-point to the lower state, we call the jump “death.” When a “dead” cell makes the jump up over the saddle-point to the upper state, we call the jump “origin of life.” When once the function φ(x) and the size N of the population in the cell are given, the probabilities of “death” and of the “origin of life” can easily be calculated. We have only to solve a linear diﬀerence equation with the appropriate boundary conditions to represent an ensemble of populations of molecules diﬀusing over the saddle-point from one side or the other. Assumption 10 (Fig. 5.12). Here we make a definite choice for the function φ(x), basing the choice on a simple thermodynamic argument. It will turn out happily that the function φ(x) derived from thermodynamics has the desired S -shaped form to produce the three equilibrium states required by Assumption 9. Thermodynamics. Assume every perfect catalyst lowers activation-energy for correct placement of a newly-placed unit by U. In a population with fraction x of units active, each catalyst is assumed to lower activation-energy by xU. This implies 1 φ(x) = , (5.1) 1 + ab−x (1 + a) is the number of species of monomer, b = exp(U/kT ) is the discrimination factor of catalysts. Fig. 5.12 Assumption 10

We assume that every catalyst in the cell works by producing a diﬀerence between the activation energies required for placing an active or inactive monomer into a mutating molecule. If the catalyst molecule is perfect, with all its monomer

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units active, then the diﬀerence in activation energies will be a certain quantity U which we assume to be the same for all perfect catalysts. If a catalyst is imperfect, in a cell with a fraction x of all monomer units active, we assume that it produces a diﬀerence xU in the activation energies for correct and incorrect mutations. We are here again making a mean-field approximation, assuming that the average eﬀect of a collection of catalysts with various degrees of imperfection is equal to the eﬀect of a single catalyst with its discrimination reduced by the average activity x of the whole population. This is another approximation which could be avoided in a more exact calculation. We assume that the monomers belong to (1 + a) equally abundant species. This means that there is one right choice and a wrong choices for the monomer to be inserted in each mutation. The eﬀect of the catalysts is to reduce the activation energy for the right choice by xU below the activation energy for a wrong choice. Thus the probability of a right choice is increased over the probability of each wrong choice by the factor bx (4.1) where b = exp (U/kT )

(4.2)

is the discrimination factor of a perfect catalyst at absolute temperature T , and k is Boltzmann’s constant. We have a wrong choices with statistical weight unity compared to one right choice with statistical weight b x . The function φ(x) is the probability of a right choice at each mutation, and therefore φ(x) =

1 1 + ab−x

(4.3)

the same S -shaped function which appears in the mean-field model of a simple ferromagnet. The formula (4.3) for φ(x) completes the definition of the model. It is uniquely defined once the three parameters N, a, b are chosen. The three parameters summarize in a simple fashion the chemical raw material with which the model is working. N defines the size of the molecular population, a defines the chemical diversity of the monomer units, and b is the quality-factor defining the degree of discrimination of the catalysts. We have now a definite three-parameter model to work with. It remains to calculate its consequences, and to examine whether it shows interesting behavior for any values of N, a, b which are consistent with the facts of organic chemistry. “Interesting behavior” here means the occurrence with reasonable probability of a jump from the disordered to the ordered state. We shall find that interesting behavior occurs for values of a and b lying in a narrow range. This narrow range is determined only by the mathematical properties of the exponential function, and is independent of all physical or chemical constants. The model therefore makes a definite statement about the stuﬀ out of which the first living cells were made. If the model has anything to do with reality, then the primaeval cells were composed of molecules having values of a and b within the calculated range.

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It turns out that the preferred ranges of values of the three parameters are Fig. 5.13: a from 8 to 10, b from 60 to 100,

(4.4) (4.5)

N from 2000 to 20000.

(4.6)

For good behavior of model. Transition from disorder to order possible with reasonable probability. 8 ≤ a ≤ 10 60 ≤ b ≤ 100 2000 ≤ N ≤ 20000 Fig. 5.13 Range of a, b, N

These ranges also happen to be reasonable from the point of view of chemistry. (4.4) says that the number of species of monomer should be in the range from 9 to 11. In modern proteins we have 20 species of amino-acids. It is reasonable to imagine that about 10 of them would provide enough diversity of protein function to get life started. On the other hand, the model definitely fails to work with a = 3, which would be the required value of a if life had begun with four species of nucleotides polymerizing to make RNA. Nucleotides alone do not provide enough chemical diversity to allow a transition from disorder to order in this model. The quantitative predictions of the model are thus consistent with the Oparin theory from which we started. The model decisively prefers protein to nucleic acid as the stuﬀ from which life arose. The range (4.5) from 60 to 100 is also reasonable for the discrimination factor of primitive enzymes. A modern polymerase enzyme typically has a discrimination factor of 5000 or 10000. The modern enzyme is a highly specialized structure perfected by three billion years of fine-tuning. It is not to be expected that the original enzymes would have come close to modern standards of performance. On the other hand, simple inorganic catalysts frequently achieve discrimination factors of 50. It is plausible that a simple peptide catalyst with an active site containing four or five amino-acids would have a discrimination factor in the range preferred by the model, from 60 to 100. The size (4.6) of the population in the primitive cell is also plausible. A population of several thousand monomers linked into a few hundred polymers would give a suﬃcient variety of structures to allow interesting catalytic cycles to exist. A value of N of the order of 10000 is large enough to display the chemical complexity characteristic of life, and still small enough to allow the statistical jump from disorder to order to occur on rare occasions with probabilities which are not impossibly small. The basic reason for the success of the model is its ability to tolerate high errorrates. It overcomes the error catastrophe by abandoning exact replication. It neither

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needs nor achieves precise control of its molecular structures. It is this lack of precision which allows a population of 10000 monomers to jump into an ordered state without invoking a miracle. In a model of the origin of life which assumes exact replication from the beginning, with a low tolerance of errors, a jump of a population of N monomers from disorder to order will occur with probability of the order of (1 + a)−N . If we exclude miracles, a replicating system can arise spontaneously only with N of the order of 100 or less. In contrast, our nonreplicating model can make the transition to order with a population a hundred times larger. The error-rate in the ordered state of our model is typically between twenty and thirty percent when the parameters a and b are in the ranges (4.4), (4.5). An error-rate of 25% means that three out of four of the monomers in each polymer are correctly placed. A catalyst with five monomers in its active site has one chance out of four of being completely functional. Such a level of performance is tolerable for a non-replicating system, but would be totally unacceptable in a replicating system. The ability to function with a 25% error-rate is the decisive factor which makes the ordered state in our model statistically accessible, with populations large enough to be biologically interesting.

V. Consequences of the Model

Time required for transition from disorder to order T = τ exp(ΔN) τ =mutation time per site N =population of monomers Δ = U(β) − U(α) Time available for transition: 1010 cells for 105 mutation-times, so T/τ ≤ 1015 Maximum population for transition Nc ∼

30 Δ

(within a factor of 3) Fig. 5.14 Critical Populations

I will not describe in this lecture the mathematical details of the model. The main result of the mathematical analysis is a formula (Fig. 5.14) T = τ exp(ΔN),

(5.1)

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for the time T required on the average for a cell to make the transition from disorder to order. Here τ is the average time-interval between mutations at each site, N is the total number of monomers, and Δ is a number which we can calculate, depending only on the parameters a and b. If Δ were of the order of unity, then the exponential in (5.1) would be impossibly large for N greater than 100. We would then be in the situation characteristic of error-intolerant systems, for which the transition to order is astronomically improbable for large N. However, when the parameters a and b are in the ranges (4.4) (4.5), which correspond to models with high error-tolerance, it turns out that Δ is not of the order of unity but lies in the range from 0.001 to 0.015. This is the feature of the model which makes transition to order possible with populations as large as 20000. Although (5.2) is still an exponentially increasing function of N, it increases much more slowly than one would naively expect. According to (5.1) there is a critical population-size Nc such that populations N of the order of Nc or smaller will make the disorder-to-order transition with reasonable probability, whereas populations much greater than Nc will not. I choose to define Nc by 30 (5.2) Nc = , Δ so that the exponential factor in (5.1) is e30 ∼ 1013

for

N = Nc

(5.3)

The coeﬃcient 30 in (5.2) is chosen arbitrarily. We do not know how many droplets might have existed in environments suitable for the origin of life, nor how long such environments lasted, nor how frequently their molecular constituents mutated. The choice (5.2) means that we could expect one transition to the ordered state to occur in a thousand mutationtimes among a collection of 1010 droplets each containing Nc monomers. It is not absurd to imagine that 1010 droplets may have existed for a suitably long time in an appropriate environment. On the other hand, if we considered droplets with molecular populations three times larger, that is to say with N = 3Nc , then the exponential factor in (5.1) would be 1039 , and it is inconceivable that enough droplets could have existed to give a reasonable probability of a transition. The critical population Nc thus defines the upper limit of N for which transition can occur, with a margin of uncertainty which is less than a factor of three. The critical population-sizes given by (5.2) range from 2000 to 20000 when the parameters a and b lie in the ranges 8 to 10 and 60 to 100 respectively. The properties of our model can be conveniently represented in a two-dimensional diagram Fig. 5.15 with the parameter a horizontal and the parameter b vertical. Each point on the diagram corresponds to a particular choice of a and b. Models which satisfy the triple-crossing condition (assumption 9) and possess disordered and ordered states occupy the central region of the diagram, extending up and to the right from the cusp. The cusp at a = e2 = 7.4,

b = e4 = 54.6,

(5.4)

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Fig. 5.15 Variety of Models

marks the lower bound of the values of a and b for which a disorder-order transition can occur. The critical population-size Nc is large near to the cusp and decreases rapidly as a and b increase. The biologically interesting models are to be found in the part of the central region close to the cusp. These are the models which have high error-rates and can make the disorder-order transition with large populations. To illustrate the behavior of the model in the interesting region near to the cusp, I pick out one particular case which has the advantage of being easy to calculate exactly. This is the case Fig. 5.16 a = 8,

b = 64,

(5.5)

which has the three equilibrium states 1 α= , 3

1 β= , 2

2 γ= . 3

(5.6)

The error-rate in the ordered state is exactly one-third. The value of Δ for this model turns out to be Δ = log 3 − (19/12) log2 = 0.001129, (5.7) which gives a satisfactorily large critical population-size Nc = 26566.

(5.8)

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Freeman J. Dyson a = 8,

b = 64.

This case is easy to solve exactly. Symmetrical because b = a2 . Three equilibrium states: 1 1 2 α= , β= , γ= . 3 2 3 Error-rate 1/3 in ordered state. Δ = log 3 −

19 log 2 = 0.001129, 12

equal to diﬀerence between perfect fifth and equi-tempered fifth in musical scale. Critical population size Nc = 26566. Fig. 5.16 Special Case of Model

My friend Christopher Longuet-Higgins, who happens to be a musician as well as a chemist, pointed out that the quantity Δ appearing in (5.7) is well-known to musicians as the fractional diﬀerence in pitch between a perfect fifth and an equitempered fifth. On a logarithmic scale of pitch, a perfect fifth is (log 3 − log 2) and an equi-tempered fifth is seven semitones or (7/12) log2. The smallness of the difference is the reason why the equi-tempered scale works as well as it does. The smallness of Δ is also the reason why this model of the origin of life worked as well as it does. Old Pythagoras would be pleased if he could see this example, justifying his doctrine of a universal harmony which embraces number, music and science. After this digression into Pythagorean mysticism I return to the general properties of the model shown in Fig. 5.15. The region below and to the right of the central strip represents models which have only a disordered state and no ordered state. These models have a too large (too much chemical diversity) and b too small (too weak catalytic activity) to produce an ordered state. Droplets in this region are dead and cannot come to life. I call the region “Cold Chicken Soup” because this phrase has been used to describe the composition of the Earth’s ocean in prebiotic times. The region above and to the left of the central strip represents models which have only an ordered state and no disordered state. These models have a too small (too little chemical diversity) and b too large (too strong catalytic activity) to produce a disordered state. Droplets in this region are frozen into the ordered state and cannot die. I call the region “Garden of Eden” because this phrase has been used to describe an alternative theory of the origin of life. It is possible to imagine cells evolving by random accretion of molecular components so that they drift into the central transition region either from the cold chicken soup or from the Garden of Eden. Once they reach the central region, they are capable of both life and death, and the evolution of biological complexity can begin. One striking feature of our model which is absent in modern organisms is the symmetry between life and death. In the model, the curve

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y = φ(x) = [1 + ab−x]−1

(5.9)

is invariant under the transformation x → 1 − x,

y → 1 − y,

a → (b/a)

(5.10)

In particular, the model with b = a2 has complete symmetry about the unstable saddle-point at x = y = 1/2. The ordered state and the disordered state are mirrorimages of each other. The probability of a transition from disorder to order is exactly equal to the probability of a transition from order to disorder. In the symmetrical model with b = a2 , death and resurrection occur with equal frequency. The origin of life is as commonplace an event as death. How did it happen that, as life evolved, death continued to be commonplace while resurrection became rare? What happened was that the catalytic processes in the cell became increasingly fine-tuned and increasingly intolerant of error. The curve y = φ(x) remained S -shaped but became more and more unsymmetrical as time went on. The shape of the curve in a modern cell is shown in Fig. 5.17, to be

Fig. 5.17 Application to Modern Cell

contrasted with the symmetrical curve in our hypothetical primitive cell shown in Fig. 5.11. In the primitive cell the three equilibrium states might have been α = 0.2,

β = 0.5,

γ = 0.8,

(5.11)

with an error-rate of 20% in the ordered state. In the modern cell the curve is pushed over far to the right and the equilibrium states are typically

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α = 0.05,

β = 0.999,

γ = 0.9999.

(5.12)

This position of the ordered state γ means that the error-rate in the metabolic apparatus of a modern cell is about 10−4 . The position of the saddle-point β means that an environmental insult such as a dose of X-rays which increases the error-rate to 10−3 will disrupt the fine-tuned apparatus and cause the cell to die. Death is easy and resurrection is diﬃcult, because the saddle-point has moved so close to the ordered state and so far from the disordered state. For life to originate spontaneously it was essential to have an ordered state with a high error-rate, but when life was once established the whole course of evolution was toward more specialized structures with lower tolerance of errors. I have said enough, or perhaps too much, about the properties and the consequences of my model. You may have noticed that in talking about the model I have fallen into a trap. I have fallen in love with my model. I begin to talk about it as if it were historic truth. It is of course nothing of the kind. It is not a description of events as they really happened. It is only a toy model, a simple abstract picture which will rapidly be superseded by better models incorporating some of the chemical details which I have ignored.

VI. Questions and Implications

1. Were the first creatures made of proteins or nucleic acids or a mixture of both? 2. When did random genetic drift give way to natural selection? 3. Does the model contradict the Central Dogma of molecular biology? 4. How did nucleic acids originate? 5. How did the modern genetic apparatus evolve? 6. How late was the latest common ancestor of all living species? 7. Can we find a concrete realization of the model, for example a population of 2000 amino-acids in polypeptides which can catalyze each other’s synthesis with 80% accuracy? 8. Can such a population maintain itself in homeostatic equilibrium? Fig. 5.18 Questions

I have drawn up a list of questions suggested by my model (Fig. 5.18). These questions refer not to the model itself but to the implications of the model for the subsequent course of biological evolution. I will comment briefly on each question in turn. After another twenty years of progress in biological research we may perhaps know whether my tentative answers are correct. 1. Were the first living creatures composed of proteins or nucleic acids or a mixture of the two? This is the central question in all our thinking about the origin of life. I have already stated my reasons for preferring proteins. I prefer proteins, partly because my

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model works well with ten species of monomer and works badly with four species, partly because amino-acids fit better than nucleotides the requirements of pre-biotic chemistry, and partly because I am attracted by the Margulis vision of parasitism as a driving force of early evolution and I like to put nucleic acids into the role of primaeval parasites. None of these reasons is scientifically compelling. The question can be answered, in the end, only by chemical experiment and paleontological observation. 2. At what stage did random genetic drift give way to natural selection? The model has life originating by neutral evolution according to the ideas of Kimura. A population crosses the saddle-point to the ordered state by random genetic drift. The model does not allow natural selection to operate, because it does not allow the island populations to grow or to reproduce. So long as there is no birth and death of cells, there can be no natural selection. However, once a cell has reached the ordered state as defined in the model, it can go beyond the model and pass into a new phase of evolution by assimilating fresh monomers from its environment. A cell which increases its population N by assimilation will quickly become stabilized against reversion to the disordered state, since the life-time of the ordered state increases exponentially with N. It can then continue to grow until some physical disturbance causes it to divide. If it divides into two cells, there is a good chance that both daughter populations contain a suﬃcient assortment of catalysts to remain in the ordered state. The processes of growth and division can continue until the cells begin to exhaust the supply of nutrient monomers. When the monomers are in short supply, some cells will lose their substance and die. From that point on, evolution will be driven by natural selection. 3. Does the model contradict the Central Dogma of molecular biology? The Central Dogma says that genetic information is carried only by nucleic acids and not by proteins. The dogma is true for all contemporary organisms, with the possible exception of the parasites responsible for scrapie and kuru and a few other diseases of the central nervous system of humans and other mammals. Whether or not the scrapie parasite turns out to be a true exception to the dogma, my model implies that the dogma was untrue for the earliest forms of life. According to the model, the first cells passed genetic information to their oﬀspring in the form of enzymes which were probably proteins. There is no logical reason why a population of enzymes mutually catalyzing each other’s synthesis should not serve as a carrier of genetic information. 4. How did nucleic acids originate? I remarked earlier on the curious fact that nucleic acids are chemical cousins to the ATP molecule which is the chief energy-carrier in the metabolism of modern cells. I like to use this fact to explain the origin of nucleic acids as a disease arising in some primitive cell from a surfeit of ATP. The Margulis picture of evolution converts the nucleic acids from their original status as indigestible by-products of ATP metabolism to disease agents, from disease agents to parasites, from parasites to symbionts, and finally from symbionts to fully integrated organs of the cell. 5. How did the modern genetic apparatus evolve?

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The modern genetic apparatus is enormously fine-tuned and must have evolved over a long period of time from simpler beginnings. Perhaps some clues to its earlier history will be found when the structure of the modern ribosome is explored and understood in detail. The following sequence of steps (Fig. 5.19) is a possible pathway to the modern genetic apparatus, beginning from a cell which has RNA established as a self-reproducing cellular parasite but not yet performing a genetic function for the cell, (a) Non-specific binding of RNA to free amino-acids, activating them for easier polymerization, (b) Specific binding of RNA to catalytic sites to give them structural precision, (c) RNA bound to amino-acids becomes transfer RNA. (d) RNA bound to catalytic sites becomes ribosomal RNA. (e) Catalytic sites evolve from special-purpose to general-purpose by using transfer RNA instead of amino-acids for recognition, (f) Recognition unit splits oﬀ from ribosomal RNA and becomes messenger RNA. (g) Ribosomal structure becomes unique as the genetic code takes over the function of recognition. This is only one of many possible pathways which might have led to the evolution of the genetic code. The essential point is that all such pathways appear to be long and tortuous. In my opinion, both the metabolic machinery of proteins and the parasitic selfreplication of nucleic acids must have been in place, before the evolution of the elaborate translation apparatus linking the two systems could begin. Origin of modern genetic apparatus. Possible pathway. 1. Nucleotides couple to amino-acids to make them more reactive (Katchalsky) 2. Nucleotides couple to catalysts to give them more precise structure 3. Nucleotides coupled to amino-acids grow into transfer RNA 4. Nucleotides coupled to catalysts grow into ribosomal RNA 5. Transfer RNA becomes specific to particular amino-acids (beginning of code) 6. Catalysts use transfer RNA instead of amino-acids for recognition 7. Catalysts become general-purpose with a supply of alternative recognition sequences 8. Recognition sequences split oﬀ and become messenger RNA, leaving the ribosome as a general-purpose catalyst with unique structure. Fig. 5.19 Questions

6. How late was the latest common ancestor of all living species? The universality of the genetic code suggests that the latest common ancestor of all living creatures already possessed a complete genetic apparatus of the modern type. The geological record tells us that cells existed very early, as long as 3 eons ago. It is generally assumed that the earliest cells which are preserved as microfossils already possessed a modern genetic apparatus, but this assumption is not based on concrete evidence. If the Oparin theory of the origin of life is true, cells came before enzymes and enzymes before genes. It is possible that the evolution of the modern genetic apparatus, as described in the discussion of questions 4 and 5, took eons to complete. The ancient microfossils may date from a time before there

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were genes and ribosomes. The pace of evolution may have accelerated after the genetic code was established, allowing the development from ancestral procaryote to eucaryotic cells and multicellular organisms to be completed in less time than it took to go from primitive cell to ancestral procaryote. It is therefore possible that the latest common ancestor came late in the history of life, perhaps as late as half-way from the beginning. 7. Does there exist a chemical realization of my model, for example a population of a few thousand amino-acids forming an association of polypeptides which can catalyze each other’s synthesis with 80 percent accuracy? Can such an association of molecules be confined in a droplet and supplied with energy and raw materials in such a way as to maintain itself in a stable homeostatic equilibrium? These are the crucial questions which only experiment can answer. But before embarking on experiments, it would be wise to explore the territory by studying computer models of molecular populations with realistic chemical reaction-rates. Computer simulations could tell us which chemicals to use in a droplet experiment with some hope of success. Computer simulations are not only cheaper and quicker than real experiments. They are also easier to interpret. The understanding of the origin of life will require a collaboration of many techniques, computer simulations of hypothetical primitive cells, molecular analyses of modern cellular structures, and experiments with chemical populations in real droplets. Each of these techniques will point the way for the others to make progress. Our quest for understanding is based solidly on the work of our distinguished predecessors, Oparin, Schr¨odinger, Eigen, Orgel, Margulis and Kimura. We have made a good beginning, even if the end is not yet in sight. In conclusion I would like to ask one more question. What will happen to my little toy model when the problem of the origin of life is finally solved? This question was answered nearly two hundred years ago by my favorite poet, William Blake : “To be an Error and to be Cast out is a part of God’s design.”

Fig. 5.20 Lecture room at University of Tokyo with Professor Freeman Dyson and Professor Ryogo Kubo in 1984

6

The Computing Machines in the Future Richard P. Feynman

Abstract This address was presented by Richard P. Feynman as the Nishina Memorial Lecture at Gakushuin University (Tokyo), on August 9, 1985.

It’s a great pleasure and an honor to be here as a speaker in memorial for a scientist that I have respected and admired as much as Prof. Nishina. To come to Japan and talk about computers is like giving a sermon to Buddha. But I have been thinking about computers and this is the only subject I could think of when invited to talk. The first thing I would like to say is what I am not going to talk about. I want to talk about the future computing machines. But the most important possible developments in the future, are things that I will not speak about. For exam- Richard P. Feynman ple, there is a great deal of work to try to develop smarter NMF c machines, machines which have a better relationship with the humans so that input and output can be made with less eﬀort than the complex programming that’s necessary today. This goes under the name often of artificial intelligence, but I don’t like that name. Perhaps the unintelligent machines can do even better than the intelligent ones. Another problem is the standardization of programming languages. There are too many languages today, and it would be a good idea to choose just one. (I hesitate to mention that in Japan, for what will happen will be that there will simply be more standard languages; you already have four ways of writing now and attempts to standardize anything here result apparently in more standards and not fewer.) Another interesting future Richard P. Feynman (1918 – 1988). Nobel Laureate in Physics (1965) California Institute of Technology (USA) at the time of this address R. P. Feynman: The Computing Machines in the Future, Lect. Notes Phys. 746, 99–113 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 6

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problem that is worth working on but I will not talk about, is automatic debugging programs; debugging means to fix errors in a program or in a machine. It is surprisingly diﬃcult to debug programs as they get more complicated. Another direction of improvement is to make physical machines three dimensional instead of all on a surface of a chip. That can be done in stages instead of all at once; you can have several layers and then many more layers as the time goes on. Another important device would be a way of detecting automatically defective elements on a chip, then this chip itself automatically rewiring itself so as to avoid the defective elements. At the present time when we try to make big chips there are flaws, bad spots in the chips, and we throw the whole chip away. But of course if we could make it so that we could use the part of the chip that was eﬀective, it would be much more eﬃcient. I mention these things to try to tell you that I am aware of what the real problems are for future machines. But what I want to talk about is simple, just some small technical, physically good things that can be done in principle according to the physical laws; I would like in other words to discuss the machinery and not the way we use the machines. I will talk about some technical possibilities for making machines. There will be three topics really. One is parallel processing machines which is something of the very near future, almost present, that is being developed now. Further in the future are questions of the energy consumption of machines which seems at the moment to be a limitation, but really isn’t. Finally I will talk about the size; it is always better to make the machines smaller, and the question is how much smaller is it still possible to make machines according to the laws of Nature, in principle. I will not discuss which and what of these things will actually appear in the future. That depends on economic problems and social problems and I am not going to try to guess at those.

1. Parallel Computers First about parallel programming, parallel computers, rather. Almost all the present computers, conventional computers, work on a layout or an architecture invented by von Neumann, in which there is a very large memory that stores all the information, and one central location that does simple calculations. We take a number from this place in the memory and a number from that place in the memory, send the two to the central arithmetical unit to add them and then send the answer to some other place in the memory. There is, therefore, eﬀectively one central processor which is working very very fast and very hard while the whole memory sits out there like a vast filing cabinet of cards which are very rarely used. It is obvious that if there were more processors working at the same time we ought to be able to do calculations faster. But the problem is that some one who might be using one processor may be using some information from the memory that another one needs, and it gets very confusing. And so it has been said that it is very diﬃcult to work many processors in parallel. Some steps in that direction have been taken in the larger conventional machines, what they call “vector processors”. When sometimes you want to do ex-

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actly the same step on many diﬀerent items you can do that perhaps at the same time. The ordinary hope is that the regular program can be written, and then an interpreter will discover automatically when it is useful to use this vector possibility. That idea is used in the Cray and in the super-computers in Japan. Another plan is to take what is eﬀectively a large number of relatively simple (but not very simple) computers, and connect them all together in some pattern. Then they can all work on a part of the problem. Each one is really an independent computer, and they will transfer information to each other as one or another needs it. This kind of a scheme is in a machine for example called Cosmic Cube, and is one of the possibilities; many people are making such machines. Another plan is to distribute very large numbers of very simple central processors all over the memory. Each one deals with just a small part of the memory and there is an elaborate system of interconnections between them. An example of such a machine is the Connection Machine made at M.I.T. It has 64,000 processors and a system of routing in which every 16 can talk to any other 16 and thus 4000 routing connection possibilities. It would appear that scientific questions like the propagation of waves in some material might be very easily handled by parallel processing, because what happens in this part of space at a moment can be worked out locally and only the pressures and the stresses from the neighbor needs to be known for each section can be worked out at the same time, and communicate boundary conditions across. That’s why this type of design is built for such a thing. But it has turned out that very large number of problems of all kinds can be dealt with in parallel. As long as the problem is big enough so that a lot of calculating has to be done, it turns out that a parallel computation can speed this up enormously, not just scientific problems. And what happened to the prejudice of 2 years ago, which was that the parallel programming is diﬃcult? It turns out that what was diﬃcult, and almost impossible, is to take an ordinary program and automatically figure out how to use the parallel computation eﬀectively on that program. Instead, one must start all over again with the problem, appreciating that we have parallel possibility of calculation, and rewrite the program completely with a new attitude to what is inside the machine. It is not possible to eﬀectively use the old programs. They must be rewritten. That is a great disadvantage to most industrial applications and has met with considerable resistance. But, the big programs belong usually to scientists or others, unoﬃcial intelligent programmers who love computer science and are willing to start all over again and rewrite the program if they can make it more eﬃcient. so what’s going to happen is that the hard programs, vast big ones, will first be programmed by experts in the new way, and then gradually everybody will have to come around, and more and more programs will be programmed that way, and programmers will just have to learn how to do it.

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2. Reducing the Energy Loss The second topic I want to talk about is energy loss in computers. The fact that they must be cooled is the limitation apparently to the largest computers; a good deal of the eﬀect is spent in cooling machine. I would like to explain that this is simply a result of very poor engineering and is nothing fundamental at all. Inside the computer a bit of information is controlled by a wire which either has a voltage of one value or another value. It is called “one bit”, and we have to change the voltage of the wire from one value to the other and have to put change on or take charge oﬀ. I make an analogy with water: we have to fill a vessel with water and get one level or to empty it to get to the other level. It’s just an analogy. If you like electricity better you can think more accurately electrically. What we do now is analogous, in the water case, to filling the vessel by pouring water in from a top level (Fig. 6.1), and lowering the level by opening the valve at the bottom and letting it all run out. In both cases there is a loss of energy because of the drop of the water, suddenly, through a height say from top level where it comes in to the low bottom level when you start pouring it in to fill it up again. In the cases of voltage and charge, there occurs the same thing. It’s like, as Mr. Bennett has explained, operating an automobile which has to start and stop by turning on the engine and putting on the brakes, turning on the engine and putting on the brakes; each time you lose power. Another way with a car would be to connect the wheels to flywheels. Stop the car and speed up the flywheel saving the energy, which can then be reconnected to start the car again. The analogy electrically or in the water would be to have a U-shaped tube with a valve at the bottom in the center connecting the two arms of the U (Fig. 6.2). When it is full here on the right but empty on the left with the valve closed, if we open that valve the water will slip out to the other side, and we close it just in time to catch it. Then when we want to go the other way we open the valve again and it slips to the other side and we catch it. There is some loss and it doesn’t climb as high as it did before, but all we have to do is to put a little water in to correct the little loss, a much smaller

Fig. 6.1

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Fig. 6.3 Fig. 6.2

energy loss than the direct fill method. But such a thing uses the inertia of the water and the analogue in the electricity, is inductance. However it is very diﬃcult with the silicon transistors that we use today to make up inductance on the chips. So this is not particularly practical with the present technology. Another way would be to fill the tank by a supply which stays only a little bit above the level lifting the water supply in time as we fill it up (Fig. 6.3), because then the dropping of water is always small during the entire eﬀort. In the same way, we could use an outlet to lower it but just taking oﬀ the top and lowering the tube, so that the heat loss would not appear at the position of the transistor, or would be small; it will depend on how high the distance is between the supply and the surface as we fill it up. This method corresponds to changing the voltage supply with time (Fig. 6.4). So if we would use a time varying voltage supply, we could use this

Fig. 6.4

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method. Of course, there is energy loss in the voltage supply, but that is all located in one place, that is simple, and there we can make one big inductance. This scheme is called “hot clocking”, because the voltage supply operates also as the clock which times everything. And don’t need an extra clock signal to time the circuits as we do in conventional designs. Both of these last two devices use less energy if they go slower. If try to move the water supply level too fast, the water in the tube doesn’t keep up with it and I have a big drop. So to work I must go slowly. Again. the U-tube scheme will not work unless that central valve can open and close faster than the time it takes for the water in the U-tube to slip back and forth. So my devices are slower. I’ve saved an energy loss but I’ve made the devices slower. The energy loss multiplied by the time it takes for the circuit to operate is constant. But nevertheless, this turns out to be very practical because the clock time is usually much larger than the circuit time for the transistors, and we can use that to decrease the energy. Also if we went, let us say, three times slower with our calculations, we could use one third the energy over three times the time, which is nine times less power that has to be dissipated. Maybe it is worth it. Maybe by redesigning using parallel computations or other devices, we can spend a little longer than we could do at maximum circuit speed, in order to make a larger machine that is practical and from which we could still get the energy out. For a transistor, the energy loss multiplied by the time it takes to operate is a product of several factors (Fig. 6.5): (1) the thermal energy proportional to temperature, kT; (2) the length of the transistor between source √ and drain, divided by the velocity of the electrons inside (the thermal velocity 3kT/m); (3) the length of the transistor in units of the mean free path for collisions of electrons in the transistor; and finally (4) the total number of the electrons that are inside the transistor when it operates. All of these numbers come out to tell us that the energy used in the transistor today is somewhere around a billion or ten billions or more times the thermal energy kT. When it switches we use that much energy. It is very large amount of

Fig. 6.5

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energy. It is obviously a good idea to decrease the size of the transistor. We decrease the length between source and drain, and we can decrease the number of the electrons, and use much less energy. It also turns out that a smaller transistor is much faster, because the electrons can cross it and make their decisions to switch faster. For every reason, it is a good idea to make the transistor smaller, and everybody is always trying to do that. But suppose we come to a circumstance in which the mean free path is longer than the size of the transistor, then we discover that the transistor doesn’t work right any more. It does not behave the way we expected. This reminds me, years ago there was something called the sound barrier. Airplanes cannot go faster than the speed of sound because, if you design them normally and try to put them in that speed, the propeller wouldn’t work and the wings don’t lift and nothing works correctly. Nevertheless, airplanes can go faster than the speed of sound. You just have to know what the right laws are under the right circumstances, and design the device with the correct laws. You cannot expect old designs to work in new circumstances. But new designs can work in new circumstances, and I assert that it is perfectly possible to make transistor systems, that is, that is to say more correctly, switching systems, computing devices in which the dimensions are smaller than the mean free path. I speak of course in principle and I am not speaking about actual manufacture. Therefore, let us discuss what happens if we try to make the devices as small as possible.

3. Reducing the Size So, my third topic is the size of computing elements and now I speak entirely theoretically. The first thing that you would worry about when things get very small, is Brownian motion; everything is shaking and nothing stays in place, and how can you control the circuits then? And if the circuits did work, it has a chance of accidentally jumping back. But, if we use two volts for the energy of this electric system which is what we ordinarily use, that is eighty times the thermal energy (kT = 1/40 volt) and the chance that something jumps backward against 80 times thermal energy is e, the base of the natural logarithm, to minus eighty power, or 10−43 . What does that mean? If we had a billion transistors in a computer (which we don’t have, we don’t have that many at all), working all of them 1010 times a second, that is, tenth of a nanosecond switching perpetually, operating for 109 seconds, which is 30 years, the total number of switching operations in that machine is 1028 and the chance of one of them going backward is only 10−43 ; there will be no error produced by thermal oscillations whatsoever in 30 years. If you don’t like that, use 2.5 volts and then it gets smaller. Long before that, the real failure will come when a cosmic ray accidentally goes through the transistor, and we don’t have to be more perfect than that. However, much more is in fact possible and I would like to refer you to an article in a most recent Scientific American by Bennett and Landauer. It is possible to make

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a computer in which each element, each transistor, can go forward and accidentally reverse and still the computer will operate. All the operation in succession in the computer go forward or backward. The computation proceeds for a while this way and then it undoes itself, uncalculates, and then goes forward again and so on. If we just pull it along a little, we can make it go through and finish the calculation by making it just a little bit more likely that it goes forward than backward. It is known that all the computations can be made by putting together some simple elements like transistors; or, if we be more logically abstract, a thing for instance called NAND gate (NAND means NOT-AND). It has two “wires” in and one out (Fig. 6.6). Forget the NOT first. What is AND? AND is: The output is 1 only if

Fig. 6.6

both input wires are 1, otherwise the output is 0. NOT-AND means the opposite. The output wire reads 1 (i.e. has the voltage level corresponding to 1) unless both input wires read 1, if both input wires read 1 then the output wire reads 0 (i.e. has the voltage level corresponding to 0). Here is a little table of inputs and outputs. A and B are inputs and C is the output. Unless A and B are both 1, the output is 1 otherwise 0. But such a device is irreversible. Information is lost. If I only know the output, I cannot recover the input. The device can’t be expected to flip forward and then come back and compute correctly anymore. Because if we know for instance that the output is now 1, we don’t know whether it came from A=0, B=1 or A=1, B=0 or A=0, B=0 and it cannot go back. Such a device is an irreversible gate. The great discovery of Bennett and, independently, of Fredkin is that it is possible to do computation with a diﬀerent kind of fundamental gate unit, a reversible gate unit. I have illustrated their idea — with this unit which I could call a reversible NAND or whatever. It has three inputs and three outputs (Fig. 6.7). Of the outputs, two, A and B , are the same as two of the inputs, A and B, but the third input works this way: C is the same as C unless A and B are both 1. Then it changes whatever C is.

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Fig. 6.7

For instance, if C is 1 it is changed to 0, if C is 0 it is changed to 1 only if both A and B are 1. If you put two in succession, you see A and B will go through, and if C is not changed in both it stays the same or if C is changed twice it stays the same. So this gate reverses itself. No information has been lost. It is possible to discover what went in if you know what went out. A device made entirely with such gates will make calculations if everything moves forward, but if things go back and forth for a while and then eventually go forward enough it still operates correctly. If the things flip back and then go forward later it is still all right. It’s very much the same as a particle in a gas which is bombarded by the atoms around it, usually goes nowhere, but with just a little pull, a little prejudice that makes a chance to move one way a little higher than the other way, the thing will slowly drift forward and reach from one end to the other, in spite of the Brownian motion that is made. So our computer will compute provided we apply a force of drift to pull the thing more likely across the calculation. Although it is not doing the calculation in a smooth way, but calculating like this, forward and backward, it eventually finishes the job, As with the particle in the gas, if we pull it very slightly, we lose very little energy, but it takes a long time to get to one side from the other. If we are in a hurry, and we pull hard, then we loose a lot of energy. And the same with this computer. If we are patient and go slowly, we can make the computer operate with practically no energy, even less than kT per step, any amount as small as you like if you have enough time. But if you are in a hurry, you must dissipate energy, and again it’s true that the energy lost to pull the calculation forward to complete it multiplied by the time you are allowed to make the calculation is a constant.

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With these possibilities how small can we make a computer? How big must a number be? We all know we can write numbers in base 2 as strings of “bits” each a one or a zero. But how small can I write? Surely only one atom is needed to be in one state or another to determine if it represents a one or a zero. And the next atom could be a one or a zero, so a little string of atoms are enough to hold a number, one atom for each bit. (Actually since an atom can be in more states than just two we could use even fewer atoms, but enough is little enough!) So now for intellectual entertainment we consider whether we could make a computer in which the bits writing is of atomic size, in which a bit is for example whether the spin in the atom is up for 1 or down for 0. And then our transistor changing the bits in diﬀerent places would correspond to some interaction between some atoms, which will change their states. The simplest would be a kind of 3-atom interaction to be the fundamental element or gate in such a device. But again, it won’t work right if we design it with the laws appropriate for large objects. We must use the new laws of physics, quantum mechanical laws, the laws that they are appropriate to atomic motion. And so we have to ask whether the principles of quantum mechanics permit an arrangements of atoms so small in number as a few times the number of gates in a computer that could still be put together and operate as a computer. This has been studied in principle, and such an arrangement has been found. The laws of quantum mechanics are reversible and therefore we must use the invention of reversible gates, that principle, that idea of Bennett and Fredkin, but we know that’s alright now. When the quantum mechanical situation is studied it is found that quantum mechanics adds no further limitations to anything that Mr. Bennet has said from thermodynamic considerations. Of course there is a limitation, the practical limitation anyway, that the bits must be of the size of an atom and a transistor 3 or 4 atoms; the quantum mechanical gate I used has 3 atoms. (I would not try to write my bits on to nuclei, I’ll wait till the technological development reaches the atoms before I need to go any further!) That leads us just with (a) the limitations in size to the size of atoms, (b) the energy requirements depending on the time as worked out by Bennett, (c) and the feature that I did not mention concerning the speed of light; we can’t send the signals any faster than the speed of light. Those are the only physical limitations that I know on computers. If we make an atomic size computer, somehow, it would mean that the dimension, the linear dimension is a thousand to ten thousands times smaller than those very tiny chips that we have now. It means that the volume of the computer is 100 billionth, 10−11 of the present volume, because the transistor is that much smaller 10−11 , than the transistors that we make today. The energy requirement for a single switch is also about eleven orders of magnitude smaller than the energy required to switch the transistor today, and the time to make the transitions will be at least ten thousands times faster per step of calculation. So there is plenty of room for improvement in the computer and I leave you, practical people who work on computers, this as an aim to get to. I underestimated how long it would take for Mr. Ezawa to translate what I said, and I have no more to say that I have prepared for today. Thank you! I will answer questions if you’d like.

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4. Questions and Answers Q: You mentioned that one bit of information can be stored in one atom, and I wonder if you can store the same amount of information in one quark. A: Yes. But we don’t have control of the quarks and that becomes a really impractical way to deal with things. You might think that what I am talking about is impractical, but I don’t believe so. When I am talking about atoms, I believe that someday we will be able to handle and control them individually. There would be so much energy involved in the quark interactions it would be very dangerous to handle because of the radioactivity and so on. But the atomic energies that I am talking about are very familiar to us in chemical energies, electrical energies, and those, that I am speaking of, are numbers that are within the realm of reality, I believe, however absurd it may seem at the moment. Q: You said that the smaller the computing element is the better. But, I think equipments have to be larger, because.... A: You mean that your finger is too big to push the buttons? Is that what you mean? Q: Yes, it is. A: Of course, you are right. I am talking about internal computers perhaps for robots or other devices. The input and output is something that I didn’t discuss, whether the input comes from looking at pictures, hearing voices, or buttons being pushed. I am discussing how the computation is done in principle, and not what form the output should take. It is certainly true that the input and the output cannot be reduced in most cases eﬀectively beyond human dimension. It is already too diﬃcult to push the buttons on some of the computers with our big fingers. But with elaborate computing problems that take hours and hours, they could be done very rapidly on the very small machines with low energy consumption. That’s the kind of machine I was thinking of. Not the simple applications of adding two numbers but the elaborate calculations. Q: I would like to know your method to transform the information from one atomic scale element to another atomic scale element. If you will use a quantum mechanical or natural interaction between the two elements then such a device will become very close to Nature itself. For example, if we make a computer simulation, a Monte Carlo simulation of a magnet to study critical phenomena, then your atomic scale computer will be very close to the magnet itself. What are your thoughts about that? A:. Yes. All things that we make are Nature. We arrange it in a way to suit our purpose, to make a calculation for a purpose. In a magnet there is some kind of relation, if you wish, there are some kind of computations going on just like there is in the solar system in a way of thinking. But, that might not be the calculation we want to make at the moment. What we need to make is a device for which we can change the programs and let it compute the problem that we want to solve, not just its own magnet problem that it likes to solve for itself. I can’t use the solar system

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for a computer unless it just happens that the problem that someone gave me was to find the motion of the planets, in which case all I have to do is to watch. There was an amusing article as a joke. Far in the future the “article” appears discussing a new method of making aerodynamical calculations: Instead of using the elaborate computers of the day, the author invents a simple device to blow air past the wing. (He reinvents the wind tunnel.) Q: I have recently read in an newspaper article that operations of the nerve system in a brain are much slower than present day computers and the unit in the nerve system is much smaller. Do you think that the computers you have talked about today have something in common with the nerve system in the brain? A: There is an analogy between the brain and the computer in that there are apparently elements that can switch under the control of others. Nerve impulses controlling or exciting other nerves, in a way that often depends upon whether more than one impulse comes in; something like an AND or its generalization. The amount of energy used in the brain cell for one of these transitions? I don’t know the number. The time it takes to make a switching in the brain is very much longer than it is in our computers even today, never mind the fancy business of some atomic computer. But, interconnection system is much more elaborate. Each nerve is connected to thousand other nerves, whereas we connect transistors to two or three others. Some people look at the activity of the brain in action and see that in many respects it surpasses the computer of today, and in many other respects the computer surpasses ourselves. This inspires people to design machines that can do more. What often happens is that an engineer makes up how the brain works in his opinion, and then designs a machine that behaves that way. This new machine may in fact work very well. But, I must warn you that that does not tell us anything about how the brain actually works, nor is it necessary to ever really know that in order to make a computer very capable. It is not necessary to understand the way birds flap their wings and how the feathers are designed in order to make a flying machine. It is not necessary to understand the lever system in the legs of a cheetah, that is an animal that runs fast, in order to make an automobile with wheels that goes very fast. It is therefore not necessary to imitate the behavior of Nature in detail in order to engineer a device which can in many respects surpass Nature’s abilities. It is an interesting subject and I like to talk about it. Your brain is very weak compared to a computer. I will give you a series of numbers, one, three, seven, oh yes, ichi, san, shichi, san, ni, go, ni, go, ichi, hachi, ichi, ni, ku, san, go. I want you to repeat them back. But, a computer can take ten thousands numbers and give me them back in reverse every other one, or sum them or lots of things that we cannot do. On the other hand, if I look at a face, in a glance I can tell you who it is if I know that person, or that I don’t know that person. But, we do not know how to make a computer system so that if we give it a pattern of a face it can tell us who he is, even if it has seen many faces and you try to teach it. We do not know how to make computers do that, yet. Another interesting example is chess playing machines. It is quite a surprise that we can make machines that play chess better than almost everybody in the room. But, they do it by trying many many possibilities. If he moves here, then I could

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move here and he can move there and so forth. They look at each alternative and choose the best. Now, millions of alternatives are looked at. But, a master chess player, a human, does it diﬀerently. He recognizes patterns. He looks at only thirty or forty positions before deciding what move to make. Therefore, although the rules are simpler in Go, machines that play Go are not very good, because in each position there are too many possibilities to move and there are too many things to check and the machines cannot look deeply. Therefore the problem of recognizing patterns and what to do under the circumstances is the thing that the computer engineers (they like to call themselves computer scientists) still find very diﬃcult, and it is certainly one of the important things for future computers, perhaps more important than the things I spoke about. Make a machine to play Go eﬀectively. Q: I think that any method of computation would not be fruitful unless it would give a kind of provision on how to compose such devices or programs. I thought the Fredkin paper on conservative logic was very intriguing, but once I came to think of making a simple program using such devices I came to a halt because thinking out such a program is far more complex than the program itself. I think we could easily get into a kind of infinite regression because the process of making out a certain program would be much more complex than the program itself and in trying to automate the process the automating program would be more complex and so on. Especially in this case where the program is hard wired rather than being separated as a software, I think it is fundamental to think of the ways of composition. A: We have some diﬀerent experiences. There is no infinite regression; it stops at a certain level of complexity. The machine that Fredkin ultimately is talking about and the one that I was talking about in the quantum mechanical case are both universal commuters in the sense that they can be programmed to do various jobs; this is not a hard-wired program; they are no more hard-wired than an ordinary computer that you can put information in, that the program is a part of the input, and the machine does the problem that it is assigned to do. It is hard-wired but it is universal like an ordinary computer. These things are very uncertain but I found a minimum. If you have a program written for an irreversible machine, the ordinary program, then I can convert it to a reversible machine program by a direct translation scheme, which is very ineﬃcient and uses many more steps. Then in real situations, the number of steps can be much less. But at least I know that I can take a program with 2 steps where it is irreversible, convert it to 3n steps of a reversible machine. That is many more steps. I did it very ineﬃciently; I did not try to find the minimum. Just a way. I don’t really think that we’ll find this regression that you speak of, but you might be right. I am uncertain. Q: Won’t we be sacrificing many of the merits we were expecting of such devices, because those reversible machines run so slow? I am very pessimistic about this point. A: They run slower, but they are very much smaller. I don’t make it reversible unless I need to. There is no point in making the machine reversible unless you are trying very hard to decrease the energy enormously, rather ridiculously, because with only 80 times kT the irreversible machine functions perfectly. That 80 is much

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less than the present day 109 or 1010 , so I have at least 107 improvement in energy to make, and can still do it with irreversible machines! That’s true. That’s the right way to go, for the present. I entertain myself intellectually for fun, to ask how far could we go in principle, not in practice, and then I discover that I can go to a fraction of a kT of energy and make the machines microscopic, atomically microscopic. But to do so, I must use the reversible physical laws. Irreversibility comes because the heat is spread over a large number of atoms and can’t be gathered back again. When I make the machine very small, unless I allow a cooling element which is lots of atoms, I have to work reversibly. In practice there probably will never come a time when we will be unwilling to tie a little computer to a big piece of lead which contains 1010 atoms (which is still very small indeed), making it eﬀectively irreversible. Therefore I agree with you that in practice, for a very long time and perhaps forever, we will use irreversible gates. On the other hand it is a part of the adventure of science to try to find a limitations in all directions and to stretch a human imagination as far as possible everywhere. Although at every stage it has looked as if such an activity was absurd and useless, it often turns out at least not to be useless. Q: Are there any limitations from the uncertainty principle? Are there any fundamental limitations on the energy and the clock time in your reversible machine scheme? A: That was my exact point. There is no further limitation due to quantum mechanics. One must distinguish carefully between the energy lost or consumed irreversibly, the heat generated in the operation of the machine, and the energy content of the moving parts which might be extracted again. There is a relationship between the time and the energy which might be extracted again. But that energy which can be extracted again is not of any importance or concern. It would be like asking whether we should add the mc2 , rest energy, of all the atoms which are in the device. I only speak of the energy lost times the time, and then there is no limitation. However it is true that if you want to make a calculation at a certain extremely high speed, you have to supply to the machine parts which move fast and have energy but that energy is not necessarily lost at each step of the calculation; it coasts through by inertia. A (to no Q): Could I just say with regard to the question of useless ideas? I’d like to add one more. I waited, if you would ask me, but you didn’t. So I answer it anyway. How would we make a machine of such small dimension where we have to put the atoms in special places? Today we have no machinery with moving parts whose dimension is extremely small or atomic or hundreds of atoms even, but there is no physical limitation in that direction either. And there is no reason why, when we lay down the silicon even today, the pieces cannot be made into little islands so that they are movable. And we could arrange small jets so we could squirt the diﬀerent chemicals on certain locations. We can make machinery which is extremely small. Such machinery will be easy to control by the same kind of computer circuits that we make. Ultimately, for fun again and intellectual pleasure, we could imagine machines tiny like few microns across with wheels and cables all interconnected by wires, silicon connections, so that the thing as a whole, a very large device, moves

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not like the awkward motion of our present stiﬀ machines but in a smooth way of the neck of a swan, which after all is a lot of little machines, the cells all interconnected and all controlled in a smooth way. Why can’t we do that ourselves?

Fig. 6.8 Scenes of the lecture of Professor Richard Feynman at Gakushuin University in Tokyo in 1985

7

Niels Bohr and the Development of Concepts in Nuclear Physics Ben R. Mottelson

Abstract This address was presented by Ben R. Mottelson as the Nishina Memorial Lecture at Science Council of Japan (Tokyo), on November 9, 1985.

It is a great privilege for me to be able to join with you in this celebration of Niels Bohr, scientific revolutionary, and foresighted thinker on questions bearing on science and on the human condition as well as being our common teacher. This is indeed an occasion on which scientists in both Japan and in Denmark can feel pride and inspiration. I think especially of the early decades of this century when Nishina participated so eﬀectively in the work at Niels Bohr’s institute and then returned to Japan to set in motion the development of modern physics in Japan that has produced so Ben R. Mottelson many marvelous results. I wish to thank very warmly the NMF c Science Council of Japan, the Japanese Physical Society, and the Nishina Foundation for their kindness in providing this opportunity. In preparing for this occasion, I quickly realized that any attempt to report systematically on Niels Bohr’s many very diﬀerent contributions to modern science is more than I am competent to do and would inevitably be a program too rich and diverse to be compressed into a single lecture; I therefore decided to confine my report to a discussion of Niels Bohr’s profound contributions to the understanding of atomic nuclei and even here, as you will see, I have been forced to drastically abbreviate some parts in order to properly describe the general background of the Ben R. Mottelson (1926 – ). Nobel Laureate in Physics (1975) NORDITA (Copenhagen, Denmark) at the time of this address B. R. Mottelson: Niels Bohr and the Development of Concepts in Nuclear Physics, Lect. Notes Phys. 746, 115–135 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 7

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development and to include a little of the subsequent impact and evolution of the ideas initiated by Bohr. Let us begin at the beginning: Niels Bohr was eleven years old when Becquerel discovered the first hint of the existence of atomic nuclei in the occurrence of natural radioactivity, a kind of faintly glowing ashes left from the violent nuclear phenomena that created the heavy elements from which our solid earth and living bodies are made. Fifteen years later Rutherford used the natural radioactivity as a marvelous probe which established the profound distinction between the open, planetary structure of the atomic electrons surrounding the small, dense, enigmatic atomic nucleus in the center. This discovery made possible Bohr’s analysis of the dynamics of the electrons in the atom which lead to the discovery of quantum mechanics. However, the understanding of properties of atomic nuclei in terms of a dynamics of nuclear constituents had to wait for more than 20 years, until after Chadwick’s discovery of the neutron (1932). At last one could begin a rational theory of the structure of atomic nuclei. Immediately after the discovery of the neutron, it was Heisenberg who took the first step in developing a theory of nuclear structure by recognizing that (i) a nucleus of charge Z |e| and mass AM can be considered as a composite system built out of A protons and (A-Z) neutrons; (ii) a new force of nature (later called the ’strong’ interaction of ’nuclear’ force) is required to hold this system together. From the available evidence on nuclear masses and stability, Heisenberg, Wigner and Majarana were able to derive some basis features of this new force. The fact that the nuclear volume and binding energy are approximately proportional to the total number of neutrons and protons (in contrast to atomic binding energies that go as Z 7/3 ) implies that the nuclear forces saturate. The magnitude of the nuclear binding energies imply that the nuclear forces are much stronger than the electric forces even when one takes account of the 1/r dependence of the latter and the fact that nuclei are 104 times smaller than atoms. A comparison of the binding of the deuteron and 4 He nucleus shows that the forces are of short range (a few times 10−13 cm) (Wigner 1933). It was, of course, this last feature that Hideki Yukawa recognized as the crucial point in formulating a fundamental theory of these interactions based on the exchange of massive bosonic quanta. Yukawa’s insight was a major turning point in the whole development. For nuclear physics it provided the first insight into the microscopic origin of nuclear cohesion, and at the same time it provided a fundamental scale of length and energy at which one must expect major corrections to the picture of nuclei as built out of neutrons and protons. Especially this last point can be seen as the opening of the great development of elementary particle physics which reveals that the proton itself, when examined on a fine enough scale, has a rich and fascinating composite structure. But, now I have gotten far ahead of my story and so I must go back to the period around 1932-34 when, at last, it became possible to begin the detailed discussion of the structure of nuclei based on a picture of the nuclei as composite systems built

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out of neutrons and protons. It is at this juncture that the first nuclear accelerators begin to provide evidence on nuclear reactions produced by protons and deuterons (Cockcroft and Walton 1932, Lawrence and Livingstone 1932). However the energies available in these early machines were only suﬃcient to produce reactions in the lightest elements. At this point, Fermi (who had done theoretical work up to this time) realized that the recently discovered neutron aﬀorded a powerful tool for producing reactions in even the heaviest nuclei. The diﬃculty with neutrons was that they had first to be produced by bombarding Be with natural alpha particles and thus there were not too many of them; in the experiments in Rome the sources produced of order 107 neutrons/sec. This disadvantage was however compensated by the fact that the neutron, having no charge, can reach the nuclei of all atoms without having to overcome the repulsive electric potential barrier that surrounds the nucleus. Fermi and his collaborators took up the program of irradiating all the elements of the periodic table with neutrons; they started at the beginning of the periodic table and by March 25, 1934 they had reached 9 F and observed their first new radioactivity F(n, α)16 N(β− )16 O). With the heavier elements they soon discovered that in al(19 9 7 most every case new radioactive species were produced. It was an enormous expansion of the material available for studying nuclear processes. They showed that in most cases the radio-activity was produced by radiative capture (A Z+n → A+1 Z+γ). Having found this wealth of new activities the Rome workers began studying the relative eﬃciency with which the diﬀerent activities were produced, i.e. establishing relative cross sections for the neutron reactions with diﬀerent substances. In the course of this work one day Fermi, in an apparently unpremeditated act, inserted a piece of paraﬃn, between the source and the sample (Ag) and immediately observed a marked increase in the rate of activation. The same day he had interpreted the eﬀect as resulting from the slowing down of the neutrons in their collision with hydrogen in the paraﬃn, the slow neutron apparently having a larger cross section for capture than the fast neutrons (which had energies extending up to about 8 MeV) coming directly from the source. These developments stimulated theoretical analysis of the interaction of slow neutrons with nuclei and soon papers were published by Beck and Horsley (1935), Bethe (1935), Fermi (1935), and Perrin and Elsasser (1935). All of these authors based their analysis on the interaction of the incident neutron with a nuclear potential that was assumed constant inside the nuclear volume. These investigations provide valuable insight into the prevailing prejudices as well as the tools available for the analysis of the nuclear problem at this time and therefore the analysis is briefly recapitulated in Table 7.1. The description in terms of a single particle potential in these investigations was borrowed directly from the successful use of this description for the scattering of electrons by atoms. We may wonder whether the practitioners had other reasons of theoretical or experimental nature for believing in the appropriateness of this description. Apparently such evidence or arguments was quite lacking, as indicated by a remark in Bethe’s paper, “It is not likely that the approximation made in this paper, i.e. taking the nucleus as a rigid body and repre-

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Table 7.1 Analysis of slow neutron reactions (1935) Beck + Horsley; Bethe; Elsasser + Perrin; Fermi I wave lengths outside nucleus: En ∼ kT ∼ 0.025eV out = h¯ /(2ME)1/2 ∼ 3 × 10−9 cm inside nucleus: En ∼ V0 ∼ 50MeV in ∼ 0.6 × 10−13 cm II residence time for neutron in nucleus, tin a) traversal time, τ0 τ0 =

2R 10−12 cm = 10−22 sec ∼ vin 1010 cm/sec

b) reflection at nuclear surface TR = 1 − R in ∼ 10−4 out c) residence time

tin = τ0 (T R )−1 ∼ 10−18 sec

III gamma radiation P = radiation probability/time 4 1 Eγ = |P0 |2 Eγ = γ − ray energy 3 h¯ h¯ c ∼ 7MeV P0 = ”dipole momemt” ∼ 1017 sec−1

∼ eR ∼ 10−12 cm · e

IV Cross sections (a) tin ⇒ En ∼ thin¯ ∼ keV thus, cross sections are smooth and universal for En keV (b) σnγ ∝ tin ∝ (En )−1/2 σnγ (c) σscat = P · tin < 1

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senting it by a potential field acting on the neutron, is really adequate ... . Anyway, it is the only practicable approximation in many cases ...” The analysis in Table 7.1 implies that the (n, γ) capture cross sections should depend on the neutron energy as (En )−1/2 over a considerable range of energies and thus one obtained a direct explanation for the observed increase in activation produced by slowing down the neutrons in paraﬃn. However, almost immediately the theory began to run into diﬃculties. The capture cross sections of some elements for slow neutrons were found to be unexpectedly large (in some cases as much as 100 times the geometrical cross section of the nucleus) and the elastic scattering cross section in these cases was not exceptionally large.

Fig. 7.1 Arrangement used by the Rome group for studying the absorption cross sections of slow neutrons (Amaldi 1984). S = neutron source, P = paraﬃn block, A = absorber, D = detector

And then came the remarkable discovery of “selective absorption” (Bjerge and Westcott (1935); Moon and Tilman (1935)) which was quite outside the theoretical expectation of a smooth energy dependence of the cross section. The experimental set up for the observation of this eﬀect is the very essence of simplicity and elegance (Fig. 7) and consists of a neutron source (Be + Ra), a paraﬃn moderator, the material whose absorption is being measured and a detector directly above the absorber. The amount of neutrons removed by the absorber was monitored by the amount of radioactivity produced in the material of the detector. The first measurements with this set-up confirmed, as expected, that the substances with large cross sections for activation also were especially eﬃcient in attenuating the source. But, then it was noticed that the amount of the attenuation depended on the material being used as the monitor in the detector position. In every case it was found that when the detector was the same substance as the absorber, the observed attenuation was the greatest (see Table 7). This was the “selective absorption” interpreted in terms of the broad energy distribution of the neutron sources and the occurrence of narrow energy absorption bands characteristic of each substance. By ingenious arrangements involving the slowing down of the neutrons between absorber and detector it was possible to order the absorption bands of the diﬀerent substances and even to get measures of the widths of the bands. The observed sharpness of the absorption bands implies that

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Ben R. Mottelson abs. detector Mn Br Rh Ag I

Mn Br Rh Ag I 73 81 88 86 79

92 61 96 91 84

59 79 54 68 91

59 79 67 45 70

98 86 97 89 55

Table 7.2 Evidence for selective absorption, Amaldi and Fermi (1935)

the slow neutrons residence time in the nucleus is an order of magnitude longer than the estimate given in Table 7.1. It was Niels Bohr who saw first and most clearly that these experimental discoveries concerning the interactions of neutrons with nuclei demanded a radical revision in the basic picture of nuclear dynamics. He recognized that the assumed single particle motion, copied from atomic physics, was being falsified and he suggested in its stead an idealization which focused on the many body features and the strong coupling of all the diﬀerent degrees of freedom of the nuclear system - the compound nucleus. There are two dramatic accounts (one by Frisch and one by Wheeler) of a colloquium in Copenhagen that appears to mark a decisive turning point in the development of these ideas. First, as reported by Frisch (1968) “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 USA had tried to calculate that chance, and I remember the colloquium in 1935 when some speaker reported on that paper. 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 got up and said with an apologetic smile, “Now. I understand it all”, and he outlined the compound nucleus idea.”

Wheeler’s account appears to refer to the same occasion (Wheeler, 1979): “The news hit me at a Copenhagen seminar, set up at short notice to hear what Christian Miller had found out during his Eastertime visit to Rome and Fermi’s group. The enormous cross sections that Miller reported for the interception of a slow neutron stood at complete variance to the concept of the nucleus then generally accepted. In 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. Miller 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 led one to think of exactly the opposite idealizations: 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 through the grapevine before he gave his first formal lecture on the subject, before the Copenhagen Academy on January 27th, 1936, with a subsequent written account in Nature.”

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These recollections give a lively picture of the style of discussion at the Institute in the mid 1930’s, but I should warn you that there is rather strong evidence that the two accounts cannot refer to the same occasions and thus it is impossible that both can describe the moment of conception of the compound nucleus. This question has been carefully considered by Peierls (1985), exploiting the extensive letters and unpublished manuscripts in the Niels Bohr Archives, who has concluded that Bohr had in fact been developing his ideas about nuclear dynamics for some time. The two colloquia reported by Frisch and Wheeler are then to be seen as occasions on which Bohr saw some additional significant piece of information fall into place. Significant support for the assumption of a long gestation period for the compound nucleus ideas is contained in several letters quoted by Peierls. In a letter to Gamow (26. Feb. 1936) Bohr writes, “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 1934 immediately after Fermi’s first experiment about the capture of fast neutrons, and which I have taken up again after the latest wonderful discoveries about the capture of slow neutron”. Similarly Rutherford writes to Max Born (22. Feb. 1936) reporting on Bohr’s new ideas, “The main idea is an old one of 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”. Let us now turn more directly to the consideration of the new ideas initiated by Bohr’s article in “Nature” (1936). The core of Bohr’s thinking is the recognition that the densely packed nuclear system being studied in the neutron reactions forces one to place the collective, many body features of the nuclear dynamics at the center of attention. To illustrate these ideas I do not know of any better figures than those prepared by Niels Bohr in connection with lectures which he gave at this time and which were published in the same issue of “Nature” (as a news item) that contains his famous article. The first (Fig. 7.2) draws attention to the far reaching consequences for the course of a nuclear reaction of the assumption of a short mean free path for the nucleons. If we imagine the balls removed from the central region of the figure, the ball entering from the right will be accelerated as it enters the central depression, but just this acceleration ensures that after running across to the opposite side the ball will have enough energy to surmount the barrier on that side and run out of the nuclear region. A very diﬀerent dynamical history results if we restore the balls to the central region. Now, the entering ball (nucleon) will soon collide with one of the balls of the target and, sharing its energy with the struck ball, will no longer be able to leave the confining potential. Being reflected back it will collide and share its remaining energy with still other balls and these struck balls will also collide and ultimately the total energy will be distributed among all the balls in a distribution of the type described by the equilibrium distribution of the kinetic theory of gases. In this situation the only possibility for one of the balls to escape from the central

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Fig. 7.2

region requires the occurrence of a fluctuation in which almost all of the energy is again concentrated on a single ball which will then be able to surmount the confining potential. The unlikelihood of such an extreme fluctuation implies that the duration of the reaction phase is enormously increased (as compared with the first situation considered with only a static potential acting). This increase of the reaction time makes it possible to explain both the observed large ratio of capture to scattering cross sections for slow neutrons as well as the narrowness of the selective absorption bands. Perhaps even more important, the intermediate stage representing a kind of thermal equilibrium from which the final decay represents a rare fluctuation, ensures that the relative probability of diﬀerent final states will be governed by statistical laws and is independent of the mode of formation of the compound system. Fig. 7.3 shows Bohr’s sketch of a schematic nuclear level system. The study of radioactivity had shown that the lowest excited states in heavy nuclei are of order a fraction of 1 MeV, and Bohr assumed that these excitations represent some sort of collective vibration of the whole nucleus. With increasing excitation energy an increasing number of diﬀerent vibrational modes can be excited and the diﬀerent possibilities for partitioning the total excitation energy between these diﬀerent modes leads to an enormous increase in the total number of excited states. (Note the similarity to the mathematical problem of counting the number of ways of partitioning a given integer n into a sum of smaller integers - a problem that had been solved by Hardy√and Ramanujan who found an exponential increase in the number of partitions (n 48 )−1 − exp π(2n/3)1/2). All of these quantum states can be resonantly excited by an incoming neutron thus accounting for the dense spacing and narrowness of the levels observed in the selective absorption phenomena. The dotted line in the magnifying glass at about 10 MeV indicates the neutron separation energy, but the level scheme above and below this line are not significantly diﬀerent; indeed, the neutron escape probability is much less than the γ-emission probability for levels slightly above this energy as a result of the extreme improbability of the

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Fig. 7.3

fluctuation required to concentrate all of the excitation energy on a single particle. Only at higher energies will the neutron emission probability contribute appreciable to the width of the individual levels and lead to a broadening and eventually the overlapping of the level (indicated in the upper magnifying glass at about 15 MeV). Bohr contrasts this picture of densely spaced many particle levels in the nucleus with the spectrum of atoms excited in collisions with electrons where the incident electron will at most collide with one of the atomic electrons causing it to change its binding state from one orbit to another; the resulting spectrum contains relatively few, widely spaced, resonances. The profound reordering of the picture of nuclear dynamics implied by Bohr’s ideas was, apparently, rapidly and widely accepted in the nuclear physics community; within months the literature is completely dominated by papers applying, testing, and extending the ideas of the compound nucleus. It would take us much too far to include within the framework of this lecture a discussion of the many significant ideas and discoveries which went into this development; as a very anemic substitute for such a discussion I have attempted in Table 7.3 to list some of main landmarks in the expanding development of the subject. Each of these developments involves many deeply interesting ideas that significantly extended and exploited the general picture that Bohr had sketched. There is much too much to tell about here, so let me take a single example to illustrate the

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Fig. 7.4

flavour of this development - I take as an example the first steps in the interpretation of the fission process. The story begins already in 1934; Fermi and his collaborators had in their systematic studies irradiated Th and U with neutrons and had found induced activity. However, the results were diﬃcult to interpret since for these elements (and for them alone) it appeared that many diﬀerent activities were being produced simultaneously (compound decay curves). Four years later Fermi referred to these ex-

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periments which were being interpreted in terms of the production of “transuranic” elements in his Nobel lecture (December, 1938), but the picture was still confusing. Just a month after Fermi’s Nobel lecture, Hahn and Strassmann published the startling news that among the activities produced by neutron irradiation of U there was an isotope chemically indistinguishable from Ba (Z = 54). They say in their publication that as chemists they have to call it Ba, but as nuclear chemists a field with close connection to physics they cannot take this step since it would be in conflict with all previous experience in nuclear physics. Table 7.3 Major developments bearing on compound nucleus (1936–48) 1. Resonance formula; Breit and Wigner (1936) Γγ Γn σn (E) = πλ2 2

1 2 (E−E 0 ) + 2 Γtot

2. Level density and thermodynamic concepts Bethe; Bohr and Kalckar (1936-37) entropy α ln ρ 1 dρ ρ de 3. Nuclear decay as evaporation temperature: T−1 =

Weisskopf (1937) reciprocity arguments 4. Cross sections for “black” nucleus Bethe (1940); Feshback, Peaslee, and Weisskopf (1947) 5. Semi-empirical mass formula Weizsacher (1935) Bulk energies (volume, surface, symmetry) pairing energy 6. Collective vibration of nucleus shape oscillations density fluctuations electric dipole mode

Bohr and Kalckar (1937) Migdal (1940) Baldwin and Klaiber (1947) Goldhaber and Teller (1948)

7. Fission: The compound nuleus’ finest hour! Hahn and Strassmann (1939) Meitner and Frisch (1939) Bohr and Wheeler (1939)

On hearing of Hahn and Strassmann’s work, Frisch and Meitner immediately recognized that the experiments were revealing a new type of nuclear reaction, which could be directly’ understood in terms of Bohr’s ideas on the compound nucleus.

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Indeed, all nuclei heavier than Zr are exothermic for a reaction that divides the nucleus into two approximately equal fragments. This instability is the result of the Coulomb energy which increases as Z 2 e2 /R ∼ Z 2 /A2/3 and thus eventually overwhelms the surface energy (4πR2 ∼ A2/3 ) which holds the nucleus united and approximately spherical. For the heaviest nuclei the energy release can be estimated from the known masses and is of order 200 MeV. Thus Frisch and Meitner envisioned a process in which a heavy nucleus, acting like a charged liquid drop, divides itself, going through a sequence of more and more elongated shapes until finally the Coulomb forces take over and drive the two nascent droplets apart. When Frisch told Bohr about these ideas, Bohr was enthusiastic. As told by Frisch, he had only a brief chance to tell Bohr of their ideas before Bohr was to leave for a trip to the United States: ‘When l 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?’

As is well known, Bohr and Wheeler took up, with great energy and breadth of scope, the problem of elucidating the various aspects of the fission reactions, building on and extending the concepts of the compound nucleus. Of this very great development I can only remind you of a single little nugget, as told in the words oft Leon Rosenfeld, who accompanied Bohr on that famous trip to the USA following immediately after the interview with Frisch which I quoted above. Rosenfeld tells of a morning in Princeton shortly after their arrival: ‘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 to 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, l joined Bohr, who was walking silently, lost in a deep meditation which I was careful not to disturb. As soon as he 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 (Fig. 7.5a). 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, mentioning 238 U 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 235 U. This was intended to show the fission cross section, with non-vanishing values over the whole energy range (Fig. 7.5c). Having drawn the graph, 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 behaviour is thus entirely similar to that of thorium. Consequently, the observed slow-neutron fission must be attributed to the rare isotope 235 U: This is a logical necessity. The next step was to explain the similarity between the two

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Fig. 7.5

even-mass nuclei Th and 238 U and the essential diﬀerence respecting fissility between the even-mass and the odd-mass uranium isotope’.

The diﬀerence results from the well-known pairing eﬀect in the nuclear masses. A neutron added to a system with an odd number of neutrons forms a compound system with an additional neutron pair, and therefore with about 1 MeV more binding energy than when the neutron is added to an already paired system. In retrospect, we may have the impression that this was 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, was highly skeptical. The application, and deeper understanding of these ideas has undergone an enormous development in the fortyfive years since that time, and it would be quite beyond the scope of this lecture to even attempt an enumeration of all the important ideas that have, through the development, enriched the compound nucleus concept. However, there are two chapters in the post war development that I think I really must include; the reconciling of the compound nucleus with the occurrence of shell structure and as a second point the random matrix models. If we continue the story chronologically, the next step is the analysis in 1948 of the vastly expanded data on the systematics of nuclear binding energies by Maria Goepert Mayer, showing the unmistakable eﬀects of nuclear shell structure. The correct independent particle model, based on strong spin orbit forces, was found by Mayer and independently by Haxel, Jensen, and Suess about one year later. This development, at first sight, seemed to disastrously undermine the arguments that had

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Fig. 7.6

been employed to justify the compound nucleus concept - the mean free path of a neutron in the nucleus is long (for low energy neutrons λc ∼ 14fm) - not short, as assumed in arguing for the compound nucleus. But still the compound nucleus idea had been enormously successful. The resolution of this paradox is provided by considering the diﬀerent time scales involved in single particle motion, in scattering, and in compound nucleus formation (see Fig. 7.6). The strong reflection of slow neutrons at the nuclear surface implies that the residence time of the neutron is much longer than the traversal time (see also Table 7.1). If the collision time is short compared with this residence time, the compound nucleus will be formed and Bohr’s ideas will be applicable. This is not at all in conflict with the occurrence of shell structure and single particle motion which is a major eﬀect under the much weaker condition that the collision time is comparable to or longer than the traversal time. If we now look back over the development of nuclear physics in the period 193352 we see, besides the great discoveries of diﬀerent types of nuclear reactions and processes, a gradual clarification of the nature of that fascinating new form for matter encountered in nuclei. A deep understanding of the dynamics of this matter could not be built until one had settled on the correct starting point; is one to start from something like the localized highly correlated picture of a solid or from the delocalized orbits of particles quantized in the total volume of the nucleus? The question is, of course, intimately linked to the strength of the nuclear forces (measured in units

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of the Fermi energy which is a measure of the energy required to localize particles at the equilibrium separation). From this point of view one may feel that from the start there were strong arguments for believing that the forces are rather weak - in the two body system there is only one very weakly bound state for T = 0 and no bound state at all for T = 1 - and thus unable to produce the localization necessary for a quantum solid. We must, however, remember that in assessing this question today we are exploiting the results of a long development in which the analysis of nuclear matter could be compared with a variety of quantal systems encountered in condensed matter physics and that even with this advantage the answers are not very simple (see, for example, the necessary uncertainty in discussing the deconfinement transitions for quarks and gluons, as well as the question of a possible solid phase in the interior of neutron stars). We are here forcefully reminded that despite the impressive development of the powers of formal analysis, the important many body problems of nature have repeatedly revealed the deepseated limitations of straightforward reductionism. Each rung of the quantum ladder has revealed marvelous structures the interpretation of which has required the invention of appropriate concepts which are almost never discovered as a result of purely formal analysis of the interactions between the constituents. The recognition of single particle motion in the average nuclear potential provided a basis for developing a very detailed understanding of the nuclear dynamics, an understanding that reveals a fascinating tension between the concepts relating to independent particle motion and those referring to collective features associated with the organized dynamics of many nucleons. The compound nucleus ideas have eﬀected this development in many and far reaching ways but I shall here confine my discussion to a single example, the remarkable development of the statistical theory of quantal spectra. The experimental impetus for this development is again the neutron resonances which played such a role in the original inspiration of the compound nucleus. It is impossible for me to think about these resonances without a sense of awe at the profound generosity of nature in providing a window in the nuclear spectra at a point where the level densities are about a million times greater than those of the fundamental modes, where the quantal levels are still beautifully sharp in relation to their separation, and where the slow neutrons provide an exquisitly matched tool with which to resolve and measure the detailed properties of each resonance. The eﬀective exploitation of this tool has provided complete spectra comprising hundreds of individually resolved and measured neutron resonances, (Fig. 7.7) while corresponding developments in charged particle spectroscopy have lead to the measurement of similar spectra for proton resonances. It was Wigner (1955) who initiated thinking about this material in terms of random matrices. The idea is to provide a detailed characterization of the wavefunctions and spectra describing the quantal spectrum of the compound nucleus. The compound nucleus idea implies that the quantal states are complicated mixtures involving all the available degrees of freedom of the many-body-system (the quantal equivalent of ergodic motion in classical mechanics). Wigner suggested that significant features of these quantal spectra might be modeled by considering, for some

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Fig. 7.7

region of the spectrum, an expansion of the Hamiltonian matrix on an arbitrarily chosen finite set of basis states. The strong mixing of diﬀerent degrees of freedom and the randomness of the compound nucleus is expressed by chosing the matrix elements of the Hamiltonian matrix independently and randomly from an appropriate ensemble. We may then ask whether there are significant features in the eigenvectors and eigenvalues which reflect the strong coupling of the diﬀerent parts but are otherwise universal in the sense of being the same for almost all of the matrices generated by such a process. It turns out that the answer to this question is yes; indeed, as shown by Thomas and Porter, Mehta, Dyson, and French and co-workers, the fluctuations in level widths and spacings are just such universal properties (see Table 7.4 and the review article by Brody et al. (1981). The extensive evidence from nuclear resonances referred to above, has in recent years been shown to agree in striking detail with the prediction concerning these fluctuations based on random matrices (see Fig. 7.8) and thus to confirm the applicability of this characterization of quantal states of the compound nucleus in the regions to which it has been applied. (These ideas have also played an important role in the interpretation of experiments on laser excitation of polyatomic molecules (Stanholm; Fields) and have been invoked in the discussion of electronic properties of small metalic particles (Kubo, Gorkov and Eliashberg).) While the original formulation of this model was based on random matrices, current developments have made it possible to relate these characteristic features of quantal chaotic motion to more physical models (first to a model of electron motion

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Table 7.4 Microscopic structure of Compound Nucleus = Random Matrix 1. object of study N×N real orthogonal matrix, H constrained average and dispension of eigenvalues otherwise, maximize “entropy” = chose “most typical” matrix 2. joint probability of eigenvalues E1 −− EN P(E1 – EN ) = (norm)

N Eα − Eβ exp −C E2α

α<β

1

C - constant related to level spacing note (Dyson, 1962) complete analogy to partition function for classical electron gas in 1-d with interaction V12 ∼ ln |x1 − x2 | and harmonic confining potential 2 2 Z(x1 −− xN ) = exp − ae2 T x2i + eT Ln |xC − xi | 3. electrostatic analogy “explains” almost crystaline order of the eigenvalues a) nearest neighbors P(E) ≈

π 2D2

2 E E exp − π4 D

Wigner distribution b) number of eigenvalues in interval2L PL ≈ (2πρ)−1/2 exp − 2σ1 2 n − DL σ2 =

2 π2

ln DL + O(1)

Fig. 7.8

in a disordered medium (Efetov (1983)) and quite recently to direct semi-classical

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quantization of the classical chaotic motion based on the (unstable) periodic orbits (Berry 1985). The current questions are concerned with issues such as: how can one characterize the transition between the low energy spectrum with its many conserved quantum numbers (classically multiply periodic motion) and the compound nucleus region, exhibiting quantal chaos? and how to characterize the limitations on the random matrix model that are associated with the existence of a finite relaxation time for the nuclear configurations? In attempting to understand questions such as these nuclear physicists are joining with workers in many other areas of physics in attempting to understand more deeply the significance of classical chaos in quantal spectra and, at least for the nuclear physicists, Niels Bohr’s idea of the compound nucleus provides the crucial point of entry.

Fig. 7.9 Professor Ben Mottelson during the lecture (1985)

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Appendix. An Introduction to Prof. Mottelson’s Address (This was presented by Ryogo Kubo as the introduction for Prof. Mottelson’s address at Science Council of Japan (Tokyo), on November 9, 1985.) I am not quite sure if the name of Niels Bohr appears in physics textbooks for Japanese high schools, but I am sure that everyone knows his name if he has ever been interested in modern science. Niels Bohr was born one hundred years ago in Copenhagen, Denmark. To commemorate this, there have been meetings and symposia in various countries in the world. At the Niels Bohr Institute in Copenhagen, there have been several symposia in last few months, and the highlight was the Niels Bohr Centenary Symposium held through October 4 to 7 with attendance of over three hundred scientists from all over the world. Fortunately I was able to participate this symposium, which was very successful with important review lectures on physics, chemistry, and biology of the present day to commemorate the great man who paved the way to these modern sciences. The Centenary Lecture Meeting today is not covering so wide fields of sciences as that symposium in Copenhagen, but we are very happy that Professor Mottelson kindly accepted our invitation to give a memorial lecture on Niels Bohr and the modern physics. I imagine that one focus of the lecture would be Bohr and nuclear physics, on which Niels Bohr spent most of the latter half of his life to study. I think there is no much need to introduce the speaker today, but let me make a brief introduction. Professor Mottelson was born in Chicago, obtained PhD at Harvard, and came to Copenhagen in 1950. He has remained there most of the time since then. His cooperation with Professor Aage Bohr, the fourth son of Niels Bohr, started in 1951 and has been continued to the present. In 1975, both Professor Aage Bohr and Professor Mottelson shared the Nobel Prize with Rainwater for their remarkable achievements on the structure of nuclei. The subject of the work is the relationship between the individual motion and the collective motion in atomic nuclei. This problem in general is a central one not only in nuclear theory but also in other fields of physics of the present day. In fact, the idea of collective motion in the assembly of protons and neutrons was initiated by Niels Bohr as the famous liquid drop model of nuclei. The idea of competitive existence of individual and collective modes is an excellent example of the complementarity which Niels Bohr stressed throughout his life. In this sense also, the subject of Professor Mottelson’s lecture is most appropriate for commemoration of Niels Bohr. Some people maintain that the scientific achievement is only the important matter and it is immaterial who did this or that. It is true that science as an objective existence does not belong to any individual. However, scientific work is done by individuals and its evolution cannot be separated from the life of the man who did it. Scientific revolution always is ignited by some individuals and the way it evolves greatly depends on who did it. Even if there was no Einstein, the relativity might have been discovered by someone before 1915. Even if there was no Niels Bohr,

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the quantum theory of hydrogen atom might have been formed by someone before 1920. Indeed, there were A. Haas and J. W. Nicolson who thought something about the hydrogen atom, but Niels Bohr did it in an extremely unique way. The breakthrough Bohr achieved was not only the theory of a hydrogen atom but it was the guide which illuminated the way to the new horizon through the year of struggle to the birth of quantum mechanics. Mankind never forget this history. Copenhagen Geist penetrated the new physics and it gave birth of the new science of the new era. The Niels Bohr Institute became the center of international cooperation. Young ambitious scientists gathered here from all over the world. From Japan, which had experienced only a half century since she opened the door to the west, came Takamine, Nishina, Hori, Kimura, Sugiura, Ariyama and some others. These scientists played very important roles after they came back to Japan to create active atmosphere of research in Japan. Among these Japanese scientists who were in Copenhagen at that time, Dr. Nishina had most deep relations with Niels Bohr and the Institute. Dr. Nishina studied electrical engineering at Tokyo University and entered the Institute of Physical and Chemical Research after graduation. He went to Europe in 1921 and stayed at Copenhagen from 1923 to 1928 to work with Niels Bohr. He did much of experimental studies as well as theory. The most well-known of his work is the derivation of the Klein-Nishina formula, for scattering of gamma rays by electron using Dirac’s relativistic quantum theory. Dr. Nishina was liked very much by Bohr’s family. Children used to call him Onkel Nishina. After coming back to Japan, Dr. Nishina started the work on nuclear and cosmic ray physics at the Institute of Physical and Chemical Research. He also invited young theoreticians such as Tomonaga. His laboratory soon became the center of Japan for the study of modern physics. At that time most of the imperial universities were slow to change, so that the eﬀorts of Nishina was really important for the development of modern physics in Japan. The eﬀect was great indeed. In 1935, there was Yukawa who put forward the revolutionary idea of mesons. In several laboratories including Nishina’s laboratory and that in Osaka University, experimental studies on nuclear physics started very actively. So we expected that the day was approaching when the Japanese physics might catch up the level of Europe. It is very sad to reflect the disaster of the Second World War which completely crushed down our hope. Nevertheless, after fourty years since the war, we must not forget the fact that we owe a great deal to the valuable eﬀorts done in 1930’s by these predecessors. In this sense also we realize deeply with great appreciation how much we owe today’s Japan to Niels Bohr. After the war, during the past few decades there have been a great number of our colleagues who went Copenhagen to study at the Niels Bohr Institute. They are now the leaders at various universities and institutions. Thus, there are great number of Bohr’s pupils, grandpupils, and grand grandpupils in Japan. Niels Bohr was always very warm and kind to Japanese scientists. He came to Japan only Once in 1937. The memory of the visit was talked about repeatedly in Bohr’s family. Unfortunately I have had no chance to meet him, but once had a chance to see Mrs. Niels Bohr who told me about those Japanese scientists at Copenhagen and her visit to Japan. In the hall outside of this auditorium there are

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exhibitions of photographs of Niels Bohr which show us something about Bohr and Japan. If you have not seen them, I hope you pay a look after the lecture. The Nishina Memorial Foundation was established to commemorate Dr. Nishina and so it has kept a close relationship with Niels Bohr Institute. Some years ago when Professor Tomonaga was the President, he invited Professor Aage Bohr to Japan. Also Professor Tomonaga and his associates did much eﬀorts to support the activity of the Institute through a financial grant from the EXPO Foundation. At the present moment, two young scientists are studying at the Niels Bohr Institute by the grants given by the Nishina Memorial Foundation. Some time ago, the idea of doing something to commemorate Niels Bohr centenary here in Japan came naturally to the minds of those who have ever studied at Copenhagen. The Nishina Memorial Foundation decided to take up this idea and this Lecture is one of the outcome. Since there have been several such meetings here and there in the world, we worried very much if this can ever be realized. So, we are very grateful to Professor Mottelson for his kind acceptance of our invitation. The Science Council of Japan and the Physical Society of Japan have agreed to cosponsor this Niels Bohr Centenary Lecture Meeting, which I think very appropriate to express our everlasting esteem and gratitude to the great father of modern science, Niels Bohr. Thank you for your attention.

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From X-Ray to Electron Spectroscopy Kai Siegbahn

Abstract This address was presented by Kai Siegbahn as the Nishina Memorial Lecture at the University of Tokyo, on April 4, 1988.

1. Historic Background R¨ontgen’s surprising discovery in November 1895 can be regarded as the great break-through from classical physics to a new era, which developed into modern atomic physics. Hittorf, Lenard and Crookes made important preliminary work in this field, a fact that R¨ontgen pointed out in his report on the discovery “Uber eine neue Art von Strahlen”. He and many other scientists must have been strongly stimulated by the almost science-fiction like picture, that Crookes called forth at a meeting in Royal Society in London in 1878: “The phenomena in these exhausted tubes reveal to Kai Siegbahn physical science a new world—a world where matter may NMF c exist in a fourth state, where the corpuscular theory of light may be true, and where light does not always move in straight lines, but where we can never enter, and with which we must be content to observe and experiment from the outside.” Many of the scientists at that time worked intensely in this field and had certainly also used fluorescence screens and had by those means the conditions for the discovery of the radiation. It is, however, interesting to note how R¨ontgen at his sensational discovery investigated with scientific thoroughness the properties of the new radiation. Quickly and with superior experimental skilfulness R¨ontgen attained order in a field, that before had been completely outside human experience. It would Kai Siegbahn (1918 – 2007). Nobel Laureate in Physics (1981) University of Uppsala (Sweden) at the time of this address K. Siegbahn: From X-Ray to Electron Spectroscopy, Lect. Notes Phys. 746, 137–228 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 8

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last almost 17 years until any essentially new properties of this radiation were being added to those which R¨ontgen himself had found. One of R¨ontgen’s early observations, which would be significant in the medical use, was that when the cathode radiation in the tube scattered against platinum it appeared a harder radiation than when it scattered against aluminium, glass or other light materials. The most essential novelty for atomic physics in general was that one had found a radiation that could find its way through every kind of material and, in particular, could penetrate the before hidden interior part of the atom. In that way the necessary conditions had been created for a first analysis of the inner structure of the atom. The next break-through in the scientific field came first with the discovery of the diﬀraction of this radiation in crystals by von Laue, Friedrich and Knipping in 1912. Somewhat before, however, Barkla and others had with simple means furnished proofs of some properties of the R¨ontgen radiation, which had significance for the further development of atomic physics. After the penetration of aluminium foils the “soft” part of the radiation was quickly absorbed. Left behind was a rather homogeneous radiation. Allowing this “hard” radiation to strike an arbitrary plate, one could in the scattered radiation find three diﬀerent components (Fig. 8.1). The

Fig. 8.1 The interaction of X-radiation with matter. One component is the scattered X-radiation with the same energy as the primary radiation from the X-ray tube. The second component is characteristic of the material being studied. In optical terminology this is the fluorescence radiation which developed into X-ray emission spectroscopy. The third component consists of electrons and is the basis for modern electron spectroscopy

first component consisted of scattered radiation of the same kind as the impinging one. The second component was secondary X-radiation which was softer than the impinging one and characteristic of the irradiated material. From the study of this characteristic radiation Barkla could distinguish between two series of radiation, which he called K- and L-fluorescence radiation. For a certain element the penetration of the K-radiation was 300 times higher than for the L-radiation. From these early observations X-ray spectroscopy was generally developed by means of the more and more refined X-ray diﬀraction methods. X-ray spectroscopy made possible an atomic analysis of diﬀerent materials and led to the discovery of new elements like hafnium and rhenium. The shell structure of the atoms (Fig. 8.2) could be inves-

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Fig. 8.2 X-ray emission spectrum (in Å) from the elements showing the three series K, L and M

tigated by X-ray spectroscopy, a field in which my father was deeply involved [1] and atomic physics was put on solid grounds. The third component of the scattered radiation was found to consist of electrons, which were expelled from the irradiated material. What happened in this field of spectroscopy? For a very long time it was shadowed by the successful study of X-ray spectroscopy. In the twenties spectroscopic investigations of the secondary electrons, the “photoelectrons”, were started by e.g. H. Robinson in England and M. de Brogue in France. They showed by means of magnetic deflection of the electrons, that also this component contained information on the shell structure of the atom and that one could obtain approximate values of the binding energies for the electrons in the diﬀerent shells. This field turned out to be much more diﬃcult to master and the accuracy was small. My interest in this third component began early in the fifties. For some time I had been concerned with techniques to investigate electrons, emitted in radio-active β decay. A suitable way to investigate the γ radiation was to cover the radioactive sample by a thin lead foil and to record the expelled photoelectrons from the foil by an electron spectrometer. This work gradually led to improved resolution in nuclear spectroscopy [2]. I was finally able to observe and measure the inherent widths of conversion-electron lines due to the finite widths of the atomic levels involved in the internal conversion process during the nuclear decay. In order to observe such phenomena a resolution of 1 : 104 at these energies, around 100 keV, was required. The investigations were performed by means of a magnetic double focussing iron

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Fig. 8.3 ThB F- and I-lines. Internal conversion in the K and LI shells, respectively. At this high resolution one can notice the diﬀerent inherent widths of these β-lines

free spectrometer with large dispersion (R = 30 cm). Fig. 8.3 shows the diﬀerent internal widths of the F- and I-conversion lines in the decay of radioactive ThB, the former line converted in the K shell the latter in the LI shell. Most of the high resolution work in my laboratory during that period of time was performed with a large double focussing magnetic spectrometer with iron yoke (R = 50 cm) which was specially designed for studying complicated decay schemes of radioactive isotopes. The most complex of these was Au194 . It contained more than 100 γ-transitions, the conversion electron spectrum contained some 350 detectable lines. By means of a double counter operated in coincidence it was possible to detect lines of an intensity of 10−5 times that of the strongest lines. Fig. 8.4 shows a limited part of that spectrum. In these investigations both internal and external photoelectron spectra were taken and the final decay scheme, further checked by coincidence studies from selected nuclear levels, is reproduced in Fig. 8.5. My interest to investigate finer details in nuclear spectra continuously tempted me to go back to R¨ontgen’s original discovery and, more precisely, to the third component mentioned before and to see if new methods could be applied to atoms, molecules and solids using an X-ray tube instead of nuclear y radiation. For this purpose the above mentioned iron free double focusing instrument was constructed and adopted to investigating electron energies some orders of magnitude less than in nuclear decay. Robinson and some other scientists around 1925 had been able to establish that electrons expelled from metals by means of the photoelectric eﬀect exhibited an energy distribution that was consistent with the shell structure of atoms which had been studied in much more detail by X-ray emission and absorption spectroscopy. During the thirties and forties much of the interest in atomic physics shifted to nuclear physics. Partly because of this and partly because of the lack of adequate methods for handling the experimental problems associated with electron spectroscopy the field had waited for its development and exploration.

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Fig. 8.4 Part of the internal conversion β spectrum of Au194 . There are altogether 350 observable β lines in this complex decay, with intensity variations of 1 − 10−5

Fig. 8.5 Decay scheme of Au194 based on the internal conversion electron line and external photoelectron line spectra

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The mentioned early period is represented by the top of Fig. 8.6 which shows a photographic recording of the photoelectron spectrum of gold by Robinson [3] in 1925. The various levels in gold are distinguished in Robinson’s spectrum and also in the corresponding photometric recording. The well-known NVI , NVII doublet, extensively used for calibrations in modern electron spectroscopy, is not observed in this early spectrum, however, and obviously the electron distributions rather resemble X-ray absorption distributions than true lines. At the later part of the fifties the work in my laboratory had led to the development of an electron spectroscopy which was characterized by narrow electron lines from solid materials excited by X-radiation. The recorded electron lines were well defined by widths set by the inherent atomic widths themselves. The state of the art during this period is illustrated by the recordings of the gold spin doublet made during the early 60’s in my laboratory (to the right of Robinson’s spectrum). The same spectrum taken some years later is shown in the middle of the figure on an energy scale expanded by a factor 600 compared to Robinson’s spectrum. The improvement in resolution between the two later spectra is due to the introduction of X-ray monochromatization by means of crystal diﬀraction of the AlKα radiation. This made it possible to pass beyond the previous limit set by the inherent width of the X-ray line. The lowest part of the figure illustrates one particularly important feature of electron spectroscopy. The diﬀerence between the middle and the lowest part of the figure demonstrates the surface sensitivity of this spectroscopy. A fingerprint on the gold foil completely wipes out the gold lines and replaces them by other lines dependent on what elements happened to be on the surface layer of that finger. Electron spectroscopy is nowadays an independent alternative to X- ray and other spectroscopies and contributes with much new information about the properties of matter. In particular surface science and technology makes use of electron spectroscopy as a convenient tool to characterize surface conditions and reactions. Applications are found in many other areas in the border lines between physics and chemistry. To emphasize these aspects the acronym ESCA (electron spectroscopy for chemical analysis) was introduced [4], [5]. The historical background is covered in several more recent works [6], [7], [8], [9].

2. Some Basic Features of Electron Spectroscopy In photoelectron spectroscopy the sample is introduced into vacuum and radiated with soft X-rays, ultra-violet light or synchrotron radiation. In addition, an electron beam can supplementary be used to excite Auger electron spectra by electrons and, if properly monochromatized, for electron scattering spectroscopy. A certain number of the electrons which are expelled from their atomic bindings may leave the surface layer without energy losses, the scanning depth being set by the energy dependent mean free paths. An electrostatic lens system collects and focusses the electrons onto the slit of the electron analyser. An extended detector is situated in the focal plane where the diﬀerent electrons are simultaneously being recorded. These

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Fig. 8.6 Some steps in the development of photoelectron spectroscopy excited by X- radiation. Upper figure to the left: the recording of gold as obtained by Robinson in 1925 with its photometer curve. To the right: the “gold doublet” photoelectron lines around electron binding energies of EB∼ 85 eV as observed after that photoelectron line spectroscopy had been developed at the end of the fifties. These and any of the other lines cannot be seen in the previous spectrum. The middle spectrum shows the same spectrum when X-ray monochromatization of AlKα at 1486.6 eV (Δhν = 0.2 eV) had been introduced. The gold doublet is inserted in this figure in an expanded scale ∼ 600 times that of the Robinson spectrum. The lower figure shows the surface sensitivity of electron spectroscopy. A fingerprint has wiped out the gold lines and produced new lines

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Fig. 8.7 Scope of electron spectroscopy

events appear on the screen of a computer as a fence of separate electron lines (see Fig. 8.7). These lines characterize the examined substance, the elemental composition and the chemical bindings. Lid materials with elements over the whole periodic system can be examined and also gases down to low pressures ∼ 1 − 10−5 torr. The spectroscopy has been applied also to liquids and solutions. Extensions of electron spectroscopy are under way by using LASER radiation for citation (in particular resonance enhanced multiphoton ionization, MPI). Fig. 8.8 illustrates an atom which is bound to other atoms in molecular valence bondings, alternatively adsorbed or chemically bound to a rface. In order to eject electrons from the inner part of an atom he “core” region) harder radiation is required than for the external valance electron region. When an electron is emitted a hole is created the electron shell. This is immediately followed by a relaxation the other electrons which thereby adjust themselves to the new potential by means of a “shrinkage” and flow in the surrounding electron cloud. The hole has a certain very short lifetime (< 10−14 s) fore it is filled by an electron from some externally situated ell. The atom can dispose of the released energy either in the form of an X-ray photon or by emitting another (Auger) electron. In such a case three levels are involved (e.g. LMM etc.). Such electrons are recorded together with the primary emitted photoelectron spectrum. One advantage to excite Auger electrons by X-rays compared

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Fig. 8.8 Citation of core and valence electron spectra

to electrons is the great improvement in signal to background. These conditions are further discussed later in this survey. When a chemical compound between two or more atoms is formed a redistribution of the external valence electrons of the atoms occurs which are responsible for the chemical bonds. The electric potential around a certain atom in the molecule will then be changed, to an extent which is dependent on the specific nature of the chemical bond in the diﬀerent cases (e.g. at diﬀerent “states of oxidation”). This new electric potential influences the bond strength of the inner electrons which surrounds the atomic nucleus and the consequence of this is a “chemical shift” in the recorded electron spectrum. This information is exceedingly important in electron spectroscopy. One can for example easily distinguish, even at modest resolution, between metallic atoms and those which have been oxidized at the surface layer. Fig. 8.9 shows such a case [10]. It concerns the surface of a silicon crystal and one observes in the electron spectrum taken at modest resolution two main lines which are due to the electrons from the 2s and 2p levels, respectively, from silicon. The spectrum also contains some satellites which are due to discrete energy losses of electrons. The diﬀerence between the lower and upper figure is that the crystal surface has been tilted so that the electrons in the latter case leave the sample at a small angle from the surface. Those electrons which come from below, from the “bulk”, are then absorbed to a larger extent than those from the outer surface layer. The surface layer is favoured. One can notice how the slightly oxidized silicon layer

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Fig. 8.9 Spectrum of a slightly oxidized silicon surface. By tilting the crystal the oxide surface layer is emphasized. Plasmon lines are also observed

on the surface shows up strongly in the form of SiO2 lines to the left of the Si lines. They were only barely visible in the other spectrum. At improved resolution (Fig. 8.10) much more detailed information is obtainable concerning the depth composition at the oxidation [11]. This is a simple and commonly used method to distinguish between bulk and surface. The surface sensitivity is a small fraction of a single atomic layer, under certain conditions less than a percent of an atomic layer. The spectral resolution can be pushed much further than what is shown in Fig. 8.9 and Fit. 8.10. Fig. 8.11 gives a highly resolved spectrum of the Si2p1/2,3/2 doublet excited by means of monochromatized AlKα rays [12]. Here the doublet is completely resolved in two components instead of the unresolved one in the previous figure. The background is also very small, essentially zero. Small intensity structures can then be observed slightly above background. An increasing number of ESCA instruments are now in operation which are provided with X-ray monochromators for high resolution work. To a much less extent these are combined with a rotating anode. Still it is this combination which oﬀers the best advantages for high resolution at high intensities. Ultimately, the recorded electron linewidths are set by the inherent levels widths. The use of an X-ray monochro-

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Fig. 8.10 A study of the oxidation of a silicon surface taken at higher resolution by meas of the “tilting” method

Fig. 8.11 Well resolved 2p1/2 and 2p3/2 core lines of Si(111) at T=300 K and θ = 45◦ by means of monochromatized AlKα 1486.6 eV (Δhν = 0.2 eV) Observe the low background

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mator significantly improves the conditions for accurate deconvolutions at the analysis of the spectra, since the lines are getting narrower and the signal to background ratio is enhanced. The electron lines due to X-ray satellites situated close to the real line structures are eliminated and so is the background due to bremsstrahlung. In photoelectron spectroscopy the recorded linewidths are lifetime and vibration limited. As an example carbon lines from polymers are usually rather broad by nature (> 1 eV). If the sample is an insulator one always has to take precautions to avoid charging of the sample surface. Methods have been developed to eliminate or greatly reduce such artifacts in the spectra. Usually an electron flood gun with very low energy electrons is used to flooding the sample or one may simply use the degraded flux of electrons from the X-ray electron production at the sample by surrounding the sample by a cavity with two holes, one for the X-rays and one for the expelled photoelectrons in the direction of the slit of the analyzer. A more recent arrangement, is to use an unfocused electron gun with electrons in the 1 keV region. Another recently developed method is to use a wire net at a defined potential fairly closely situated to the sample surface. A further possibility which will be further studied would be to rotate the samples during the exposure. These methods are convenient to apply when the X-ray beam is strongly focussed onto the sample. As a general rule the samples should be made as thin as possible and be deposited on a conducting backing. Some electron spectra will demonstrate the state of the art at good resolution [13]. Fig. 8.12 shows the electron spectrum of copper. One observes the core levels with their diﬀerent widths and intensities. Close to zero binding energy the conduction band (3d4s) is recorded. This structure and similar ones from metals and alloys etc. can be separately studied in much more detail at larger dispersion (see e.g. Fig. 8.35 and Fig. 8.36). In the spectrum one also observes the Auger electron lines due to LMM transitions in the region excited by the same Alkα radiation. Fig. 8.13 shows the electron spectrum of an ionic crystal, KCl. The L and M sublevels for both elements are recorded and their linewidths are given in the figure. In the valence region (lower part) some energy loss and “shake-up” lines are shown. The shake-up line situated 5–6 eV from the Cl3s is due to a configurational interaction between the 3s2 2S ionic ground state and the 3p2 4s∗ , 3p2 4s∗ , 3p2 4p∗ and 3p2 3d∗2 S states. A strong shake-up structure situated 14 eV from the K3s is due to a configuration interaction between the 3s2 S ionic ground state and the 3p2 4s∗ , 3p2 4p∗ and 3p2 3d∗2 S states. The energy diﬀerence between the two outer bands of the cation and the anion, K3p adn Cl3p, respectively, is according to the figure 12.11 eV. This can be used to assign an ionicity for such binary crystals. Some examples of ESCA chemical shifts will be given here. The first one concerns Na2 S2 O3 , Fig. 8.14. There are two diﬀerent sulphur atoms here which, according to classical chemical language, could be asso- ciated with oxidation numbers 6+ (central) and 2− (ligand). The ESCA chemical shift between the central S-atom (to the left) and the ligand S-atom (to the right) for the 2p1/2,3/2 doublet is 6.04 eV. This is evidently a large chemical eﬀect, even larger than the atomic spin-orbit splitting, which is

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Fig. 8.12 The copper spectrum showing core photoelectron lines, Auger electron lines and the conduction band

just resolved in the spectrum. The lower part of the figure shows the corresponding shift between the 2s levels. One observes here the larger inherent linewidths of the s-levels. The chemical shift is almost the same, 5.82 eV, but may give room for a small second order eﬀect. The second example (Fig. 8.15) concerns the MgKLL Auger electron spectrum excited with AlKα radiation at diﬀerent stages of oxidation. The upper curve is a clean metal surface, the lower is the oxide (with only a trace of metal) and the middle at intermediate oxidation. Series of volume plasmons (metal plasma collective oscillations) for each Auger line are observed, some of which nearly coincide with other Auger electron lines. The MgO peak, when growing up, happens to coincide with the second Auger electron peak of the metal. For comparison, the NeKLL Auger electron spectrum is given below. This spectrum contains a great number of satellites, which can alternatively be recorded in separate experiments in the gas phase by means of electron excitation. Inserted in the figure is the Mg2p photoelectron line and the chemical shift of this during oxidation. The chemical shift eﬀect is frequently used in polymer technology for characterization of such materials. Fig. 8.16 shows the C1s core line splitting in five components in the case of Viton. The relative intensities between the lines depend on the branching ratio in the polymer chain. From the spectrum in Fig. 8.16 one can in this way distinguish between Viton 65 and Viton 80. Fig. 8.17 is a commonly used ‘test’ sample in ESCA, namely PMMA (polymethylmethacrylate). It is a polymer with wide-spread applications, e.g. in the pro-

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Fig. 8.13 The spectrum of an ionic crystal, KCl. The diﬀerent linewidths for this insulator are given in the spectrum. The ionicity is related to the energy diﬀerence 12.11 eV

Fig. 8.14 ESCA chemical shifts for S2p and S2s in Na2 S2 Q3

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Fig. 8.15 MgKLL Auger electron lines at diﬀerent stages of oxidation. Volume plasmons for each electron line are also observed. The chemical shift of the Mg2p line is inserted. The Ne Auger electron spectrum excited by electrons is inserted for comparison with Mg. This spectrum contains a great number of well resolved satellites [5]

duction of semiconductor chips by means of lithography. The polymer chain consists of the group indicated in the figure. A good instrument, e.g. one with well focussed X-rays, should be able to resolve suﬃciently well the diﬀerent carbon atoms in this group [14]. It is an insulator and therefore subject to charging if not the correct precautions have been taken to eliminate this eﬀect. The inherent widths of the photo lines are partly set by internal vibrations in this case. It is therefore not possible to distinguish all the lines completely. However, with good statistics (high intensity, low background and monochromatic X-radiation) a reliable deconvolution can be made showing four carbon components on the ‘right’ places, which is good enough for a characterization of this polymer.

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Fig. 8.16 ESCA spectra of the polymers Viton 65 and Viton 80 with diﬀerent branchings in agreement with the measured intensities

Fig. 8.17 ESCA spectrum of the polymer PMMA, polymethylmethacrylate. The deconvolution into components and their positions characterizes the polymer

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3. Monochromatization of the Exciting X-radiation. Instrumental Arrangements An ultimate factor in reaching high resolution is the monochromacy of the exciting radiation. In the X-ray region one can use X-ray lines to confine much of the available X-radiation energy into a very narrow region defined by the inherent linewidth of the Kα line of the anode material (e.g. Al or Mg). For further improvements monochromatization by means of X-ray diﬀraction against a crystal (e.g. quartz) is necessary. Regardless whether one starts with the discrete line spectrum of an anode material or the continuous spectrum of synchrotron radiation, which allows a continuously variable wavelength, it is the properties of the diﬀracting crystal which set the limit for the final resolution. Important factors here are the number of lattice planes in the crystal taking part in the diﬀraction and the suitable choice of crystal material to withstand radiation damage. Furthermore, mosaic structure of the crystal is a disadvantage for high resolution. Quartz is a particularly good choice for reaching highest resolution but is on the other hand fairly radiation sensitive and therefore not suitable in too high concentration of radiation, e.g, synchrotron radiation. In the case of AlKα radiation the Bragg angle for quartz (010) is 78◦ which means that reflexion is almost at normal incidence. Under these conditions a spherically bent crystal will approximately achieve two directional focussing, i.e. point to point imaging. The reflectivity is quite high, around 50%. Using an array of such crystals (our recent design contains 19 crystals, each with a diameter of 6 cm) on the Rowland circle, or rather on a Rowland surface, one can collect and focus a substantial solid angle of monochromatized X-radiation with high intensity for the production of photoelectrons at the position of the sample. In order to get a maximum of highly monochromatic X-radiation the primary radiation has to be emitted from as small a surface element as possible. The anode has to be watercooled and at the same time rotating in a good vacuum. In my most recent design the rotor will be magnetically suspended (see Fig. 8.18) with an asynchronous motor between the ‘active’ magnetic bearings. By means of electronic sensors the rotating body is fixed (and adjustable) in both radial and axial directions. This is a stable and safe arrangement which does not require lubrication. The design of a rotating anode is technically a demanding task. My laboratory has been dealing with such problems for a long period of time. The anode should be capable of very high speeds of rotation (> 10000 rpm) and strongly water cooled in order to be able to accept the high power levels required on a small area. With minor modifications the design according to Fig. 8.18 can be made in any desired size. As an example, at 15000 rpm and a diameter of 50 cm the rotor has a speed at the periphery of ∼ 400 m/sec, i.e. well above the velocity of sound. Far even higher speeds the strengths of the rotor itself, if necessary, can be further improved in the future by using composite materials. Dependent on the chosen spot size of the electron gun and the particular anode material one might be able to dissipate a power of ∼ 50 kW due to an eﬃcient water cooling of the rotor periphery. The heat generated at the surface of the rotor is distributed over the whole periphery

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Fig. 8.18 The design of a new high speed, magnetically suspended, water cooled rotating anode. This high intensity X-ray generator is provided with two electron guns and several diﬀerent anode materials along the rotor periphery to generate diﬀerent X-ray wavelengths

but on top of that a quickly decaying transient temperature spike is developed each time a certain surface element is passing the electron beam spot. Because of this the very high rotor speeds are required. Other precautions have to be taken to create, preserve and to continuously inspect the surface conditions necessary to achieve high X-ray emission intensities. For this purpose the rotor house is provided with appropriate arrangements. On the external part at the periphery of the rotor, which is being exposed to the focussed electron beam, diﬀerent anode materials can be deposited, in particular aluminium. Since AlKα radiation is focussed at an angle of 78◦ in the first order of diﬀraction it is interesting to: see what other X-ray lines of other materials could be used which have approximately the same Bragg angle at higher orders. Going from one anode

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material to another at multiples of 1486.65 eV, the energy of the AlKα line, requires then only minor mechanical adjustments from the standard position. Doubling the X-ray energy results in a larger escape depth of the produced photoelectrons in the sample. The cross section for photoelectron production in the sample is getting down, unfortunately, but of some particular interest is the fact that the number of planes involved in the diﬀraction in the quartz is increasing. This has as a consequence that the theoretically attainable resolution is increasing. By means of the detailed dynamical theory of X-ray diﬀraction the rocking curves for quartz (010) (and other crystals) can be calculated for diﬀerent wavelengths. Fig. 8.19 summarizes the results [15]. Possible anode materials having approxi-

Fig. 8.19 Calculated rocking curves for several X-rays reflected against quartz (010) near 78◦ at diﬀerent orders. The width of the rocking curve narrows at increasing energy

mately the same Bragg angle (78◦ ) in diﬀerent orders are: AlKα (first order), AgLα (second order), TiKα, ScKβ (third order) and MnKα, CrKβ (fourth order). According to Fig. 8.19 the widths of the theoretical rocking curves are: 135 meV, 77 meV, 25 meV and 27 meV, respectively. As pointed out above the photoelectron intensities are decreasing and, furthermore, since the energies of the photoelectrons are increased the demands put on the resolving power of the electron spectrometer is correspondingly increased. Full use of the theoretically attainable higher resolution at higher orders according to Fig. 8.19 will be at the expense of a great reduction in intensity. How far one can really reach the theoretical limit remains to be seen. For the case of AlKα the theoretical limit of 135 meV is almost reached by the actually obtained value of 0.21 eV according to Fig. 8.20. Instruments in electron spectroscopy can be constructed in a great variety of different ways, dependent on the modes of excitation, types of samples, research problems etc. On the market there are presently a number of designs available. They are usually tailor made for surface studies under ultrahigh vacuum conditions to be used on a routine basis. A typical trend today is to simultaneously make use of complementary multipurpose techniques for surface characterization like LEED, SIMS, TDS etc. Handling of gases or liquids requires eﬃcient diﬀerential pump-

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Fig. 8.20 Achieved monochromatization of the AlKα doublet reflected near 78◦ against a set of spherically bent thin quartz wafer crystals (010)

ing and special designs. Synchrotron radiation, when available, is particularly well suited for excitation of photoelectron spectra and necessary when complete tunability is required. Commercial instruments take advantage of devoted laboratory sources like soft X-ray anodes adopted to photoelectron spectroscopy, ultra-violet discharge lamps and monochromatized and focussed electron beams. Tunable laser sources will provide new possibilities for investigations by means of multiphoton ionization and tunability in the valence region. High spectral resolution is important in all cases. In the soft X-ray region the monochromatization can be achieved in its lower part by means of optical grating techniques as is done at synchrotron storage rings and in its higher part (> 1 keV) by means of crystal diﬀraction. A recent laboratory design in my laboratory for this purpose is shown in Fig. 8.21. It consists of the previously mentioned water cooled swiftly rotating anode (Fig. 8.18) with two electron guns, the X-radiation produced by one of them being directed into an X-ray monochromator. The purpose of the other one is to enable other X-ray experiments to be done. The spherically bent thin quartz crystals are mounted on a common zerodur block which can be moved in the horizontal direction around a vertical axis situated at the side of the block. Such a movement changes the Bragg angle and adjusts the crystal surfaces to stay on the Rowland circle (R = 100 cm) when the house of the rotating anode is correspondingly moved along a prescribed curve on the rotor table. The diﬀerent anode materials are deposited as 3–6 mm wide strips aside of each other along the periphery of the rotor. The electron gun can be tilted from outside to direct the electron beam towards the diﬀerent anode materials. In accordance to the position of the electron beam spot on the anode the crystal block is simultaneously slightly tilted around a horizontal axis supported by a strong ball bearing. By these arrangements the focussed and diﬀracted X-ray beam for diﬀerent wavelengths will always hit the sample on the same spot in front of the electrostatic lens system. The movements can automatically be performed by step motors. The construction admits the use of the five anode materials Al, Ag, Ti, Cr and Mn in diﬀerent orders as discussed above. The use of further auxiliary anode materials like Y, Zr or Mo to produce ultrasoft Mζ X-radiation in the 130–190 eV region can in principle be arranged within the same scheme. In that case a separate concave mirror or grating could be introduced in front of the crystal assembly. One should then make use of the presently quickly developing multilayer techniques which, at

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Fig. 8.21 The rotating anode-monochromator (RAMON) arrangement and the lens system of the electron analyzer. The monochromator provides additional radiation sources for W and laser excitation focussed at the same spot on the sample. There is a fine-focus electron gun for additional Auger electron excitation and microscopic scanning of the sample. Samples can be introduced either from two sample preparation systems from the back side or via a vacuum lock devise joining this part of the instrument with the other part of the total instrument

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nearly normal reflexion, may enhance the intensity by some orders of magnitude due to a much increased reflectivity and also solid angle. This technique still waits for its full exploration. The monochromator house is provided with further arrangements for W and laser light which can be directed onto the same spot on the sample as do the X-rays. Other external radiation sources, inclusively synchrotron radiation, can also be handled in the monochromator house. The lens system is a five-component system provided with an exchangeable auxiliary einzel-lens close to the lens entrance slit. In order to direct the beam accurately to a given small entrance slit at the analyzer an octopole electric deflector is mounted inside the long central section of the lens system. The lens system is surrounded by two concentric μ metal shields, as is the analyzer. This einzel-lens is not always required for ordinary spectroscopic work. It is provided with a collimating slit to achieve a magnified real electron optical image at the entrance slit to the analyzer. This is to achieve lateral resolution. Developments in order to realize high lateral resolution (< 100 μm) combined with good energy resolution are presently under way in several laboratories. Arrangements for this purpose can be made in many diﬀerent ways. In the present case the magnification achieved by the einzel-lens may be about 10–20 times, dependent on the chosen geometry. If the X-ray spot on the sample surface is concentrated to be 0.2 ×1 mm2 , which is feasible with the present high intensity X-ray generator combined with the focussing monochromator, this small spot will emit photoelectrons at a very high intensity. The conditions are therefore ideal for achieving high lateral resolution. To achieve this one can choose a suitable magnification by means of the magnifying electron optical lens system. The simplest case is shown by the arrangement in Fig. 8.21. Additional lenses would give higher magnification at the expense of intensity. It is therefore of prime importance to start with a high brilliance at the sample spot to be investigated. A swiftly rotating anode as in Fig. 8.18 is particularly well suited for this purpose. With 20 times magnification the electron image at the entrance slit of the analyzer would become 20 mm × 4 mm2 . If the analyzer is accurately adjusted it will produce a real image in the focal plane of the same dimensions. There are several ways to proceed from here. For example, one can use a slit at the entrance of the analyzer which has a width of 0.1 mm. Then the analyzer will accept electrons only coming from a 5μm wide strip of the sample. With a perfectly chosen optical system with negligible aberration errors in regard to both lens system and analyzer a point to point image is produced in the focal plane of the analyzer which has simultaneously dispersed the energy spectrum from each point on the sample. By means of the electric octopole deflector the illuminated sample surface can be scanned. In such a deflector the two orthogonal deflections are completely independent of each other [16]. If the sample has a large area the region corresponding to the X-ray spot is being selected by means of the sample manipulator. The position sensitive multichannel-plate detector is in this “photoelectron microscope” electronically an integrated part of the total system. Obviously, the high lateral resolution mode of operation is realized only at a great expense of intensity. If this is not required, the lens system can be used under

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much more relaxed conditions, the main purposes being a high collection eﬃciency and good optical retardation properties for achieving high intensity and high energy resolution, respectively. A view of the total ESCA instrument with its accessories is shown in Fig. 8.22. The spherical analyzer (R = 30 cm) is provided with two separate lens and detector systems, one for electrons being bent in the horizontal plane and the other in the vertical plane. Two separate experimental sets up are then available and samples can be studied in anyone of them. There is a connection between the two through a valve. There are several diﬀerent modes of excitations within the system and also complementary techniques, in particular for surface studies. Since diﬀerential pumping has been introduced in the sample houses the instrument is also equipped for studying gases and liquids as well as solids. In the sample chamber which analyzes the electrons in the vertical plane there are provisions for UV excitation by means of a set of one toroidal mirror and four toroidal gratings adjustable from outside which covers the energy range between 10–5 eV. In the same chamber there is a two-stage high resolution electron monochromator, variable between ∼ 1 eV – 6 keV for electron scattering in the 90◦ direction, an Auger gun and an ion gun with a Wien selective filter. Provisions for electron flooding for electric neutralization of surfaces are included. Laser radiation can be introduced. Samples can be introduced into the chamber through diﬀerent ways. One introduction port is connected to a preparation chamber which in turn communicates with an MBE system. The other port is a fast sample inlet directly into the measuring position of the analyzer through a vacuum lock devise. This sample chamber is connected through a valve on top of the sample chamber to a further apartment, containing facilities for complementary surface techniques, like LEED etc. A long range manipulator carries the sample into diﬀerent measuring positions and provides the means for angular studies and temperature regulation. A horizontal rod brings the sample into the second part of the instrument where the electrons are analyzed in the horizontal plane. The primary mode of excitation here is the monochromatic X-radiation and the other radiation facilities previously described in Fig. 8.20. There is a further focussed scanning Auger gun situated close to the sample. The latter is transferred from the introduction rod to a manipulator in front of the lens slit. This sample house communicates with a chamber which branches into two directions backwards. One is a separate preparation chamber (with its own sample inlet devise) for the normally occurring sample preparations like evaporation, sputtering, CVD etc, the other is a specially designed inlet system for liquids and solutions, which admits direct communication “on line” between the liquid sample in the spectrometer and chemical experiments to be performed in the laboratory. The pump system consists of several turbo pumps arranged to achieve diﬀerential pumping in various parts of the instrument and a cryopump with high pump capacity (1500/sec). For liquid studies of water solutions a special cool trap is justified.

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Fig. 8.22 A total view of the ESCA-LASER instrument. There are several separate preparation facilities “on line” of the instrument. One is for ordinary chemical and adsorption operations and the other is for the preparation and introduction of liquid samples. These facilities concern the first part of the instrument as shown in the previous figure. The sample house for the second part of the instrument is shown in the figure in front of the analyzer with its various sources of excitation. It communicates with an UHV preparation chamber connected to a molecular beam epitaxy (MBE) apparatus. This sample house is furthermore provided with a fast inlet for samples of diﬀerent kinds carrying them directly into measuring position in front of the lens slit. There are altogether five diﬀerent ways to introduce samples into diﬀerent parts of the instrument

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Fig. 8.23 shows a vertical view of another and smaller apparatus which is mainly designed for studying gases (gas cells) and molecular beams (supersonic jets). Since it is constructed for UHV performance surface studies can, however, also be performed. The cross section in Fig. 8.23 shows an energy variable electron monochromator, in two subsequent steps (to avoid space charge limitation). This is identical to the one in the bigger instrument. The electron beam is crossing the vertical molecular beam. The inelastic scattered electron beam is analyzed, after passing the lens system, by a spherical analyzer with a radius of curvature of 36 cm. Other radiation sources are situated around the sample house. There is polarized laser radiation (from two tunable lasers) pumped by an excimer laser crossing the molecular beam. The photoelectrons being produced by two-colours resonance enhanced multi-photon ionization (REMPI) are directed into the same analyzer. One can either use the analyzer or a time-of-flight arrangement which is attached to the back side of the analyzer. This is primarily intended for mass analysis of ionic fragments and for this purpose it is provided with a mass reflector to achieve high mass resolution [17]. For electrons, the reflector electrodes are adjusted from outside to be symmetrically located around the electron beam and used for additional focussing. The electron detector is then located further away along the tube. The electron detector in the focal plane of the analyzer is normally an extended 6 cm long multichannel plate detector. It can be replaced by a Mott scattering detector (with an accelerating voltage of 20 kV) to record the polarization of the electrons [18]. The intensity is then reduced by a factor of 1000. This alternative is shown in the figure. Opposite to the laser beam entrance in the sample house there is a four-component UV polarizer which induces photoelectrons either in the molecular beam or in a gas cell. This polarizer can also be attached to the big instrument because of the adopted modular design concept. By rotating the polarizer around its axis the electric vector of the photons can be automatically turned around. There are four further directions available for excitation or spectral studies around the sample house, one being e.g. an Auger electron gun, another an ion gun. A third flange can be used for optical fluorescence spectroscopy and a fourth for high intensity UV excitation close to the magic angle. The system is flexible enough to enable other types of experiments to be performed. For gas or molecular beam experiments the top of the sample house is used for a pulsed gas nozzle inlet or gas cell introduction. For surface studies this space is available for an additional chamber including LEED etc. plus a sample manipulator. The main pump which accepts the molecular beam is a 1500, cryopump. An alternative to the above described experimental arrangement is shown in Fig. 8.24, this time as a horizontal section. Here the instrument has been combined with a conveniently sized version of the previously described X-ray generator and monochromator or an external radiation source, such as synchrotron radiation. Again there are several alternative ports available for diﬀerent sources of excitation and sample introduction.

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Fig. 8.23 Side view of the second and smaller instrument. In this section one notices the analyzer with its lens system and a two-stage electron monochromator on the other side. At the back side of the analyzer an ion reflector is mounted for TOF mass spectrometry. It can be used also for TOF electron spectroscopy without the reflector. The laser beam is directed normally to the plane of the figure, crossing the molecular beam coming from a pulsed gas nozzle on top of the sample chamber. A UV polarizes is situated on the back side of the chamber along the direction of the laser beam

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Fig. 8.24 Top view of the instrument shown in Fig. 8.23. This is an alternative mounting, where the same analyzer as in the previous figure is turned 90◦ to be in the horizontal plane. It can then be provided with a rotating anode and monochromator (RAMON). The UV polarizer is shown in this section

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4. Surface and Interface Shifts In some cases the electron binding energy diﬀerence between the surface and bulk is suﬃciently big so that, at high resolution, one obtains, for each level, two separate lines. Such shifts are not due to ordinary chemical shifts, e.g. due to oxidation as in Fig. 8.9, but to the fact that the uppermost surface atoms do not have any neighbour atoms at the vacuum side, whereas the bulk atoms have neighbours on both sides. In the example given in Fig. 8.25 [19] the surface-bulk shift for Yb metal is An application of this phenomenon can be found in the study of the diﬀusion of a surface layer into the bulk of a substrate. Fig. 8.26 shows how this diﬀusion can be followed as a function of time in the case of a surface layer of gold being deposited on a bulk substrate of Zn, Cd and In [20]. The upper curves show the well-known gold doublet discussed before in Fig. 8.6. After a while the intensities of these lines decrease and two new lines appear somewhat shifted relative to the original ones. Finally, the original lines have disappeared and left room for a shifted doublet. The gold atoms are now situated in the bulk of the substrate metal. As we shall see it is possible to reach interfaces slightly below the surface layer of a compound for inspection. In the cases when the top layer of interest consists of only a few atomic layers one can use the very soft X-radiation which can be

Fig. 8.25 Core level shifts between surface and bulk of the 4 f levels in ytterbium at 300 K excited at hν = 40.81 eV

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Fig. 8.26 Diﬀusion of evaporated Au into Zn, Cd and In as a function of time

conveniently handled and monochromatized by optical gratings (say < 500 eV). In the more general case, when also the bulk composition is of interest, one example being an interface which is situated somewhat deeper in the bulk (> 10Å), one should use harder X-radiation in order to increase the mean free path of the produced photoelectrons. This is a normal situation in practice and is usually encountered in semi-conductor investigations and studies of layered compounds. The relative surface sensitivity is then reduced but instead the depth sensitivity is increased. Alternatively, one has to remove by various means (e.g. ion bombardment) successively the outer atomic layers in order to reach the material in the bulk, e.g. an interface. This is a commonly used procedure but is also well known to present some problems which can cause interpretational complications. From this point of view it is useful to have access to harder, well monochromatized X-radiation (> 1.5 keV) which was discussed in the previous section and to make use of the sample “tilting” method for depth composition scanning. The experimental accuracy in the determination of electron peak positions have gradually improved to such an extent that the binding energies that can be extracted from electron spectra often can be given with errors in the 0.1 eV range and even less for metals and much less (1 meV) for gases. It is then of importance to carefully consider problems related to the choice of reference levels to connect electron spectroscopic data with other data. Core electron binding energies for a metal are measured relative to the Fermi level. In order to relate this binding energy to that referred to the vacuum level of the free atoms one should add a metallic work function φ. One can also proceed by means of a thermochemical approach. One then assumes a complete screening of the positive hole left behind in the metal lattice at the photoelectron emission due to the good mobility of the conduction electrons. This is a generally accepted assumption in electron spectroscopy to treat the relaxation

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in metals. The ‘equivalent core’ model is extensively used. It states that the core ionized atom is treated as an impurity atom with nuclear charge Z + 1. With these assumptions a Born-Haber cycle can be performed in accordance to a treatment by B. Johansson and N. Mårtensson [20]–[26]. One then connects the binding energy shift ΔEC to macroscopically measurable quantities like the cohesive energies and solution energies in metals. ΔEC is the shift between the metal core level referred to M and the corresponding free atom referred to the vacuum level the Fermi level EC,F ECA according to (see Fig. 8.27): M ΔEC = ECA − EC,F

(1)

The Born-Haber cycle gives the relation imp

(Z) Z+1 Z+1 + Ecoh − Ecoh − EZ+1 (Z) ΔEC = I(Z)

(2)

Here M denotes the metal, A the atom, C the core, F the Fermi level, z the atomic number and I the appropriate valence ionization energy (usually the first ionization imp energy). Ecoh is the cohesive energy and EZ+1 (Z) is the solution energy of the impurity atom (Z + 1) in (Z) metal. The dominating contributions to the shifts are the diﬀerence in cohesive energy between the (Z + 1) and Z metal and the ionization energy of the (Z + 1) atom. The same treatment as for metallic bulk can also be applied to surface core-level shifts. The surface atoms experience a diﬀerent potential compared to the layers below because of the lower coordination number. This results in somewhat diﬀerent

Fig. 8.27 The Born-Haber cycle for a metal connecting the binding energy shift between a metal core level referred to the Fermi level and the corresponding free atom referred to the vacuum level

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core level binding energies. One can extend the previous Born-Haber cycle model to account for the surface-bulk core level shift. Empirically, the surface cohesive energy is approximately 80% of the bulk value. The result is then:

imp Z+1 Z ΔECS,B = ECsurf − ECbulk = 0.2 Ecoh − Ecoh − EZ+1 (Z) (3) This equation obviously relates the surface chemical shift and the heat of surface segregation of a (Z + 1) substitutional impurity in the Z metal. In a recent investigation performed by N. Mårtensson et al. [27] a quantitative study of metal-metal adhesion and interface segregation energies by means of electron spectroscopy was made. They were able to study layer dependent core level shifts for Yb epitaxially grown on Mo(110) for the first three layers. They used the surface sensitive 100 eV radiation from the MAX synchrotron. Well resolved Yb 4f lines could be recorded simultaneously for the interface layer between Yb/Mo, for the nearest bulk Yb and for the free Yb surface according to Fig. 8.28.

Fig. 8.28 Yb 4f electron spectra for 2, 3 and 4 monolayers of Yb deposited on Mo(110). Excitation at hν = 100 eV synchrotron radiation

These measured shifts provide new quantitative information on the energetics of adhesion and interface segregation which would be very diﬃcult to obtain by other means. When making similar assumptions as above concerning screening etc. one arrives to an expression for the shift between the interface and the surface which reflects the eﬀect of a free Yb surface when a Mo surface is adhered to it. This shift is denoted the “adhesion” shift ΔEBAdh . The shift between the interface and the bulk is denoted similarly the “interface” ΔEBInt . One finds that Z∗,M Z,M ΔEBAdh = εAdh − εAdh

(4)

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i.e. the adhesion shift is the diﬀerence in adhesion energy/atom of Z and Z* to the substrate. The appropriate quantitative comparison between experiment and theoretical treatment is performed in the above quoted paper. Using eq. (4) an adhesion energy diﬀerence of 1.15 eV/Yb atom is obtained which should be compared to the measured shift ΔEBAdh = 1.19 eV. The fact that at high resolution the various shifts between the surface layer, the bulk and the interface layer can be observed so distinctly as in Fig. 8.28 is gratifying. Hopefully, the techniques may be applicable over other areas of the Periodic System even when the shifts are smaller. A necessary condition for this is that the required high spectral resolution can be achieved. A further interesting illustration of this quality is a recent finding by A. Nilsson and N. Mårtensson [28]. A closer inspection of the line forms (and also positions) at high resolution (AlKα, Δhν = 0.2 eV) of adsorbates reveals temperature dependent vibrational eﬀects which can be correlated to the actual sites of the adsorbed molecules in the substrate surface. They observe extra line broadenings on the “wrong” sides of the core lines (i.e. on the high energy side) of oxygen and carbon, when CO is adsorbed on a clean N(100) surface. This phenomenon corresponds to hot bands in W excited free molecules and is consequently temperature dependent. The magnitude of this broadening can be explained as due to strongly site dependent vibrational eﬀects which are coupled to the final state energies of the adsorbate through vertical transitions at the ionization. Other possible eﬀects for line broadenings have previously been discussed as results of soft electron-hole pairs emission within a 2π*-derived resonance at the sudden perturbation of the core hole. The eﬀects observed by Nilsson and Mårtensson seem to be of a diﬀerent origin and if so could have interesting implications not only for detailed surface studies by means of photoelectron spectroscopy but also for other surface methods like NEXAFS and photon induced desorption. Recently, a new and faster alternative to the conventional all semiconductor npn transistor has been proposed. This substitutes a very thin layer of metal for the base of a standard transistor, thereby strongly reducing the transit time for electrons from collector to emitter. For such an optimized SMS transistor the theoretical cutoﬀ frequency could be as high as 30 GHz instead of 4 GHz for a GaAs transistor. This SMS transistor consists of a thin layer of cobalt disilicide sandwiched between two thicker layers of silicon, serving as emitter and collector enclosing the CoSi2 base. Another possible choice is to use a platinum silicide. Previously the metal-GaAs interface has been studied by electron spectroscopy [29]–[32] with the localized core levels used to trace the band bending of the valence band at the interface. For a silicon-suicide interface, however, the problem presented is more diﬃcult because the metal phase itself, which is the platinum suicide, contains silicon that has to be distinguished from the semiconductor silicon. A high resolution is then necessary. In an investigation in our laboratory [33] this problem was studied at a resolution of the monochromatized AlKα line (1487 eV) of ca 0.23 eV. It was then possible to resolve the semiconductor Si2p3/2 core line from the silicide Si2p lines of the Si-Pt suicide sample. In this way a direct determination of the Schottky barrier could be made. At this resolution the electron spectrum revealed that the suicide consisted

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of two chemically diﬀerent forms, namely PtSi and PtSi2 . The spectra showed that on top of the silicide there was a layer of mixed silicon oxides. It was also found that this oxidation took place more easily than for clean Si surfaces, indicating that the presence of metal atoms in the underlying suicide layer might have a certain catalytic promoting influence on the oxidation of silicon. The ESCA shifts can to a first approximation be interpreted as corresponding to the potential shift connected with the rearrangement of the valence electron density. In this way one can by means of ESCA trace the potential distribution that causes the Schottky barrier for a particular metal-semiconductor interface and one can actually measure its value, which in this case was found to be 0.82 ± 0.05 eV. This fits neatly to what has been found by others for PtSi-Si junctions with other methods. The principle of the measurement of the Schottky barrier is illustrated by Fig. 8.29. The barrier height φB is obtained by subtracting the distance between the Fermi level and the silicon valence band from the band gap. From the figure, φB = Eg − EBINT (Si2p) − ΔE

(5)

From an experimental point of view it is necessary that the suicide film is thin enough and that the excitation radiation is hard enough so that the Si bulk line is still observed. The energy resolution at the required fairly high photon energies din this case 1487 eV) is suﬃciently high to resolve the Si bulk line from the other Si2p lines and to allow the observation of the sharp Fermi edge.

Fig. 8.29 Principle of ESCA measurement of a Schottky barrier φB . The abbreviation v.b. is for valence band; subscripts F, b and g are for Fermi, bulk and gap, respectively; superscript int is for interface

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As emphasized above in surface science not only the top layer but also the composition and the chemical bonds between atoms close to and below the top surface layer are of importance. When some element has a concentration profile within the electron escape depth, i.e. when there are surface layers of diﬀerent composition with a thickness less than the escape depth, the peak amplitude of that element shows a dependence of the exit angle. The surface concentration profile, in accordance with the previous example can then be investigated. Another such a study which was of medical interest dealt with blood-compatible surfaces [34], [35]. The systems studied were colloidal heparin, or dextran sulphate stabilized with hexadecyl ammonium chloride, deposited onto steel substrates, and chemically related substances. By using the mentioned angular dependence (tilting) techniques, it was found that the intensity ratio for the S2p peaks from disulfide and sulphate exhibit angular dependence for albumin-covered heparin-glutar and dextran sulphate-glutar surfaces. This indicate that the disulfide groups are positioned closer to the external surface than the sulphate groups. In a series of experiments on a similar problem cationic polyethyleneimine was adsorbed on sulphated polyethylene surfaces at diﬀerent pH, varying from 4.0 to 9.0. From the angular dependence of the amine:protonated amine peak ratio (see Fig. 8.30) it was possible to conclude that there was an accumulation of charged

Fig. 8.30 Angular dependence of a surface layer of amino-protonated-amine and the resulting surface construction

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amine groups towards the sulphate surface at high pH. The angular dependence of the intensity ratio N/N+ (neutral amine:protonated amine) furthermore showed that adsorption at pH 4.0 gave a higher relative amount of charged groups and that this amount was independent of the exit angle. Adsorption at pH 9.0 gave a relatively larger amount of neutral amine groups and a N/N+ ratio that was dependent on the exit angle. A straightforward interpretation of these results is that the configuration of PEI when adsorbed at pH 4 is essentially flat on the surface while adsorption at pH 9.0 gives a ‘layered’ configuration with the charged groups (N+ ) closer to the sulphated surface and the neutral groups further out according to the right part of Fig. 8.30. The fact that the number of charged amino groups remains constant leads to the conclusion that the adsorption could be considered as an ion exchange reaction. The results also imply that polymer surfaces with diﬀerent densities of sulphate groups would adsorb diﬀerent amounts of PEI. So it would be possible to make polymer surfaces with diﬀerent densities of amine groups not only by adsorption at diﬀerent pH but also by varying the sulphate group density. Core-level binding-energy shifts at surfaces and in solids have been reviewed by W.F. Egelhoﬀ Jr. [36].

5. Studies of Gases by Monochromatic X-radiation Electron spectra of gaseous molecules are favourable to study at good resolution since the usually occurring additional solid state broadenings in bulk matter is absent. Furthermore, the energy calibration procedure is simplified by the possibilities of mixing the sample gas with conveniently chosen standard calibration gases. Fig. 8.31 is an example of how this is performed [37]. It is an aromatic molecule with a fluorine and an amino group attached to the benzene ring in para position, para-aminofluorobenzene. In order to study the chemical shifts in this compound CF4 , N2 and CO2 were mixed with the sample gas. In the spectrum one can determine the chemical shifts accurately. Even the diﬀerent carbons in the benzene ring can be distinguished, namely those which are neighbours to the substitutes. As an example of an electron spectrum of a gaseous phase and how it changes at condensation we take mercury [13]. If a droplet is introduced into the electron spectrometer the vapour pressure at room temperature, ca 10−3 torr, is suﬃcient to produce a spectrum. This is shown in Fig. 8.32. All levels in the Hg atom which can be reached by the AlKα radiation are recorded. The line widths in the spectrum are the inherent atomic widths. Many of the lines are followed by more or less observable satellites. These are due to “shake-up” phenomena during the photoelectron emission process [38] or to inelastic scattering of electrons. A typical example is given in Fig. 8.33 for two of the main lines in the mercury spectrum [13]. Close to zero binding energy one observes a group of lines denoted by OIV , OV , PI . Fig. 8.34 shows an enlargement of this group, in the gaseous phase (upper fig-

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Fig. 8.31 The core electron spectrum of gaseous para-aminofluorobenzene. CF4 , N2 and CO2 have been used as calibration gases mixed with the gas sample under study

Fig. 8.32 Electron spectrum of Hg vapour by means of AlKα excitation

ure) and when the Hg vapour has been condensed on a “cold finger”. One observes a broadening of the lines in the condensed phase. This is due to the “solid state broadening” caused by the mutual influence of the closely spaced atoms. A particularly dramatic eﬀect is observed for the PI (or 6s) level which experiences a continu-

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Fig. 8.33 Shake-up spectrum of Hg NVI , NVII . The first few lines are due to inelastic scattering (pressure dependent) in the mercury gas. Remaining lines are due to the internal excitation of the mercury ion (shake-up) . Lower figure shows the same part of the spectrum after condensation

ous spreading with a well defined edge on the high energy side. This is the Fermi edge of the conduction band of mercury which consequently is due to the seemingly unimportant atomic PI line in the gas phase spectrum.

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Fig. 8.34 The eﬀect of condensation on electron lines close to zero binding energies. Upper spectrum from Hg vapour, lower spectrum from solid Hg

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6. Conduction and Valence Bands The previous example directs our attention to the valence region. This can be studied at diﬀerent excitation energies. It is usually advisable to use fairly high excitation energy to avoid possible mixing with states close to the band edge. At suﬃciently high excitation energy the shape of the band electron spectrum starts to converge. At low excitation energies the shapes reflect interesting phenomena which are indeed important. There exists a lot of information from such studies [39]–[42] but we will not discuss these here. We will only give some typical examples of bands obtained at high excitation energy, namely with AlKα at 1487 eV (Δhν = 0.2 eV. Fig. 8.35 shows the conduction band of gold taken at high resolution and Fig. 8.36 the corresponding band of silver. Both show characteristic structures which reasonably well can be reproduced by density of states calculations. Electron spectroscopy has been applied also to alloys, semiconductors and insulators. Fig. 8.37 is an example of the conduction bands of palladium and copper and their alloys at diﬀerent compositions [13], [43]. One observes the shifts of the core levels at alloying and also changes in level widths and line asymmetries. The conduction band gradually changes from one pure metal to the other. The valence spectrum of the diﬀerent uranium oxides UO2 , UO3 , U3 O8 and uranium + UO2 are shown in Fig. 8.38. They are examples of semiconductors and insulators and exhibit quite diﬀerent spectra [44]. Empty bands can be studied by the techniques mainly developed by V. Dose. One then makes use of the reverse photoelectron eﬀect, i.e. an impinging electron beam is varied in energy until photons of a certain energy is appearing in a detector. We refer here to recent accounts due to V. Dose [45], N.V. Smith [39] and F.J. Himpsel [46].

7. Excitation of Gases with UV Radiation It is particularly advantageous to use VUV radiation from rare gas discharge lamps which contain a large number of sharp and intense UV lines for excitation of electron spectra from the valence regions of molecules [47]. Fig. 8.39 shows the valence electron spectrum of CO2 [42], [43]. One can notice the vibrational structure of the molecular ion. In favourable cases even the rotational fine structures are visible. In order to observe such finer details one has to go to the very limit of resolution. This limit is set by several independent factors, both due to the lamp conditions and the sample gas itself. In the lamp the most important contributions are due to Doppler broadening, self-reversal and self-absorption. The lamp gas and the interior of the lamp has to be very clean. It is advantageous if a discharge can be maintained at very low gas pressures, for example by means of a magnetically confined microwave discharge tuned to the electron cyclotron resonance condition. In the sample gas the main contributions come from the space charge caused by the produced

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Fig. 8.35 The conduction electron band of gold. Monochromatic AlKα excitation (Δhν = 0.2 eV)

Fig. 8.36 The conduction electron band of silver. Monochromatic AlKα excitation (Δhν = 0.2 eV)

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Fig. 8.37 Cu2p3/2 and Pd3d5/2 and the conduction bands for the pure metals and for diﬀerent compositions of these alloys. The Pd core lines are asymmetric due to excitation of electron-hole pairs in the conduction band. The Cu core lines are almost symmetric. The conduction bands as well as the core lines are changing at alloying

Fig. 8.38 The valence electron spectra of the uranium oxides UO2 , UO3 , U3 O8 uranium + U02 . Monochromatic AlKα excitation

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Fig. 8.39 HeI at 21.2182 eV (and NeI) excited valence electron spectrum of CO2

ions and furthermore from external electric gradients over the sample. Rotational fine structures usually result in unresolved line envelopes. The space charge eﬀect is a main obstacle particularly in the case of pulsed laser excitation but also in other cases and special schemes have to be used to minimize these eﬀects. The spectrometer resolution itself is naturally a further limiting factor. Presently, the resolution for UV excitation is normally not much better than 10 meV but can be improved to around 5 meV. Fig. 8.40 shows an example of the latter case for argon when NeI has been used for excitation [15]. It is likely that this limit can be improved further by using supersonic jet beams, better light sources, precautions as to the sample conditions and the surroundings etc. Fig. 8.41 shows the HeI excited valence electron spectrum of H2 O vapour [13]. The resolution in this case was enough to distinguish isotopic diﬀerences between H and D and O16 and O18 . Also rotational structures can be observed in this and some other cases. Fig. 8.42 shows the spectrum of benzene excited by HeI radiation [37]. An expanded, high resolution study of the last band 1e1g , around 9.5 eV is shown in Fig. 8.43. It is a challenge for future to try to resolve such structures which are presently dominating features in UV excited photoelectron spectroscopy. Improved spectroscopical techniques are required. Finally we show the influence of the energy of the exciting radiation on the appearance of the valence orbital spectrum [37]. Fig. 8.44 is the complete valence spectrum of SF6 excited by AlKα (Δhν = 0.2 eV) (upper spectrum). The middle spectrum shows the region 15–28 eV excited by HeII at 40.8 eV. The lower spectrum the region 15–21 eV excited b HeI at 21.22 eV. One observes the large variations of

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Fig. 8.40 3p doublet electron lines from Ar gas excited by NeI (hν = 16.8483 and 16.6710 eV). To the right: Light source and spectrometer adjusted for max resolving power of 5.7 meV

the relative electron line intensities when the energy of the exciting radiation is varied. In particular the 1t1g electron line experiences a large increase in intensity going from AlKα to HeII excitation and then a remarkable decrease in intensity going from HeII to HeI excitation. A general rule found in experimental studies of spectra excited by AlKα on one hand and W on the other is that the former (harder radiation) enhances s-like molecular orbitals, whereas the latter (softer) p-like orbitals. These wavelengths dependent intensity rules can be quantified and are applicable over quite extended energy regions.

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Fig. 8.41 The electron bands of D2 16 O, H2 16 O and H2 18 O, corresponding to ionization in the 1b1 and 2a1 orbitals. For the 2 A1 state a vibrational progression of the ν2 bending mode consists of 20 members. The diﬀerence between H2 and D2 is obvious. Also, there is a small but measurable diﬀerence between O16 and O18

Fig. 8.42 Valence electron spectrum of benzene, excited by HeI. Scan spectrum

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Fig. 8.43 High resolution spectrum of the outermost orbital 1e1g electron lines in benzene. Observe the recorded detailed structures compared to the corresponding scan spectrum in Fig. 8.42. A challenge for future to resolve this structure further

Fig. 8.44 The valence electron spectrum of sulphur hexafluoride excited by AlKα at 1486.7 eV (Δhν = 0.2 eV) , HeII at 40.814 eV and HeI at 21.218 eV, respectively. Observe the large variations of the relative intensities, in particular the 1t1g line, showing a resonance

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8. Vibrational Fine Structures in Core Electron and X-ray Emission Lines The importance of monochromatization of the exciting radiation and resolution in core electron spectroscopy is further exemplified in Fig. 8.45 and Fig. 8.46. They show the C1s line in CH4 at modest and high (monochromatized radiation) resolution [15], respectively. The slightly asymmetric is line in the first figure splits up at high resolution into three (actually a fourth line can also be seen) well resolved lines. This splitting is caused by the vibration produced when a core electron of the centrally located carbon atom is emitted. The new equilibrium corresponds to a shrinkage of about 0.05 Å, and the Franck-Condon transitions which take place then give rise to the observed vibrational fine structure with intensities given by the Franck-Condon factors. The existence of vibrational fine structures as a result of electron emission from molecules initiated a series of experiments in our laboratory in 1971 to look for similar eﬀects in ultrasoft X-ray emission [48]. For this purpose a specially designed grazing incidence spectrometer with electron excitation in a diﬀerentially pumped gas cell was constructed. The first observation of this vibrational fine structures in X-ray emission spectra for free molecules was found for nitrogen gas [49]. Fig. 8.47 and Fig. 8.48 show a photographic recording and a photometer diagram of this phenomenon. Similar investigations were undertaken for a number of other small molecules. Fig. 8.49 can illustrate this in the above mentioned case of CO2 [50]. An analysis can be performed assuming diﬀerent atomic distances and the best fit to experimental data yields the new equilibrium for the ion in question. More recently this field has been much developed by J. Nordgren et al. with applications also in new areas of research [51, 52].

Fig. 8.45 C1s of gaseous CH4 with monochromatization of the AlKα at moderate spectral resolution. The core line is observed to be slightly asymmetric

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Fig. 8.46 C1s of gaseous CH4 with monochromatized (Δhν = 0.2 eV) AlKα-radiation and at high spectral resolution. The line is split up in core vibrational components which now can be subject to a more detailed deconvolution procedure using simultaneously recorded Ar lines as “window curves”

Fig. 8.47 X-ray emission spectrum of nitrogen gas, showing vibrational structures from resolved valence orbitals

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Fig. 8.48 Photometer curve for the nitrogen X-ray spectrum with calculated line profiles

Fig. 8.49 Vibrational structure of the CK X-ray of CO2

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9. Angular Distributions The angular distribution of photoelectrons from free molecules or from surfaces are of importance, since these data give information on the symmetry properties of valence orbitals and, in the case of surfaces, on the geometrical arrangements of adsorbed molecules on the crystal substrates. Fig. 8.50 shows the principle of such an experiment when linearly polarized UV radiation, for example HeI at 21.21 eV, is used for the excitation of the photoelectrons. Photoelectrons from an nσ orbital can according to selection rules result in επ or εσ final orbitals. If the photons are directed along the axis of the CO molecule, taken as an example, only the επ alternative is possible. Turning the plane polarized electric vector of the photon beam around and recalling that the επ orbital has a maximum along the electric vector and a nodal plane perpendicular to this direction one should be able to record a zero amplitude in the photoelectron intensity when the electric vector is perpendicular to the emission direction towards the slit of the electron spectrometer. From such an experiment one can conclude that the CO molecule is actually standing up perpendicularly to the surface in this case. Experiments of this kind have in general to be combined with extensive calculations concerning continuum wave functions and deformations of molecular shapes at surfaces (e.g. using cluster calculations). Such calculations are known to be difficult to make (very extended basis sets are required) and presently contain great uncertainties. It is likely that new experimental work done for a suﬃciently large number of test cases can shed new light on the validity of various such calculations and also eventually lead to semiempirical approaches in somewhat more complicated cases than the simple example discussed here. The angular distributions of photoelectrons emitted from free molecules can be studied either by varying the angle between the direction of the incoming photons

Fig. 8.50 Principle for using polarized photons to determine the geometry of adsorbed molecules on a single-crystal surface by the photoelectron intensity dependence

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and the emitted photoelectrons or by using plane polarized light in a fixed geometry and observing the intensity variations of the photoelectrons as a function of the angle between the electric vector of the photon beam and the electron emission direction. This latter scheme is much to be preferred from all points of view provided that a photon polarizer of suﬃcient intensity and beam quality can be realized [35]. Fig. 8.51 shows the most recent design (combined with a UV lamp excited by mi-

Fig. 8.51 Ultraviolet monochromator with several toroidal gratings covering the energy range 10 eV < hν < 51 eV. Alternatively, the UV radiation is polarized by four succeeding mirrors one of which being a toroidal mirror for focussing, one a plane grating and the other two plane mirrors. The polarizer is automatically turned around its axis, thereby stepwise changing the direction of the electric vector

crowaves) from my laboratory which follows up our previous experience. The new design was briefly mentioned in connection with Fig. 8.24. It consists of four optical elements in the following sequence: one plane mirror, one further plane mirror, one plane grating, one toroidal mirror. This device can be automatically rotated around its axis in a programmed fashion by a step motor. The focussing in the toroidal mirror compensates for the reflection losses, and also makes it possible to use a large distance between the light source, polarizer and sample without sacrificing intensity. It is important to minimize the contamination of the reflecting elements, which otherwise makes the polarization to decrease with time. By means of a set of gratings, suitable photon energies can be selected, using diﬀerent gases in the light source (H2 , He, Ne, Ar, Kr). The photon energy region 10–51 eV can then be covered in small steps. Some examples illustrate the situation for free molecules. For plane- polarized radiation, the intensity distribution of the photoelectrons is given by

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˜ 2 Πu in CO2 Fig. 8.52 A β parameter (anisotropy) spectrum of a vibrational sequence of A

I(θ) = Io (1 + β/4(3P cos2θ + 1))

(6)

where P is the degree of polarization. The “asymmetry” parameter β can then be calculated from the measured photoelectron intensity parallel and perpendicular to the plane of polarization according to β = 4 I|| − I⊥ / I|| (3P − 1) + I⊥(3P + 1)

(7)

The good intensity of the polarized radiation makes it possible and meaningful to calculate the asymmetry parameter S point by point, to generate a “β parameter spectrum” (βPS). Fig. 8.52 is a typical βPS showing part of a vibrational sequence ˜ 2 Πu in CO2 [53]. of A or CO2 , the β parameter was measured for some 40 vibrational states, several of which had not been observed earlier as ordinary photoelectron lines. The βPS ˜ 2 Πg is shown in Fig. 8.53. The prominent β peak at corresponding to the state X 13.97 eV was found to correspond to the excitation of a single quantum of the antisymmetric stretching mode. In the ordinary spectrum, this line is barely visible s a shoulder on a much more intense peak but can be observed here because of its diﬀerent β value. This excitation is normally forbidden in photoelectron spectra, but ˜ 2 Πu . The large it can attain measurable intensity through interaction with the state A ˜ diﬀerence n β-value between this line and the allowed lines in the X-state is characteristic for peaks that get an enhanced intensity through interaction with another state. The β-value in such cases tends to come closer to that of the perturbing state than to the state to which it belongs. ˜ 2 Πg state in the CS+ was investigated by means of a number of photon The X 2 lines between the H Lyα (10.20 eV) and HeIIa (40.8 eV). Besides he more often used lines from NeI (16.84 eV), HeIa and NeII (26.91 V) a number of lines from

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˜ 2 Πg n CO2 around a β peak at 13.97 eV. Fig. 8.53 Parameter spectrum corresponding to the state X The enhanced β slue is due to an interaction with the state 2 Πu

discharges in Ar, Kr and Xe were used in the energy region 10.5–13.5 eV. Very rapid oscillations in the β value for the adiabatic transition were observed for kinetic energies of the photoelectron < 4 eV. At the same time the intensity of the vibrational excitation varied. Both these phenomena have to be explained by assuming that the ionization occurs at certain photon energies via autoionizing states. In inelastic scattering events (for example in CS2 ) one can distinguish between longlived intermediate scattering states, which result in a change from non-zero β to zero β and shortlived intermediate scattering states keeping a non-zero β after scattering [54]. The energy dependence of β close to the threshold for photoionization shows considerable fluctuations. This was studied in some detail for Ar, Kr and Xe. For Kr a deep dip in β for Kr 4p3/2 occurred at a photoelectron energy of 581 meV. The βPS could be followed down to a photoelectron energy of 15 meV. Such fluctuations can be ascribed to resonances with series of autoionizing states. When Xe is excited by means of UV radiation from a discharge in N2 one can study the β parameter spectrum close to the ionization threshold, in particular in the region between the thresholds for ionization of the p3/2 and p1/2 states. There is a suﬃciently large number of closely spaced UV lines from N2 in the discharge available for ionization of Xe at all photon energies of interest. As can be seen in Fig. 8.54 the photoelectron spectrum taken parallel to and perpendicular to the electric vector of the N2 photon beam both reflect the complicated structure of the exciting photon spectrum coming from N2 in the discharge source, ‘scanned’ by the p level of Xe in the photoelectron spectrometer. However, from the ratio of the intensities at each photoelectron energy the β parameter spectrum of Xe can be derived, as shown in the upper part of the figure. This β PS contains an interesting sequence of minima, consisting of a converging series of resonances. This can be understood in terms of a series of autoionizing states in Xe, which converges towards the p1/2 ionization limit. The figure also shows that the β parameter can be measured down to a few meV above the ionization threshold.

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Fig. 8.54 Parameter spectrum of Xe in the region between the threshold for ionization of the p3/2 and p1/2 states with the use of N2 in the light source

In conclusion one may expect an expanding area of research related to the angular dependence of photoelectrons as a function of energy both close to threshold and at higher energies by means of polarized V light either from UV lamps or tunable synchrotron radiation, polarized tunable and laser light and the possibilities of using a Mott detector for the measurements of the emitted photoelectrons spin directions contribute to the interesting developments in this field [56], [57].

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10. ESCA Diﬀraction The angular distributions of photoelectrons from core levels by using photons in the X-ray region (e.g. AlKα or synchrotron radiation) are manifested in the ESCA diﬀraction patterns. These studies can be made either by recording the angular distributions at a fix X-ray energy (e.g. AlKα) or at a fixed angle and varying the wavelength of the radiation. This latter procedure requires access to the variable synchrotron radiation. Fig. 8.55 shows an early example of an ESCA diﬀraction pattern from a NaCl single crystal [58]. In this experiment, we noted that core and valence levels in a selected element of a crystal could be studied separately and the corresponding diﬀraction pattern be recorded. This was also demonstrated for the Auger electron diﬀraction.

Fig. 8.55 ESCA diﬀraction for a NaCl single crystal: (a) Cl2p3/2 , Ekin =1055 eV; (b) NaKLL(1 D2 ), Ekin =990 eV

A number of such studies are now available from several laboratories in which both the polar and the azimuthal angles have been carefully scanned. It has also been found that it is feasible to apply the method to (epitaxially) adsorbed surface species, in which case one gets structural and geometrical information of the adsorbed species related to the sastrate lattice [59], [60]. A dominating contribution to the observed patterns is caused by interference through scattering along principal crystal axes. When applied to adsorbed species,

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e.g. CO on a Ni(001) surface, this constructive interference occurs along the array of atoms. If there are many atoms in the row the first atomic scattering can enhance and focus the intensity but subsequent atoms in the row may deenhance the intensity. The diﬀraction pattern then saturates when the adsorbed layer is about 3 ML [61], [62], [63], [64]. Since the photoelectron or the Auger electron line is specific for each element and even for its chemical bonding it is obvious that one is dealing with a new convenient surface diﬀraction method. Another advantage is that for the energies concerned, say around 500 eV, it turns out that simple single scattering cluster (SSC) theory is suﬃcient (even for lower energies). The theoretical treatment is similar to the extended X-ray absorption fine structure (EXAFS). Improvements of this simple model have been made based on spherical wave scattering. In order to make full use of the experimental situation one should arrange for a good angular resolution (< 2◦ ) [65]. Under these circumstances it seems possible to reach structural information with a resolution of perhaps ±0.1 Å. Using SSC calculations with plane wave (PW) scattering one can conclude, as an example, that in the case of CO on a Ni surface as discussed before the CO molecules are tilted less than 12◦ from the surface normal. Further improvements in experiments and corrections for multiple scattering may result in better geometrical accuracy. If Cu is grown epitaxially in successive layers on Ni(001) the diﬀraction pattern for the CuLMM line is observed [61], according to Fig. 8.56 which also contains the SSC-PW calculations for comparison. The results for the Cu3p line are similar [66]. The ESCA diﬀraction will be much more used as a surface structure tool when the experimental conditions are improved in the future. As an indication of such improvements Fig. 8.57 demonstrates the sharpening of the diﬀraction pattern for Ni2p3/2 when the angular definition is increased from ±3◦ to ±1.5◦ in the case of Ni(001) [65]. New applications have recently been found in the study of spin-polarized photoelectron diﬀraction [67]. In this case core level multiplet splitting was used to produce internal spin-polarized sources of photoelectrons which subsequently can scatter from arrays of ordered magnetic moments in magnetic materials. According to findings by C.S. Fadley et al, such spin polarized photoelectron diﬀraction provides a new tool for probing short-range magnetic order. Surface structurally informative results have been obtained using synchrotron radiation, in which case the patterns are recorded in the normal direction of the crystal varying the wavelength of the synchrotron radiation. The procedures are described in papers from SSRL (D.A. Shirley et al.) [68], [69] and BESSY (D.P. Woodruﬀ, A.M. Bradshaw et al.) [70], [71]. As a recent example a study of the structure of the formate (CO2 H) species on copper surfaces can be quoted [70]. Fig. 8.58 shows how this species is adsorbed on Cu(100) and (110) surfaces. The results are shown in Fig. 8.59.

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Fig. 8.56 Experimental Cu 2p3d3d Auger line polar diﬀraction scan compared to SSC-PW calculations for successive layers of epitaxial growth of Cu on Ni(001). Similar results are obtained for Cu3p

11. Studies of Liquids and Ionic Solutions Above I have given a few examples of some current electron spectroscopic studies of free molecules (gases) , solids (bulk) and surfaces. The latter state is characterized by so many special features that it deserves the notation as a state of aggregation of its own. The third type of condensed state of aggregation is the liquid state. The application of ESCA on liquids started in my laboratory in 1971. We made an arrangement for a continuous flow of a thin “liquid beam” in front of the slit in the spectrometer. The liquid beam, subject to diﬀerential pumping, was irradiated by X-rays and the resulting spectrum was recorded. Our first study concerned liquid formamide, HOCNH2 . We were able to record both the core spectrum and the valence spectrum [72], [73]. It has been possible to master the experimental problems to record liquid spectra of suﬃciently good quality to enable more reliable conclusions to be drawn. Core line spectra of at least as good quality as previously

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Fig. 8.57 The eﬀect of improved angular resolution on the diﬀraction pattern of the AlKα excited Ni 2p3/2 photoelectron line from Ni(001). Azimuthal scans at θ = 47◦ for an aperture of ±3.0◦ and ±1.5◦ , respectively

obtained for solids can now be produced for a great number of diﬀerent solvents in which chemicals are dissolved. The scope is very wide and most of the applications essentially remain to be done [74]. The experimental problem is to keep the liquid surface fresh all the time in vacuum and to eliminate the influence of the vapour phase. This is accomplished by renewing the liquid in front of the electron spectrometer slit continuously either by a translational or a rotational movement. In the first case one can form the above mentioned liquid beam in the vacuum in front of and along the slit of the spectrometer. Such a liquid beam or a wetted wire is then continuously subject to X-radiation. The vapour phase is diﬀerentially pumped in the same way as gaseous samples are handled. In this way the expelled photo- or Auger electrons from the liquid can pass the gas phase spending only a short distance before they reach the slit and the analyzer. The liquid surface can also be renewed by the continuous rotation of the liquid exposing the renewed surface layer to the X-ray flux. Again, the expelled photoand Auger electrons are passing the gas phase at a short distance to the slit before the electrons are being analyzed at high vacuum. Generally, one obtains two electron lines, a line doublet, for each level, one originating from the liquid phase and the other from the same molecules in the vapour phase. This gives the opportunity to refer the liquid lines to the vacuum level of the free molecules by a suitable calibration procedure in the gas phase. For more com-

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Fig. 8.58 The perpendicular geometry of the formate species on Cu(100) and (110) surfaces

Fig. 8.59 Diﬀraction of O1s and C1s at normal emission from formate on Cu(100) and (110) surfaces. The dashed curve corresponds to results of single scattering plane wave calculations from a Cu atom 2.0 Å behind the emitter. The OCO bond angle is evaluated to be 134◦

plicated structures, e.g. when the structures contain chemical shifts the vapour lines can be removed by a simple trick: A small potential of 10 or 20 V is applied to the metallic substrate of the liquid relative to the first slit. The vapour lines will then be broadened to the extent set by the applied electric field over the vapour volume and will more or less disappear in the continuum whereas the liquid lines which emanate from a well defined potential, will be correspondingly shifted but not broadened. In order to reduce the intensity of the vapour line the exciting radiation should preferably be directed from the side towards the liquid. Very eﬃcient diﬀerential pumping on the gas phase is particularly important for liquids like water solutions with high vapour pressures.

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Fig. 8.60 Liquid spectrum of ethanol; core and valence electron spectrum

Fig. 8.61 Core and Auger electron spectrum of a solution of Na+ I− (5M) in glycol

Fig. 8.60 shows a spectrum of liquid ethanol [75], showing the chemically split C1s line from the ethyl group, the O1s line and the orbital valence electron spectrum of the molecule. Fig. 8.61 shows a core- and Auger electron spectrum of a solution of Na+ I− (5M) in glycol [76]. The shifts of the Na+ lines with respect to the gas phase (solvation shifts) were obtained from separate photoelectron spectroscopical atomic gas phase data combined with calculated atom-ion shifts (using scf techniques). Fig. 8.62 shows the liquid ESCA spectrum of SrBr2 (1M) [77]. The Br− -gas value was likewise obtained from a molecular photoelectron spectroscopical value coupled with a calculated molecule-atom shift and an atom-ion shift. Fig. 8.63 is the ESCA spectrum of HgCl2 (0.2 M) in C2 H5 OH [77]. Observe again the ESCA chemical shift between the two carbon atoms in the ethyl group. As previously discussed electron spectroscopy gives information about the electric charges around atoms, which change the potential at the formation of diﬀerent chemical compounds of a given element. The change of charge at the photoelectron emission of one unit for photoelectron lines and two units at the Auger process is followed by a reorganization of the atomic electrons when the hole state is being

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Fig. 8.62 Liquid spectrum of SrBr2 in glycol (1M)

Fig. 8.63 Liquid spectrum of HgCl2 (0.2M) in ethanol at −85◦ C

formed. This is the origin of the reorganization or relaxation energy. One can show that the diﬀerence in reorganization energies between two compounds can be determined by measuring both the photoelectron energy shifts and the Auger electron energy shifts. The reorganization energy is on the other hand directly related to the solvation energy of a certain ion in a solution. The solvation energy is defined as the energy diﬀerence between charging an ion in vacuum and in the solvent. It is possible to perform Born-Haber cycles to get relationships between solvation energies and measurable quantities from electron spectroscopy on solutions. Since the solvation energy is essentially the energy associated with the reaction of the solvent against a dissolved ion it corresponds to the previously discussed reorganization or relaxation energy. The molecules of a solvent can react twofold

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against a dissolved ion: either by a very fast electronic polarization or by a relatively slower reorientation of their electric dipoles. The reorganization energy which is being measured in the fast ESCA process is the electronic part of the order of 10−15 sec, whereas the dipolar reorientation takes much longer time to be included in the ESCA process. Therefore, the two contributions to the chemically measurable solvation energy can be separated into independent parts. Recent systematic studies by ESCA shows that at low valence states of the ion the two contributions are about equal, whereas at higher valence states the electronic polarization contribution is becoming the more important part. The experimental ESCA studies of liquids can be complemented by model calculations of the solvation shifts of core levels. It is reasonable to assume that solvation binding energies and Auger energy shifts of ion energy levels are to be described by a model that combines the long-range continuum-like behaviour of the solvent with a short-range molecular interaction between the ion and first solvation shell of molecules. In particular, to study the latter part and also to investigate the importance of the long-range interaction, ab initio calculations have been made on Na+ solvated clusters surrounded by an increasing number of molecule [78]. For a proper comparison with experimental data in solution it is desirable to perform calculations up to and including a fully solvated cluster with six solvent molecules. This is practically possible only for water ligands and carefully chosen basis sets. Calculations for other solvent molecules (such as methanol) must then be made for a more limited number of molecules and results extrapolated to full clusters. The main results of the calculations show that the experimental cluster solvation energies for Na+ (H2 O) are reproduced with good accuracy by using a basis set of moderate size including polarization functions of p-type on ligand molecules. The calculated binding and Auger energy solvation shifts for the cluster are smaller by at least 20% compared with experimental values obtained in solution. The discrepancy is substantially larger for the Auger shift. This reflects the importance of long-range electronic polarization in the description of the solvent environment of small cations in solution. This electronic polarization becomes increasingly important for higher charge states of the ion. A cluster model is generally insuﬃcient to reach the values obtained in ionic solutions by electron spectroscopical means. Replacing H2 O as ligand with CH3 OH results in an increase of the binding energy and Auger shifts of ∼20%. This may be explained as an eﬀect of the increasing number of polarizable valence electrons in the cluster. The methanol cluster (with the same number of molecules as the water cluster) can be considered as a structure with more than one solvation shell. Of particular interest is the study of water solutions [79] in which case the high vapour pressure is an experimental obstacle. Fig. 8.64 is the first example showing the liquid and the gas oxygen is lines from water in a saturated LiCi solution. The vapour phase line has been removed in the upper spectrum by applying a small potential on the liquid water backing as discussed above. The valence region is within reach also by means of the He radiation. There have been problems here for liquids for some time with respect to line shapes and signal:background ratio, which so far have complicated the applicability of this ap-

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Fig. 8.64 Spectrum of liquid water at 254 K. The O(1s) water-gas line is removed by applying a potential on the backing of the liquid sample. The remaining O(1s) is from liquid water alone

proach. These experimental problems now seem to have been removed. In a new attempt using HeI radiation on formamlde (which previously [72], [73] was the first spectrum which was recorded with X-ray excitation by means of the above mentioned liquid beam technique) Keller et al. [80] have shown that in addition to X-radiation also UV radiation can produce valence electron spectra of quite good quality (see Fig. 8.65). They furthermore used a beam of thermal metastable He atoms from the same He discharge lamp to excite electron spectra (MIES) at the uppermost surface of the liquid, shown at the bottom of the figure. The upper spectrum was a previously obtained spectrum by means of HeI radiation. From a comparison between their two diﬀerently excited spectra Keller et al, draw additional conclusions about the position of the formamide compound in the surface. An interesting further pathway would now be to try using polarized XUV radiation and perhaps laser radiation for excitation. Auger electron spectra excited by an electron beam also remain to be done and so do electron scattering experiments. The technique of a variable take-oﬀ angle for the emitted electrons which was discussed before (e.g. Fig. 8.9 and Fig. 8.10) can be applied to liquids in order to scan the ionic concentrations as a function of the distance from the surface. This was done in an experiment on the system on (ButN)+4 I− desolved in HCONH2 (0.5 M) [81]. Fig. 8.66 shows the C1s lines for the solvent and solute at two diﬀerent take-oﬀ angles, 10◦ and 55◦ . The full-drawn curves represent the expected line profiles for the bulk concentration relation between the two components (peak area 1:3). As one can see the spectra instead show pronounced surface segregation. The results can be put on a quantitative basis by making some reasonable approximate assumptions an-

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Fig. 8.65 Valence electron spectrum of liquid formamide excited by HeI and by metastable thermal He* impact (MIES). The upper curve is the previously obtained spectrum by HeI

ticipating an exponential decrease of the solute concentration with increasing depth in the solution. The result is shown in Fig. 8.67. One notices the strong change of concentrations over a depth of some 15 Å, being the mean segregation depth in this case.

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Fig. 8.66 C(1s) spectra for two diﬀerent take-oﬀ angles (θ = 55◦ and θ = 10◦ ) for the system (But4 N)+ I− in HCONH2 (0.2M). The full-drawn curves represent in both spectra the profile expected for the bulk concentration relation between the two components (peak area 1:3). The spectra show a very pronounced surface segregation of the solute within the sampling depth of the photoelectrons

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Fig. 8.67 Depth concentration profile in the system (But4 N)+ I− /HCONH2 deduced from the spectra in Fig. 8.66. The profile is based on the assumption of an exponential decrease of the solute concentrations with increasing depth in the solution. The data give a mean segregation depth of 15 Å and a ratio between surface and bulk solute concentration of 3:1

12. New Extensions of Electron Spectroscopy by Means of Laser Excitation More recently the modes of excitation by means of X and UV photons have been complemented by the use of laser radiation. There are two ways to proceed here: The first one is to use various non-linear optical media to achieve frequency doubling or higher harmonics of the laser radiation in order to reach wavelengths far down into the VUV region. These possibilities are getting gradually more promising because of improvements in laser technology. There are now available much more eﬃcient crystals for frequency doubling than before, e.g. the BBO crystal. Furthermore, some gases have turned out to be quite eﬃcient for frequency tripling e.g. Hg, Xe, Kr, Ar and Ne (see Fig. 8.68) [82]. Although the pathway towards higher frequencies can proceed only at a great loss of intensity the starting point with a pulsed laser is so good that the final result after frequency multiplication (tripling or even more) still yields tunable laser intensities decent for excitation of photoelectron spectra in the wavelength region around 1000 Å and even far below. This technique has already been used in some preliminary studies. The number of extremely monochromatic and tunable photons can be in the region of 1010 per pulse. This alternative obviously opens up interesting new possibilities and oﬀers opportunities for very high resolution, both for molecular studies and for band studies, e.g. in the semiconductor field. According to Fig. 8.68 the penetration into the VUV proceeds quite well by using e.g. a mercury cell until one reaches the region ∼105 nm when it is hindered by the cut-oﬀ of the LiF window. Already this extended wavelength region in the VUV is of great interest for optical molecular studies, since this wavelength region has been much less explored than at longer wavelengths. Furthermore the extremely narrow

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bandwidth and the tunability of the laser represents no doubt a new and most powerful tool as a UV monochromator in optical spectroscopy. It can also be used for photoelectron spectroscopy at very high resolution. Fig. 8.69 shows an experimental arrangement due to U. Heinzmann et al. for photoionization yield measurements using a mercury cell for resonant sum- and diﬀerence-frequency mixing [83]. Two tunable lasers are used and the two beams are merged via a dichroic mirror into the mercury cell. The vapour pressure is 1.5 mbar Hg mixed with 4 mbar Ne. The bandwidth is 4.5 · 10−4 nm. A second arrangement due to R. Zare et al. is shown in Fig. 8.70 [84]. In this case the the frequency-doubled dye laser beam is traversing the non linear optical rare gas medium in the form of a jet beam (produced by a pulsed nozzle). In this way windows can be avoided since a strong diﬀerential pumping on this pulsed nozzle chamber can be arranged. One may anticipate that arrangements of these types will be further developed. Already, wavelength regions around 50 nm have provisionally been reached. The photon intensities are quite good in the upper part of this VUV wavelength region even for photoelectron spectroscopy but decreases rapidly towards the lower part of the region. Still, the prospects are good to eventually achieving suﬃcient photon intensities to enable the work with tunable laser photon beams in photoelectron spectroscopy far down in the XUV region as powerful alternatives to the presently available discharge lamps and synchrotron radiation sources. The second way to proceed is to use multiphoton ionization (MPI) or, preferably, resonance enhanced multiphoton ionization (REMPI). These processes are now sufficiently well understood to be applicable in electron spectroscopy. Although the field is new and far from being maturized there exist already a few comprehensive survey articles based on recent developments by e.g. K. Kimura [85] and R. Compton and J. Miller [86]. The experiments are performed by means of pulsed lasers

Fig. 8.68 Spectral regions for frequency tripling in rare gases and in mercury

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Fig. 8.69 Scheme for a tunable laser source for photoionization measurements using a mercury cell for resonant frequency mixing according to U. Heinzman et al

Fig. 8.70 Scheme for frequency tripling by means of a pulsed rare gas jet and diﬀerential pumping according to D. Zare et al

in the optical region. The laser power usually needed is in the region of 106 –1010 watts/cm2 . The best way to proceed is to use two tunable lasers pumped by an excimer or YAG laser. The first laser is tuned to hit a resonance in the molecule (in a supersonic jet beam). The power is adjusted so that few if any events lead to further photon absorption from this laser pulse which would result in photoionization and dissociation in a fairly complicated pattern. The second laser is tuned to ionize the excited

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Fig. 8.71 Multiphoton ionization (MPI) spectrum of jet-cooled chlorobenzene. The ion current is recorded as a function of laser wavelength

molecule in one step. The resulting electron spectrum (around a few eV in extension) is recorded either in a time of flight (TOF) fashion or by means of an ordinary electron spectrometer. Provisions can be made to record also the molecular ion mass spectrum. An early study of the resonance enhanced multiphoton ionization of chlorobenzene was made by R. Zare et al. [87]. In his paper one finds references to some early works by other groups, e.g. Compton and Miller; Meek, Jones and Reilly; Kimman, Kruit and van der Wiel and Achiba, Sato, Shobatake and Kimura etc. Fig. 8.71 shows the ion current as a function of laser wavelength for chlorobenzene as obtained by R. Zare. The procedure is to select one of the resonances and then to record the corresponding photoelectron spectrum. There are several advantages to use this highly controllable method of excitation to get the correct vibrational assignments, which are often diﬃcult to make, using ordinary UV photoelectron spectroscopy. Fig. 8.72 shows some of the recorded photoelectron spectra for chlorobenzene obtained by TOF techniques at diﬀerent laser wavelengths when the laser was tuned to fulfil the conditions for REMPI. For comparison Fig. 8.73 shows the complete HeI excited valence orbital electron spectrum of chlorobenzene [88]. The band near the binding energy 9 eV is shown in more detail in Fig. 8.74. The diﬀerent orbital vibrational modes with their assignments and vibrational energies can be extracted from these data and be compared to the REMPI results. Another case studied by Kimura and Achiba et al. [89] is shown in Fig. 8.75 and Fig. 8.76 and concerns Fe(CO)5 . Fig. 8.75 shows the ion current produced by the laser as a function of wavelength. One can then select any of the peaks and take the associated photoelectron spectrum. Some of these are shown in Fig. 8.76. In order to collect a substantial fraction, ∼50%, of the produced photoelectrons in REMPI a magnetic bottle reflector has been devised [90]. A recent study concerning

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Fig. 8.72 REMPI electron spectra from four selected resonances in chlorobenzene according to Fig. 8.71. Vibrational progressions and energy spacings are listed

(2+1) REMPI photoelectron spectroscopy on Rydberg states of molecular bromine is an illustration of this method [91]. A particularly interesting possibility is oﬀered when the second laser is tuned to produce zero kinetic energy electrons. After a small time delay (a few μsec) the still remaining zero energy electrons are swept out from the production volume by an electric pulse into the electron spectrometer. The collection eﬃciency can approach 100% [92]. In this case the time-of-flight alternative is suitable. For high resolution it is important to produce only a few electron-ion pairs per pulse, otherwise the Coulomb forces will broaden the linewidths. Without this and other precautions the attainable resolution will be equal or worse than for ordinary XUV photoelectron spectroscopy (> 10 meV). The ideal laser arrangement is a high repetition rate and short pulses < 1 nsec, even psec. In favourable cases the electron linewidths in such ionization studies can approach those set by the laser linewidths. The attainable resolution under optimum conditions using zero energy (threshold) photoelectrons can in fact be so much increased that the rotational sublevels of the intermediate resonance level can be studied in detail. This has been achieved by K. M¨uller-Dethlefs

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Fig. 8.73 Valence electron spectrum of chlorobenzene excited by HeI

Fig. 8.74 The 1a2 and 3b1 bands of chlorobenzene with vibrational assignments to be compared to the results in Fig. 8.72

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Fig. 8.75 Ion current as a function of wavelength for Fe(CO)5

Fig. 8.76 Some selected REMPI electron spectra for Fe(CO)5 corresponding to resonances in Fig. 8.75

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Fig. 8.77 Two-colour laser induced zero kinetic energy (ZKE) photoelectron spectra in the (NO+ ) X ← NO A photoionization process. The rotational lines are fully resolved

et al. who report a resolution of ∼ 1 cm−1 (∼ 0.1 meV) in the case of NO [92] and benzene [93]. Fig. 8.77 shows a NO spectrum where rotational components have been completely resolved [94]. A new and very promising development of the above techniques has recently been introduced by E.W. Schlag et al. which is a combined resonance enhanced multiphoton dissociation spectroscopy (RE-MPDS) and multiphoton ionization [95]. This technique has been applied to the benzene cation [96].

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Laser-photoelectron spectroscopy can be arranged in several diﬀerent ways. As an example one variant is to study mass-selected negative cluster ions using the tunable laser for photodetachment. This has been done for negative cluster ions of silicon and germanium in the 3-12-atom range by R.E. Smalley and coworkers [97] with interesting results. J.V. Coe et al. [98] have studied the photoelectron spectra of negative cluster ions NO− (H2 O)n by laser induced photodetachment (n = 1, 2) with 2.54 eV photons. The spectra resemble that of free NO− but are shifted to successively lower electron kinetic energies. Since intermediate levels can be reached in REMPI by two or several photon absorptions such levels can be excited and observed by the following ionization either through the electrons or ions, which are forbidden optical transitions in ordinary fluorescence spectroscopy because of selection rules. Thus a very wide spectroscopical area is now available for study, as an extension to previous optical molecular spectroscopy. The recording of the dissociated molecular fragments by TOF techniques yields further information about molecular dynamics. These latter phenomena have been reviewed by D.A. Gobeli et al. [99] and by U. Boesl [17]. The interplay between the observed ionization and successive fragmentation can be described by and compared to diﬀerent models, one of the most useful being the so called “ladder” model [17]. This model gives a reasonable account for many of the successively observed ions in the mass spectra under laser irradiation. A powerful “soft” ionization laser technique using an ion reflector for energy focussing to record mass spectra even of biomolecules at high resolution (R=10000) and under controlled ionization conditions has been developed by E.W. Schlag and coworkers [100] (see Fig. 8.78). Fig. 8.79 shows a recent example of such spectra. This is a state selective technique with extreme sensitivity in the femtogram class. For surface desorption studies [101] for example it is an ideal tool which no doubt will be widely used in the next future. This scheme has been adopted in the instrument shown in Fig. 8.23. Mo Yang and J. Reilly [102] have proposed a scheme for very high resolution mass spectroscopy of desorbed molecules, e.g. aniline. They compare the diﬀerent conditions when the laser beam is striking the surface directly or is being internally reflected against the surface according to Fig. 8.80. In the first case the desorbed species are ionized in the gaseous phase after desorption, in the second case directly at the well defined surface. The first mass spectrum gets more complicated than the second one. In particular, the second alternative provides a very precisely defined geometry for starting the time of flight measurement. Using the reflector method and picosecond techniques they suggest that it might be possible to achieve higher resolution than before, 105 or perhaps even higher. It is interesting to consider the combination of laser excitation and various simultaneous excitation by other means. Such studies have been performed on sodium atoms under the simultaneous excitation by laser and synchrotron radiation [103]– [105].

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Fig. 8.78 Two-step arrangement for high resolution TOF mass spectroscopy using an ion reflector. Molecular desorption takes place in the first step by an IR laser. The desorbed complete molecules are cooled in the jet beam. They are ionized by the pulsed tunable laser in a ‘soft’ fashion, i.e. at low power. This mode produces pure molecular ions. Gradually the laser intensity is increased to achieve ‘hard’ ionization, producing fragmented molecular ions in a controlled fashion

The experimental arrangement previously shown in Fig. 8.23 and 24, is designed for the purpose of exciting from various directions a molecular beam (or a surface) by two-colour polarized laser radiation in addition with excitations of Auger electron spectra by means of a focussed electron gun, polarized VUV photons of diﬀerent wavelengths from the previously mentioned VUV polarizer. Furthermore, highly monochromatic electrons with variable energy from 1 eV up to 5 keV are produced by the electron monochromator with the electron beam directed to the slit of the electrostatic lens system with the subsequent high resolution electron energy analyzer provided with a multidetector system or a Mott detector for the determination of the electron spin polarization. This electron analyzer is in common for all the diﬀerent modes of excitation. Apart from the separate modes of excitation the arrangement might enable combinations of the diﬀerent excitation sources. For example, energy loss spectra by means of the electron monochromator and the following electron spectrometer can, in principle, be combined with laser excitation or Auger electron spectra studied under simultaneous laser excitation etc. Intensity problems will be encountered due to the reduced detection eﬃciency inherent in such double modes of excitations. Still, such experiments are particularly interesting to consider for the future.

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Fig. 8.79 Comparison of mass spectra of L-tyrosine by diﬀerent method of ionization. a) Electron beam induced mass spectrum. The pure molecular ion peak at m = 181 is quite weak. b) ‘Soft’ laser induced mass spectrum according to the scheme in Fig. 8.78. The pure molecular ion is the only one being formed. c) ‘Partially hard’ laser ionization at λ = 272 nm producing characteristic ion fragments in a controlled fashion. d) Chemical ionization (CI) using methane, corrected for the methane background

Finally, a recent experiment will be briefly discussed here where picosecond double excitation techniques have been applied to study shortlived interface states in the band gap between the valence and the conduction bands in a time resolved fashion due to R. Haight et al. [106]. The laser system provides tunable picosecond pulses by means of a NdYAG laser and an excimer laser according to Fig. 8.81. After passing a KDP crystal the laser pulses are frequency doubled and one “probe” signal is further frequency multiplied by passing a tube filled with one of the noble gases shown in Fig. 8.68. Another laser pulse passes a variable time delay and is reflected colinearly with the probe pulse into the UHV sample chamber. The two picosecond pulses so produced are impinging on a GaAs crystal. According to Fig. 8.82 the first pulse is used as an optical pump to populate the shortlived interface states by electrons from the valence band. Before these states decay, i.e. within the picosecond region, they are ionized into the vacuum by the “probe” XUV pulses with energies up to 13 eV. This results in an electron spectrum which is recorded in a TOF arrangement which is capable of recording also the angular distribution. This and similar schemes are of considerable interest for the future to explore the region of shortlived interface states by means of tunable twophoton ionization.

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Fig. 8.80 UV laser induced surface ionization (anilin) with prisma internal reflexion using TOF mass spectroscopy. a) shows the result when the laser beam is reflected against the surface and b) when it is internally reflected. In the latter case very high mass resolution can be achieved by a TOF arrangement with reflector

The two-photon excited electron emission from semiconductors has been reviewed by J.M. Moison [107].

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Fig. 8.81 Layout for a tunable picosecond laser system, yielding one ‘pump’ signal in the optical region and one ‘probe’ signal, after frequency tripling in a rare gas non linear medium. This signal is tunable up to an energy of 13 eV. This system oﬀers the opportunities to study time resolved photoelectron spectra from laser excited interfaces and surfaces. System due to R. Haight et al

Fig. 8.82 Photoelectron spectroscopy of two-colour picosecond laser excited and ionized interface states (see Fig. 8.81). The short arrow corresponds to optical transitions by the pump pulse. The longer arrows show the photoelectron transitions induced by the XUV probe

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13. Electron Scattering Spectroscopy Electrons of a few keV energy as a primary source of excitation are mostly used to produce Auger electron spectra from surfaces. The scattered electron background is a dominating feature. Because of the very high intensity of electrons available from an electron gun the Auger line structures can be visualized thanks to the good statistics simply by diﬀerentiating the electron energy distribution once or twice. One advantage by using an electron beam for excitation is the fact that it can easily be focussed onto a small spot on the specimen and therefore it gives a very good lateral resolution. There are certain limitations encountered with this technique due to the radiation damage caused by the electron beam. For materials like metals etc. this circumstance is of minor importance, but for organic and other materials the situation is diﬀerent. Gases again are not subject to this limitation and Auger and autoionization spectra from gaseous samples are therefore convenient to study [5]. In these cases the signal:background is quite good and no diﬀerentiation is necessary. Fig. 8.83 shows a highly resolved Auger electron spectrum for ArLMM transitions [108], [109]. At suﬃciently high resolution and with exciting energy just above the threshold for Auger electron emission one can notice typically asymmetric line profiles (Fig. 8.84).

Fig. 8.83 Argon L2 ,3 M2 ,3 M2,3 Auger electron spectrum, excited by electrons at two diﬀerent excess energies (2750 eV for top spectrum and 30 eV for bottom) above threshold. The shifts and asymmetries of the lines are caused by the ‘post-collision’ interaction (PCI) eﬀect

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Fig. 8.84 Comparison between the experimentally obtained and a calculated line shape according to an assumed dynamics of the PCI eﬀect on a time scale of femto-sec

This is due to ‘post-collisional’ eﬀects during the electron emission. The phenomenon is now well understood in terms of an interaction between the two slow remaining electrons after the excitation of the shell in question. Under the above conditions this results in an expelled low energy electron from that shell. The primary electron loses most of its energy and the ejected fast Auger electron leaves the molecular ion which is screened by the two mentioned remaining slow electrons. Depending on the details of the dynamics one can calculate the time behaviour of the screening and this gives rise to the asymmetric line shape [110], [111]. Conversely, the above study of the Auger electron line shape gives information about the dynamics on a time scale of ∼ 10−15 sec. Chemical shift investigations of electron excited Auger electron spectra for free molecules are fairly scarce compared to those for solid materials. As was mentioned before a combination of such shift data from both the photoelectron and the Auger spectra provides the information to determine the relaxation energies. As an example [112] Fig. 8.85(a) shows the KLL Auger electron spectrum of SO2 and Fig. 8.85(b) the chemical shifts for the S KL22,3 Auger lines and the S 2p1/2,3/2 photoelectron lines for a gas mixture of SF6 , SO2 and COS. The Auger lines were excited by electrons, the photo lines by monochromatic AlKα radiation. Such spectra can be evaluated with high accuracy at good experimental conditions, by the use of eﬃcient diﬀerential pumping, molecular gas beams or low pressure gas cells [113], [114]. Electron energy loss spectroscopy has developed into a very useful technique to record excited states of species irradiated by an electron monochromator. A recent comprehensive review of the applications in surface science is given by G. Ertl and J. K¨uppers [115]. Low electron energy loss spectroscopy gives direct information on e.g. vibrational modes of surfaces and of adsorbates on substrates, in particular developed by H.Ibach and coworkers [116]. High resolution can be achieved by monochromatization to around 5–10 meV (HREES).

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Fig. 8.85 (a) Sulphur KLL Auger electron spectrum of SO2 , excited by an electron beam (5 kV, 5 μA)

HREES is a frequently used alternative to IR or Raman spectroscopy for surfaces. It is interesting to note that more recently it has become possible to overcome the previous limitation in this technique to study surfaces of insulators, e.g. thick polymers or oxides. P.A. Thiry et al. [117] found that if such a surface was simultaneously irradiated with unfocussed ∼1 keV electrons the charging problem was eliminated and the electron loss spectra at specular reflection and at a primary electron beam energy around 6 eV approached the previous resolution for conductors. Fig. 8.86 shows the loss spectrum for MgO(001) and Fig. 8.87 for polyethylene. A comparison with the corresponding results from IR and Raman spectroscopy showed that not all the bands visible in HREES were excited in the optical modes due to selection rules. Otherwise the agreement was good. Although HREES is normally used as a particularly surface sensitive technique it has more recently been found that at low electron energy < 10 eV and at specular reflection, also interfaces in the important case of semiconductors can be reached. This is due to the long range of the electric fields of the scattered electrons and the polarization of the material. The resultant dipolar interaction excites or annihilates long wavelength optical phonons, called Fuchs-Kliever modes. By increasing the electron energies and using non-specular geometry the conditions favour instead short range scattering. This extension of HREES towards the studies of interfaces of layered semiconductor compounds in a superlattice of GaAs-Al0.3 Ga0.7 , such as for optoelectronics devices, has been demonstrated by P.A. Thiry et al, [118]. Another field of interest in the very low energy electron scattering region around 5 eV is VLEED fine structure. Such structures occur only at these low energies and disappear after showing up a few components. At the same time the lines decrease in linewidth according to a 1/n3 ratio which applies to the Rydberg series. The spectroscopic techniques to observe these phenomena requires high resolution (better

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Fig. 8.85 (b) Auger electron lines, SKLII LIII (1 D2 ) obtained from a gas mixture of SF6 , SO2 and COS (top figure). For comparison the S2p photoelectron spectrum (AlKα, Δhν = 0.2 eV) is shown in the bottom figure. The chemical shifts are in this case larger for the photoelectron lines than for the Auger electron lines. In other cases it may be the opposite. Relaxation energies are extractable from such studies

than 50 meV) and an angular resolution of < 0.5◦ . To describe this fine structure a model can be used where the electrons in the surface region experience an image barrier potential. The barrier structure for metals are now understood but it remains to study the surface barriers for semiconductors and insulators with high resolution VLEED techniques. This field has recently been reviewed by R.O. Jones and P.J. Jennings [119]. When the beam from the electron monochromator traverses a gas follo by an electron analyzer (as in Fig. 8.23) the molecular excitations ca be recorded both in the valence region and in the core region. Fig. 8.88 shows a typical electron impact energy loss spectrum in the valence region for H2 [120]. The excitation energy in this case is 30 eV. This is a well recognized field for studying electron molecular int actions which is under continuous development. Basic problems are e.g. related to accurate cross section measurements [121], [122]. Improved molecular beam methods and combinations with laser technique are promising pathways. With further increased spectral resolution one may hope to be able to resolve and investigate rotational and other fine structures and to discover resonance states etc.

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Fig. 8.86 Electron energy-loss spectrum (HREES) of 6.1 eV electrons after re- flection on a MgO(001) surface (insulator). The charging problem has been eliminated by means of an auxiliary unfocussed electron flood gun at 2.8 keV and 1 μA

Fig. 8.87 Electron-loss spectrum (HREES) of a massive sample of the insulateor polyethylene using an electron flood gun in the keV region

In the core region the energy loss spectroscopy corresponds to X-ray absorption spectroscopy and has developed during recent years to become an interesting complement to this. Fig. 8.89 shows a typical example in the case of ammonia and the methyl amines around the absorption edges of N1s [123]. Fig. 8.90 is a similar recording of the valence region, which concerns tetramethylsilane [124]. Extended absorption fine structures in X-ray absorption spectroscopy, EXAFS, has been a useful technique for geometrical structure information for several years thanks to the availability of tunable synchrotron beams. More recently, the possibil-

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Fig. 8.88 Electron energy loss spectrum for H2 gas. The strong singlet state excitations and the elastic peak are shown

Fig. 8.89 Short range electron energy loss spectra of the N1s region of ammonia and the methyl amines

ities to make use of electron beams for similar purposes as a complement to X-rays have been investigated in the electron reflexion mode. Fig. 8.91 is an overview of the various parts which can be distinguished in a scattered electron spectrum from a surface with the primary electron energy Ep . Close to the elastically scattered electrons forming the Ep peak one finds the mentioned

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Fig. 8.90 Valence shell electron energy-loss spectrum of tetramethylsilane. Estimated positions of the first members of the Rydberg series are shown below the spectrum

EELS spectrum, containing e.g. vibrational information etc. Next structure, EELFS, is the region of core electron excitation and ionization with its fine structure which is the equivalent to the X-ray absorption edge and its near and extended fine structures, XANES and EXAFS (there are also other alternative acronyms for those structures).

Fig. 8.91 Energy distribution of electrons scattered from a sample with primary electrons Ep

A more recent interest is concerned with the fine structures in the neighbourhood of Auger lines, denoted by J. Derrien et al. [125], [126] by EXFAS, (extended fine structure of the Auger spectral lines). Also from this structure one can extract geometrical information similar to EXAFS and EELFS. Fig. 8.92 and Fig. 8.93 exemplify these findings. Fig. 8.92 shows the Cr Auger spectrum containing the LVV, LMM and MVV (V are valence levels) Auger transitions. The lower part of the figure is a magnified part of the MVV Auger spectrum in which one observes several extended Auger fine structure components (EXFAS).

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Fig. 8.93 demonstrates the close relationship between EXFAS, EXAFS and EELFS. It shows the Fourier transforms of the M2,3 VV transition in cobolt (first and second derivatives) for EXFAS, EXAFS (the M23 edge and EELFS. All three techniques yield the same nearest-neighbour distances. The connection between the various fine structures and their appropriate evaluations in terms of near neighbour distances are discussed by G. Ertl and J. K¨uppers in their above mentioned book on low energy electrons and surface chemistry [115].

Fig. 8.92 Auger electron spectrum of a clean Cr film (upper figure) . Magnification of the MVV Auger electron line region shows several extended fine Auger electron structures (lower figure)

Fig. 8.93 Fourier transforms of EXFAS recorded on cobalt above the M2,3 VV transition detected in both the first-derivative (a) and second-derivative mode (b). The EXAFS Fourier transform of the same edge is shown in (c) and the EELFS in (d). All three techniques (EXFAS, EXAFS and EELFS) give the same nearest-neighbour distance

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Fig. 8.94 Scenes of the lecture of Professor Kai Siegbahn at the University of Tokyo (1988)

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The “appearance potential” techniques (APS) is complementary to the just mentioned ones to get geometrical distances. One can either record the changes in soft X-ray emission SXAPS or the changes (disappearance) of the elastically reflected electrons (DAPS). Another possibility is to record the appearance of Auger electrons (AEAPS). Extended fine structures have been observed in SXAPS but due to the low fluorescence yield of X-rays AEAPS and DAPS are somewhat more eﬃcient. Electron scattering spectroscopy is an interesting and powerful alternative which supplements other approaches which are presently being made by means of synchrotron radiation, e.g. XANES and EXAFS etc. It also oﬀers great potentialities for surface studies, complementary to optical methods.

References 1. M. Siegbahn: Spektroskopie der R¨ontgenstrahlen, Springer, Berlin 1931. 2. K. Siegbahn: Beta- and Gamma-Ray Spectroscopy, North Holl. Publ. Co, Amsterdam 1955; Alpha-, Beta and Gamma-Ray Spectroscopy, North Holl. Publ. Co, Amsterdam 1965. 3. H . Robinson, Phil. Mag. 50, 241, 1925. 4. K. Siegbahn, C. Nordling, A. Fahlman, R. Nordberg, K. Hamrin, J. Hedman, G. Johansson, T. Bergmark, S.-E. Karlsson, I. Lindgren, B. Lindberg: ESCA, Atomic, Molecular and Solid State Structure Studied by Means of Electron Spectroscopy. Nova Acta Regiae Societatis Scientiarum Upsaliensis, Uppsala 1967. 5. K. Siegbahn, C. Nordling, G. Johansson, J. Hedman, P.F. Hed´en, K. Hamrin, U. Gelius, T. Bergmark, L.O. Werme, R. Manne, Y. Baer: ESCA Applied to Free Molecules, North Holland Publ. Co., Amsterdam 1971. 6. J.G. Jenkin, R.C. Leekey and J. Liesegang, J. Electron Spectr. Rel. Phen. 12, 1, 1977. 7. T.A. Carison (ed.): Benchmark Papers in Phys. Chem. and Chem. Phys. 2, Dowden, Hutchinson and Ross 1978. 8. H. Siegbahn and L. Karlsson: Photoelectron Spectroscopy, Handbuch der Physik XXXI, W. Mehihorn (ed.), Springer, Berlin Heidelberg 1982 9. K. Siegbahn, Les Prix Nobel, Stockholm, 1981; Rev. Mod. Phys. 54, 709; Science 217, 111, 1982. 10. R. Maripuu, Thesis, Acta Universitatis Upsaliensis no. 696, 1983. 11. T.D. Bussing, P.H. Holloway, Y.X. Wang, J.F. Moulder and J.S. Hammond, J. Vacuum Science and Techn. B6, no. 5, 1514, 1988. 12. U. Gelius, L. Asplund, E. Basilier, S. Hedman, K. Helenelund and K. Siegbahn, Nucl. Instr. and Meth. B1, 85, 1983. 13. K. Siegbahn: Electron Spectroscopy - An Outlook, J. Electron Spectr. Rel. Phen. 5, 3, 1974. 14. M. Kelley, 551, (private communication) 1988.

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15. K. Siegbahn: Some Current Problems in Electron Spectroscopy and references therein, Atomic Physics 8 (ed. I. Lindgren, A. Ros´en and S. Svanberg), Plenum Press, 1983. 16. E.F. Ritz Jr., Recent Advances in Electron Beam Deflection, Advances in Electronics and Electron Physics 49, 299, 1979. 17. U. Boesl, Habilitationsschrift: “Resonante Laseranregung and Massenspektrometrie”, Technischen Universit¨at M¨unchen, Garching, 1987. 18. F.C. Tang, X. Zhang, F.B. Dunning and G.K. Walters, Rev. Sci. Instr. 59, 504, 1988. 19. A. Nilsson, N. Mårtensson, J. Hedman, B. Eriksson, R. Bergman and U. Gelius, Proc. of ECOSS-7, Surf. Sci. 1985. 20. N. Mårtensson, Thesis, Uppsala 1980. 21. B. Johansson and N. Mårtensson, Phys. Rev. B21, 4427, 1980. 22. J.S. Jen and T.D. Thomas, Phys. Rev. B13, 5284, 1976. 23. J.Q. Broughton and D.C. Perry, J. Electron Spectr. Rel. Phen. 16, 45, 1979. 24. R. Nyholm, Thesis, Uppsala 1980. 25. P. Steiner, S. H¨ufner, N. Mårtensson and B. Johansson, Solid State Commun. 37, 73, 1981. 26. N. Mårtensson, B. Reihl and 0. Vogt, Phys. Rev. 25, 824, 1982. 27. N. Mårtensson, A. Stenborg, 0. Bj¨orneholm, A. Nilsson and J.N. Andersen, Phys. Rev. Lett. 60, 1731, 1988. 28. A. Nilsson and N. Mårtensson, Solid State Comm. in press. 29. J.R. Waldrop, S.P. Kovalczyk and R.W. Grant, J. Vac. Sci. Technol. 21, 607, 1982. 30. R.S. Bauer, Phys. Rev. Lett. 43, 663, 1983. 31. G. Margaritondo, Surf. Sci. 132, 469, 1983. 32. R. Purtell, G. Hollinger, G.W. Rubloﬀ and P.S. Ho, J. Vac. Sci. Technol. A1, 566, 1983. 33. U. Gelius, K. Helenelund, L. Asplund, S. Hedman, P.A. Tove, K. Magnusson and I.P. Jam, Inst. of Physics Rep. UUIP-1101, 1984. 34. B. Lindberg, R. Maripuu, K. Siegbahn, R. Larsson, C.G. G¨olander and J.C. Eriksson, Inst. of Phys. Rep. UUIP-1066, 1982. 35. N. Larsson, P. Steiner, J.C. Eriksson, R. Maripuu and B. Lindberg, J. Colloid Interface Sci. 75, 1982. 36. W.F. Egelhoﬀ Jr., Core-Level Binding-Energy Shifts at Surfaces and in Solids, Surface Science Reports 6, no. 6–8, 1987. 37. K. Siegbahn, Electron Spectroscopy for Solids, Surfaces, Liquids and Free Molecules, Ch. 15 in Molecular Spectroscopy (ed. A.R. West), Heyden and Son Ltd., London 1977. S. Svensson, B. Eriksson, N. Mårtensson, G. Wendin and U. Gelius, 38. J. Electron S pectr. Rel. Phen. 47, 327, 1988. 39. G.V. Hansson and R.I.G. Uhrberg, Proc. 8th Int. COnf. on Vac. UV Rad. Phys., Physica Scripta T17, 1987. 40. G.V. Hansson and R.I.G. Uhrberg, Photoelectron Spectroscopy of Surface States on Semiconductor Surfaces, Surface Science Reports 9, no. 5–6, 1988.

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41. D.E. Eastman and Y. Farge (ed.), Handbook on Synchrotron Radiation, North Holl. Publ. Co., Amsterdam 1983 and further on. 42. H. Winnik and S: Doniach, Synchrotron Radiation Research, Plenum Press, New York, 1980. 43. N. Mårtensson, R. Nyholm, H. Cal´en, J. Hedman, Phys. Rev. B24, 1725, 1981. 44. J. Verbist, J. Riga, J.J. Pireaux and R. Caudano, J. Electron Spectr. 5, 193, 1974. 45. V. Dose, Momentum-Resolved Inverse Photoemission, Surface Science Reports 5, no. 8, 1986. 46. F.J. Himpsel in Semiconductor Interfaces: Formation and Properties (ed. G. LeLay, J. Derrien and N. Boccara), 196, Springer, Berlin-Heidelberg, 1989. 47. D.W. Turner, C. Baker, A.D. Baker and C.R. Brundle, Molecular Photoelectron Spectroscopy, Wiley-Interscience, London, 1970. 48. K. Siegbahn, Perspectives and Problems in Electron Spectroscopy, Proc. of Asilomar Conf., 1971 (ed. D.A. Shirley), North Holl. Publ. Co, Amsterdam 1972. 49. L.O. Werme, B. Grennberg, J. Nordgren, C. Nordling and K. Siegbahn, Phys. Rev. Lett. 30, 523, 1973; Nature 242, 453, 1973. 50. J. Nordgren, L. Selander, L. Pettersson, C. Nordling, K. Siegbahn and H. Agren, J. Chem. Phys. 76, no. 8, 3928, 1982. 51. J. Nordgren, J. de Physique 48, Colloque C9, suppl. 12, 1987 52. J.-E. Rubensson, N. Wassdahl, R. Brammer and J. Nordgren, J. Electron Spectr. Rel. Phen. 47, 131, 1988. 53. H. Veenhuizen, B. Wannberg, L. Mattsson, K.-E. Norell, C. Nohre, L. Karlsson adn K. Siegbahn, UUIP-1107, Inst. of Phys. Reports 1984. 54. K.-E. Norell, B. Wannberg, H. Veenhuizen, C. Nohre, L. Karlsson, L. Mattsson and K. Siegbahn, UUIP-1109, Inst. of Phys. Reports 1984. 55. B. Wannberg, H. Veenhuizen, K.-E. Norell, L. Karlsson, L. Mattsson and K. Siegbahn, UUIP-1110, Inst. of Phys. Reports, 1984. 56. U. Heinzmann, Physica Scripta T17, 77, 1987. 57. G. Schonhense, Appl. Phys. A41, 39, 1986. 58. K. Siegbahn, U. Gelius, H. Siegbahn and E. Olson, Phys. Lett. A32, 221, 1970; Physica Scripta 1, 272, 1970. 59. C.S. Fadley: Angle-Resolved X-ray Photoelectron Spectroscopy, Progress in Surface Science 16, no. 3, 275, 1984. 60. C.S. Fadley, Physica Scripta T17, 39, 1987. 61. W.F. Egelhoﬀ Jr., Phys. Rev. B30, 1052, 1984; J. Vac. Sci. Technol. A2, 350, 1984. 62. H.C. Poon and S.Y. Tong, Phys. Rev. B30, 6211, 1984. 63. W.F. Egelhoﬀ Jr., J. Vac. Technol. A4, 758, 1986. 64. W.F. Egelhoﬀ Jr., Vac. Technol. A6, no. 3, 730, 1988. 65. R.C. White, C.S. Fadley and R. Trehan, J. Electron Spectr. 41, 95, 1986. 66. E.L. Bullock and C.S. Fadley, Phys. Rev, B31, 1212, 1985. 67. B. Sinkovic and C.S. Fadley, Phys. Rev. B31, no. 7, 4665, 1985; J. Vac. Sci. Technol. A4, no. 3, 1477, 1986. 68. J.J. Barton, S.W. Robey and D.A. Shirley, Phys. Rev. B34, 778, 1986.

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69. C.C. Bahr, J.J. Barton, Z. Hussain, S.W. Robey, J.G. Tobin and D.A. Shirley, Phys. Rev. B35, 3773, 1987. 70. D.P. Woodruﬀ, C.F. McConville, A.L.D. Kilcoyne; Th. Lindner, J. Somers, M. Surman, G. Paolucci and A.M. Bradshaw, Surface Science 201, 228, 1988. 71. Th. Lindner, J. Somers, A.M. Bradshaw, A.L.D. Kilcoyne and D.P. Woodruﬀ, Surface Science 203, 333, 1988. 72. H. Siegbahn and K. Siegbahn, J. Electron Spectr. 2, 319, 1973. 73. H. Siegbahn, L. Asplund, P. Kelfve, K. Hamrin, L. Karlsson and K. Siegbahn, J. Electron Spectr. 5, 1059, 1974; Ibid, 7, 411, 1975. 74. H. Siegbahn, J. Phys. Chem. 89, 897, 1985. 75. H. Siegbahn, S. Svensson and M. Lundholm, J. Electron Spectr. 24, 205, 1981. 76. H. Siegbahn, M. Lundholm, S. Holmberg and M. Arbman, Physica Scripta 27, 431, 1983. 77. H. Siegbahn, M. Lundholm, S. Holmberg and M. Arbman, Chem. Phys. Lett. 110, no. 4, 425, 1984. 78. M. Arbman, H. Siegbahn, L. Pettersson and P. Siegbahn, Mol. Physics 54, no. 5, 1149, 1985. 79. M. Lundholm, H. Siegbahn, S. Holmberg and M. Arbman, J. Electron Spectr. 40, 165, 1986. 80. W. Keller, H. Morgner and W.A. M¨uller, XIV Int. Conf, on the Physics of Electronic and Atomic Collisions, 605, 1985 (eds. D.C. Lorents, W. Mayerhof and J. Petterson), North Holl. Co., Amsterdam, 1986. 81. S. Holmberg, R. Moberg, Zhong Cai Yuan and H. Siegbahn, J. Electron Spectr. 41, 337, 1986. 82. R. Hilbig, G. Hilber and R. Wallenstein, Applied Physics B41, 225, 1986. 83. T. Huth, A. Mank, N. B¨owering, G. Sch¨onhense, R. Wallenstein and U. Heinzmann, personal communication. 84. T.P. Softly, W.E. Ernst, L.M. Tashiro and R.N. Zare, Chem. Phys. 116, 299, 1987. 85. K. Kimura: Molecular Dynamic Photoelectron Spectroscopy using Resonant Multiphoton Ionization for Photophysics and Photochemistry, International Reviews in Physical Chemistry, 1986. 86. R.N. Compton and J.C. Miller: Multiphoton Ionization Photoelectron Spectroscopy, Oak Ridge, Tennessee, 1986. 87. S.L. Anderson, D.M. Rider and R.N. Zare, Chem. Phys. Letters 93, no. 1, 11, 1982. 88. I. Reineck, C. Nohre, R. Maripuu, P. Lodin, K.E. Norell, H. Veenhuizen, L. Karlsson and K. Siegbahn, UUIP-1084, Uppsala Inst. Phys. Reports, 1983. 89. Y. Nagano, Y. Achiba and K. Kimura, J. Chem. Phys. 84, no. 3, 1063, 1986. 90. P. Kruit and F.H. Read, J. Phys. E16, 313, 1983. 91. B.G. Koenders, G.J. Kuik, Karel E. Drabe and C.A. de Lange, Chem. Phys. Lett. 147, no. 4, 310, 1988. 92. K. M¨uller-Dethlefs, M. Sander and E.W. Schlag, Z. Naturforsch. 39a, 1089, 1984. 93. L.A. Chewter, M. Sander, K. M¨uller-Dethlefs and E.W. Schlag, J. Chem. Phys. 86, no 9, 4737, 1987.

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94. M. Sander, L.A. Chewter, K. M¨uller-Dethlefs and E.W. Schlag, Phys. Rev. A36, no. 9, 4543, 1987. 95. R. Weinkauf, K. Walter, U. Boesl, E.W. Schlag, Chem. Phys. Lett. 141, 267, 1987. 96. K. Walter, R. Weinkauf, U. Boesl and E.W. Schlag, personal communication. 97. O. Chesknovsky, S.H. Yang, C.L. Pettiette, M.J. Craycraft, Y. Liu and R.E. Smalley, Chem. Phys. Lett. B8, nr. 23, 119, 1987. 98. J.V. Coe, J.T. Snodgrass, C.B. Freidhoﬀ, K.M. McHugh and K.H. Bowen, J. Chem. Phys. 87 (8), 4302, 1987. 99. D.A. Gobeli, J.J. Yang and M.A. E1-Sayed, Chem. Rev. 85, 529, 1985. 100. J. Grotemeyer and E.W. Schlag, Angew. Chemie 27, no. 4, 447, 1988. 101. Liang Li and D.M. Lubman, Rev. Sci. Instr. 59, 557, 1988. 102. Mo Yang and J.P. Reilly, Anal. Instr. 16, 133, 1987. 103. J.M. Bizau, F. Wuilleumier, D.L. Ederer, J.C. Keller, J.L. LeGouit, J.L. Picqu´e, B. Carr´e and P.M. Koch, Phys. Rev. Lett. 55, 1281, 1985. 104. J.M. Bizau, D. Cubaynes, P. Gerard, F.J. Wuilleimier, J.L. Picqu´e, D.L. Ederer, B. Carr´e and G. Wendin, Phys. Rev. Lett. 57, no. 3, 306, 1986. 105. M. Ferray, F. Gounand, P. D’Oliveira, P.R. Fournier, D. Cubaynes, J.M. Bizau, T.J. Morgan and F.J. Wuilleumier, Phys. Rev. Lett. 59, no. 18, 2040, 1987. 106. R. Haight, J.A. Silberman and M.I. Lilie, Rev. Sci. Instr. 59, no. 9, 1941, 1971. 107. J.M. Moison, Semiconductor Interfaces: Formation and Properties (ed. G. LeLay, J. Derrien and N. Boccara), Proc. in Physics 22, Springer, Berlin-Heidelberg, 1987. 108. K. Helenelund, S. Hedman, L. Asplund, U. Gelius and K. Siegbahn, Physica Scripta 27, 245, 1983. 109. K. Helenelund, Thesis, Acta Universitatis Upsaliensis no. 757, 1984. 110. W. Sandner, J. Phys. B, At. Mol. Phys. 19, L863, 1986. 111. R. Huster, W. S andner and W. Mehlhorn, J. Phys. B, At. Mol. Phys. 20, L, 1987. 112. L. Asplund, P. Kelfve, B. Blomster, H. Siegbahn, K. Siegbahn, R.L. Lozes and U.I. Wahlgren, Physica Scripta 16, 273, 1977. 113. L. Asplund, Thesis, Acta Universitatis Upsaliensis no 479, 1977 114. P. Kelfve, Thesis, Acta Universitatis Upsaliensis no 483, 1978 115. G. Ertl and J. K¨uppers, Low Energy Electrons and Surface Chemistry, VCH Verlagsgesellschaft, Weinheim, 1985. 116. H. Ibach and D.L. Mills, Electron Energy Loss Spectroscopy and Surface Vibrations, Academic Press, New York, 1982. 117. P.A. Thiry, J.J. Pireaux, M. Leihr and R. Caudano, J. Physique 47, 103, 1986. 118. P.A. Thiry, M. Liehr, J.J. Pireaux and R. Caudano, Ph. Lambin, J.P. Vigneon, A.A. Lucas and T. Kuech, J. Vac. Sci. Technol. B4, no. 4, 1028, 1986. 119. R.O. Jones and P.J. Jennings, Surface Science Rep. 9, 165, 1988. 120. S. Trajmar, XIV Int. Conf. on the Phys. of Electronic and Atomic Collision, 77, 1985 (ed. D.C. Lorents, W.E. Meyerhof and J.R. Petersson), North Holland, Amsterdam, 1986. 121. E.N. Lassettre and A. Skerbele, Methods of Experimental Physics 3, 868, 1974.

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122. E.N. Lassettre, Chem. Spectr. and Photochem. in the Vac. Ultr. Viol., 43, (ed. C. Sandorfy, P.J. Ansloos and M.B. Robin, Reidel Publ. Co., Boston, 1974. 123. R.N.S. Sodhi and C.E. Brion, J. Electr. Spectr. 36, 187, 1985. 124. R.N.S. Sodhi, S. Daviel, C.E. Brion and G.G.B. de Souza, J. Electr. Spectr. 35, 45, 1985. 125. J. Derrien, E. Chainet, M. de Crescenzi and C. Noguera, Surface Science 189/190, 590, 1987. 126. J. Derrien, Semiconductor Interfaces: Formation and Properties (ed. G. LeLay, J. Derrien and N. Boccara), 102, Springer, Berlin-Heidelberg, 1987.

9

Theoretical Paradigms for the Sciences of Complexity Philip W. Anderson

Abstract This address was presented by Philip W. Anderson as the Nishina Memorial Lecture at the 50th Anniversary Seminar of the Faculty of Science & Technology, at Keio University (Tokyo), on May 18, 1989.

I may not be a very appropriate representative for the subject of Materials Science here in a conference focusing on technology and the applications of science to human problems. I am not, strictly speaking, a materials scientist in the narrow sense of these words, and much as I admire and applaud the applications of science in technology, that is not what I do. I am a theoretical physicist much of whose work has involved trying to understand the behavior of more or less complex materials such as metals, magnets, superconductors, superfluids, and the like. I thought that perhaps you Philip W. Anderson c would enjoy hearing, in the brief time I have here, not about NMF these investigations or about wonderful materials of the future — as far as I am concerned, from an intellectual point of view, the very impractical and obscure low-temperature phases of the mass-3 isotope of helium are at least as fascinating materials as anything the future is likely to bring — but rather about some of the wider implications of the kind of thing I do. In particular, I have been an active participant for several years in an enterprise called the Santa Fe Institute whose charter involves action in two main directions;

Philip W. Anderson (1923 –). Nobel Laureate in Physics (1977) Princeton University (USA) at the time of this address P. W. Anderson: Theoretical Paradigms for the Sciences of Complexity, Lect. Notes Phys. 746, 229–234 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 9

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(1) We believe that the growth points of science lie primarily in the gaps between the sciences, so that we believe in fostering cross-disciplinary research in growth areas which are not well served by the conventional structure of the universities or the funding agencies, I use the word cross-disciplinary to emphasize that we are not trying to create new disciplines (like materials science or biomolecular engineering), which often rigidify into new, even narrower intellectual straightjackets, but that we approach problems by cross-coupling between scientists well grounded in their disciplines but thinking about problems outside or between them — as has often been fertile in materials science, with the coupling of good physicists, good chemists and good engineers. (2) We believe that there are many common themes in the study of complex systems wherever they occur, from the relatively simple ones which I have encountered in solid state physics or in astrophysical situations, through complex non-linear dynamical systems such as one encounters in hydrodynamics, through biological organization, to complex biological regulatory systems such as the immune system or the nervous system, and on into population biology, ecology, and into human interactions in, for instance, economic systems. Much of our work — not all of it, to be sure — fits under the general rubric of the study of Complex Adaptive Systems; systems which by virtue of their complexity are capable of adapting to the world around them. It would carry me too far afield to describe all of our activities in Santa Fe; one, for instance, which I have enjoyed very much is a program mixing physical scientists such as myself with a group of theoretical economists in the hope of inventing new directions for the science of economics. Rather, I would like to describe a few of the paradigms for dealing with complex systems, in general, which have come from, or are related to, my science of condensed matter physics and which seem to be generalizable to a great many other types of systems. Let me list three of them here and try to describe each in a few words, relate it to the appropriate part of condensed matter theory, and then show how the idea may be generalized. (1) The Emergent Property of Broken Symmetry. (2) The Paradigm of the “Rugged Landscape” (3) Scale-Free Behavior: Critical Points, Fractals, and 1/ f noise. There are several other paradigms — e.g., hierarchical organization, pattern selection, marginal stability, classifier algorithms among others; but surely this is enough ideas for one short talk. (1) Broken symmetry is actually the basic underlying concept of solid state physics. It seems at first simple and obvious that atoms will want to stack themselves into regular arrays in three dimensions, like cannonballs. Thus one does not recognize that the formation of a crystal lattice is the most-studied and perhaps simplest example of what we call an “emergent property”: a property which is manifested only by a suﬃciently large and complex system by virtue of that size and complexity. The particles, (electrons and nuclei) of which a crystal lattice is made do not have rigidity, regularity, elasticity — all the characteristic properties of the solid: these are actually only manifest when we get “enough” particles together and cool

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them to a “low enough” temperature. In fact, there are kinds of particles — atoms of either isotope of helium, or electrons in a metal, for instance — which simply do not normally stack at all and remain fluid right down to absolute zero. This illustrates one of the most important facts about broken symmetry; quantum-mechanical as well as thermal fluctuations are inimical to it. Why do we call the beautifully symmetric crystalline state “broken” symmetry? Because, symmetrical as it is, the crystal has less symmetry than the atoms of the fluid from which it crystallized: these are, in the ideal case, featureless balls which translate and rotate in any direction, while the crystal has no continuous rotation or translation symmetry. Mathematically, the properties of the crystal are only to be derived in the socalled “thermodynamic” or “→ ∞” limit of every large system. Of course, for many purposes a very small cluster of atoms, of the order of a few thousand, can behave in somewhat crystalline ways, but the structure at a finite crystal is not really stable against thermal or quantum fluctuations. Thus the characteristic crystalline properties of rigidity, elasticity, (as opposed to the shear flow of a viscous fluid) and anisotropy (as e.g., birefringence) are true emergent properties, properties which are only properties of the large and complex systems. It turns out that many, if not most, of the interesting properties of condensed matter systems are emergent broken symmetry eﬀects. Magnetism is a well-known example; so is superconductivity of metals and the very similar superfluidity of the two forms of helium and of neutrons in a neutron star. The anisotropic properties of liquid crystals, useful in calculator displays, are yet another fascinating example. Broken symmetry is encountered in several other contexts. One important one is in the theory of the “Big Bang” during which, it is proposed, one or more broken symmetry transitions took place in the state of the vacuum, changing the nature and number of elementary particles available at each one, greatly modifying the energetic of these primeval events, and leaving behind one or more forms of debris — the fashionable one these days being “cosmic strings”. The early history of broken symmetry in the vacuum was dominated by the Japanese-American physicist Yoichiro Nambu. Some scientists have proposed that driven dynamical systems can exhibit broken symmetry eﬀects; I find the analogy between the emergent behavior of equilibrium and of non-equilibrium system less than compelling. Broken symmetry does not; generalize in any straightforward way to form a model for the origin of life, for instance; it stands, rather, as an explicit proof of the existence of emergence. (2) The paradigm of the “rugged landscape” was discussed in connection with another condensed matter physics problem, the rather obscure phenomenon known as “spin glass”. It is almost unnecessary to go into the long and controversial history of the spin glass problem itself, except that it involves the possibility of a phase transition at which the spins in a random magnetic alloy “freeze” into some random configuration. The attempt was initially to find a simple model for the still mysterious behavior of ordinary glass when freezing into a solid-like but disordered state; but it turned out the disordered magnetic alloy had its own diﬀerent and complex behavior.

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The model one uses abstracts the movable spins in the magnetic alloy as having two possible states, up(+) or down(−), like the 0 or 1 of a binary bit Each spin S i is presumed to interact in a random fashion “Ji j ” with many other spins, causing a “frustrated” Hamiltonian (9.1) H Ji j S i S j in which there are many conflicting terms to optimize and it is not easy to visualize the lowest energy state. Ji j is a random variable, equally often positive or negative. It is the values of the energy H -plotted in the multidimensional “configuration space” of the state variable {S i } — which constitutes the “rugged landscape”. The task of finding a low-energy state is one of seeking for deep valleys in this “rugged landscape”, but it can be proved that this task is computationally very diﬃcult, because one gets stuck in one of the many diﬀerent local minima with no hint as to where to go to find a better state. In fact, this problem is a prime example of one of the most important classifications of computational complexity, the “NP complete” case. It has already suggested an important new algorithm for solving complex “combinatoric optimization” problems which arise in many emergency situations such as complex chip design: the method of simulated annealing. Combinatorial optimization problems in the presence of conflicting goals are very common in everyday life: almost every personal or business decision, from ordering from a menu to siting a new factory, is of this nature: so of course information on the basic nature of these problems is of great value. Unique to our approach is the recognition of the “freezing” phenomena, the possibility of being stuck indefinitely in a less than optimum solution. Two places where the rugged landscape point of view is catching on are in evolutionary biology and in the theory of neural networks — “generalized brains”. S. Kaufmann has particularly emphasized the “rugged landscape” approach to problems of molecular evolution, both in the original origins of life and in proposing systems of “directed evolution” to produce organisms with particular traits. In the evolutionary analogy, which was pioneered by Stein and myself, and picked up by S.Kaufmann, the genetic material is the state-vector {S i } in a multidimensional configuration space. A very important point is that given the “freezing” phenomenon, it may be better to improve by complexifying — adding dimensions to the configuration space — than by optimization within one’s obvious capabilities. The reanimation of neural network theory which has recently occurred due to Hopfield’s introduction of spin glass like ideas is both so well known and so far afield from my subject that I do not want to go into it more deeply than that. (3) Scale-free phenomena. Here is a paradigm which has had two joint inputs, initially far apart but growing closer with time. The first is from mathematics: the fundamental ideas coming from a number of mathematicians such as Hausdorﬀ but the applicability to real world situations (which, to a natural scientist, is far more important) being discovered by Mandelbrot. As Mandelbrot points out, there are many real world objects which have the property of non-trivial scale invariance — properly called anomalous dimension-

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ality, but which he calls fractality. Such objects look the same geometrically no matter what scale they are observed at; in general that is true only in a statistical sense. For instance, he shows that many coastlines have the same geometry at any scale; the same is true of clouds and of many mountain landscapes. This alone is not enough — after all, a simple continuum in any dimension is scale-invariant. The second property is that the size of the object vary with scale in a non-integer way. For instance, he shows that the length of coastlines depends on the length of the ruler used to measure them as L ∝ −p where P ∼ .2. Mandelbrot gives many beautiful examples, in his books, of fractal objects, and others have discovered additional ones — for instance, the shape of the breakdown paths in a dielectric subjected to too high a voltage, which is an example of Diﬀusion-Limited Aggregation (DLA), a process of pattern growth common to many systems, and discussed by T. Witten and others. Another important case is the “strange attractor” observed in chaotic, low-dimensional dynamic systems as discussed by Ruelle and co-workers. But in general Mandelbrot has not approached — at least successfully — the question of why fractals are so common and so important in nature. A second independent observation of scale-invariance is due to condensed matter theorists, specifically Kadanoﬀ, Widom, and Wilson, in the study of “critical points” of phase transition between diﬀerent thermodynamic phases, such as liquidgas critical points, superfluid-normal fluid transitions, magnetic critical points, etc. It came to be realized that, at these critical points, again the structure of the substance — in terms of the fluctuations back and forth between liquid and gas — is scale-invariant in the same sense: there are “droplets” of absolutely all sizes from one molecule to comparable to the size of the entire sample. This is the basic nature of critical behavior and the famous “critical fluctuations” which may be beautifully demonstrated experimentally. It turned out that some of Mandelbrot’s fractals are formally equivalent to critical points — e.g., the DLA system, which leads to a critically percolating cluster. It is the recent suggestion of Per Bak, that a great many examples of fractals in nature are systems at or near a critical point, in that he feels that many kinds of systems, when driven hard enough, will maintain themselves at a critical point. He calls this phenomenon “self-organized criticality” and the idea is the center of considerable controversy but also great interest. In particular, Bak points out that many systems in nature exhibit a kind of random fluctuation or “noise” which can also be thought of as scale-free but in time, not space — the ubiquitous “1/ f noise” of many diﬀerent kinds of systems. (Actually, in general 1/ f 1±p when p is a small number ∼ .1–.2.) This kind of noise is technologically very important. Going from the practical and turning to the gigantic, others have proposed that the large-scale structure of the universe may have fractality over some range. In conclusion, then, let me summarize the point of view I — we, if I may include others at SFI — am taking towards the study of complexity. From the beginning of thought, the system of Pythagoras, the medieval scholasticists, Descartes and his universality of mechanism (and from him stem the ideas of many modern particle physicists, for instance) — it has been a temptation to try to create a universal system — a Theory of Everything. It is precisely in the opposite direction that we search

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– we try to look at the world and let it tell us what kinds of things it is capable of doing. How, actually, do complex systems behave, and what do these behaviors have in common? The search for the universal must start from the particular.

10

Some Ideas on the Aesthetics of Science Philip W. Anderson

Abstract This address was presented by Philip W. Anderson as the Nishina Memorial Lecture at the 50th Anniversary Seminar of the Faculty of Science & Technology, at Keio University (Tokyo), on May 18, 1989.

The educated layman is used to thinking of science as having aesthetic values in two senses. Often he can recognize the grandeur and sweep of the scientific vision: the cosmological overview of the universe, the long climb of evolution towards complexity, the slow crunch of the tectonic plates, the delicately concentrated energy of the massive accelerator. Also, many visual images from science have aesthetic meaning: images of galaxies, of the complex structures of crystals or of the double helix, the fascinating diversity of organisms and their traces in Nature. What I want to dis- Philip W. Anderson c cuss here, however, is the internal, intellectual aesthetic of NMF science, which is often what the scientist himself alludes to when he calls a certain piece of science “sweet” or “beautiful”. This is very often a comprehension of internal intellectual connections among diverse phenomena or even fields of science — that the same intellectual structure, for instance, may govern the formation of elementary particles and the flow of electricity in a superconducting wire; another may relate a complex magnetic alloy with the functioning of neuronal circuits. In summary, I will try to describe what the scientist (or, at least, one scientist) finds beautiful in science.

Philip W. Anderson (1923 –). Nobel Laureate in Physics (1977) Princeton University (USA) at the time of this address P. W. Anderson: Some Ideas on the Aesthetics of Science, Lect. Notes Phys. 746, 235–243 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 10

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During the debate over the Hydrogen Bomb in the early 1950’s which eventually led to J.R. Oppenheimer’s downfall, he opposed Teller’s “crash” eﬀorts to design such a bomb on some combination of technical and moral grounds. But when Stan Ulam, working with Teller, proposed a new configuration, Oppenheimer seems to have withdrawn his opposition, remarking that the new design was “so technically sweet” — i.e., so “beautiful”, that it had to be done. This is only a widely publicized incident involving scientists making essentially aesthetic judgments and allowing them to influence their actions; I happen to feel that it is a disgraceful one, but that is beside the point here. All scientists, I think, who are worthy of their calling, have some aesthetic feeling about it, specifically about what is beautiful science and what is not. It is this aesthetic component of science which I want to discuss here. I am sure that I shall tread on many toes, nor am I absolutely sure that I have got it right in any case; in fact, I would feel that I have done my job if I simply succeed in opening a discussion. In aesthetic matters there is a widespread prejudice summarized in the saying “each to his own taste”, but, in fact, I happen to feel there are real criteria both in the arts and in science. Let me first dispose of some common layman’s misconceptions. The most common would surely be that science is not only value-free but without scope for imagination and creativity. It is seen as the application of a systematic “scientific method” involving wearing a white coat and being dull. I feel that too many young people come into science with this view, and that too many fields degenerate into the kind of work which results: automatic crank-turning and data-collecting of the sort which Kuhn calls “normal science” and Rutherford “stamp-collecting”. In fact, the creation of new science is a creative act, literally, and people who are not creative are not very good at it. (Equally, one often finds people miscast in scientific careers who do not realize that the second most important skill is communication: this seems to be a special problem for Japanese scientists. Science is the discovery and communication of new knowledge.) A second layman’s problem is the attempt to project his own aesthetic system into science. I have, several times, been asked by artists, for instance, about striking images which can be made from scientific objects, and, of course, in popularizing science every TV program is eagerly hunting for this kind of thing. Science itself contains a fifth column of practitioners — often otherwise respectable — who like to create pretty images, sometimes by computer tricks, or to emphasize the grandeur of the scientific vista by playing games with large numbers. To play pretty games or to inspire awe with large or small magnitudes is perhaps a legitimate, if tricky, way to enhance popular support for science (but what happens to the equally important but unglamorize subjects?) but it has little or nothing to do with science itself. It is true that diﬀerent fields of science attract people who are, to some extent, swayed by subject matter: astronomers do like to look at the stars and contemplate deep space, biologists often seem to enjoy the diversity of forms of life, elementary particle physicists are convinced they alone are plumbing the “really” fundamental, etc. But within each science, and across the spectrum of the sciences, it is still possible to distinguish the “sweet” from the ugly.

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A third misconception is promulgated by certain sociologists of science, who seem to feel that science is a purely sociological phenomenon, with no intrinsic truth value at all: that scientists’ aesthetic and cultural prejudices create the form which science takes, which is otherwise arbitrary. This is mainly refuted by the fact that science works in a real sense: it grows exponentially because it is useful and eﬀective, which means that it produces, one way or another, a true picture of the real world. These sociologists have studied science being done, which is, of course, a confusing set of interactions among highly fallible people with strong prejudices; but they have not enough insight into the subject matter or into the qualitative diﬀerences among fields and among people to recognize the rapid disappearance of the shoddy or dishonest result. It is significant that the average scientific paper is cited less than once in the literature, while some are cited thousands of times: some are right, some are wrong, most are meaningless. To the sociologist of science, observing from the outside, the uncited paper and the “classic” appear equally significant. As we will see, fortunately, the “aesthetic” aspect of science has much to do with values which are also related to its validity and truth, so I am not saying that aesthetics leads scientists to distort the meaning of their work. I do not deny the regrettable fact that some scientific fields do become detached from the values of the rest of science and lose sight of certain basic reality principles: we have, in the past few months, seen an example of precisely this problem in the field of electrochemistry, which I am told is one of these. But the advancing edge of sciences adhere to unavoidable reality principles. Having disposed of the negative, let us ask: can we find a theory of aesthetic value which is at all common between the arts as normally understood, and the sciences? The arts, of course, have their equivalent of the facile games I referred to in the sciences: sentimental verse, picture postcard art; there is, of course, a great body of aesthetic theory on which I am certainly not an expert; but I have over a number of years, picked out a number of statements which I think are significant. In sculpture and painting, the critic Berenson has made much of what he calls “Tactile Values”, which seems to mean giving the viewer a sense of personal involvement in the action or motion or scene depicted. A similar, if quite diﬀerent, statement by a sculptress friend once impressed me strongly: she felt that all successful sculpture, no matter how abstract, referred back’to the human body. Finally, also in the visual arts, the use of iconography and symbol is a common bond between ultramodern painters such as Jasper Johns and Frank Stella, and classic painters and sculptors, especially religious art but also classical oriental painting. In the modern paintings, the iconography is self-created by repetition of certain motifs, but it is firmly there. All of these kinds of remarks bring out two theses which I want to put forward and test (1) That even in abstract art there must be a “content” or “substrate” to which the viewer is expected to relate. Nothing serious is beautiful in a vacuum; in fact, this is thought now to be a property of the human mind: that it can not think, can not perceive, can not communicate except about something: the mere act of communication requires context.

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(2) To be beautiful, a piece of art should have more to it than surface content. It should be enriched by more than one layer of meaning. This brings me to a theory of aesthetics in literature and poetry which very much intrigued me, the ideas of T.S. Eliot and the Cambridge school of critics such as David Daiches. Eliot uses the word “ambiguity” to express himself, perhaps a misleading use of this word which often, in English, means “fuzziness” or lack of clarity; whereas Eliot was always absolutely certain of what he meant. What he really meant was that good poetry should have as many levels of meaning packed into the same words as possible. In his poem “The Wasteland” for instance, there are characters carrying out certain actions on the surface, which is at least clear enough that much of the poem may be read directly as a series of stories. There is also a surface level of absolutely gorgeous use of language. There is, underneath those two levels, a sense of despair at the moral emptiness of the modern world of the time; and still under that, if we read quite carefully, there are a series of references to myth, especially the Grail legends and those involving the Fisher King. On a more obvious level, his play “The Cocktail Party” has quite obvious Christian symbolism superposed on an apparently clever, brittle drawing-room comedy. But in this, in Japan, I am probably telling you nothing new: in the land of the Haiku, the delicate use of ambiguity and crossreference needs no explanation. Leonard Bernstein’s Harvard lectures give some beautiful examples of this kind of cross-reference or multiple meaning in, especially, Stravinsky’s music; I am not an expert on music and can give you no further examples. But a kind of music I do know well, classic American Jazz, is again a case of multiple-layered meaning and multiple reference. Characteristically, the surface meaning of jazz is a sentimental love song or a naive hymn; this is then overlaid with an ironic twist which pokes fun at its sentimentality or simplicity, and possibly also emphasizes a less respectable meaning of the lyrics; and, finally, there is the contrapuntal improvisation which is a pure, rather abstract musical object, only weakly related to the original tune and often bringing in cross-references to other pieces of music: quotes from Souza marches, bugle calls, or even well-known classical pieces. As far as I understand the concepts of structuralism and of deconstructionism, my point of view is diametrically opposite to these; I have a feeling that these ideas devalue art and, when applied to science, often have the same eﬀect as the sociological relativism which I have already deplored. Let me then set out the criteria for beautiful science which I am going to try to abstract from these ideas about beautiful art. (1) Reality principle: The work must refer to the external world, not just to the contents of the scientist’s (artist’s) mind. In this I make a real distinction between mathematics and science. Mathematics creates its own world, and because of the long history of mathematics there is a shared substrate of ideas within which crossreference is possible. But I think any mathematician would agree that beauty in mathematics lies in tying together pre-existing material, rather than in meaninglessly arcane postulational systems.

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On the other hand, natural science is the science of nature, not of imaginary worlds; I do not, for instance, feel that cellular automata are part of nature, so that study of their properties must be judged as mathematics, not as science. I have, myself an aesthetic prejudice in favor of science which takes nature as she is, not that which studies artifacts made by the scientist himself such as gigantic accelerators or fusion machines. I accept that this is personal, not universal, and that clever technology can be beautiful to many people. (2) Craftsmanship is always an element of beauty, in science as in art. The act of creation must be non-trivial and it must be done well. Much ultra-modern art fails on this score, as a visit to, say, the L.A.County museum can easily convince one. The lucky fellow who happens on a new substance or a new eﬀect may win a prize, but we, as scientists, do not really value his contribution unless he displays other characteristics: Edison, as scientist, is not a model we really admire. In science, however, one often finds that the discoverer does not necessarily craft his discovery optimally: BCS theory, for instance, was first expressed in its ugliest form, and only refined by Bogoliubov, Nambu and others into a thing of Beauty. We accept this as the nature of the beast, and it is perhaps not unknown in art; for instance, the Dutch school discovered counterpoint, but Bach exploited its possibilities beyond their abilities. (3) Next is the principle of maximal cross-reference, i.e. my “ambiguity” equivalent. This refers both to diﬀerent levels of meaning and to breadth of reference in the real world. I will talk about examples later, but perhaps I can continue with the BCS theory as a relatively simple one. Once re-expressed in Bogoliubov-Nambu form, it became almost evident that BCS could be a model for a theory of elementary particles as well as of its “surface” meaning, theory of superconductivity. Once expanded by Gor’kov in Green’s function form, it not only allowed many new insights into the phenomenology of superconductivity, but acquired a second meaning as not just a “model”, parameterized theory but a “microscopic”, computable theory. And, finally, Bohr, Mottelson and Pines extended the idea to nuclear matter, and Brueckner, Morel and myself to the anisotropic superfluid 3 He, bringing, in the end, two enormously fertile and unexpected references into the picture. Where does the beauty reside? Of course, not entirely in the original paper which solved the problem of superconductivity, although indeed that was a well-crafted, very exciting paper. Not in any single object or work: not even any historian of science will be capable of dissecting the entire web of connections brought forth by the phrase “BCS”. Perhaps, in some abstract sense, in the citation network: who cites whose paper and why? Science has the almost unique property of collectively building a beautiful edifice: perhaps the best analogue is a medieval cathedral like Ely or Chartres, or a great building like the Katsura detached palace and its garden, where many dedicated artists working with reference to each other’s work jointly created a complex of beauty. (4) I want finally to add one criterion which is surely needed in science and probably so in art: a paradoxical simplicity imposed on all the complexity. There is the famous story of Ezra Pound editing T.S. Eliot’s “Wasteland”: that he reduced

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its total length by nearly half, without changing any of the lines that he left in, and greatly improved the poem thereby. In science, even more than in art, there is a necessity to achieve maximal simplicity, not just an aesthetic preference. The subjects with which we deal, and the overall bulk of scientific studies grow endlessly; if we are to comprehend in any real sense what is going on, we must generalize, abstract, and simplify. Together with the previous criterion, this amounts to a very basic dictum for good science, pot just beautiful science. We must describe the maximum amount of information about the real world with the minimum of ideas and concepts. In a way, we can think of this as a variational problem in information space: to classify the maximum amount of data with the minimum of hypotheses. Of course, this is just “Occam’s razor” of not unnecessarily multiplying hypotheses, which in fact has been given a mathematical formulation in modern computer learning theory by Baum and others. In this case, our aesthetic concept is severely practical as well. Again returning to our canonical example of BCS theory, in its original formulation it was not at all clear what the minimal set of hypotheses was: whether the crucial feature was the energy gap, or the zero-momentum pairing idea, or what? With refinement, which came in response to the Russian work and to the Josephson eﬀect, gradually we discarded details and recognized that the one core concept is macroscopic quantum coherence in the pair field, which when coupled with a fermi liquid description of the normal metal leads inevitably to one of the versions of BCS theory. The beauty of the theory lies in the immense variety and complexity of experimental fact which follows from these two concepts. But without the existence of all that variety of experimental fact, and of the painful, exhilarating process of connecting it in to the main mass, the concept alone seems to me to be a meaningless, relatively uninteresting mathematical game. It is in the interplay, the creative tension between theory and experiment, that the beauty of science lies. Let me give a few examples of beautiful science to try to clarify my ideas further. To begin with, let me hop entirely outside my own specialty and recall an incident from a recent book by Francis Crick. He was describing a dinner meeting at which Jim Watson was to be the feature speaker, and he describes Jim being plied with sherry, wine and after-dinner port, and then struggling with a presentation of their joint work on the double helix. The practical details he got through, but when it came time to summarize the significance, he just pointed at the model and said — “It’s so beautiful... so beautiful”. And, as Crick says, it was. Why? As a model of one of the true macromolecules of biology it did, of course, embody brilliant technical advances and insights, and in addition as a structure itself it contains the creative tension of simple repetition yet complex bonding. But of course, he meant far more than that: that with the structure in hand, it was possible to first envisage that the detailed molecular mechanism of heredity, and of the genome determining the phenotype, could eventually be solved. At that point not much further had been solved — one was just at the stage of proving that the obvious mechanism of DNA replication on cell division was really taking place, by quantitative measurements of DNA amounts — but that the original piece of the puzzle lay there in that model was hardly to be doubted. Crick and Watson, to their

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credit, did see — and did, especially Crick, later participate in and formulate — the whole complex of ideas that was likely to arise from their work. Crick and Brunner called this the Central Dogma, and the role played by macroscopic quantum coherence in BCS theory is played by the Central Dogma in this theory. The “Central Dogma” is, of course (1) DNA → DNA (2) DNA → mRNA transcription and (3) mRNA → protein gene expression (3) implies a code Some of this was already known in a vague way: that genes determined protein sequence, for instance, so if the gene was DNA, DNA → protein was obvious — but was it? Crick points out that Watson and he were the first to make up the standard list of 20 amino acids, as a response to their realization that a code must exist. Some of the most beautiful — because simple — scientific reasoning in history went into the determination of the code. Enough said — Jim Watson’s alcoholic musing was right. (2) Again, to go outside my specialty, one of the truly beautiful complexes in science is the gauge principle of particle physics: the realization that all four of the known interactions are gauge interactions, in which the form of the forces coupling the particles follows from symmetry and not vice versa. A very nice discussion of this area is to be found in C.N. Yang’s scientific autobiography, written as an annotation of his collected papers. Mathematicians will tell you that they invented gauge theory anywhere from 50 to 100 years before the physicists in the form of something called “fiber bundles”. I do not take this seriously — see my remarks about the “reality principle”. A theory as a mathematical object is simply a statement about the contents of someone’s mind, not about nature. Another point worth noting is that quite often the physicist — or other scientist, as in the case of probability theory — invents his own mathematics which is fairly satisfactory for his purposes, and only later finds the relevant branch of mathematics — as with Einstein and non-Euclidean geometry. Gauge was first used as a formally symmetric way of writing Maxwell’s equations, and formal manipulation with it played a significant role in early attempts to produce a “projective” unification of gravity and electromagnetism. But the gauge idea proper stems from the work of Dirac, Jordan and others in reformulating quantum electrodynamics. What was done was to combine the early ideas of Wigner and Weyl on the role of symmetry in quantum mechanics with the “locality” principle of Einstein’s general relativity. Quantum mechanics connects symmetry and conservation laws: time-invariance = energy conservation, rotation-invariance = angular momentum, etc; but from the Einsteinian point of view, the elementary interactions must allow only local, not global, symmetries. The appropriate symmetry principle for charge conservation is phase-invariance of a complex field; but to make phase-invariance local we must introduce the gauge field A and write all derivatives as i¯h∇ − ec A. The dynamical theory of the vector potential A is then just electromagnetic theory. This is the message of gauge theory: out of three concepts one gets one.

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Conservation laws, symmetries, and interactions are not three independent entities but one. Next — from the physicist’s side, this is where the mathematicians make their unjustifiable claims — Yang and Mills realized that the gauge theory was not unique, in that the symmetry involved did not need to be Abelian; but such a theory introduces gauge fields which carry the conserved quantity. After many false starts it became clear that the appropriate theory for strong interactions was color gauge theory, quantum chromodynamics based on the group S U(3). Here yet another thread was brought in by T’Hooft, Gross, Politzer and others: the proof that gauge theories of this sort are asymptotically free and hence renormalizable. To make a long story short, with yet one more beautiful idea, that of broken symmetry, we now contemplate a world in which all four basic interactions are gauge theories: the threedimensional S U(3), the 2 + 1 dimensional S U(2) × U(1) of the electroweak theory, and the 4-dimensional gauge theory which is Einstein’s gravity. Whether the fact that the dimensions add up to 10, an interesting number in string theory, is significant is still much under discussion. One can hardly not, even at this stage, sit back and marvel at the beauty and intricacy not just of this simple structure but of its history and its cross-connections to many other ways of thinking. One could go on following almost any thread of modern science and find an equivalent beauty at the center of it. One more instance will allow me to be a bit self-indulgent: topology, dissipation, and broken symmetry. This starts with four apparently independent but individually beautiful pieces of work. First, the dislocation theory of strength of materials, when Burgers Taylor and others first invented the concept of the dislocation or line defect of the crystalline order, then — using very modern-sounding topological arguments — proved that it was topologically stable, and finally showed that motion of dislocations was the limiting factor in the strength of most materials. Second chronologically was the beautiful work of Jaques Friedel’s grandfather, G. Friedel, in identifying the defects in liquid crystals — specifically the “nematic” liquid crystal, so-called because the defects appeared threadlike. Third was the domain theory of ferromagnetism, and especially the beautiful sequence of work of Shockley and Williams showing how the motion of domain walls — planar defects where magnetization rotates — accounts for hysteresis loops in magnetic materials. Finally, there are the gorgeous conceptual breakthroughs of Feynman, and then Abrikosov, where Feynman, in particular, invented the superfluid vortex line and showed that it could account for the critical velocity of superfluid helium, while Abrikosov described the vortex state of superconductors and I later pointed out that motion of the vortices implied resistance. Oddly enough, it was the discovery of superfluidity in 3 He which triggered the realization that these were all the same phenomena. Almost simultaneously, Volovik and Mineev, and Toulouse and Kleman developed the general topological theory of defects in condensed phases, encompassing the physics developed over 100 years prior to 1975 in a single structure, classifying the possible topologies of maps of real space into the space of the order parameter of the condensed phase. For instance, for liquid helium the order parameter has a free phase so one must map space onto

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a circle; if that map is non-trivial, it implies that at some line in space the order parameter vanishes. This means that the defects are vortex lines. Then Toulouse and I made the general connection between motion of topological defects and the breakdown of a generalized rigidity of the system, implying dissipation: which couples together all these energy dissipation mechanisms. The great generality of this kind of structure has been exploited in the theory of “glitches” in the spinning neutron stars or pulsars: giant slippages of the vortex structure implied by the superfluidity of the neutron matter in such a star, beautifully isomorphic with the “flux jumps” which are the bane of superconducting magnet designers. More or less at the same time, topology became fashionable in elementary particle physics, with the revival of the “Skyrmion” model of the fermion particle, and the fashion for “θ vacua” and “instantons”. This is one of these fascinating cross-connections, although the topological ideas have not yet had their satisfactory resolution in particle theory. As I already said, pick up almost any thread near the frontiers of modern science and one will find it leading back through some such sequence of connections. For example, an equally glorious story can be made of the separate investigations which, together, make up the present synthesis called “plate tectonics”. But if there is beautiful science, is there also ugly science? I regret to say that this also exists and often flourishes. It does so most commonly when a field falls out of eﬀective communication with the rest of science; one often find fields or subfields which have lost contact with most of science and survive on purely internal criteria of interest or validity. The behaviorist or Skinnerian school of experimental psychology was a notorious example; I suspect that these days we are seeing an exposure of the entire field of electrochemistry to the pitiless light of real science. And certain recent incidents in the field of superconductivity have inclined me to believe that there is an isolated school of electronic structure calculators who have been avoiding contact with reality for some years. Finally, there is, of course, pseudoscience, which will always be with us: parapsychology, “creation science”, “cognitive science”, “political science”, etc. — Crick once made the remark that one should always be suspicious of a field with “science” in its title. I leave you with the final thought, that the essentially aesthetic criteria I have tried to describe for you may often be an instant test for scientific validity as well as for beauty.

11

Particle Physics and Cosmology: New Aspects of an Old Relationship Leon Van Hove

Abstract This address was presented by Leon Van Hove as the Nishina Memorial Lecture at the University of Tokyo, on April 11, 1990.

1. Introduction It has been a great pleasure to visit Japan as a guest of the Nishina Memorial Foundation, and I am deeply honoured to deliver the Memorial Lecture dedicated to the illustrious Japanese physicist Yoshio Nishina. I have chosen to speak on the relationship between physics and cosmology, not a new subject but one that experienced in the last decade a flurry of exciting developments triggered by the new results and speculations which marked the rapid progress in particle physics in the 70’s and 80’s. The aim of cosmology is to study the large-scale struc- Leon Van Hove c ture of the Universe and to reconstruct its early history on NMF the basis of the astronomical observations and of the laws of physics. The historical element is crucial in the study. When astronomers observe distant objects, the signals they detect have travelled a long time and therefore reflect the state of these objects in the deep past. Furthermore, astronomers cannot look very far in space nor very deep in the past. During the early and most interesting phase of its expansion, the Universe was presumably filled with very hot and dense matter which absorbed and thermalized all electromagnetic radiation including all information-carrying signals. Cosmology is therefore an historical discipline condemned to work with highly incomplete records. Using the laws of physics, the cosmologist can only speculate Leon Van Hove (1924 – 1990). CERN (Geneva, Switzerland) at the time of this address L. Van Hove: Particle Physics and Cosmology: New Aspects of an Old Relationship, Lect. Notes Phys. 746, 245–259 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 11

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on how the Universe could have evolved and what its large-scale structure could be. Consistency with observations and logical consistency are of course demanded, but plausibility arguments and assumptions play a big role despite their unavoidable lack of objectivity. The deepest one goes into the past, the largest is the dependence on theoretical speculations. In the last decade such speculations have proliferated to an amazing degree, throwing into doubt at one time or another almost everything that seemed generally accepted in the cosmological models of the 60’s and 70’s, and inventing for the expansion of the Universe a variety of possible “scenarios” which compete for scientific recognition. A striking impression of the change in cosmological thinking is given by contrasting S. Weinberg’s classic “The First Three Minutes” (1977) [1] with A. Linde’s very recent “Particle Physics and Inflationary Cosmology” (1990) [2]. A closer appreciation of the highly diversified evolution of cosmological thinking in the 80’s can be gained from the successive Proceedings of the ESO-CERN Symposia on “Astronomy, Cosmology and Fundamental Physics” (Geneva 1983, Garching bei M¨unchen 1986, Bologna 1988)( [3], [4], [5]). My aim in this lecture is not to review those many speculative developments. I shall concentrate on general features common to most of them, on items where knowledge has advanced reliably (although usually not enough to give unique answers) and on some unsolved problems for which progress can be expected in the coming decade or so.

Fig. 11.1 Scene at the lecture room of the University of Tokyo (1990)

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2. Matter in the Expanding Universe As evidenced by all observations, the spatial distribution of “visible”, i.e., electromagnetically detectable matter in the Universe is extremely inhomogeneous, with many sorts of clustering (stars, galaxies, clusters and superclusters of galaxies, voids, filaments and / or sheets, gas clouds, etc, etc). So far, attempts to define a characteristic length for the space structure are inconclusive because they tend to give results of the order of the largest distances observed. Despite the inhomogeneities, the very simple Hubble expansion law continues to hold on the average up to the largest observed distances. In amazing contrast with the high degree of inhomogeneity of visible matter, the microwave background radiation (MBR) must have an extremely homogeneous space distribution. As recently measured by the COBE satellite, its spectrum is blackbody to very high precision (T = 2.7 K). Apart from the dipole anisotropy due to our “peculiar” motion with respect to the local average comoving frame, the MBR is highly isotropic (to a level of 10−4 , soon to be improved by COBE). All this is only understandable if the space distribution of the MBR is very homogeneous. To form a theoretical picture of this contrasting situation, one usually assumes that, despite the observed inhomogeneity of visible matter, there is an average homogeneity of all matter over very large, as yet unobserved distances. Averaging over such distances one can assume the expanding Universe to be described by an homogeneous (Robertson-Walter) metric with a time-dependent scale factor a(t) [a(t) represents the distance at time t between two comoving local frames; choosing two other such frames only multiplies a(t) by a constant]. The Einstein equations of General Relativity then give H 2 = 8πGρ/3 + k/a2 + Λ,

H ≡ a−1 da/dt

(11.1)

with H(t) the Hubble “constant” (constant in space, not in time), G Newton’s constant, ρ(t) the non-gravitational energy density including all mass contributions, k the curvature constant and A the cosmological constant (currently the latter is the subject of wide-ranging discussions and speculations). The units used in eq. (11.1) are such that h/2π = c = 1. At present the estimated value of ρ for visible matter (of order of 0.1 ÷ 1 GeV/m3 , i.e., 0.1 ÷ 1 nucleon / m3 on the average) gives for the first term of (11.1), 8πGρ/3, no more then a few percent of the observed value H 2 ∼ 4 × 10−36 sec−2 , which itself is still very uncertain (at least by a factor 2) whereas k/a2 and Λ are believed to be H 2 in absolute value. Unless we live in a special era of the expansion, one expects 8πGρ/3 to be very close to H2 , and the popular “inflationary” scenarios of the early expansion have made this an attractive prediction. Hence the current strong belief that our present Universe contains lots of “dark”, i.e., invisible matter, and the multitude of attempts to try to detect and identify it. Dark matter could come in many sorts: ordinary matter (protons, nuclei, electrons) too cold to emit visible light (as is the case for the planets), and / or massive neutrinos (masses of a few tens eV are of interest), and / or so far unknown types of particles for which many candidates

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have been proposed in the last 15 years by theorists trying to extend and improve the Standard Model of particle physics. The usual basis for the reconstruction of the history of the expanding Universe is eq. (11.1) supplemented by d(ρa3 )/dt p da3 /dt = 0 (11.2) (p = pressure) which expresses energy conservation for a comoving domain of volume a3 under the simplest thermodynamic assumption, namely adiabatic expansion (no entropy creation). Eqs. (11.1) and (11.2) can be solved for a(t) and ρ(t) if the pressure p is a known function of the energy density ρ. Before the dark matter issue came up, this was straightforward for the present Universe where ρ was supposed to be the mass density of visible matter (protons, nuclei, electrons, all with nonrelativistic velocities in the comoving frame) plus very small contributions due to photons and massless neutrinos. If this were the whole story, or if most dark matter consisted of neutrinos, the pressure term in eq. (11.2) would be negligible, (p a3 ), p would be ∝ a−3 and eq. (11.1) would give a ∝ t2/3 , at t early enough for k/a2 and Λ to be negligible. Another extreme case of great simplicity obtains if most dark matter consists of (almost) massless particles having extremely weak nongravitational interactions. The pressure is then p ∼ ρ/3 and eqs. (11.1, 11.2) give ρ ∝ a−4 , a ∝ t1/2 (the latter again when k/a2 and Λ are negligible). The dark matter problem illustrates the great importance of neutrino physics for cosmology. As is well known, another case in point concerns primordial nucleosynthesis. A major step forward has been taken last year, when the new e+ e− colliders (SLC at SLAC, LEP at CERN) operating on the Z0 peak established that the number of neutrino species produced with standard electroweak coupling is three. This number corresponds to the species known from earlier experiments and agrees with the number needed to account for primordial nucleosynthesis. Unfortunately, progress is much slower on the equally important problem of neutrino masses. The 1988 Particle Data Table report the upper bounds 18 eV, 250 eV and 35 MeV for the electron -, muon - and tau - neutrinos respectively. After an ITEP group (Moscow) reported some years ago a non-vanishing νe mass in tritium decay (their present value is 26 ± 5 eV), a number of new experiments were undertaken with results so far compatible with zero mass. Regarding the muon - and tau - neutrinos, the experimental problems are even much more formidable, and it will at best be a long time before the neutrino side of the dark matter problem is solved.

3. The Visible and Invisible Parts of the Universe Our large-scale astronomical observations are entirely based on electromagnetic radiation, mostly visible light and radio waves (one day, perhaps, gravitational waves will be detected, widening immensely our cosmological horizon!). At present, electromagnetic radiation travels almost undisturbed through intergalactic space because

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there is very little ionized matter to absorb it. But this was not so in the past, when the MBR, instead of its present T = 2.7 K = 2.3 × 10−4 eV (we put Boltzmann’s constant =1), was blackbody radiation at temperatures T 3000 K = 0.26 eV and was able to ionize matter. The latter was then an electron-ion plasma, in thermal equilibrium with the photons and opaque to electromagnetic radiation on astronomical scales. By the Hubble redshift, the temperature of the photon blackbody spectrum scales like 1/a(t). We must therefore conclude that we have no astronomical observations on the state of the Universe at times t < tdec when a(t) was < a(tdec ) ∼ (2.7/3000) a(tpres), where tpres refers to the present and the “decoupling time” tdec refers to the period, where matter became electrically neutral and the photons decoupled from it. Consequently, since in our units light travels with velocity 1, the visible part of the Universe has a diameter Dvis ∼ tpres − tdec . To estimate Dvis we must solve eqs. (1,2) between tdec and tpres , which requires assumptions concerning dark matter. The two simple cases considered in section 2 give C = constant (11.3) ρ ∼ C a−n , with n = 3 and 4. As long as one avoids recent times so that the k/a2 and Λ terms can be neglected, eqs. (11.1) and (11.3) give n−1 dρ−1/2 /dt = L L ≡ (8πG/3)

1/2

(11.4)

= 1.2 × 10

−19

= 7.8 × 10

GeV

−44

−1

sec

(11.5)

(11.4) is integrable. It gives the time interval t2 − t1 between an early and a later phase of the expansion (t1 < t2 ) in terms of the corresponding energy densities ρ1 , ρ2 : t2 − t1 = (ρ2 −1/2 − ρ−1/2 )/nL

(11.6)

The uncertainties on the ρ values are much larger than the uncertainties on n (n = 3 or 4) and the diﬀerence between our crude approximation (11.4) and the full equations (11.1), (11.2). Eq. (11.6) is therefore good enough to estimate the time development of the expansion. For example, for t1 − tdec and t2 − tpres , (11.6) gives Dvis ∼ tpres − tdec ∼ (ρpres 1/2 nL)−1

(11.7)

because ρdec ρpres . We adopt ρpres ∼ 10 ÷ 50 GeV/m3

(11.8)

which would correspond to some 10 to 50 nucleons per cubic meter if all the matter is nucleonic, instead of the estimated 0.1 ÷1 nucleon/m3 of visible matter. Eq. (11.7) then gives

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Dvis ∼ (1 ÷ 2)1023 km tpres − tdec ∼ (1 ÷ 2)10

10

years

(11.9) (11.10)

Eq. (11.9) gives the estimated size of the visible part of the Universe. Up to a few years ago, most cosmologists assumed the visible and invisible parts of the Universe to have the same properties (assumption of overall homogeneity). Recent considerations on the possible eﬀects of quantum fluctuations at very early times have led to a change in attitude, and a popular trend of theoretical cosmology is now to discuss highly inhomogeneous scenarios for the invisible part of the Universe (see section 7). The vast array of current speculations encompasses changes not only in the state of matter, but in the fundamental physical constants, the laws of physics, and even in the dimensionality of spacetime! Needless to say, there are no observational indications for such dramatic eﬀects. Let us now discuss times before tdec and in particular what is commonly called the “age of the Universe”, widely quoted to have a value of order (11.10). For t < tdec , and as long as the Standard Model of particle physics applies (i.e. for temperatures up to ∼1 TeV = 103 GeV, the highest energy attained by an existing accelerator, the Fermilab Tevatron), the pressure in eq. (11.2) can be taken ∼ ρ/3, so that eq. (11.3) applies whith n = 4. As mentioned in section 5, there is a phase transition at T ∼ 200 MeV, which causes a sudden change in the coeﬃcient C of (11.3). Taking this change into account shortens the estimate (11.6) by an amount of order 10−5 sec, totally negligible for our present discussion. We therefore apply (11.6) with n = 4 to the interval tdec − tTeV where tTeV is the time where the temperature was 1 TeV tdec − tTeV ∼ (ρdec −1/2 − ρTeV −1/2 )/4 L ∼ (4ρdec 1/2 L)−1

(11.11)

ρdec is of order 1 GeV/cm3 and ρTeV ∼ 10 TeV4 ∼ 2 × 1050 TeV/cm3 . Hence tdec − tTeV ∼ 3 × 1013 sec = 0.95 × 105 years

(11.12)

and adding to (11.10) we have tpres − tTeV ∼ (1 ÷ 2)1010 years

(11.13)

The latter estimates would not be aﬀected if tTeV is replaced by any earlier time t1 such that ρ ∝ a−4 holds between t1 and tTeV because tTeV − t1 ∼ (ρTeV −1/2 − ρ1 −1/2 )/4L ≤ (4ρTeV 1/2 L)−1 ∼ 4 × 10−13 sec

(11.14)

a totally negligible time compared to (11.12) and (11.13). In the present cosmological discussions, it is the early epoch, of duration 10−13 sec and characterized by temperatures 1 TeV but presumably already with a ρ ∝ a−4 type expansion, which best deserves the name of Hot Big Bang (HBB), whereas the so called “age of the Universe” is the time elapsed since then, of order (1 ÷ 2)1010 years. The present trend is to abandon the view, very popular in the last

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decades, according to which that epoch started with a space-time singularity [ρ1 = ∞ and a(t1 ) = 0 in the above equations] marking the “beginning” of the Universe. The main reason for this change of attitude is the diﬃculty to understand in such a scenario the observed isotropy of the MBR. As explained in section 7, a radically diﬀerent ρ(t) versus a(t) behaviour is needed to account for this property. There are undoubtedly many theoretical possibilities, including scenarios where the Universe pre-existed and the HBB relevant to the part visible to us resulted from a local quantum fluctuation [6]. This completes our discussion of the limited space-time domain of the Universe about which we can claim to have a fair degree of knowledge. Our main aim was to point out the uncertainties still aﬀecting what many regard to be the standard, i.e., well established part of cosmology. We did not even discuss the inhomogeneity of all visible matter, simply because no convincing solution is yet known to the problem of explaining its origin.

4. Production of Exergy From now on we take t to be the time after the Hot Big Bang (HBB) as defined in the previous section. At time t ∼ 1 sec, the temperature of matter and of radiation (photon gas) in the Universe had dropped to T ∼ 1 MeV = 1.2 × 1010 K and departures from thermal equilibrium began to appear. Matter was then composed of nucleons (protons and neutrons), electrons, positrons, (anti-) neutrinos, and possibly exotic particles now belonging to dark matter. At T ∼ 1 MeV the rate of collisions controlled by the weak interactions, i.e., those involving neutrinos, dropped below the expansion rate and very rapidly these collisions became so rare as to be negligible. The neutrinos became in eﬀect a non-interacting gas, each of them with a momentum redshifted by the expansion proportionally to a−1 with a = a(t) the scale parameter. Also the neutron to proton ratio ceased to be given by the ratio of the Boltzmann factors, exp(−Δm/T) with Δm = mn − mp = 1.3 MeV. The n/p ratio became constant, except for a small initial decrease due to the decay of free neutrons which stopped at t ∼ 3 min when all remaining neutrons were stabilized by being bound in light nuclei, mainly 4 He (about 25 % of nucleons were then bound in nuclei, the others being free protons), the so-called primordial or big bang nucleosynthesis. The formation of heavier nuclei was negligible because of the very low densities and reaction rates; it could only occur at much later times (t > 105 to 106 years) when stars had formed and high reaction rates became possible in their dense and hot interior. While the neutrinos and nucleons were falling out of equilibrium from t ∼ 1 sec onward, the electromagnetic interaction maintained thermal equilibrium much longer between photons, electrons and positrons and it also maintained the protons and light nuclei in kinetic equilibrium with them, i.e., the velocity distribution of protons and nuclei remained the equilibrium one for the same temperature T . This situation persisted until the formation of neutral atoms at t ∼ 105 years. Most

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positrons had disappeared by annihilation with electrons as early as t ∼ 15 sec (T ∼ 0.3 × 109 K). From then on the remaining electrons were as numerous as the protons (electric neutrality), about one electron and one free or bound proton per 109 to 1010 photons. Although in kinetic equilibrium as mentioned above, the nucleons after t ∼ 1 sec were out of chemical equilibrium, i.e., their distribution in nuclei diﬀered from the equilibrium one for the photon temperature T . As explained by Eriksson et al.7) chemical equilibrium of the nucleons would have corresponded to almost 100 % free protons at T > 3.3 × 109 K, almost 100 % 4 He at 3.0 × 109 K > T > 2.5 × 109 K and almost 100 % 56 Fe at T < 2.2 × 109 K, in each case with the appropriate numbers of electrons to have electric neutrality. The changes between these equilibrium compositions would have taken place in very narrow temperature intervals, but this would have required nuclear fusion rates faster than the expansion rate a−1 da/dt of the Universe, and the actual fusion rates were very much slower. This is the cause of the non-equilibrium feature which preserved free protons and delayed the synthesis of heavy nuclei until the late times (t > 106 years) when star formed and started to burn. As was done in [7], it is interesting to determine quantitatively the amount of non-thermalized energy which became available after t ∼ 1 sec due to the nonequilibrium feature just discussed. This quantity is a special case of what has been called exergy, the maximum amount of non-thermal energy (mechanical work) which can be extracted from a physical system (in our case the nucleons in the Universe) under the prevailing conditions (here the photon gas as heat bath), without violating the laws of thermodynamics. Eriksson et al. [7] find that the nuclear exergy, i.e., the exergy related to the strong, electromagnetic and weak interactions of the nucleons, amounts to 7.8 MeV per nucleon, and this reserve of non-thermalized energy was formed in the first day of the expansion (1 sec < t < 24 hours). It increased steadily during this interval, mainly during the first minutes, except for a small drop of ∼ 0.6 MeV/nucleon at helium formation (t ∼ 3 min). A very small decrease of 10 eV/nucleon took place much later, at t ∼ 105 years when atoms formed. Of course, gravitation provides another source of exergy. It is not important in normal stars but is large if neutron stars or black holes are formed.

5. Hadronic Phase Transition According to general considerations and Quantum Chromodynamics lattice calculations, hadronic (i.e. strongly interacting) matter at high temperature (T 200 MeV) takes the form of a quark-gluon plasma, whereas at low temperature and net quark number density it takes the form of a gas of well-separated hadrons inside which the (anti) quarks and gluons are confined. The lattice calculations predict that the phase transition is probably of 1st order and occurs at T c ∼ 200 ± 50 MeV. Furthermore, the discontinuities Δρh , Δsh of the hadronic energy density ρh and entropy density share probably large, perhaps of the order of the values of ρh , sh on the low, hadron

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gas side of the transition. This is for small or vanishing net quark number density, the case appropriate to the early Universe. The transition temperature T c ∼ 200 MeV was reached at a time tc ∼ 10−5 sec after HBB. It is probable that the hadronic transition took place through nucleation, i.e., formation and growth of bubbles of hadron gas in the quark-gluon plasma, a smooth process described by eqs. (11.1) and (11.2) with constant pressure p, and taking place in a time interval from tc to a time of order (1.5 ÷ 2)tc. While it is now generally regarded to be unlikely that the hadronic phase transition had any lasting consequence on the expansion of the Universe, the discussion of possible eﬀects led to some interesting considerations, two of which will be briefly mentioned. Due to our ignorance of the non-perturbative aspects of Quantum Chromodynamics (the field theory of quarks and gluons, and hence of all hadronic phenomena), we cannot exclude the possibility that the hadronic phase transition could have been violent, for example with strong supercooling and sudden release of large amounts of latent heat over times of microsecond order. This could generate chaotic pulses of gravitational waves which would have travelled through space since time tc , with very little damping but with the strong redshift resulting from the Hubble expansion. The present frequency range of the pulses would then be 1 year−1 . Quite remarkably, high-precision timing measurements of millisecond pulsars can probe this range of gravitational wave frequencies, although detection of a signal would of course not yet mean that it would have originated from the hadronic phase transition. Other explanations would exist, e.g., “cosmic strings” as postulated by some models of galaxy formation.(8) Another possible consequence of nucleation in the hadronic phase transition could be the occurrence of large inhomogeneities in the space distribution of nucleons, persisting as long as the neutron-to-proton ratio was in thermal equilibrium with the electron-neutrinos, i.e., until t ∼ 1 sec (T ∼ 1 MeV). Up to that time, the nucleons oscillated very rapidly between the proton and the neutron states, their oscillating electric charge preventing them from diﬀusing through the dense electron plasma from the nucleon-rich to the nucleon-poor regions. After t ∼ 1 sec, the neutrons could only become protons by the very slow process of beta decay (lifetime 891 ± 5 sec, another particle property of great importance for cosmology). Being electrically neutral, they could then diﬀuse to the nucleon-poor regions, leaving the protons behind. These curious phenomena have been modelled in considerable detail in the last few years, the most remarkable finding being that among the nuclides produced by primordial nucleosynthesis, the very rare lithium-7 turns out to be very sensitive to inhomogeneities in the nucleon distribution. The primordial 7 Li abundance can in fact be related to the actual parameters of the hadronic phase transition, especially its critical temperature T c .(9) It should also be recalled, of course, that the ultra-relativistic heavy ion beams available at Brookhaven and CERN (now up to sulphur, in a few year’s time lead at CERN and gold at Brookhaven) provide a more direct access to the study of the hadronic phase transition through the detailed experimental and theoretical investigation of nucleus-nucleus collisions 10].

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6. Baryon Asymmetry and Standard Model Modern particle physics suggests that the observed asymmetry between matter and antimatter in the present Universe (much less antimatter than matter) can have originated from a symmetric situation at early times, under a variety of conditions including non-equilibrium features of the early expansion. This has become an very active domain of research, and many diﬀerent models have been explored. Quite a few gave an asymmetry compatible with the observed sign and magnitude (1 nucleon and 0 antinucleon per 109 to 1010 photons in the present Universe), but none makes definite predictions, not even for the sign. In fact the present situation is that the existing asymmetry is used as one among several constraints which astrophysics imposes upon modern unified theories of particles and interactions. The common premise in this work is that the net baryon number B (number of baryons minus number of antibaryons) was originally negligible and evolved to the present value during an early phase of the expansion. It should be realized that from t ∼ 10−12 sec (T ∼ 1 TeV) onward B was conserved in good approximation and the baryon asymmetry had the form nq − nq¯ , (10−10 to 109 ) nall with the n’s the number densities for quarks, antiquarks and all particles. Now nall ∼ n photons and nq¯ nq . but at t 10−5 sec one had nq + nq¯ ∼ nall and hence nq − nq¯ nq . If the observed baryon asymmetry of the Universe is to have evolved out of a symmetric situation, various conditions must be fulfilled. Firstly, of course, the basic interactions must violate B conservation, and this is the point discussed below. Secondly, both C and CP invariance must also be violated (C is charge conjugation which exchanges matter with antimatter, P is space reflection); indeed since C and CP reverse the sign of B, the appearance of B 0 in a Universe which started with B = 0 can only result from interactions violating B, C and CP. As is well known both C and CP are violated in particle physics. The third condition is a consequence of the CPT theorem, which holds for all relativistic field theories with local interactions and asserts exact invariance for the combined CPT transformation (T is time reversal). A consequence of the CPT theorem is that a system in thermodynamical equilibrium with vanishing chemical potentials is CPT-symmetric, and therefore symmetric between matter and antimatter. Indeed, the hamiltonian is CPT-symmetric by the theorem, and the sum over states covers equally states which diﬀer by space reflection (P), by time reversal (T ), and in case of zero chemical potentials by charge symmetry (C). This remains true (by definition) for any adiabatic, i.e., reversible evolution of such a system. The appearance of a CPT-asymmetric situation out of a symmetric one therefore requires departure from equilibrium. In the 80’s, most work on the baryon asymmetry of the Universe (BAU) consisted in going beyond the Standard Model of particle physics and inventing new field theories with lagrangians implying baryon number violation (BNV). Typically such theories are able to produce the BAU at very high temperatures (T 107 TeV). They disregard the fact that ’t Hooft had shown already in 1976 the existence of BNV in the Standard Model as an exceedingly weak non-perturbative eﬀect (proton lifetime poorly predicted but much longer than anything measurable). More recently, it was

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noted that this Standard Model BNV, which is due to tunnelling between topologically inequivalent vacua through a potential barrier of the order ∼ 10 TeV (tunnelling probability ∼ 10−173 at temperatures T < 20 GeV), could have been much stronger when the Universe was at temperatures T 10 TeV [11] There is so far no reliable way to calculate high temperature BNV in the Standard Model, the diﬃculty lying in the non-perturbative, topological source of the violation. Progress is being made, however. Thus, Ringwald has recently estimated the increase with energy of the Standard Model BNV eﬀects in quark-quark collisions 12]. It turns out to be very rapid, but the strongest BNV eﬀects appear in channels with large numbers of W and Z bosons. This problem is one of the most interesting challenges for positive temperature field theory, and its importance for cosmology is obvious. If Standard Model BNV is important at T 10 TeV, it is clear that the whole problem of the occurrence of the BAU must be reconsidered. Any BAU created by non-Standard-Model interactions at higher T could be erased by the time T drops below 10 TeV. Conversely, a baryon symmetric Universe at very high T could develop a baryon asymmetry, perhaps the observed one, by purely Standard Model eﬀects in the T ∼ 10 TeV range.

7. New Physics in the Early Expansion As mentioned at the end of section 3, the old HBB scenario in which the Universe began at a time t1 where ρ1 = ∞, a(t1 ) = 0 is now generally rejected, the main reason being its failure to explain the observed isotropy of the MBR. This isotropy is only understandable if the MBR is very homogeneous over the whole visible part of the Universe. This homogeneity must have existed for the photons and the electron-ion plasma at the decoupling time tdec , when the size of the now visible part of the Universe was (11.15) Ddec = Dvis a(tdec )/a(tvis ) With the estimates of section 3 we find (remember c = 1) Ddec − (0.6 ÷ 3)107 years

(11.16)

The large uncertainty is again due to the dark matter problem. Before tdec , the photons and the charged particles were in thermal equilibrium, at least locally. Their homogeneity over the distance ddec at time tdec can be understood if interactions had time to act over Ddec before tdec . The eﬀects of interactions cannot propagate faster than light, so that Ddec must be smaller than the maximum distance Dmax (tdec ) which can be covered before tdec by a signal travelling with light velocity (the so-called horizon distance). An elementary calculation based on the RobertsonWalker metric gives Dmax (tdec ) = a(tdec )

tdec

dt/a(t)

(11.17)

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where the integral extends over all times before tdec (i.e., from −∞ or from any finite initial time as the case may be). With (11.16) the condition Ddec < Dmax (tdec ) gives Dmax (tdec ) 6 × 106 years. With (11.17) this can also be written tdec a˙ (tdec ) dt/a(t) 30, a˙ = da/dt (11.18) where we have used the value of a˙ (tdec )/a(tdec ) given by eq. (11.1) with ρ = ρdec − 1GeV/cm3 and k = Λ = 0. As explained in section 3 we can rely on the Standard Model to describe the expansion between the time tTeV when the temperature was 1 TeV and the decoupling time tdec . Neglecting the small correction due to the hadronic phase transition we have ρ ∝ a−n , n = 4. We use eq. (11.6) with t2 = t > t1 = tTeV and we choose the origin of time so that −1

tTeV = 4Lρ1/2 (11.19) TeV (this is a more precise definition of the choice mentioned at the beginning of section 4). Solving for a(t) ∝ [ρ(t)]−1/4 we get a(t) ∝ t1/2 ,

Hence

tdec

a˙ (tdec )

tTeV < t < tdec

(11.20)

dt/a(t) = 1 − (tTeV/tdec )1/2 < 1

(11.21)

tTeV

and the bulk of the inequality (11.18) must come from t < tT eV : tTeV dt/a(t) 29 a˙ (tdec ) or equivalently a˙ (tTeV )

tTeV

dt/a(t) > N

N ∼ 29(ρTeV /ρdec )1/4 ∼ 6 × 1014 1

(11.22) (11.23)

This very large value of the bound N signals how deeply diﬀerent the pre-tTeV expansion must have been from the law, a ∝ t1/2 extrapolated back to t = a = ρ−1 = 0, for which the lefthand side of (11.22) is = 1 ! The fact that N 1 is the celebrated “horizon problem” of early cosmology (this denomination refers to the the “horizon distance” Dmax mentioned above). We now discuss model-independent aspects of the “horizon condition” N 1, before mentioning briefly two popular approaches to its solution. We first ask: can the condition be fulfilled by a power law a ∝ tq (q > 0) beginning at t = 0 ? The answer is of course yes, the condition on q being q > N/(1 + N). From ρ ∝ (˙a/a)2 we deduce ρ ∝ a−n with n = 2/q < 2(N + 1)/N. The adiabatic expansion condition, eq. (11.2), then gives

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p = (n − 3)ρ/3 < −(1 − 2/N)ρ/3 ∼ −ρ/3 i.e., a negative pressure, unusual physics indeed! The same feature holds if the pretTeV expansion is exponential, a ∝ exp(H0 t) with H0 a positive constant (this is a so-called inflationary expansion scenario which could have started at t = −∞; ρ is then constant, ρ = 3H0 2 /8πG, and p = −ρ is again negative). More generally, even without the adiabatic assumption and under the sole condition of continuous expansion (˙a >0), we now show that the horizon condition (11.22) with N 1 implies the very unexpected property that the non-gravitational energy contents of comoving volumes increases dramatically in the pre-tTeV period. This energy varies as ρa3 . It decreases with time or is essentially constant under normal conditions (ρa3 ∝ t−1/2 for a ∝ t1/2 , ρa3 constant for a ∝ t2/3 ). The argument is very simple. Using eq. (11.1) with k = Λ = 0, we can write the lefthand side of (11.22) as ˜ a˜ , a˙˜ ): follows (we abbreviate tTeV and the corresponding values of ρ, a, a˙ , by t˜, ρ, a˙˜

t˜

dt/a = a˙˜

a˜

ain

da/(a˙a) =

a˜

(ρ˜ ˜ a2 /ρa2 )1/2 da/a

(11.24)

ain

ain is the initial value of a(t) taken at t = −∞ or at a finite initial time as the case may be. The horizon condition (21, 22) implies that the quantity (11.24) is 1. This can only be realized in essentially two ways which are not exclusive: ˜ a2 and a fortiori i) Either there was in the pre-tTeV expansion a phase with ρa2 ρ˜ 3 3 ˜a . ρa ρ˜ ii) Or ain was a and ρa2 was of order ρ˜ ˜ a2 for a range of a-values a˜ , so that 3 3 ρa ρ˜ ˜ a in that range. In [13], where the above argument was first published, it is shown to hold also in presence of the curvature term k/a2 of eq. (11.1). Under the adiabatic expansion assumption, eq. (11.2), the strong increase of ρa3 of course means negative pressure at pre-tTeV times. If this assumption is discarded, eq. (11.2) is replaced by d(ρa3 )/dt = −p da3 /dt + T d(s a3 )/dt + dE g/dt

(11.25)

where s represents the entropy density and the term containing it corresponds to irreversible production of heat. The term dEg/dt represents any conversion of gravitational into non-gravitational energy not covered by the previous terms. Equation (11.25) shows that the “new physics” causing the increase of ρa3 is not necessarily related to negative pressure. Strong irreversible processes creating large amounts of entropy, perhaps at the cost of gravitational energy, could equally well dominate the pre-tTeV expansion. We end this section with a few remarks on specific models proposed so far for the pre-tTeV expansion. In the first half of the 80’s, theoretical cosmologists favoured extensions of the Standard Model with a strong first-order phase transition at temperatures 1010 TeV, the high temperature phase being characterized by a very large positive value ρ0 of ρ and a pressure p = −ρ0 . This high temperature phase created a

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period of exponential expansion a ∝ exp(H0 t) with H0 = (8πGρ0/3)1/2 . These were the first inflationary scenarios; they ran into considerable diﬃculties and became very complicated, with a corresponding loss of popularity. More recently a simpler class of models emerged, based on the assumption that the early expansion was controlled by the interaction of gravitation with one or preferably several scalar fields having very large expectation values at pre-tTeV times. Many scenarios are possible (see for example [2]) and current work explores their possibilities without claims to produce realistic models. When the scalar-field expectation values A1 , A2 , . . . are constant over a suﬃciently large space domain, one adopts a Robertson-Walker metric for the domain, and all one has to solve is a simple system of diﬀerential equations for the time variation of the Ai and of the scale factor a(t). The masses and initial values can easily be selected to obtain a pretTeV expansion with the desired properties. There is no built-in initial singularity of spacetime, and the interactions of the scalar fields do not play an essential role. While such models have a strong ad hoc character, a nice feature is that they permit a simple discussion of the long-wavelength fluctuations of the scalar fields. Being redshifted by the expansion, these fluctuations can get “frozen”, with the result that random diﬀerences appear between the expectation values of the Ai in widely separated space domains. This is called “chaotic inflation” and can generate, beyond the limits of the part of the Universe visible to us, large scale inhomogeneities in the spatial distribution of matter and in some of its physical properties.

Concluding Remarks Some sixty years ago, Cosmology was revolutionized by the discovery of the Hubble expansion, Friedmann’s homogeneous expanding solutions of the Einstein equations became the basis for physical models of the Universe (remarkably enough, the pioneer in this respect was a young priest, G. Lemaˆıtre, see the historical account of [14], especially pp. 57 and 58). This led to the Hot Big Bang “orthodoxy” of the 60’s and 70’s, with microwave background radiation and the Big Bang nucleosynthesis as splendid successes. Are we experiencing a similar revolution with the tremendous increase of cosmological research in the 80’s? In absence of major breakthroughs it is certainly too early to say, but great intellectual excitement is created by the emergence of many new lines of speculation confronting the accumulation of extremely impressive observational results. Whereas maximum homogeneity and, more generally, basic simplicity (at the cost of incompleteness) characterized most of the cosmological models up to the 70’s, the scene is now dominated by the opposite characteristics of complexity and inhomogeneity at the largest dimensions. Furthermore, the theoretical situation is in a constant state of flux, many of yesterday’s proposals being overshadowed by new, equally tentative ideas. In the meantime - and this is in my opinion a most important redeeming feature in the midst of so much speculation - slow but tenacious, high quality work is being

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done by observational cosmologists and experimental physicists, while phenomenological theorists carefully evaluate their results and confront the various interpretations, the only way to advance in the diﬃcult quest for new cosmological knowledge of lasting significance.

References 1. S. Weinberg, “The First Three Minutes”, A. Deutsch (London) 1977. 2. A. Linde, “Particle Physics and Inflationary Cosmology”, Harwood (Chur) 1990. 3. Proceedings of the First ESO-CERN Symposium, “Large-Scale Structure of the Universe, Cosmology and Fundamental Physics” (CERN, Geneva, 21–25 November 1983), eds. G. Setti and L. Van Hove, CERN Report, 1984. 4. Proceedings of the Second ESO-CERN Symposium, “Cosmology, Astronomy and Fundamental Physics”, (ESO, Garching bei M¨unchen, 17–21 March 1986), eds. G. Setti and L. Van Hove, ESO Conference and Workshop Proceedings No. 23, 1986. 5. Proceedings of the Third ESO-CERN Symposium, “Astronomy, Cosmology and Fundamental Physics”, (Bologna, 16–20 May 1988), eds. by M. Caﬀo, R. Fanti, G. Giacomelli and A. Renzini, Kluwer (Dordrecht) 1989. 6. See for example [2]. 7. K.-E. Eriksson, S. Islam and B.-S. Skagerstam, Nature 296 (1982) 540. 8. D.C. Backer and S.R. Kulkarni, Physics Today (March 1990) p.26. See especially “Millisecond Pulsars as Cosmology Probes”, p.34 9. H. Reeves [5], p.67. 10. H. Satz in [5], p.131. 11. J. Kripfganz and A. Ringwald, Z. Phys. C44 (1989) 213 and references therein. 12. A. Ringwald, “High Energy Breakdown of Perturbation Theory in the Electroweak Instanton Sector”, preprint DESY 89–074 (1989), to appear in Nucl. Phys. B. 13. L. Van Hove, Nova Acta Leopoldina, 60 (1989) 133. This is the text of a lecture delivered in 1983 at the Leopodina Academy, Halle (DDR). 14. R.W. Smith, Physics Today (April 1990) p.52

12

The Experimental Discovery of CP Violation James W. Cronin

Abstract [This address was presented by James W. Cronin as the Nishina Memorial Lecture at the University of Tokyo, and at Yukawa Institute for Theoretical Physics in September, 1993.] The discovery of CP violation was a complete surprise to the experimentalists that found it as well as to the physics community at large. This small eﬀect means that the symmetry means that the symmetry between the behavior of matter and antimatter is not exact. The experiment that made the discovery was not motivated by the idea that such a violation might exist. I will describe in some detail how it came to be performed in the context of of the fast moving pace of particle physics in 1963. I will review how we actually did the experiment using extracts from personal notebooks. I will discuss some diﬃculties we had with the apparatus and the anxiety some of us had to be sure we were correct. Such considerations are rarely revealed in a formal publication but are the realities of doing science. I will then discuss the aftermath of the experiment and the great eﬀorts that continue to this day to understand the origin of the CP violation, which remains a mystery. The search for the origin of CP violation motivates many of the proposals for new particle facilities.

Introduction I am honored to be invited to Japan to give the Nishina Memorial Lecture. Yoshio Nishina was instrumental in introducing modern physics to Japan, name is also familiar to all of our students at the University of Chicago who required to repeat the Compton eﬀect in their experimental course. In doing they compare their results with the famous James W. Cronin c Dept. of Physics, Univ. of Chicago James W. Cronin (1931 – ). Nobel Laureate in Physics (1980) University of Chicago (USA) at the time of this address J. W. Cronin: The Experimental Discovery of CP Violation, Lect. Notes Phys. 746, 261–280 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 12

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Klein-Nishina formula which was of the earliest calculations in quantum electrodynamics [1]. I am pleased to have this opportunity to recall the discovery of CP violation. It has forced me to go back and look at old notebooks and records. It amazes me that they are rather disorganized and very rarely are there any dates on them. Perhaps this is because I was not in any sense aware the verge of an unanticipated discovery. In the second reference [2] some of the discovery. I give a list of literature on this subject which provides diﬀerent perspectives on the discovery. I will begin with a review of some of the important background which is necessary to place the discovery of CP violation in proper context.

Precursors The story begins with the absolutely magnificent paper of Gell-Mann and Pais published in early 1955 [3]. By chance I was a witness to the birth of this paper. In the spring of 1954 Murray Gell-Mann was lecturing to a small class at the University of Chicago on his scheme for organizing the newly discovered elementary particles [4]. Simultaneously Nakano and Nishijima were proposing similar ideas [5]. Among the students in this class was Enrico Fermi. As Gell-Mann was going through his scheme he mentioned that the neutral θ0 meson was distinct from its antiparticle θ¯0 because of a postulated strangeness quantum number which was conserved in strong interactions. The decay of the θ0 and θ¯0 was by weak interaction to two pions. Fermi asked, “How can θ0 and θ¯0 be distinct if they have a common decay mode.” GellMann did not have a ready response but the comment surely remained on his mind, for in the fall of 1954 he wrote the famous paper with Pais on the particle mixture phenomenon in the θ0 - θ¯0 system. They gave the paper a very formal title, “Behavior of Neutral Particles under Charge Conjugation”, but they knew in the end that this was something that concerned experiment. So they provided the last paragraph which reads: “At any rate, the point to be emphasized is this: a neutral boson may exist which has a characteristic θ0 mass but a lifetime τ and which may find its natural place in the present picture as the second component of the θ0 mixture.” One of us, (M. G.-M.), wishes to thank Professor E. Fermi for a stimulating discussion.”

The reference to Fermi acknowledges his comment which was the key remark that led Gell-Mann and Pais to write this paper. Gell-Mann and Pais pointed out pointed out that while the θ0 and θ¯0 were the appropriate states for the strong interactions, the states of definite lifetime were linear combinations: 1 θ1 = √ θ0 + θ¯ 0 2 and

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Fig. 12.1 Decay of a long-lived K meson observed in a cloud chamber at the Brookhaven Cosmotron (ref 5)

1 θ2 = √ θ0 − θ¯ 0 2 These are eigenstates of the charge conjugation operator C with eigenvalues of ±1. If C is conserved in the weak decay then one of these linear combinations is forbidden to decay to two pions and has only three body decays accessible to it (for example θ2 → π− + μ+ ν). The phase space available to three bodies is less than for two so that the lifetime for the θ2 was expected to be much longer than the θ1 . It did not take Leon Lederman long to test the remarkable prediction of GellMann and Pais. A neutral particle with a much longer lifetime than the θ0 and no two body decay modes was predicted. With Lande, Booth, Impeduglia, and Chinowsky a successful experiment was carried out at the Brookhaven Cosmotron. Their paper entitled “Observation of Long-Lived Neutral V Particles” was published in 1956 [6]. It is interesting to read the acknowledgement in this paper. “The authors are indebted to Professor A. Pais whose elucidation of the theory directly stimulated this research. The eﬀectiveness of the Cosmotron staﬀ collaboration is evidenced by the successful coincident operation of six magnets and the Cosmotron with the cloud chamber.”

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Figure 12.1 shows an event in the cloud chamber which was located in a corn crib out in the back yard of the Cosmotron. The event shows manifestly a three body decay because both charged decay tracks emerge on the same side of the beam. A third neutral particle is required to balance the transverse momentum. By 1961 the combined world data showed that the upper limit for two body decays was 0.3 % of all decays [7]. The paper of Gell-Mann and Pais used conservation of charge conjugation to argue for the necessity of a long-lived neutral K meson. (After 1957 the name θ had been replaced by K.) With the discovery of parity violation the conclusion was unaltered when the charge conjugation conservation was replaced by the combined conservation of charge conjugation and parity (CP) [8]. The consequence was that the long-lived neutral K meson (K2 ) was forbidden to decay to two pions. There was another important consequence, the phenomenon of regeneration, which was described in a paper entitled, “Note on the Decay and Absorption of the θ0 ” by Pais and Piccioni [9]. This paper deduced one of the beautiful aspects of the particle mixture theory. Neutral K mesons displayed in passing through matter a behavior very similar to light passing through a birefringent material. When a K2 passes through matter the positive and negative strangeness components are attenuated by diﬀerent amounts. On emerging from the matter the balance between the positive and negative components is altered so that there is a superposition of K2 and short-lived K mesons (K1 ). The K1 ’s decay to two pions immediately beyond the absorbing material. Oreste Piccioni, with colleagues at the Berkeley Bevatron, demonstrated this phenomenon experimentally in a propane filled bubble chamber [10]. The introduction to their paper pays tribute to the theory of Gell-Mann and Pais. “It is by no means certain that, if the complex ensemble of phenomenon concerning the neutral K mesons were known without the benefit of the Gell-Mann - Pais theory, we could, even today, correctly interpret the behavior of these particles. That their theory, published, in 1955, actually preceded most of the experimental evidence known at present, is one of the most astonishing and gratifying successes in the history of the elementary particles.”

After regeneration had been established, Adair, Chinowsky and collaborators placed a hydrogen bubble chamber in a neutral beam at the Brookhaven Cosmotron to study the eﬀect in hydrogen [11]. Figure 12.2 shows their result. In this experiment, as in subsequent ones, the vector momenta of the two charged tracks in the decay are measured. Assuming each track is a pion, the direction and mass of a parent particle is calculated. Two body decays of K mesons will produce a peak in the forward direction at 498 MeV. The three body decays will produce a background that can be estimated by Monte Carlo and extrapolation. The forward regenerated peak was found to be too large by a factor of 10 to 20. Adair gave a very creative explanation; he postulated a fifth force which was very weak but had a long range and hence had a small total cross section with a large forward amplitude. It also diﬀerentiated between positive and negative strangeness producing a strong regeneration. If confirmed this would have been a major discovery.

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Fig. 12.2 Anomalous regeneration in hydrogen (ref 10) “Angular distribution of events which have a 2π-decay Q-value consistent with K01 decay, and a momentum consistent with the beam momentum. All events are plotted for which 180 MeV ≤ Q ≤ 270 MeV, p ≥800 MeV/c. The black histogram presents those events in front of the thin window. The solid curve represents the contribution from K02 decays”

The Experiment At this time both Val Fitch and I were working at experiments. Val had spent much of his career working Brookhaven on separate with K mesons and was steeped in the lore of these particles which had already revealed so much about nature. Val was one of the first to measure the individual lifetimes of the various decay modes of the charged K mesons. To avoid trouble with parity one thought that the two pion and three pion decay modes were actually due to diﬀerent particles [12]. On the occasion of Panofsky’s visit to Brookhaven he and Val detected the K2 mesons by electronic means [13]. The Adair experiment appeared in preprint form while Val was just finishing an experiment on the pion form factor at the AGS and I was just finishing an experiment on the production of p mesons at the Cosmotron. At the heart of this experiment was a spark chamber spectrometer designed to detect p mesons produced in hydrogen at low transverse momentum [14]. My development of spark chambers for use at accelerators was a direct consequence of the work of Fukui and Miyamoto on the “discharge chamber” [15]. At that time optical spark chambers were a new tool in which one could, by selective electronic trigger, record the trajectories of the desired events out of a very high rate background [16]. The spectrometer was state of the art at the time [17]. Val, so experienced with K mesons, came to me and suggested that together we use our spectrometer to look for Adair’s anomalous regeneration. Progress in

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physics thrives on good ideas. I enthusiastically agreed with Val’s suggestion. Jim Christenson, a Ph. D. student, and R´ene Turlay, who was visiting from Prance, joined Val and me on the experiment. In addition to checking the Adair eﬀect, it was an opportunity to make other measurements on K2 with much greater precision. The spectrometer I had built with Alan Clark, Jim Christenson, and Ren´e Turlay was ideally suited for the job. It was designed to look at pairs of particle with small transverse momentum. This was just the property needed to detect two body decays in a neutral beam. We also had a 4-foot long hydrogen target which would be a perfect regenerator. The spectrometer consisted of two normal 18 × 36 beam-line magnets turned on end so that the deflections were in the vertical plane. The angle between the two magnets was adjustable. Spark chambers before and after the magnet permitted the measurement of the vector momentum of a charged particle in each arm of the spectrometer. The spark chambers were triggered by a coincidence of scintillators and a ˇ water Cerenkov counter behind each spectrometer arm. This apparatus could accumulate data much more rapidly than the bubble chamber and had a mass resolution which was five times better. Another fortunate fact was that we had an analysis system ready to measure the spark chamber photographs quickly. We had homemade projectors and measured, instead of points, only angles of tracks and fiducials. The angular measurement was made with a Datex encoder attached to an IBM Model 526 card punch. The least count of the angular encoder was 1.5 mrad. In addition we had bought a commercial high-precision bubble chamber measuring machine which would become important in the checking of our results. It should be noted that our support came from the Oﬃce of Naval Research. It was only later that the military stopped supporting fundamental research. We looked around for a neutral beam at both the Cosmotron and the AGS. The most suitable beam was one used by the Illinois group [18]. The beam was directed towards the inside of the AGS ring to a narrow, crowded area squeezed between the shielding of the machine and the wall of the experimental hall. The area was dubbed “Inner Mongolia” by Ken Green one of the builders of the AGS. This area was mostly relegated to parasitic experiments working oﬀ the same target that produced the high energy small angle beams for the major experiments. The beam was produced on an internal target at an angle of 30◦. Figure 12.3 is a sketch of the setup that I placed in my notebook when we were planning the experiment. An angle of 22◦ between the neutral beam and each arm of the spectrometer matched the mean opening angle of K02 → π+ + π− decays at 1.1 GeV/c which was at the peak of the spectrum at 30◦ . It also allowed room for the neutral beam to pass between the front spark chamber of each spectrometer arm. Heavily outlined is the decay region used for the Monte Carlo estimates of the rates. Fainter lines show the outline of the hydrogen target. Our proposal was only two pages. It is reproduced in an Appendix. The first page describes essentially what we wanted to do. It reads in part:

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Fig. 12.3 Sketch of the spectrometer arrangement from notebook of J.W. Cronin

“It is the purpose of this experiment to check these results with a precision far transcending the previous experiment. Other results to be obtained will be a new and much better limit for the partial rate of K02 → π+ + π− ,. . . ”

One notes that we referred to a limit; we had no expectation that we would find a signal. We also proposed to measure a limit on neutral currents and study coherent regeneration. On the second page of the proposal one reads: “We have made careful Monte Carlo calculations of the counting rates expected. For example, using the 30◦ beam with the detector 60 ft. from the A.G.S. target we could expect 0.6 decay events per 1011 circulating protons if the K2 went entirely to two pions. This means that we can set a limit of about one in a thousand for the partial rate of K2 → 2π in one hour of operation.”

This estimate turned out to be somewhat optimistic. We moved the spectrometer from the Cosmotron to the AGS in May 1963. It just barely fit inside the building. We began running in early June. There was no air conditioned trailer. The electronics, all home-made, was just out on the floor in the summer’s heat. Figure 12.4 shows the only photograph that we have of the apparatus. Most prominent are the plywood enclosures which contained the optics for the photography of the spark chambers. One can discern the two magnets set at 22◦ to the neutral beam. Also visible are the few racks of electronics. The individual in the picture is Wayne Vernon, a graduate student, who did his thesis with Val on a subsequent experiment. Figure 12.5 shows schematically the experimental arrangement for the CP invariance run. A large helium bag was placed in the decay region. By the time we were ready to begin the CP run on June 20, 1963 we had a better number for the flux of K2 ’s in the beam. The observed yield of K2 in the beam turned out to be about

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Fig. 12.4 The only existing photograph of the apparatus set up in the 30◦ neutral beam at the Brookhaven AGS

one-third of the original estimate given in the proposal. The best monitor was a thin scintillation telescope placed in the neutral beam upstream of the decay region which counted neutrons. Figure 12.6 is taken from my notebook. I estimated that there were 106K2 per neutron count (in units of 105 ). The Monte Carlo eﬃciency to detect a K→ 2π decay was 1.5 × 10−5. Thus to set a limit of the order of 10−4 , 666 neutron counts were needed. For safety I suggested 1200 neutron counts.

Fig. 12.5 (a) Schematic view of the arrangement for the CP run

The page of our data book from the day that the CP run began is shown in Fig. 12.7. Only ten minutes into the run one finds the note: “Stopped run because neutron monitor was not counting - found anti and collector transistors blown in coin. circuit - replaced - A.O.K.”

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Fig. 12.5 (b) Detail of the spectrometer

Fig. 12.6 Page from notebook of J. W. Cronin estimating the amount of time to set a limit of 10∼4 for the branching ratio K2 → π+ + π− /K→all

This was not a smooth run - it was the real world! “3a is now meaningless - won’t write” “Film ran out sometime (?) before this - noticed it at this point - sometime before 131700 it would seem! Sorry.” “at 0445, noticed rubber diaphragm on camera lens (#3 side) was oﬀ - perhaps pictures taken till now are no good?” “found top of helium bag in beam at end of above run. - put more He in.”

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And so it was - not smooth but working nevertheless. We ran for about 100 hours over five days. The AGS ran very well. We collected a total of more than 1800 neutron monitors, more than the 1200 we thought we needed. During about a month of running, data were taken on many aspects of K2 ’s including a measurement of the K1 - K2 mass diﬀerence and the density dependence of the coherent regeneration in copper. And, of course, a week of data was taken with the hydrogen target to search for the anomalous regeneration.

Analysis We stopped running at the end of June and gave our first results at the Brookhaven Weak Interactions Conference in September. We reported on a new measurement of the mass diﬀerence. As I recall we did not give high priority to the CP run in the early analysis, but it was Ren´e Turlay who began to look at this part of the data in the fall. A quick look at the hydrogen regeneration did not reveal any anomaly.

Fig. 12.7 Page from the data book at the beginning of the CP violation run, June 20,1963

All the events which were collected in the CP invariance run were measured with the angular encoder. This was complete by early 1964 and Ren´e Turlay produced the curves shown in Fig. 12.8. There were 5211 events that were measured and successfully reconstructed. The top curve shows the mass distribution of all the events assuming each charged track was a pion. Shown also is the Monte Carlo expectation for the distribution. The relative eﬃciency for all K2 decay modes compared to the decay to two pions was found to be 0.23. The bottom curve shows the angular distribution of the events in the eﬀective mass range of 490 to 510 MeV. The curve was plotted in bins of cos θ = 0.0001, presumably consistent with the angular resolution that could be obtained with the angular measuring machines. There appeared

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to be an excess of about 50 events expected. We then remeasured those events with cos θ ≥0.9995 on our precision bubble chamber measuring machine. In looking over my old notebooks I found a page which is reproduced in Fig. 12.9. When the data measured with the angular encoder were plotted in finer bins of cos θ of .00001 the angular resolution was much better than bins of 0.0001 suggest. There was a clear forward peak and a “CP limit” of 2.3 × 10−3 was indicated at the top of the page on the basis of 42 events. Note that the mass range was from 480 to 510, larger than Fig. 12.8. The most significant statement on the page is: “To draw final conclusions we await the remeasurement on the Hydel”. Hydel was the trade name of the precision bubble measuring machine.

Fig. 12.8 (a) Experimental distribution in m* compared with Monte Carlo calculation. The calculated distribution is normalized to the total number of observed events, (b) Angular distribution of those events in the range 490 ≤ m* ≤ 510 MeV. The calculated curve is normalized to the number of events in the complete sample

The events were remeasured and we published the results. In our paper the key figure was the third one which is reproduced as Fig. 12.10. Here the angular distribu-

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Fig. 12.9 Page from notebook of J. W. Cronin with comment on the first results of the analysis of the CP events measured with the angular encoder

tion of the events was plotted for three mass ranges with the central range centered on the K1 mass. This was our principal evidence of the eﬀect [19]. I found it quite convincing. Perhaps being more naive than my colleagues and not fully appreciating the profound consequences of the result, I was not at all worried that the result might be wrong. We had done an important check to be sure of the calibration of the apparatus. We had placed a tungsten block at five positions along the decay region to simulate with 2π decays of regenerated K1 ’s the distribution of the CP violating events. We found the mass, angular resolution and spatial distribution of the events observed with the helium bag to be identical with the regenerated K1 events. From our own measurements of regeneration amplitudes the regeneration in the helium was many orders of magnitude too small to explain the eﬀect. We reported a branching ratio of (2.0 ± 0.4)×10−3, a result that within the error has not changed to this day. We also reported in this paper a value of the parameter that has come to be known as η+− . Wu and Yang introduced a new nomenclature which has remained [20]. The short and long lived K mesons are KS and KL . The parameter η+− is the ratio of the amplitude, amp(KL → π+ + π− ), to the amplitude, amp(KS → π+ + π− ). Two weeks after our publication the Illinois group published a paper entitled, “Search for CP Nonconservation in K02 Decays” [21]. It reported some evidence for the two pion decay of the K2 . The data were taken in the same AGS beam at an earlier date. It was an experiment that was designed to study the form factor of the three body decays. While their experiment was not optimized for CP studies they

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Fig. 12.10 Angular distribution in three mass ranges for events with cos θ ≥ 0.9995

reported some ten events in a mass range of 500 Mev to 510 MeV which were consistent with two body decays. One important aspect was the fact that in the Illinois apparatus the decay products passed through some material. Two of the events in the forward peak showed one of the decay products interacting in material. This identified the decay products as strongly interacting. At the time of the discovery there were all kinds of ideas brought forth to save the concept of CP violation. Among these theories were situations where the apparent pions in the CP violation would not be coherent with the pions of a K1 decay. Thus it was important to first establish the coherence of the CP violating decays. There was an experiment carried out by Val Fitch and his collaborators [22] which has not received the proper attention of those who have reviewed the field. In this experiment Val showed explicitly that there was constructive interference between regenerated K1 decays and the CP violating decays. The idea was clever and grew out of our extensive experience with the regeneration phenomenon. A long low density regenerator, made of thin sheets of beryllium, was prepared with a regeneration amplitude which just matched the CP amplitude. The experiment showed definitively that there was maximal constructive interference, and strengthened the idea

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Fig. 12.11

that in the constitution of the long-lived K there was a small admixture of CP-even state in what is predominately CP-odd state. A second important measurement was the observation of a 0.3% diﬀerence in the decay rates KL → π− + e+ + ν and KL → π+ + e− + ν¯ [23]. This experiment showed explicitly the asymmetry between matter and antimatter that CP violation implies.

Progress Since the Discovery Since the discovery of CP violation there has been an enormous amount of work both on the neutral K meson system and on searches for time reversal violation in many systems. So far no eﬀects have been found outside the neutral K meson system. Technological improvements over the last 29 years have permitted very sensitive experiments on the CP violating parameters of the K meson system. Routinely, event samples containing millions of CP violating decays in both neutral and charged modes have been obtained. The mass plots for both the neutral and charged CP violating decays from a recently reported Fermilab experiment [25] are presented in Figure 12.12. Not only does one marvel at the large number of events but other details as well. For example the plot for KL → π+ + π− shows a tail towards lower mass while its neutral counterpart does not. This tail is due to the inner bremstrahlung, KL → π+ + π− + γ which cannot occur in the neutral decay mode.

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Fig. 12.12 Mass plots from a recently published Fermilab experiment ( [23]). (a) KL → π+ + π− ; (b)KL → π0 + π0

In recent years great there has been emphasis on the measurement of the relative strength of the CP violation in the decay to neutral pions compared to charged pions. These are characterized by the amplitude ratios η00 and η+− respectively. An observed diﬀerence in η00 and η+− means that there is a second independent CP violating parameter. The Number of possible theories for the origin of CP violation would be reduced, in particular the superweak theory of Wolfenstein would be ruled out [24]. This diﬀerence is usually expressed by a small quantity: | /| =

1 1 − |η00|2 /|η+− |2 . 6

(12.1)

A non-zero value of this quantity would indicate a “direct” CP violation and represent real progress in understanding CP violation. A recent high precision experiment at Fermilab [25] has reported | /| =(7.4±5.9)×10−4. An experiment of comparable precision at CERN [26] has a preliminary value of (23 ± 7)×10−4. While it appears that the value of | /| is larger than zero, both laboratories are planning more sensitive experiments to confirm this conclusion. The most attractive “explanation” for CP violation lies in the innovative ideas of Cabbibo [27], and Kobayashi, and Maskawa [28]. The paper of Kobayashi and Maskawa is remarkable in that it postulated a third family of quarks which was required in order to have a CP violating phase. This was done at a time when there was only evidence for an up, down, and strange quark! The weak decays of the quarks are described by a 3×3 CKM matrix. The most recent theoretical calculations

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which include all the experimental constraints on the CKM matrix suggest a positive value for / in the range from (1 to 30)×10−4 which is compatible with the present experimental result [29]. The constraints imposed by the neutral K meson system on the CP violating phase in the the CKM matrix lead to the prediction of large CP violating eﬀects in some of the rare decay modes in the neutral B meson system. High luminosity e+ e− colliders (B factories) have been proposed at Cornell University and SLAC in the United States and at KEK in Japan to observe these eﬀects [30]. It will be necessary to observe these CP violating eﬀects in the B mesons to be certain that the origin of CP violation really rests in a phase in the CKM matrix. CP violation is concerned with the most fundamental aspects of space and time. It is no surprise, then, that this small eﬀect stimulated a closer relation between cosmology and particle physics. Sakharov [31] in 1967, very early after the discovery of CP violation, pointed out a mechanism whereby the early universe, composed of equal amounts of matter and antimatter could evolve to a matter dominated universe with a baryon to photon ratio of ∼ 10−9 . He stated the three essential conditions: 1) Baryon nonconservation, 2) CP violation, and 3) appropriate non-equilibrium conditions related to the cooling rate of the universe and the appropriate interaction rates. This paper was far ahead of its time and received little attention. Serious consideration of the role of CP violation in the evolution to a matter dominated universe began with the paper of Yoshimura [32]. There followed a great activity which sought to understand the relation of CP violation to the evolution of the universe. It seems that the CP violation observed in the K meson system is not directly responsible for the development of a matter dominated universe [33]. Nevertheless the discovery of CP violation in the K meson system has been influential in the union of cosmology physics.

Final Remarks I would like to conclude with some personal remarks, although I know Nature is not going to pay any attention to what I think. I would be very disappointed if the origin of CP violation only resides in a phase of the CKM matrix, which has as much or as little significance as the other constants which refer to the mixing of the quark states between the weak and the strong interactions. I would like to think that there is some more fundamental relation between the manifest CP violation in the neutral K meson system and the significant fact that our galaxy and most likely our universe is matter dominated. It may not be so. When parity violation was discovered many thought that the fact that our biological molecules show a handedness was related to the manifest handedness of the weak interaction [34]. But subsequent experiments and theoretical considerations do not support this possibility [35]. Indeed it is almost certain that the CP violation observed in the K meson system is not directly responsible for the the matter dominance of the universe, but one would wish that it is related to whatever was the mechanism that created the matter dominance.

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The history of CP violation is not complete. It is gratifying to see that CP violation remains one of the major topics of research in particle physics. Let me repeat the conclusion of a previous lecture given in 1980 which remains as timely today [36]. “We must continue to seek the origin of the CP symmetry violation by all means at our disposal. We know that improvements in detector technology and quality of accelerators will permit even more sensitive experiments in the coming decades. We are hopeful, then, that at some epoch, perhaps distant, this cryptic message will be deciphered.”

Appendix Proposal for K02 Decay and Interaction Experiment J. W. Cronin, V. L. Fitch, R. Turlay (April 10, 1963)

I. Introduction The present proposal was largely stimulated by the recent anomalous results of Adair et al., on the coherent regeneration of K01 mesons. It is the purpose of this experiment to check these results with a precision far transcending that attained in the previous experiment. Other results to be obtained will be a new and much better limit for the partial rate of K02 → π+ + π− , a new limit for the presence (or absence) of neutral currents as observed through K2 → μ+ + μ− . In addition, if time permits, the coherent regeneration of K1 ’s in dense materials can be observed with good accuracy.

II. Experimental Apparatus Fortuitously the equipment of this experiment already exists in operating condition. We propose to use the present 30◦ neutral beam at the A.G.S. along with the di-pion detector and hydrogen target currently being used by Cronin, et al. at the Cosmotron. We further propose that this experiment be done during the forthcoming μ-p scattering experiment on a parasitic basis. The di-pion apparatus appears ideal for the experiment. The energy resolution is better than 4 Mev in the m∗ or the Q value measurement. The origin of the decay can be located to better than 0.1 inches. The 4 Mev resolution is to be compared with the 20 Mev in the Adair bubble chamber. Indeed it is through the greatly improved resolution (coupled with better statistics) that one can expect to get improved limits on the partial decay rates mentioned above.

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III. Counting Rates We have made careful Monte Carlo calculations of the counting rates expected. For example, using the 30◦ beam with the detector 60-ft. from the A.G.S. target we could expect 0.6 decay events per 1011 circulating protons if the K2 went entirely to two pions. This means that one can set a limit of about one in a thousand for the partial rate of K2 → 2π in one hour of operation. The actual limit is set, of course, by the number of three-body K2 decays that look like two-body decays. We have not as yet made detailed calculations of this. However, it is certain that the excellent resolution of the apparatus will greatly assist in arriving at a much better limit. If the experiment of Adair, et al. is correct the rate of coherently regenerated K1 ’s in hydrogen will be approximately 80/hour. This is to be compared with a total of 20 events in the original experiment. The apparatus has enough angular acceptance to detect incoherently produced K1 ’s with uniform eﬃciency to beyond 15◦ . We emphasize the advantage of being able to remove the regenerating material (e.g., hydrogen) from the neutral beam.

IV. Power Requirements The power requirements for the experiment are extraordinarily modest. We must power one 18-in. × 36-in. magnet for sweeping the beam of charged particles. The two magnets in the di-pion spectrometer are operated in series and use a total of 20 kw.

References 1. O. Klein and Y. Nishina, Z. Physik 52 (1929) 853 2. R. K. Adair, “CP Non Conservation- The Early Experiments”,Proceedings of the Blois Conference on CP Violation in Particle Physics And Astrophysics, ed. J. Tran Thanh Van, Editions Eronti´eres,(1990) p 37 ; A. Pais,“CP ViolationThe First 25 Years”, ibid, p 3; J. W. Cronfn, Physics Today 35 (July 1982) 38 ; V. L. Fitch “Symmetries in Physics (1600-1980)”,Proceedings of the Conference at San Felice de Guixols, Spain(1983) ed. M. Doncel, University of Barcelona,1987; A. Franklin, Historical Studies of the Physical Sciences 13 (1983) ,207 3. M. Gell-Mann and A. Pais, Phys. Rev. 97 (1955) 1387 4. M. Gell-Mann, Phys. Rev. 92 (1953) 833. 5. T. Nakano and K. Nishijima, Prog. Theo. Phys. 10 (1953) 581 6. K. Lande, E. T. Booth, J. Impeduglia, L. M. Lederman, and W. Chinowsky, Phys. Rev. 103 (1956) 1901.

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7. D. Neagu, E. O. Okonov, N. I. Okonov, N. I. Petrov, A. M. Rosanova, and V. A. Rusakov, Phys. Rev. Lett. 6 (1961) 552. 8. T. D. Lee, R. Oehme, and C. N. Yang, Phys. Rev. 106 (1957) 340. 9. A. Pais and O. Piccioni, Phys. Rev. 100 (1955) 1487. 10. R. H. Good, R. P. Matsen, F. Muller, O. Piccioni, W. M. Powell, H. S. White, W. B. Fowler, and R. W. Birge, Phys. Rev. 124 (1961) 1223. 11. L. B. Leipuner, W Chinowsky, R. Crittenden, R. Adair, B Musgrave, and F. T. Shively, Phys. Rev. 132 (1963) 2285. 12. V.Pitch and R. Motley, Phys. Rev. 105 (1957) 265. 13. W. K. H. Panofsky, V. L. Fitch, R. M. Motley, and W. G. Chesnut, Phys. Rev 109 (1958) 1353. 14. A. R. Clark, J. H. Christenson, J. W. Cronin, and R. Turlay, Phys. Rev. 139 (1965) B1557. 15. S. Fukui and M. Miyamoto, Nuovo CimentO ll (1959) 113. 16. J. W. Cronin and G. Renninger, Proceedings of the International Conference on Instrumentation for High Energy Physics (Interscience Publishers Inc.,New York, 1961) (1960) 271. 17. J. H. Christenson, A. R. Clark, and J. W. Cronin, IEEE Trans. Nucl. Sci. NS-ll (June 1964) 310. 18. L. Creegie, J. D. Fox, H. Frauenfelder, A. O. Hanson, G. Moscati, C. F. Perdrisat, and I. Todoroﬀ, Phys. Rev. Lett. 17 (1966) 150. 19. J. H. Christenson, J W. Cronin, V. L. Fitch, and R. Turlay, Phys. Rev. Lett. 13 (1964) 138. 20. T. T. Wu and C. N. Yang, Phys. Rev. Lett. 13, 380 (1964): 21. A. Abashian, R.J. Abrams, D. W. Carpenter, G. P. Fisher, B. M. K. Nefkens, and J. H. Smith, Phys. Rev. Lett. 13 (1964) 243. 22. V. L. Fitch, R. F. Roth, I. Russ, and W. Vernon, Phys. Rev. Lett. 15 (1965)73. 23. J. Marx et al., Phys. Lett. 32B (1970) 219. 24. L. Wolfenstein, Phys. Rev. Lett. 13 (1964) 562. 25. L. K. Gibbons et al., Phys. Rev. Lett. 70 (1993) 1203. 26. G. Barr, Proceedings of the Joint International Lepton-Photon Symposium and Europhysics Conference on High Energy Physics (World Scientfic), eds S. Hegarty, K. Potter, E. Quercigh 1 (1991) 179. 27. N. Cabbibo, Phys. Rev. Lett. 10 (1963) 531 28. M. Kobayashi, and T. Maskawa, Prog. of Theor. Phys. 49 (1973) 652. 29. B. Winstein and L. Wolfenstein, Rev. Mod. Phys. to be published. 30. SLAC Reports 0359, 0372 (1991); Cornell reports CLNS-91-1043, 1047, 1050(1991); Report KEK Task Force Report on Asymmetric B Factory at KEK,(Feb 1990) 31. A. D. Sakharov Zh. Eksp. Teor. Fiz. Pis’ma Red. 5 (1967) 32; [JETP Lett. 5(1967) 24]. 32. M. Yoshimura, Phys. Rev. Lett 41 (1978) 281. 33. R. D. Peccei, Proceedings of the Blois Conference on CP Violation in Particle Physics and Astrophysics, ed. I. Tran Thanh Van, Editions Ftonti´eres (1990) p615. 34. H. Krauch and F.Vester, Naturewissenschaten 44 (1957) 49.

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35. R. A. Hegstrom, A. Rich and J.Van House, Nature 313 (1985) 391. 36. J. W. Cronin, Rev. Mod. Phys. 53 (1981) 373.

13

The Nanometer Age: Challenge and Change Heinrich Rohrer

Abstract [This address was presented by Heinrich Rohrer as the Nishina Memorial Lecture at the University of Tokyo, on June 25, 1993.] The new players in the emerging nano-world are individual, selected objects of the size of some 50 nm down to molecules and atoms. The new aspect of science and technology on the nanometer scale is that these objects are treated as individuals, not as ensemble members. To a great extent, this requires real-space methods. Local probe methods, such as scanning tunneling microscopy and its derivatives, are therefore a key to the nanoworld. Major challenges of the new nanometer world are to exploit the new possibilities that arise from nanometer dimensions, to interface the macroscopic world to nano-individuals, to establish new concepts for working with very large numbers of nano-individuals and large sets of control parameters, to create the basis for broad interdisciplinarity, and to prepare society for the tremendous changes anticipated in a nanometer world.

I. Introduction Miniaturization is one of the key driving forces for science and technology on the nanometer scale. Figure la shows the progress of miniaturization for two examples from the data processing industry. In the past two decades, miniaturization has progressed exponentially. The challenge in the coming decade, Period 1 in Fig. 13.1a, will be to find methods suitable for the mass production of Gbit chips from those present-day elements that can already be miniaturized suﬃciently and assembled in small quantities. In Period 2, say, 10 to 20 years from now, the challenge will be to develop Heinrich Rohrer c NMF Heinrich Rohrer (1933 – ). Nobel Laureate in Physics (1986) IBM Research Division. Zurich Research Laboratory (Switzerland) at the time of this address H. Rohrer: The Nanometer Age: Challenge and Change, Lect. Notes Phys. 746, 281–296 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 13

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Fig. 13.1 (a) Progress of miniaturization in information technology. [From H. Rohrer, II Nuovo c Cimento 107A, 989 (1994) Societ` a Italiana di Fisica] (b) Developments in solid-state technology and chemistry: Miniaturization builds on ever smaller individuals; increased complexity of ensemble members distinguishes macro-molecular chemistry [From E. Rohrer, Ultramicroscopy 42–44, 1 (1992)]

new types of elements. In both periods the investment into new technologies versus anticipated possible return will be a central problem. Eventually miniaturization, the division into ever smaller blocks, will come to an end in Period 3. Regarding storage, we do not know at present of any way involving less than, say, 1000 atoms in solid-state technology and some hundred in DNA*. Whether it will ever be possible to store information in nuclear degrees of freedom —– who knows. For data processing, heat dissipation per logic operation of least the thermal energy, kT, is a principal limit for any practical computation. While solid-state science and technology have moved down from the millimeter to the nanometer scale, chemistry has simultaneously and independently progressed from the level of small, few-atom molecules to macromolecules of biological size (see Fig. 13.1b). Supra-molecular chemistry might eventually provide the functional elements for the assembly scenario in the post-miniaturization period. Biological elements in general might be impractical, but biological concepts will guide us to new ways of thinking and doing things. Numerical approaches have taken a similar development like that of chemistry, from atoms and small molecules to ever larger nano-objects. They will be of great importance in understanding properties, functions and processes on the nanometer scale because on the one hand theory has little symmetry and no fixed dimensionality to build on and on the other hand functions and processes of nanometer-sized elements depend critically on their immediate environment.

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II. The New Nanometer World The nanometer age can thus be considered as a continuation of an ongoing development: for example, miniaturization in solid-state technology, increasing complexity in chemistry and numerically intensive computation. However, the new possibilities and novel aspects when working with nanometer dimensions go far beyond that —– beyond, e.g., “smaller, faster, cheaper” in information technology. Dealing with chemical bonds rather than bulk mechanical properties leads to a new nanomechanics with, for example, strains for the onset of plastic deformation an order of magnitude larger than those in the bulk. Mechanical resonance frequencies in the MHz to GHz range and thermal and diﬀusion response times below nanoseconds should very well complement fast electronics. Moreover, these fast relaxation times allow the creation of new materials and new structures. Local electric fields of up to several volts per angstrom, which are attainable in a scanning tunneling microscope (STM) configuration, and chemical interaction forces at angstrom distances are the basis for manipulation and modification on the atomic and the molecular level. Forces on the nano-scale are therefore a key to the nano-world. In addition, the extremely high electric fields provide convenient access to local nonlinear phenomena might also revive applications of thin ferroelectrical films. Other interesting and challenging aspects of nano-scale dimensions are: Quantum eﬀects will become important; we have to deal with tera and peta individuals; we often will think in terms of single electrons rather than currents; the immediate environment is a vital part of the nano-individual and not just a linear, minor perturbation; parallel operation will become the norm, and assembly and self-organization will replace miniaturization procedures. Progress after miniaturization will be based on increased complexity. A promising route could be the assembly of molecular-sized functional elements into complex functional units. A primary task of science is to find appropriate self-assembling techniques and ways to interface the macroscopic world with molecular-sized functional elements for communication and control or modification of their functions. This will lead to an extremely fruitful, interdisciplinary eﬀort that is expected to add new dimensions to biology as well as to supramolecular chemistry. The coming nanometer age can, therefore, also be called the age of interdisciplinarity. Major tools for the nanometer world comprise beam methods (microscopy and lithography with beams of electrons, ions, photons, atoms, maybe sometime even with neutrons and positrons), local probe methods (STM and its derivates), computational methods and new nano-materials. The beam methods are the chief fabrication methods of current microtechnology, which they will carry deep into the nanometer age. In the nano-world, these methods might be the key for producing the patterns necessary for self-assembly and self-organization of and for communication with nano-individuals. The computational methods will be central for theory, as mentioned above, both in terms of understanding properties and processes on the nanometer scale as well as in context with new concepts of handling very large numbers of nano-individuals and many degrees of freedom in systems of nanoindividuals. New nano-materials are required for machining on the nanometer scale

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as well as for providing appropriate supports of nano-objects, be they particular biological molecules, macro molecules from supramolecular chemistry or building blocks from solid-state technology.

III. Local Probe Methods Local probes are the “finger tips” to interact with nano-individuals, very much in the same way as we sense and handle macroscopic materials with our fingers. The positions and the properties of objects and functions as well as of processes associated with them are sensed, conditioned or changed by interactions between the probe and the object, see Fig. 13.2. The “localization” of the experiment is given by the active size of the probe and by the interaction distance, i.e., the distance between those parts of object and probe that interact. In the following, “object” is also used for part of an object, e.g., a surface area of atomic dimensions. For an exponential distance dependence of the √ interaction, the localization is of the order of (D + R) /κ, where R is an eﬀective probe size, D an eﬀective interaction distance, and 1/κ therefore have to be of atomic dimension. For tunneling between two bare metal surfaces, 1/κ is about 0.4 Å, thus most of the tunneling current flows between atomic-sized regions of tip and sample as indicated in Fig. 13.2. In principle, it is very easy to produce an atomically sharp probe. Any tip, pointed or not, usually has a rough apex —– unless great care is taken to produce a flat tip —– of which one atom can be brought closest to the nano-object. However, at the beginning it was not so easy to keep this very last atom in place during the

Fig. 13.2 Schematic of local probe methods. The circles represent atoms of the parts of probe and object, respectively, closest to each other. The probe is moved in the x,y and z-direction. A possible y-scan trace is indicated by the dashed line [From H. Rohrer, Jpn. J. Appi Phys. 32, 1335 (1993)]

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experiment, but now everybody has a recipe for doing so, and stability of the tip apex no longer is a serious problem. The distance dependence of the interaction is the key to the sample topography. Scanning at constant interaction gives a constant-interaction contour that reflects the sample topography, provided the interaction is laterally homogeneous. However, the ability of gaining access to inhomogeneities down to the atomic scale is one of the unique and attractive features of the local approach and of atomic-scale imaging. The more inhomogeneous the objects of interest are, i.e., for the truly “colorful” and interesting objects, the more important it becomes that the probe-object distance can be controlled independently of the experiment to be performed. Also, a local probe measurement usually includes diﬀerent interactions. In tunneling, for example, the interactions are the overlaps of tip and sample electronic wave functions at equal energy —– inelastic processes are smaller by several orders of magnitude —– thus diﬀerent electronic states with diﬀerent wave-function overlaps contribute to the total tunnel current. The art of local probe methods is then to find one interaction to control the probe-object distance and one to perform the experiment, and to separate either interaction from all the others, i.e., separation into a control and a working interaction, respectively. Ideally, the control interaction should be monotonous and, for imaging, laterally homogeneous. It is, therefore, the appropriate interaction for imaging the topography. For most of the classical surface-science-type STM experiments, the interaction separation can be handled to a great extent by tunneling spectroscopy. The preparation methods yield compositionally well-defined surfaces of long-range homogeneity. Short-range inhomogeneities are periodic or easily recognizable, such as steps and defects —– yet by no means does this imply “easy” experiments. In most other cases, however, interaction separation is essential for understanding images. In general, separation requires simultaneous measurement of two or more quantities. In magnetic force imaging, for example, the separation of the magnetic forces and their lateral variation from the other forces and topographic eﬀects can be achieved by introducing a well-defined Coulomb force. For ambient imaging, a procedure to separate the topography from electronic and elastic eﬀects has recently been proposed that requires the simultaneous measuring of force and compliance on a constant tunnel current contour. Artifacts can arise when the various interactions involved yield diﬀerent image resolution. Then the interaction with least resolution —– or the least inhomogeneous interaction from the imaging point of view —– is the most suitable one to be used as control interaction. It should be noted that “topography” is not a clear-cut notion. Topography as the smoothed average position of surface atoms, although probe-independent, is of limited practical value for surfaces with diﬀerent atoms of diﬀerent sizes. A best compromise for the topography and thus also for the probe-object distance might be the point of zero force or point of contact between object and probe apex atom, although this topography can be tip dependent. The corresponding control interaction is then the total force between object and probe apex atom. Unfortunately this force is not accessible in a force measurement, which yields only forces between the object and the entire probe. Working in a liquid eliminates or substantially re-

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Fig. 13.3 Local probe methods for imaging (a–c), as part of a specific experimental configuration on the nanometer scale (d–f), and as a tool (g–i) [From H. Rohrer, Surface Sci 299/300, 956 (1994)]

duces some of the less local forces, however, molecules squeezed between probe and sample can complicate matters. Nevertheless, determining the point of contact by, for example, an abrupt change in damping or eﬀective lever compliance appears at present to be a truly meaningful way to define within some tenths of an angstrom and control the probe-object distance. Subsurface sensitivity is achieved when the interaction extends into the object, e.g., the electrostatic interaction of a conducting or polarizable probe with an electronic charge in an insulating layer. This, however, results in a loss of resolution, since physically the probe cannot come closer than the object surface. Other subsurface methods include ballistic electron emission microscopy (BEEM), in which ballistic electrons injected by a tunnel tip probe electronic properties at buried interfaces, and local luminescence of quantum-well structures, where the emitted light from the recombination of injected electrons is characteristic of both the surface band bending and the band gap in the interior. A first set of applications of local probe methods deals with measurements, i.e., to monitor displacements, to determine when contact occurs, to measure local properties and to perform imaging (see Figs. 13.3a-c). The interactions should of course not aﬀect the properties under consideration, although they might change others. A second set uses special aspects of the probe-object configuration. In Fig. 13.3d, the nonlinearity of the tunnel junction mixes diﬀerent light frequencies. This can

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be used to image a property via the nonlinearity of the junction or to use a particularly strong local nonlinearity for frequency mixing per se. In Fig. 13.3e, a local plasmon mode characteristic of the tip-sample system is excited by the tunneling electron, which on decay emits a photon. In Fig. 13.3f, the injected electrons are used to probe a buried interface by BEEM or to investigate surface and bulk semiconductor band edges, for example, in quantum-well structures. Finally, the local probe can serve as manipulator or as machining tool. Rearranging adsorbed atoms and molecules on surfaces has resulted in most remarkable structures such as atom corrals. In Fig. 13.3g an atom is switched back and forth between tip and surface —– the atom switch. Extraction (Fig. 13.3h) and deposition of clusters and even of individual atoms have opened an exciting area of surface modification. Finally, control of processes and functions (Fig. 13.3i) is one of the ultimate aims of science and technology on the nanometer scale

IV. Competence and Challenges Let me now give some examples that illustrate the competence we have already achieved with local probe methods and the challenges lying ahead.

A. Measuring and Imagine We have already acquired considerable competence with simple model systems. Atomic resolution imaging of structural, electronic and mechanical properties and of the growth and diﬀusion phenomena under various conditions, ranging from ultrahigh vacuum to electro-chemical environments, has become standard. The first example, Fig. 13.4, shows a scanning tunneling microscope image of C60 or “bucky balls” adsorbed on Au(110), the case sketched in Fig. 13.3a. For convenience, I take an example from our Laboratory that illustrates various approaches to imaging. Excellent results of C60 imaging have been obtained at many diﬀerent places, in Japan in particularly by the group at the Tohoku University. On the lefthand side of Fig. 13.4, regions of uncovered gold with mostly individual gold rows 8 Å apart, which are the (1 × 2) reconstruction of the bare gold surface can be seen. The zigzag structure on the right-hand side is due to a monolayer of adsorbed C60 , which forms a (5 × 6) reconstruction, i.e., a five and six times larger periodicity than unreconstructed Au(110). The C60 molecules at the boundary zones appear much larger. Remember that STM just images electronic states. Why the electronic states at the energy of the present tunneling experiments of the isolated or edge molecules appear more extended is not known at present. At room temperature, the bucky balls rotate rapidly and no internal structure can be observed by STM. At 50 K, the rotation is frozen in and three types of structures associated with diﬀerent frozen-in states of the molecule on the substrate can

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Fig. 13.4 STM image of a monolayer of C60 molecules on Au(110), courtesy of J.K. Gimzewski, S. Modesti and R.R. Schlittler. IBM R¨uschlikon

Fig. 13.5 (a) STM image of “frozen-in” C60 molecules on Au(110), displaying three characteristic shapes, courtesy of J.K. Gimzewski, IBM R¨uschlikon. (b) Photon map of an Au(110) surface covered with an annealed monolayer of C60 . The area is 60 Å×60 Å[From R. Berndt, R. Gaisch, W.D. Schneider, J.K. Gimzewski, B. Reihl, R.R. Schlittler and M. Tschudy, “Photon Emission from Adsorbed C60 Molecules with Sub-Nanometer Lateral Resolution,” Appl. Phys. A 57, 513 c (1993) Fig. 13.3b, Springer-Verlag 1993]

be observed, as shown in Fig. 13.5a. This example demonstrates the diﬃculty of interpreting STM images of more complex systems. The imaged electronic states reflect those of the molecules, of the substrate and, to some extent, even of the tip, and cannot be related in a straightforward way to the icosahedron shape of the C60 Figure 13.5b shows the light emitted from the adsorbed C60 molecules. The tunneling electron excites a local plasmon due to the particular tip-sample configuration (example for Fig. 13.3e). The plasmon, on decay, emits a photon, thus making a “bucky bulb” out of a bucky ball.

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The second example shows the cross-sectional STM view (Fig. 13.6) of a sequence of alternating thin layers of GaAs and AlGaAs. The larger band gap of AlGaAs provides the potential that confines the electrons into two, one or zero dimension, called quantum wells (for alternating thin layers), quantum wires and quantum dots, respectively. Questions of interest to be answered by an STM experiment concern the structural and electronic width of the GaAs-AlGaAs interface, the distribution of dopants and of Al, the band gaps and band bending. The GaAs appears bright because tunneling into it is easy, while the AlGaAs appears dark owing to the smaller number of electric states at the given energy of the tunnel electrons. Thus, bright and dark indicate high and low electron state densities rather than topographic features. Likewise, the apparent roughness of AlGaAs is of electronic rather than topographic nature. The blow-up (Fig. 13.7a) shows that the compositional transition from the GaAs layer to the AlGaAs is very sharp, the band gap, however, varies much more smoothly (Fig. 13.7b). Figures 13.4 to 13.7 were examples of scanning tunneling microscopy, which requires conducting probes and objects. In force microscopy, the probe-sample interaction is a force. Resolution in force microscopy is generally a little bit less than in scanning tunneling microscopy, e.g., atomic resolution so far is the exception rather than the standard. However, its ease and breadth of application, in particu-

Fig. 13.6 STM view of a cleaved quantum well structure with a constant tunnel current trace between the two arrows at the top. The fine mesh of bright spots corresponds to the As atoms. The overall bright areas are GaAs, the dark ones AlGaAs regions. Image courtesy of M. Pfister, M.B. Johnson, S.F. Alvarado and H.W.M. Salemink, IBM R´uschlikon

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lar for nonconducting objects, make it the most widely applied method at the time being. Figure 13.8 shows a force image of magnetic tracks. For less simple systems, however, separation and individual control of the interactions involved in a local experiment are crucial for understanding the imaging process and interpreting the image. Images can be beautiful and interesting, but then so is a sphinx. Force measurements are expected to play a central role for further progress in local characterization methods. Further challenging issues concern magnetic properties and chemical specifity on a nanometer scale, and the combination of nano in space and time.

B. The Solid-Liquid Interface Local probe methods can be performed in nearly any environment in which the local probe can be moved with respect to the object and which does not screen the interaction between probe and object. They have brought a quantum leap for in situ characterization in ambient or liquid environments not accessible to electron and ion microscopies and have laid the foundation for nano-electrochemistry. The electrode-electrolyte interface is tremendously rich, with all its reconstructions and other structural and compositional phenomena of no lesser variety than those of the solid-vacuum interface in classical surface science. Moreover, the composition of the electrolyte brings an additional degree of freedom, reflected, for example, in the electrolyte-dependent reconstructions. Thus nanoelectrochemistry has pioneered the nanoscopic approach to the solid-liquid interface in general. The central importance of understanding and controlling the solid-liquid interface on a nanoscopic scale, however, extends far beyond the classical topic of electrochemistry. Liquids provide new ways to treat and control surfaces. Capillary and van der Waal’s forces acting on cantilever force sensors in force microscopy are best controlled in liquids. We can also think of surface control through passivation with a liquid and simultaneous local surface modification using, for example, specific molecules in the liquid. A new surface science will emerge that can deal with “real” surfaces at ambient conditions and in liquids, and which is based on the extremely high resolution of local probe methods and their adaptability to diﬀerent environments. This could open the present surface science of homogenized, well-prepared, well-controlled and reasonably well-defined surfaces to a large variety of “real” surfaces and interfaces that can be inhomogeneous on the smallest possible scale. Important for such a new type of surface science, however, is a much improved chemical analysis capability of local probe methods. Characterization of “real” surfaces and interfaces will involve diﬀerent types of experiments, since initially much less is known about the state of such surfaces and interfaces than about that of wellprepared and controlled surfaces. For interaction separation, the experiments have to be performed simultaneously, especially because “real” interfaces can neither be reproduced on a local scale nor suﬃciently controlled for sequential local experi-

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Fig. 13.7 (a) The interface between the AlGaAs in the lower left and the GaAs in the upper right is “atomically” sharp. The apparent roughness of the AlGaAs is the roughness of the electronic states due to the statistically distributed Al; the large bright features are associated with the electrons of adsorbed oxygen atoms. Image courtesy of H.W.M. Salemink, IBM R¨uschlikon. (b) Current onset related to the valence band across a AlGaAs/GaAs interface. The valence edge energy was derived from tunneling spectroscopic curves taken simultaneously with an atomic resolution image similar to that in (a). The drawn curve (S) refers to the value as calculated for this particular surface. Note that the transition takes place over a length of scale of 3.5 nm (about six atom rows) [From H.W.M. Salemink et al, Phys. Rev. B 45, 6946 (1992)]

Fig. 13.8 Force image of a magnetic track. In bright and dark stripes, the magnetization points in opposite directions. The magnetic pattern was imaged by magnetic forces, the topography of the track by electrostatic forces. Image area: 6 × 6μm. Image courtesy of Ch. Sch¨onenberger and S.F. Alvarado, IBM R¨uschlikon

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ments. The local approach will also produce very large data sets for representative surface samples, calling for increased speed and parallel operation as well as for new ways of handling and analyzing such volumes of data. Local probe methods give us the ability to interact with individual functional molecular units, be it to study or to control their functions and the processes associated with them. The functionality of most of them, such as those of biological molecules, depends critically on an appropriate liquid environment. Therefore, mastering the solid-liquid interface on a nano-scale is crucial to the application of local probe methods to in vivo biology. Lastly, the liquid provides the third dimension for eﬃcient self-assembly and self-organization of large molecules on surfaces. Such “selfprocedures” will play a central role in the emerging nano-age, where we will have to build and interact with tera and peta nanometer-sized objects on an individual or at least on a distinctly selective basis. The liquid-solid interface, quite generally, is a crucial element for interfacing the macro-scopic world to nano-individuals —– one of the primary objectives and challenges of science and technology on the nanometer scale.

C. Manipulation and Modification Manipulation and modification on the nanometer or even atomic scale have made tremendous progress in the past couple of years. They aim at creating new types of nanometer-sized structures and functional units for scientific and practical purposes. In Fig. 13.9, 48 Fe atoms adsorbed on a Ni(110) surface have been arranged to form a “quantum corral.” The electronic surface waves are reflected at the Fe atoms, giving rise to a standing-wave pattern, which modulates the tunneling current accordingly. This example might not have much practical value, but is a beautiful illustration of what can be done by controlled manipulation of atoms. The more practical eﬀorts are viewed by some mainly as a road leading to large-scale integrated systems, e.g., petabyte memories. Whether simple scratching with storage densities of Gbits/cm2 , see Fig. 13.10 atom extraction or deposition at 100 Tbits/cm2, see Fig. 13.11, or other methods with performances somewhere in between will ever lead to viable large-scale storage application is an open issue. This will depend crucially on the possibility of producing miniaturized nano-tools suitable for parallel operation, for example of thousands to millions of tips as reading and writing heads, as well as on the progress in current technologies. However, even more exciting might be the prospects of creating sophisticated and complex nano-structures and nano-machines by manipulation and modification. Such nano-machines would be used for specific experiments or could perform specific tasks that cannot be reasonably executed or are even impossible by other means. The simplest nano-machine —– although it is far from being simple —– could be a functionalized tip with a specific test molecule attached that is used for recognition of other molecules (see also below, in Sub-

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Fig. 13.9 A circular quantum corral. This STM image shows 48 iron atoms that were positioned into a 124-Å-diameter ring on a copper (111) surface. The iron atoms scatter the surface-state electrons of the copper surface, resulting in the quantum confinement of the electrons to the corral. The wave structure in the interior of the corral is due to the density distribution of three of the eigenstates of the corral that happen to lie very close to the Fermi energy. Image courtesy of D. Eigler, IBM Research Division, Almaden

Fig. 13.10 “HEUREKA” scratched with the dynamical ploughing technique (“Woody Woodpecker” approach) into a compact disc. The holes are information pits in the compact disc. The letter size is 700 nm, and the indentation depth is 10 nm, corresponding to approx. 100 Gbits/cm2 [From T.A. Jung et al., Ultramicroscopy 42–44, 1446 (1992)]

section E). Mbit to Gbit memories of micro- to millimeter dimension, everything included, could have many applications for “local” tasks. Finally, the multibillion-

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dollar human genome project could essentially be miniaturized, in a first step, to a local-probe DNA imaging station and in a second step to a biological DNA reading unit with an appropriate interface to the human world. We have again “smaller, faster, cheaper”, but applied to complex tasks not to individual elements. For instance, the cost of memory bits in a nano-machine plays a lesser role than for mass storage. Local probe methods appear indispensable in the exploratory stage of the nano-world. Once standard, however, fabrication of nano-machines and their control might be achieved by other means.

Fig. 13.11 STM image of a MoS2 surface: (a) Pristine and (b) after extraction of individual atoms to form the word NANO SPACE. This corresponds to a storage density of 100 Tbits/cm2 . Image courtesy of S. Hosaka, Central Research Laboratory, Hitachi Ltd., Tokyo

D. Nanotools and a New Standard Miniaturized sensors and actuators requiring nano- to picometer precision and control are another rewarding challenge. They will serve as local measuring and control stations and as sensory organs, hands and feet of nano-robots, i.e., small robots working with nm-to-pm precision. An example is the micro-calorimeter, which measures p Joules of reaction heat in msec, and we can readily envisage the ability to measure f Joules in μ sec. Quite generally, the nanometer will become the new standard of precision. Micrometer precision was a crucial element for the later part of industrialization and for the beginning of the technology age. The notion of a nanometer world, however, still encounters considerable reservation in the western industrial world at large, al-

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though already accepted as the new standard for microtechnology of the near future, To change that is indeed a challenge. It might help to remember that the micrometer had no significance for a farmer plowing his field with an ox and plow 150 years ago —– nor for the ox or the plow. Nevertheless, the micrometer changed plowing —– it is the precision standard for the tractor.

E. Interfacing Molecules

Fig. 13.12 Program for “interfacing molecules” by chemical activation (functionalizing) of probe and substrate, (a) “Bare” configuration, (b) “functional” environment, (c) activation of substrate, here by a self-assembled monolayer, (d) configuration (c) in proper environment, (e) configuration (d) with activated probe. Steps (a) to (e) connect a functional object via the functional probe with the outside world. In (f) a functional molecule is the new probe. [From H. Rohrer, Surface Sci. 299/300, 956 (1994)]

Interfacing the macro-world with nano-individuals is one of the great challenges. Figure 13.12 sketches a program for the case of functional biological macromolecules. In the first step shown in Fig. 13.12a, neither the substrate nor the probe are activated; the molecule is physisorbed directly onto the substrate. This step is used for qualitative imaging and for exploring communication with the molecule. In Fig. 13.12b, object and probe are immersed into an appropriate liquid environment. Of interest here is the immobilization in a liquid environment for imaging the “true” shape of the molecule and for communication. In Fig. 13.12c, the molecule is immobilized on a self-assembled monolayer —– a problem currently of interest. The next steps include immobilization in the proper environment on a chemically

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activated substrate (Fig. 13.12d) and finally activation of the probe (Fig. 13.12e and f).

F. Other Challenges Progress into the nanometer age depends critically on improved interdisciplinary thinking and acting, both within science and between science and engineering. The thinking starts in the heads of scientists and in those of open-minded money agencies, the acting begins in formulating interdisciplinary projects and subsequent cooperation between scientists who are well trained in their disciplines. Interdisciplinarity is mainly a matter of the attitude of the scientific community —– not of science politics. Being able to handle and control condensed matter —– “dead” or living —– on an atom-by-atom or molecule-by-molecule basis and on a time scale of individual processes opens tremendous perspectives, but also fears. Both engender the wish for controlling science, whatever the motivation may be. The destiny of society, however, lies in the proper use of science, not in its control.

Fig. 13.13 STM image of a monolayer self-assembled from dodecanethiol on Au(lll), (a) as assembled and (b) annealed. Monomolecular channels form spontaneously during annealing and might be useful for directed immobilization of functional molecules (process sketched in Fig. 13.12c) [Reprinted with permission from E. Delamarche, B. Michel, H. Kang and Ch. Gerber, Langmuir (1994, in press). Copyright 1994 American Chemical Society.]

14

From Rice to Snow Pierre-Gilles de Gennes

Abstract [This address was presented by Pierre-Gilles de Gennes as the Nishina Memorial Lecture at the University of Tokyo, on April 3, 1998.] We present here some general features of granular materials, of their importance, and of the conceptual diﬃculties which they exhibit. For static problems, we insist on the diﬀerence between textures, which represent frozen correlations between grains, and stress tensors. We argue that in systems like heaps and silos, texture is present, but the main features of the stress distribution do not depend on it, and a description using an isotropic medium is a good starting point. We also discuss avalanche flows, using a modified version of the equations of Bouchaud et al, which might be valid for thick avalanches.

1 Examples of Granular Matter Solid of particles are omnipresent: from the rings of Saturn to the snow of our mountains. Granular materials represent a major object of human activities: as measured in tons, the first material manipulated on earth is water; the second is granular matter [1]. This may show up in very diﬀerent forms: rice, corn, powders for construction (the elinkers which will turn into concrete), pharmaceuticals, · · · . In our supposedly modern age, we are extraordinarily clumsy with granular system spends an unreasonable amount of energy, and also leads to Pierre-Gilles de Gennes an extremely wide distribution of sizes. Transporting a gran- NMF c ular material is not easy: sometimes it flows like an honest

Pierre-Gilles de Gennes (1932 – 2007). Nobel Laureate in Physics (1991) Coll´ege de France at the time of this address P.-G. de Gennes: From Rice to Snow, Lect. Notes Phys. 746, 297–318 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 14

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fluid, but sometimes (in hoppers) it may get stuck: the reopening procedures are complicated —– and often dangerous. Even storage is a problem. The contents of bags can clump. Silos can explode, because of two features: a) Fine powders of organic materials in air often achieve the optimum ratio of organic/ambient oxygen for detonations. b) Most grains, when transported, acquire charge by collisions (tribo electricity: high voltages build up, and create sparks. From a fundamental point of view, granular systems are also very special. The general definition is based on size. We talk of particles which are large enough for thermal agitation to be negligible. Granular matter is a zero temperature system. In practice, Brownian motion may be ignored for particles larger than one micrometer: this is our threshold. A heap of grains is metastable: ideally, on a flat horizontal support, it should spread into a monolayer (to decrease its gravitational energy). But it does not! It can be in a variety of frozen states, and the detailed stress distribution, inside the heap, depends on sample history. (We come back to these static problems in section 2). The dynamics is also very complex: my vision of avalanches is presented in section 3 —– but it is probably naive and incomplete. Not only we do have a great variety of grains: but also a great variety of interactions, commanding the adhesion and the friction between grains. For instance, during dry periods, the grains of sand in a dune have no cohesion, and under the action of wind, the dune moves [2]. In more humid intervals, the grains stick together through minute humidity patches, and they are not entrained by the wind: the dunes stop, thus relieving the plantations from a serious threat. In the present text, we shall concentrate on dry systems, with no cohesion, which give us a relatively well defined model system.

2 Statics 2.1 The General Problem Over more than a hundred years, the static distribution of stresses in a granular sample has been analyzed in departments of Applied Mechanics, Geotechnical Engineering, and Chemical Engineering. What is usually done is to determine the relations between stress and strain on model samples, using the so called triaxial tests. Then, these data are integrated into the problem at hand, with the material divided into finite elements. There is one complication however. To define a strain in a sample, we must know an unstrained reference state. This is easily found for a conventional solid, which has a shape. It is less clear for a powder sample: a) the way in which we filled the container for the triaxial test may play a role. b) when we trans-

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pose the triaxial data to the field, we are in fact assuming that our field material has had one particular mechanical history. I tend to believe that, in a number of cases, the problem of the reference state can be simplified, because the sample has not experienced any dangerous stress since the moment, when the grains “froze” together: this leads to a quasi elastic description, which is simple. I will try to make these statements more concrete by choosing one example: a silo filled with grain.

2.2 The Janssen Picture for a Silo The problem of a silo (Fig. 14.1) is relatively simple. The stresses, measured with gauges at the bottom, are generally much smaller than the hydrostatic pressure ρgH which we would have in a liquid (ρ: density, g : gravitational acceleration, H: column height). A first modelisation for this was given long ago by Janssen [3] and Lord Rayleigh [4]. a) Janssen assumes that the horizontal stresses in the granular medium (σ xx , σyy ) are proportional to the vertical stresses: σ xx = σyy = k j σzz = −k j p(z)

(14.1)

where k j is a phenomenological coeﬃcient, and p = −σzz is a pressure. b) An important item is the friction between the grains and the vertical walls. The walls endure a stress σrz . The equilibrium condition for a horizontal slice of grain (area πR2 ,Height dz) gives: −ρg +

∂p 2 = σrz |r=R ∂z R

(14.2)

(where r is a radical coordinate, and z is measured positive towards the bottom). Janssen assumes that, everywhere on the walls, the friction force has reached its maximum allowed value − given by the celebrated law of L.da Vinci and Amontons([5]): σrz = −μ f σrr = −μ f k j p (14.3) where μ f is the coeﬃcient of friction between grains and wall. Accepting eqs (14.1) and (14.3), and incorporating them into eq. (14.2), Janssen arrives at: ∂p 2μ f + k j p = ρg (14.4) ∂z R This introduces a characteristic length: λ=

R 2μ f k j

and leads to pressure profiles of the form:

(14.5)

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Fig. 14.1 A silo filled with grains, up to a height H. The grains are assumed to undergo very small vertical displacements u, for which an elastic description makes sense. They rub against the lateral walls

p(z) = p∞ [1 − exp(−z/λ)]

(14.6)

with p∞ = ρgλ. Near the free surface (z < λ) the pressure is hydrostatic (p ∼ ρgz). But at larger depths (z > λ) p → pin f ty : all the weight is carried by the walls.

2.3 Critique of the Janssen Picture This Janssen picture is simple, and does give the gross features of stress distributions in silos. But his two assumptions are open to some doubt.

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a) If we take an (excellent) book describing the problem as seen from mechanics department [6], we find that relation (14.1) is criticized: a constitutive relation of this sort might be acceptable if x, y, z were the principal axes of the stress tensor —– but in fact, in the Janssen model, we also need non vanishing oﬀ diagonal components σ xz , σyz . b) For the contact with the wall, it is entirely arbitrary to assume full mobilisation of the friction, as in eq.([3]). In fact, any value σrz /σrr below threshold would be acceptable. Some tutorial examples of this condition and of its mechanical consequences are presented in Duran’s book [1]. I discussed some related ambiguities in a recent note [7].

2.4 Quasi Elastic Model When a granular sample is prepared, we start from grains in motion, and they progressively freeze into some shape: this defines our reference state. For instance, if we fill a silo from the center, we have continuous avalanches running towards the walls, which stop and leave us with a certain slope. As we shall see in section 3, this final slope, in a “Closed cell” geometry like the silo, is always below critical: we do not expect to be close to an instability in shear. In situations like this, we may try to describe the granular medium as a quasi elastic medium. The word “quasi” must be explained at this point. When we have a granular system in a certain state of compaction, it will show a resistance to compression, measured by a macroscopic bulk modulus K. But the forces are mediated by small contact regions between two adjacent grains, and the contact areas increase with pressure. The result is that K(p) increases with p. For spheroidal objects and purely Hertzian contacts, one would expect K ∼ p1/3 , while most experiments are closed to K ∼ p1/2 [9]. Tentative interpretations of the p1/2 law have been proposed [10 ], [11]. Thus, following [12], we assume now that we can use an elastic description of the material in the silo -since we do not expect any slip band in the silo. To start, we introduce a displacement field u (r ); for instance, with a laboratory column, ∼ ∼ we would define a reference state with a filled horizontal column, then rotate it to vertical, and measure some very small displacement u of the grains towards the bottom. The only non vanishing component. of u is uz . We further assume, for the moment, that our medium can be described locally as isotropic, with two Lame coeﬃcients, or equivalently a bulk modulus K, plus a shear modulus μ. We can then write the vertical and horizontal constraints in the standard form: 4μ ∂uz σzz = K + (14.7) 3 ∂z 2μ ∂uz σ xx = σyy = K − (14.8) 3 ∂z

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Comparing the two, we do get a Janssen relation, with: kj =

σ σ xx 3K − 2μ = = σzz 3K + 4μ 1 − σ

(14.9)

where σ is the Poisson ration. In our picture, K and μ may still be functions of the scalar pressure −(σ xx + σyy + σzz ), or equivalently of p(z). Here we assume, for simplicity, that σ is independent of p. This will have to be checked in the future. How do we get the stress σrz ? We have: σrr = 2μ

∂uz ∂z

(14.10)

and this imposes: 1 uz = u0 (z) − C(z)r2 (14.11) 2 where u0 is the value at the center point, and the correction C is obtained by comparison with eq. (14.2): r ∂p (14.12) σrr = −2μCr = ρg + 2 ∂z giving: C(z) = (4μ)

−1

∂p ρg − ∂z

The correction −1/2Cr2 in eq. (14.11) must be compared to u0 . Taking derivatives, we find:

∂ 2 CR 1 dp R ∂z =R ∂ p dz λ ∂z (u0 )

(14.13)

(14.14)

thus, the whole description is strictly consistent if λ R or μ f 1.

2.5 State of Partial Mobilisation At this stage, we have (to our best) answered the first critique to the Janssen model. Let us now turn to the description of friction. Following ref. [7], we are led to replace the macroscopic threshold law of eq. [3] by a more detailed law, involving the displacement uz = u near the wall surface. The idea is that, for very small distortions, the friction force is harmonic —– proportional to u. But when u is larger than a certain anchoring length Δ, the friction force saturates to the Amontons limit. In ref. [7], I used a specific model of bistable asperities (Caroli Nozi´eres) to substantiate this assumption. But, more general friction systems (involving some plastic

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deformations at the contact points) are also compatible with this description. Thus, we are led to write: u −σrz = σrr μ f ψ (14.15) Δ where ψ(x) is a crossover function with ψ(x) ∼ x for x → 0 and ψ(x) → 1 for |x| 1. The few data available on macroscopic friction systems with smooth surfaces suggest Δ ∼ 1 micron (comparable to the size of an asperity). For our grains, rubbing against the wall of a silo, Δ is largely unknown. When |u| < Δ, we say that the friction is only partly mobilised. a) Let us assume first that we have no mobilisation. Then p(z) is hydrostatic: p = ρgz, and we have a local deformation: ∂u ρgz = ∂z K˜

(14.16)

where K˜ = K + 4μ/3. This is associated with a boundary condition at the bottom of the silo: u(z = H) = 0 (14.17) The result is a displacement at the free surface:

u s ≡ u(z = 0) = ρgH 2 / 2 K˜

(14.18)

our assumption of weak mobilisation is consistent if u s < Δ, or equivalently H < H ∗ , where H ∗ is a critical column height, defined by: ˜ (ρg) H ∗2 = 2 KΔ/

(14.19)

Typical, with Δ =1micron, we expect H ∗ ∼30cm. b) What should happen if our column is now higher than H ∗ ? Let us assume now that friction is mobilised in most of the column. If H > λ, this implies that p ∼ p∞ : thus, the deformation must be: du p∞ = (14.20) dz K˜ Let us investigate the bottom of the silo, putting z = H − η. At η =0, we have u =0. Thus, using eq. (14.20), we reach: u ηp∞ 2ηλ = = ∗2 Δ H ΔK˜

(14.21)

We see that the bottom part is not mobilised (u < Δ) up to a level: η = η∗ ≡

H ∗2 ∗ H <λ 2λ

(14.22)

Eq. (14.22) holds only if p(z) is close to p∞ in the region of interest: this imposes η∗ < λ, or equivalently H ∗ < λ. In the opposite case, the pressure field p(z), in the ˜ interval 0< η < η∗ , would again be hydrostatic, with u ∼ ρgη2 /K.

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η∗ = H ∗

H∗ > λ

(14.23)

The Janssen model holds only if H η∗ . The conclusion (for all values of H ∗ /λ) is that Janssen can apply only for heights H H ∗ . This is probably satisfied in industrial silos, but not necessarily in laboratory columns. Certain observed disagreements between p(z), measured in columns, and the Janssen model, may reflect this [13]. The authors of ref. [13] have also made an important observation: the temperature cycles between day and night lead to significant modulations of p(z). This, as they point out, must be a dilation eﬀect: the diﬀerential dilations experienced by the grains and the wall can easily lead to vertical displacements u which are comparable to the anchoring length: mobilisation may be very diﬀerent during night and day.

2.6 Stress Distribution in a Heap Below a heap of sand, the distribution of normal pressures on the floor is not easy to guess. In some cases, the pressure is not a maximum at the center point! This has led to a vast number of physical conjectures, describing “arches” in the structure [14] [15] [16]. In their most recent form [16], what is assumed is that, in a heap, the principal axis of the stress are fixed by the deposition procedure. Near the free surface, following Coulomb [6], it is usually assumed that (for a material of zero cohesion) the shear and normal components of the stress (τ and σn ) are related by the condition: τ = σn μi = σn tan θmax (14.24) where μi is an interval friction coeﬃcient and tanθmax is the resulting slope. In a 2 dimensional geometry, this corresponds to a principal axes which is at an angle 2θmax from the horizontal (Fig. 14.2) [6]. The assumption of ref. [16] is that this orientation is retained in all the left hand side of the heap (plus a mirror symmetry for the right hand side). Once this is accepted, the equilibrium conditions incorporating gravity, naturally lead to a “channeling of forces” along the principal axes, and to a distribution of loads on the bottom which has two peaks. This point of view has been challenged by S.Savage [17] who recently gave a detailed review of the experimental and theoretical literature. He makes the following points: a) for 2 dimensional heaps (“wedges”) with a rigid support plane, there is no dip in the experiments. b) if the support is (very slightly) deformable, the stress field changes deeply, and a dip occurs. c) for the 3d case (“cones”) the results are extremely sensitive to the details of the deposition procedure. Savage also describes finite element calculations, where one imposes the Mohr Coulomb conditions (to which we come back in section 3) at the free surface of a wedge. If we had assumed a quasi elastic description inside, we would have found an inconsistency: there is a region, just below the surface, which becomes instable

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towards shear and slippage. Thus Savage uses Mohr Coulomb in a finite sheet near the surface, plus elastic laws in the inner part: with a rigid support he finds no dip. But, with a deformable support, he gets a dip. In my opinion, the Savage picture contains the essential ingredients. There may exist an extra simplification, however -which I already announced in connection with the silos. If we look at the formation of the heap (as we shall do in section 3) we find that the slope angle upon disposition should be lower than the critical angle θmax . Thus our system is prepared in non critical conditions: all the sample may then be described as quasi elastic. This, in fact, should not bring in very great diﬀerences from the Savage results. I suspect that, what the physicists really wanted to incorporate, is the possible importance of an internal texture [18]. If we look at the contacts (1,2,· · ·,i,· · · ,p) of a grain in the structure, we can form two characteristic tensors: one is purely geometrical and defines what I shall call the texture: (i) x(i) (14.25) Qαβ = α xβ i

(where xα are the distances measured from the center of gravity of the grain). The other tensor is the static stress: 1 (i) (i) (i) (i) xα F β + xβ F α (14.26) σαβ = 2 i where F∼(i) is the force transmitted at contact (i). There is no reason for the axes of these two tensors to coincide. For instance, in an ideal hexagonal crystal, one major axes of the Q tensor is the hexagonal axis, while the stresses can have any set of principal axes. In the heap problem, I am ready to believe that the deposition process freezes a certain structure for the Q tensor, but not for the stress tensor. The presence of a non trivial Q tensor (or “texture”) can modify the quasi elastic model: instead of using an isotropic medium, as was done here in eqs (14.7,14.8) for the silo, we may need an anisotropic medium. In its simplest version, we would assume that the coarse-grained average Qαβ has two degenerate eigenvalues, and one third eigenvalue, along a certain unit vector (the director) n(r ). Thus, a complete ∼ ∼ discussion of static problems, in the absence of strong shear bands, would involve an extra field n defined by the construction of the sample. But this refinement is, in a ∼ certain sense, minor. Texture eﬀects should not alter deeply the quasi elastic picture.

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Fig. 14.2 The Coulomb method of wedges to define the angle θmax at which an avalanche starts

3 Dynamics: Avalanche problems 3.1 Onset and Evolution of Surface Flows 3.1.1 The Coulomb View As already mentioned in section 2, C.A.Coulomb (who was at the time a military engineer) noticed that a granular system, with a slope angle θ, larger than a critical value θmax , would be unstable. He related the angle θmax to the friction properties of the material. For granular materials, with negligible adhesive forces, this leads to tgθmax = μi , where μi is a friction coeﬃcient [6]. The instability generates an avalanche. What we need is a detailed scenario for the avalanche. We note first that the Coulomb argument is not complete: a) it does not tell us at what angle θmax + ε the process will actually start b) it does not tell us which gliding plane is preferred among all these of angle θmax as shown on Fig. 14.2. I shall propose an answer to these questions based on the notion of a characteristic size ξ in the granular material. 1) Simulations [19] [20] and experiments [21] indicates that the forces are not uniform in a granular medium, but that there are force paths conveying a large fraction of the force. These paths have a certain mesh size ξ, which is dependent on the grain shapes, on the friction forces between them, etc, but which is typically ξ ∼ 5 to 10 gram diameters d.

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2) We also know that, under strong shear, a granular material can display slip bands [22]. The detailed geometry of these bands depends on the imposed boundary conditions. But the minimum thickness of a slip band appears to be larger than d. We postulate that the minimum size coincides with the mesh size ξ. We are then able to make a plausible prediction for the onset of the Coulomb process: the thickness of the excess layer must be of order ξ: and the excess angle ε must be of order ξ/L, where L is the size of the free surface. Thus, at the moment of onset, our picture is that a layer of thickness ∼ ξ starts to slip. It shall then undergo various processes: (i) the number of grains involved shall be fluidized by the collisions on the underlying heap (ii) it shall be amplified because the rolling grains destabilize some other grains below. The steady state flow has been studied in detailed simulations [23]. It shows a sharp boundary between rolling grains and immobile grains: this observation is the starting point of most current theories. The amplification process was considered in some detail by Bouchaud et al. in a classic paper of 1994 (referred to here at BCRE [24][25]. it is important to realise that, if we start an avalanche with a thickness ξ of rolling species, we rapidly reach much larger thicknesses R: in practice, with macroscopic samples, we deal with thick avalanches (R ξ). We are mainly interested in these regimes —– which, in fact, turn out to be relatively simple.

3.1.2 Modified BCRE Equations [26] BCRE discuss surface flow on a slope of profile h(x, t) and slope tgθ θ = ∂h/∂x, with a certain amount R(x, t) of rolling species (Fig. 14.3). In ref. [24], the rate equation for the profile is written in the form: ∂h = γR (θn − θ) (+diﬀusionterms) ∂t

(14.27)

This gives erosion for θ > θn , and accretion for θ < θn . We call θn the neutral angle. This notation diﬀers from BCRE who called it θr (the angle of repose). Our point is that diﬀerent experiments can lead to diﬀerent angles or repose, not always egal to θn . For the rolling species, BCRE write: ∂h ∂R ∂R = − + v (+diﬀusionterms) ∂t ∂t ∂x

(14.28)

where γ is a characteristic frequency, and v a flow velocity, assumed to be non vanishing (and approximately constant) for θ ∼ θn . For simple grain shapes (spheroidal) and average levels of inelastic collisions, we expect v ∼ γd ∼ (gd)1/2, where d is the grain diameter and g the gravitational acceleration. Eq. (14.28) gives [∂h/∂t] as linear in R: this should hold at small R, when the rolling grains act independently.

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Fig. 14.3 The basic assumption of the BCRE picture is that there is a sharp distinction between immobile grains with a profile h(x, t) and rolling grains of density R(x, t). R is measured in units of “equivalent height”: collision processes conserve the sum h + R

But, when R > d, this is not acceptable. Consider for instance the “uphill waves” mentioned by BCRE, where R is constant: eq. (14.27) shows that an accident in slope moves upward, with a velocity vup = γR. It is not natural to assume that vup can become very large for large R. This lead us (namely T. Boutreux, E. Rapha¨el, and myself [26] to propose a modified version of BCRE, valid for flows which involve large R values, and of the form: ∂h = vup (θn − θ) (R > ξ) (14.29) ∂t where vup is a constant, comparable to v. We shall not see the consequences of this modification. Remark: in the present problems, the diﬀusion terms in eq. (14.28) turn out to be small, when compared to the convective terms (of order d/l, whereL is the size of the sample): we omit them systematically.

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3.1.3 A Simple Case A simple basic example (Fig. 14.4) is a two dimensional silo, fed from a point at the top, with a rate 2Q, and extending over a horizontal span 2L: the height profile moves upward with a constant velocity Q/L. The profiles were already analysed within the BCRE equations (14.25). With the modified version, the R profile stays the same, vanishing at the wall (x = 0): R=

xQ L v

(14.30)

but the angle is modified and diﬀers from the neutral angle: setting ∂h/∂t = Q/L, we arrive at: Q (Q > vξ) θn − θ = (14.31) Lvup Thus, we expect a slope which is now dependent on the rate of filling: this might be tested in experiments or in simulations.

Fig. 14.4 Feeding of a two dimensional silo with a flux Q over a length L, leading to a growth velocity w(z) = Q/L.

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3.2 Downhill and Uphill Motions Our starting point is a supercritical slope, extending over a horizontal span L with and angle θ = θmax + (Fig. 14.2). Following the ideas of section 1, the excess angle is taken to be small (of order ξ/L). It will turn out that the exact values of is not important: as soon as the avalanche starts, the population of rolling species grows rapidly and becomes independent of (for small): this means that our scenarios have a certain level of universality. The crucial feature is that grains roll down, but profiles move uphill: we shall explain this in detail in the next paragraph.

3.2.1 Wave Equations and Boundary Conditions It is convenient to introduce a reduced profile: ˜ t) = h − θn x h(x,

(14.32)

Following BCRE, we constantly assume that the angles θ are not very large, and write tgθ ∼ θ: this simplifies the notation. Ultimately, we may write eqs (14.28) and (14.29) in the following compact form: ∂R ∂R ∂h˜ = vup + v ∂t ∂x ∂x

(14.33)

∂h˜ ∂h˜ = −vup (14.34) ∂t ∂x Another important condition is that we must have R > 0. If we reach R = 0 in a certain interval of x, this means that the system is locally frozen, and we must then impose: ∂h˜ =0 (14.35) ∂t One central feature of the modified eqs. (14.33), (14.34) is that, whenever R > 0, they are linear. The reduce profile h˜ is decoupled from R, and follows a very simple wave equation:

˜ t) = v x − vupt h(x, (14.36) where w is an arbitrary function describing uphill waves. ˜ t) which moves It is also possible to find a linear combination of R(x, t) andh(x, downhill. Let us put: ˜ t) = u(x, t) R(x, t) + λh(x, (14.37) where λ is an unknown constant. Inserting eq. (14.37) into eq. (14.33), we arrive at:

∂h˜ ∂u ∂u − v = vup − λ vup + v ∂t ∂x ∂x

(14.38)

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Thus, if we choose: λ=

vup v + vup

(14.39)

we find that u is ruled by a simple wave equation, and we may set: u(x, t) = u(x + vt)

(14.40)

We can rewrite eq. (14.37) in the form: R(x, t) = u(x + vt) − λw(x − vupt)

(14.41)

Eqs (14.36) and (14.41) represent the normal solution of our problem in all regions where R > 0. This formal solution leads in fact to a great variety of avalanche regimes.

3.2.2 Comparison of Uphill and Downhill Velocities Our equations introduce two velocities: one downhill (v) and one uphill (vup ). How are they related? The answer clearly depends on the precise shape (and surface features) of the grains. Again, if we go to spheroidal grains and average levels of inelasticity, we may try to relate vup and v by a naive scaling argument. Returning to eq. (14.27) and (14.29) for the rate of exchange between fixed and rolling species, we may interpolate between the two limits (R < ξ and R > ξ): ∂h R = γξ (θ − θn ) f (14.42) ∂t ξ where the unknown function f has the limiting behaviours: f (x → 0) = x f ( 1) = f∞ = constant

(14.43)

This corresponds to vup = f∞ γξ. Since we have assumed v ∼ γd, we are led to: vup /v ∼ f∞ ξ/d

(14.44)

If, even more boldly, we assume that f∞ ∼ 1, and since ξ is somewhat larger than the grain size, we are led to suspect that vup may be larger than v.

3.2.3 Closed Versus Open Systems Various types of boundary conditions can be found for our problems of avalanches:

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Fig. 14.5 Two types of avalanches: a) open cell b) closed cell

a) At the top of the heap, we may have a situation of zero feeding (R = 0). But we can also have a constant injection rate Q fixing R = Q/v. This occurs in the silo of Fig. 14.4. It also occurs at the top of a dune under a steady wind, where saltation takes place on the windward side (14.2), imposing a certain injection rate Q, which then induces a steady state flow on the steeper, leeward side. b) At the bottom end, we sometimes face a solid wall —– e.g. in the silo; then we talk about a closed cell, and impose R = 0 at the wall. But in certain experiments with a rotating bucket, the bottom end is open (Fig. 14.5). Here, the natural boundary condition is h =constant at the bottom point, and R is not fixed. Both cases are discussed in ref. [26]. Here, we shall simply describe some features for the closed cell system.

3.3 Scenario for a Closed Cell The successive “acts” in the play can be deduced from the wave eqs. (14.40, 14.41) plus initial conditions. Results are shown in Fig. (14.6) – Fig. 14.10). During act 1, a rolling wave starts from the top, and an uphill wave starts from the bottom end. In act 2, these waves have passed each other. In act 3, one of the waves hits the border. If v+ > v, this occurs at the top. From this moments, a region near the top gets frozen, and increases in size. If v+ < v, this occurs at the bottom: the frozen region starts there and expands upwards. In both cases, the final slope θ f is not equal to the neutral angle θn , but is smaller: θ f = θn − δ = θmax − 2δ

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Fig. 14.6 Closed cell “act 1”. The slope in the bottom region is described by eq. (14.40)

3.4 Discussion 1) The determination of the whole profiles h(x, t) on an avalanche represents a rather complex experiment [27]. But certain simple checks could easily be performed. a) With an open cell, the loss of material measured by R(0, t) is easily obtained, for instance, by capacitance measurement (14.28). The predictions of ref. [26] for this loss are described on fig. (14.10). R(0, t) rises linearly up to a maximum at t = L/v, and then decreases, reaching 0 at the final time L(1/v+1/vup). The integrated amount is: 1 1 2 (14.45) M ≡ R(0, t)dt = λδL2 + 2 v vup

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Fig. 14.7 Closed cell “act 2”. The sketch has been drawn for vup > v. (When vup < v, the slope ∂R/∂x in the central region becomes positive)

Unfortunately, the attention in ref. [28] was focused mainly on the reproducibility of M, but (apparently) the value of M and the shape of R(0, t) were not analysed in detail. b) With a closed cell, a simple observable is the rise of the height at the bottom h(0, t): this is predicted to increase linearly with time: ˜ t) = δv+ t h(0, t) = h(0,

(14.46)

up to t = L/v+ , and to remain constant after. Similar measurements (both for open or closed cells) could be done at the top points, giving h(L, t).

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Fig. 14.8 Closed cell “act 3”. The case vup > v. A frozen patch grows from the top

c) A crucial parameter is the final angle θ f . In our model, this angle is the same all along the slope. For an open cell, it is equal to the neutral angle θn . For a closed cell, it is smaller: θ f = θn − δ. Thus the notion of an angle of repose is not universal! The result θ f = θn − δ was already predicted in a note [28], where we proposed a qualitative discussion of thick avalanches. The dynamics ( based on a simplified version of BCRE eqs) was unrealistic —– too fast —– but the conclusion on θ f was obvious: in a closed cell, the material which starts at the top, has to be stored at the bottom part, and this leads to a decrease in slope.

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Fig. 14.9 Closed cell “act 3”(vup < v). Here a frozen patch grows from the bottom

d) One major unknown of our discussion is the ratio vup/v. We already pointed out that this may diﬀer for diﬀerent types of grains. Qualitative observations on a closed cell would be very useful here: if in its late stages (act (14.3)) the avalanche first freezes at the top, this means vup > v. If it freezes from the bottom, vup must be < v. 2) Limitations of the present model: a) our description is deterministic: the avalanche starts automatically at θ = θmax , and sweeps the whole surface. In the open cell systems (with slowly rotating drums) one does find a nearly periodic set of avalanche spikes, suggesting that θmax is well defined. But the amplitude (and the duration) of these spikes varies (28): it may be that some avalanches do not start from the top. We can only pretend to represent the full avalanches. What is the reason for these statistical features? (i) Disparity in grain size tends to generate spatial in inhomogeneities after a certain number of runs (in the simplest cases, the large grains roll further down and accumulate near the walls). (ii)

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Fig. 14.10 Flux profile predicted at the bottom of an open cell

Cohesive forces may be present: they tend to deform the final profiles, with a θ(x) which is not constant in space. (iii) Parameters like θm (or θn ) may depend on sample history. b) Regions of small R. For instance, in a closed cell, R(x, t) → 0 for x → 0. A complete solution in the vicinity of R = 0 requires more complex equations, interpolating between BCRE and our linear set of equations, as sketched in eq. (14.42). Boutreux and Rapha¨el have indeed investigated this point. It does not seem to alter significantly the macroscopic results described here. c) Ambiguities in θn . When comparing thick and thin avalanches, we assumed that θn is the same for both: but there may, in fact, be a small diﬀerence between the two. Since most practical situations are related to thick avalanches, we tend to focus our attention on the “thick” case —– but this possible distinction between thick and thin should be kept in mind. Acknowledgements I have greatly benefited from discussions and written exchanges with J.P. Bouchaud, J. Duran, P. Evesque, H, Herrmann, and J. Reichenbach.

References 1. For a general introduction to granular materials, see J. Duran “Poudres et grains” (Eyrolles, Paris 1996). 2. The basic book here is “Physics of blown sand and sand dunes” by E.R. Bagnold (Chapman and Hall, London 1941). 3. H.A. Janssen, Z. Vereins DeutschEng. 39 (35), p. 1045 (1895). 4. Lord Rayleigh, Phil Mag 36, 11, 61, 129, 206 (1906).

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5. See for instance “Friction: an introduction”, P. Bowden and D. Tabor (Doubleday, NY 1973). 6. R. Nedermann, “Statics and kinematics of granular materials”, Cambridge U. Press, 1992. 7. P.G. de Gennes, C.R. Acad. Sci. (Paris), (1997). 8. P. Evesque, J. Physique I (France), 7, p. 1501 (1997) 9. J. Duﬀy, R. Mindlin, J. App. Mech. (ASME), 24, p. 585 (1957). 10. J. Goddard, Proc. Roy. Soc. (London), 430, p. 105 (1990). 11. P.G. de Gennes, Europhys. Lett., 35, p. 145-149 (1996) 12. P. Evesque, P.G. de Gennes, submitted to C.R. Acad. Sci. (Paris). 13. L. Vanel, E. Cl´ement, J. Lanuza, J. Duran, to be published. 14. S.F. Edwards, C.C. Mounfield, Physica, A 226, p. 1, 12, 25 (1996). 15. J.P. Bouchaud, M. Cates, P. Claudin, J. Physique II (France), p. 639 (1995). 16. J.P. Wittmer, M. Cates, P. Claudin, J. Physique I (France), 7, p. 39 (l997). 17. S.B. Savage, in “Powders and grains” (Behringer and Jenkins, eds), p. 185 (Balkema, Rotterdam) (1997). 18. H. Herrmann, “On the shape of a sand pile”, Proceedings of the Carg`ese Workshop (1997), to be published. 19. F. Radjai et al, Phys. Rev. Lett., 77, p.274 (1996). 20. F. Radjain D. Wolf, S. Roux, M. Jean, J.J. Moreau, “Powders and grains” (a. Behringer, J. Jenkins eds), p. 211, Balkema, Rotterdam (1997). 21. C.H. Liu, S. Nagel, D. Shechter, S. Coppermisth, S. Majumdar, O. Narayan, T. Witten, Science, 269, p. 513 (1995). 22. J. DesrueS, in “Physics of Granular Media.” (D. Bideau, J. Dodds eds),p. 127 (Nova Sci. Pub., Les Houches Series (1991). 23. P.A. Thompson, G.S. Grest, Phys. Rev. Lett., 67, p. 1751 (1991). 24. -J.P. Bouchaud, M. Cates, R. Prakash, S.F. Edwards, J. Phys. (France), 4, p. 1383 (l994). -J.P. Bouchaud, M. Cates, in “Dry granular matter”, Proceedings of the Carg`ese workshop, (1997), H. Hermann ed. (to be published). 25. P.G. de Gennes, in “Powders and grains” (R. Behringer, J. jenkins eds), p. 3, Balkema,, Rotterdam (1997). 26. T. Boutreux, E. Rapha¨el, P.G. de Gennes, to be published. 27. H. Jaeger, C. Liu, S. Nagel, Phys. Rev. Lett., 62, p. 40 (1988). 28. T. Boutreux, P.G. de Gennes, C.R. Acad. Sci. (Paris), 324, p. 85-89 (1997)

15

SCIENCE — A Round Peg in a Square World Harold Kroto

Abstract [This address was presented by Harold Kroto as the Nishina Memorial Lecture at Yukawa Institute for Theoretical Physics, on November 5, 1998.] I have various possible presentations that I could give depending on what I feel I should speak about - in fact I have about four hours worth so I had better get started. I am going to start with Science and what it means to me and what it means to many other people.

1 Patterns and Symmetries In this first image Fig. 15.1 we see Dr. Jacob Bronowski playing with his grandchild. I would like to know how many of you in the audience actually played with this toy when you were children. Can you put your hands up? I see from the response that quite a lot of you had one. Now how many gave this toy to your children? Well, there is one mother, who shall be nameless, who gave such a toy to her son and when the child picked up the cube he tried to put it through the round hole and forced it so much that it went through and then he picked up a Harold Kroto triangular brick and forced that through the round hole too. Harold c Kroto Then his mother started to get a bit worried and decided to take the child to see a psychiatrist. After some discussion the psychiatrist said, “Hmmm, it seems that this kid really has the same solution to any problem, doesn’t he. There is really only one career suitable for him. I suggest he should become a politician · · · · · · , Mrs. Blair”. Harold Kroto (1939 –). Nobel Laureate in Chemistry (1996) University of Sussex (United Kingdom) at the time of this address H. Kroto: SCIENCE — A Round Peg in a SquareWorld, Lect. Notes Phys. 746, 319–347 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 15

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Fig. 15.1 Trying to put a cube through a round hole

However, such symmetric shapes and structures are really quite interesting. Consider for instance these stone artifacts that were discovered in Scotland Fig. 15.2; they appear to have been carved some two or three thousand years ago and were found at the site of the first Glasgow Rangers versus Celtic soccer match. In those days the spectators were much more cultured and they carved the rocks into beautiful symmetric shapes before they threw them at the opposition supporters. It is however clear that an appreciation of symmetry lies buried deep within us. If we look at the work of Piero della Francesca Fig. 15.3 we see here a drawing of a truncated icosahedron - in fact it is the same pattern as a soccer ball. And in the work of Leonardo da Vinci we see the same structure. So these symmetric structures seem to have fundamental significance. The symmetry patterns somehow reach down deep into our consciousness. Let us consider a passage to be found in the “First Chemistry Book” - Plato’s Timaeus. I hope you all realise that this is the first. I didn’t realize until very late in life that is the only decent chemistry book that has ever been written. For instance in this book Plato says the following:

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Fig. 15.2 Ancient rocks carved into symmetric shapes

In the first place it is clear to everyone(!) that fire, earth, water and air are bodies, and all those bodies are solids, and all those solids are bounded by surfaces, and all rectilinear surfaces are composed of triangles Fig. 15.4.

In this way Plato arrived at the Greek Periodic Table. It had five elements - one more than Mrs. Thatcher seems to have known about judging by the financial support she gave UK chemistry when she was in power. Anyway this is a very bold statement and echos of such boldness are to be heard in a paragraph from a key paper by Van Vleck (Rev. Mod. Phys.23 (1951), 213). It says that practically everyone knows that the components of total angular momentum of a molecule relative to axes x,y and z fixed in space satisfy commutation relations of the form, J x Jy − Jy J x = i¯h Jz . Now, I went down Yasukuni-dori yesterday and I asked everybody I met whether they knew this fact and, believe it or not, not a single person did know anything about it. Actually, I confess no one knew anything about it in Brighton either. Anyway, I decided that I had better learn this if Van Vleck thought everyone knew about it. Then I came to page 60 of Condon and Shortly’s book on The Theory of Atomic Spectra; not only is it a great book but it is also a most elegantly printed one, page 60 is one of the most beautiful in the book and also perhaps the most important. The equations are the elegant mathematics of Dirac’s treatment of the interaction of radiation with matter - I expect you all to have understood the derivation by the end of today and to be able to work out the relations. This page details the derivation of the selection rules for the way that light and matter interact and so govern such things as the colour of materials etc. I think the page is not only very beautiful from a scientific viewpoint but also from a visual aesthetic one - the typeface is elegant and powerful too. It took a while to understand the derivation. If you go through the Quantum Theory of angular momentum, which you have to do if you want to understand spectroscopy, you come to this relationship Fig. 15.5 which details the result that there are 2J+1 components of angular momentum.

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Fig. 15.3 Truncated icosahedron in Piero della Francesca’s work

Almost the whole of chemistry falls out from this result, i.e.: When J is 0, 2J +1 = 1, when J is 1 it is = 3, and then 5, · · · and so on and in this way the structure of Mendeleev’s Periodic Table is revealed. Basically we are able to rationalise the observations that the first row has 2 × 1 elements, the second has 2 × (1 + 3), the third has 2 × (1 + 3 + 5) etc. · · · . So, basically, in the mathematical symmetries there are to be found truly fundamental aspects of the governing laws of Nature and the Physical World. That is the first part of what I wanted to say, the second is that our appreciation of these fundamental abstract patterns lies deeply buried in the human conscious mind.

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Fig. 15.4 Plato’s elements: earth, fire, water and air. The dodecahedron cannot be an element because its pentagon faces cannot be constructed out of right-angled triangles, Plato’s true elements

2 Scientists in Society Today one problem is that basic science is expensive and governments are forever trying to control the way it is done. Let me say something about chemists. John Cornforth’s 75th anniversary address to the Australian Chemical Society is one of the most wonderful article that I have ever read. John is a truly wonderful scientist and a great humanitarian who shared the Nobel Prize with Prelog in 1975. He is at Sussex and is a good friend. “Chemists who create new compositions of matter have transformed to an even greater extent the modern world: new metals, plastics, composites and so on. The list is much longer and chemists created the material for them all and physicists and mathematicians and biologists and earth scientists can tell similar stories. Scientists are embedded in the fabric of modern society and most of them spend their whole careers responding to the demands of the state or the market. They are so useful that the overwhelming majority who are non-scientists assume that is what they are there for. To an increasing extent the majority is insisting that scientists ought to concentrate more on what society says it wants from them and as for the teachers of science in the schools and universities, their business is to train people who will continue to satisfy those wants.”

Steacie was a Great Canadian scientist - he was the chief architect of the National Research Council of the 1950–70 period — the Golden Years alas now gone. If you read the book of his collected speeches which was published by University of Toronto press, you win find many observations which strike resonant chords with our world today. I can’t do justice here to his many ideas and insights but I highlight one described by Babbitt who edited the book,

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Fig. 15.5 Aspects of symmetry: angular momenta and the periodic table. The arrows in the boxes represent spin states

“· · · (This) makes it abundantly clear that he was implacably opposed to any attempt to formulate a broad general plan for science (it is impossible - my addition)“

You can tell politicians and others that till you’re blue in the face but they will not believe you - more to the point it will fall on deaf ears. I suspect that many scientists do the science without a clear idea of how they actually do it. Governments legislate on scientific matters and are often aided by prominent scientists who think they know how it should be done - and I suspect do not - especially as I believe there are many diﬀerent ways and one general strategy may be good for one type of scientist and their science and may be disastrous for another. “· · · Committees set up to advise on general areas are of relatively little value in comparison with the committee of experts set up to advise on a particular problem· · · ”

In the book on Steacie, Babbitt says: “· · ·like Polanyi, he (Steacie) believes in the spontaneous coordination of independent initiatives and the exercise of those informal mechanisms which traditionally have been used by academies: the scientific meeting and the expert committee”.

From the father to the son and here I now quote John Polanyi:

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“· · ·As with the free market in goods, it is the individual entrepreneur who is the best judge of where opportunities lie. This is because the working scientist is in close touch with the growing points of the field. Additionally, the scientist can be depended on to make the most careful investment of his time since it is he or she who will be punished in the event of a bad choice of topic”.

This is of course correct, unless you are able in your research report to disguise failure by finding a successful result. My views on this matter are coloured strongly by the great diﬃculty I have in carrying out research. I once commented to a colleague at NRC Canada (The Japanese scientist Takeshi Oka who was already at that time a superb researcher - he is now at the University of Chicago): “Only about one in ten of my experiments seems to work.” I shall always remember his reply: “That’s a very good percentage!” So, here we are. We are playing a game in which we have to end up with a successful research project and the likelihood of success is about 10%. So the secret is to show that you have been successful when in actual fact the experiment may not have worked or it may have evolved in some completely diﬀerent direction and we have to assure some committee people that it actually worked well in the way we originally predicted it would. It’s a bit’of a problem if the real success rate is 10%, but that is in fact that’s what happens. I believe that the very best research involves problems and research projects which went wrong in the sense that totally unexpected results were obtained. In his book on The Future of Capitalism Theroux gives advice to Government on their strategy. “· · ·The proper role of governments in capitalist societies in an era of man-made brain power is to represent the interests of the future to the present, but today,s governments are doing precisely the opposite. They are lowering investment in the future to raise consumption in the present· · · ”

3 Fundamental Science This is the problem here and in Britain too. Last week in the UK there was the launch of a corporate plan for science - just what Steacie steadfastly resisted and I maintain is not possible. Furthermore we find statements such as : “· · ·I would be suspicious of a scientist who could not explain why the work was being done in the first place· · · ”

Well, such suspicion certainly applies to me as I did have no idea that : i) My work in the early 70’s (with John Nixon) would result in a whole new field of phosphorus chemistry which is flourishing today; ii) That our laboratory studies (with David Walton) on long carbon chains (originally carried out for some personally fascinating and rather esoteric quantum dynamical reasons) would lead to a radioastronomy programme (with Takeshi Oka, Lorne Avery, John McLeod and Norm Broten at

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NRC) which revealed whole new perspective on the molecular composition of the interstellar medium and iii) that a little personal idea to simulate the conditions in a red giant carbon star would result in the serendipitous discovery of C60 , Buckminsterfullerene (with Jim Heath, Yuan Liu, Bob Curl and Rick Smalley). Furthermore an industrial member of the EPSRC Users panel balks when it comes to blue skies thinking. He says: “I’m uncomfortable with the idea of blue skies research because it implies an activity with little sense of direction.”

Well, I was north of San Francisco in the Napa Valley a few months ago and there was a beaten up old Volvo in a parking lot and on the bumper was a truly wonderful statement that sums up my sentiment on all cultural matters and science in particular: It was a quotation from the Song of Aragorn by J.R.R. Tolkien: “· · · Not all those who wander are lost· · ·”

As I pondered this I thought how apposite for I was in Sam Francisco and these other guys are somewhere else (applause). We might ask the question: What is fundamental science? In the article John Cornforth beautifully describes a famous and archetypal example - one that will strike a chord with everybody. “Here is an actual and far more typical case. Some people decided to examine the eﬀects of an electric field on living cells. They generated this field between two platinum surfaces and immersed in a liquid culture medium. The cells died, but the people who did the experiment were real scientists who resisted the obvious conclusion and found that the cells were not being killed by the electric field but were being poisoned by tiny traces of dissolved platinum. They mentioned their findings to a colleague who looked for, and found, a stronger eﬀect on cancer cells. A search in the chemical literature for a soluble compound of platinum turned up a substance that had been made one hundred years ago by a chemist in another country whose interest was simply platinum chemistry· · · .”

[There isn’t much platinum chemistry, you know, that’s what you learn in the textbooks - it’s a fairly unreactive element and so a bit diﬃcult to work with - but this scientist found some.] “This compound was even more eﬀective against cancer cells. In the event, a large number of people are alive today who would be dead but for this constructive but unfocussed curiosity of several scientists separated by discipline, nation and time. The factors combined in this success were curiosity, scepticism, good communication· · · [that means you don’t hide your results. You publish them. You don’t keep them secret from your competitors - and the publication of results.]· · · Together these produced an outcome that nobody predicted or expected and that is the essence of research. But it has always been diﬃcult to persuade those who finance research that predictable results are worthless and the best hope is to employ the team that makes the vital connections between other people’s results and sometimes their own.”

I would like to talk a little about the discovery of C60 , Buckminster-fullerene. It was more black than blue skies research perhaps more accurately due to the darkness of space research. In the 1970’s with colleagues, Anthony Alexander, Colin Kirby and David Walton at Sussex we synthesized and studied some long carbon chain

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molecules. Then with Takeshi Oka, Lorne Avery, Norm Broten and John McLeod at NRC in Ottawa we used a radiotelescope to probe the black clouds of dust and gas which lie scattered across the Galaxy. These are very black areas of the sky where few stars can be seen. The Greeks used to think of the sky as an upsidedown glass dish and the stars as diamonds stuck into the inside surface of the dish. The black regions where no stars could be seen are holes in the dish - the glass smashed by an Tottenham supporter who had heaved a brick through the glass dish - and through the hole one could see deep into space. Now of course we know better - it was an Arsenal supporter. More seriously however when we looked at these areas with a radio telescope, we found carbon chain molecules in some of the clouds and they are really quite interesting and abundant. Particularly interesting is the question “Why are they there?”. My own view which diﬀered from the generally accepted one is that they had been formed in the atmosphere of a cool red giant carbon star which had ejected the molecules into the interstellar medium. We were very excited about the discovery and in this slide [not available] I show a photograph of the group from those times. I like it particularly because this picture shows that I once had hair. I am not sure if Lorne ever had any hair. It was a fantastic time for me. As luck would have it, in 1984 I visited Rice University at the invitation of a friend, Bob Curl. On arrival he told me that I really should visit Rick Smalley’s laboratory where Rick had developed a superb new innovative technique for studying clusters. Basically, a laser is focused on a disc of refractory material such as aluminium or iron, and as a pulse of helium passes through this 1 mm diameter channel over the disc the laser fires producing a plasma. As the plasma cools it forms clusters which are swept into a vacuum chamber so that they can be studied by mass spectrometry. On seeing this apparatus I began to wonder whether it could produce a plasma similar to that in a carbon star if the metal disc were replaced by a carbon one. Later that evening I suggested this to Bob Curl and he said he would discuss the possibility of a joint study with Rick. In fact, carbon stars create all the carbon in your body, the carbon (and oxygen and nitrogen atoms too, etc.) of every single person here were all produced in a star aeons ago. So, basically, now you know who your real mother is. Some 17 months went by and then in August 1985 I got a phone call from Bob to tell me that they were about to try my experiment and he asked whether I wanted to come over to Houston or did I want them to send me the results. Needless to say I wanted to do my experiment myself and I arrived in Texas within three days. I met Jim Heath, Yuan Liu and Sean O’Brien who were the graduate students working on the apparatus at the time and did all the technical work. They were the experts in running what was a complicated apparatus doing all the technical manipulation of the apparatus. This allowed me to put my feet up on the desk and concentrate on the PC display and focus on the results as they appeared on the screen. The students did all the hard work and Bob, Rick and I got the prize - But don’t worry if you

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are a student you get your chance later, when you are professors you can get your students to do the work for you.

Fig. 15.6 An interloper denoted as C+60

Fig. 15.7 Hexagonal tiles. Sat and contemplated every morning

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However, there was good news and bad news - the good news was that we were able to show that the carbon chains could form under the laser induced plasma conditions - just as I had expected. The bad news was there was an interloper - here Fig. 15.6. I wrote C+60 (?) On my Printout. What was it? Well, to cut a long story short if you think about graphite, the most important thing about it that You remember from the textbooks is that it’s supposed to consist of stacks of completely flat sheets of carbon atoms linked together in a hexagonal network. At the time I was staying with Bob Curl and I thought I should show you the floor of Bob Curl’s loo which consists of hexagonal tiles Fig. 15.7. Each morning I would sit· · · and contemplate this floor· · ·. I would wonder exactly what could be going on. How could the number 60 relate to this floor. Furthermore something else crossed my mind and it dated back to a visit to Canada in 1967 - in fact a French (Canadian) Connection. Here Fig. 15.8 is Buckminster Fuller’s Dome designed for the US pavilion at Expo 67 in Montreal. Maybe he had been sitting looking at a similar floor and had wondered how to curve a hexagonal network into a round cage. Buckminster Fuller however knew the secret of how to do it. Anyway, we also wondered whether a graphitic network might have curled into a ball. There was something else that I remembered. This was an object that I had made for my children several years before. It was this stardome. - It was a spheroidal polyhedron but I remembered that it had not only had hexagonal faces but it also had pentagonal faces. On the night of - let me think - the 9th Rick went back home and played around with hexagons and then remembered that I had described the object and in particular the fact that I had described the pentagons. Only when the pentagons were included did the structure curl and close and create this fantastic structure out of paper. When we saw it we knew it just had to be right. It was so beautiful, how could it be wrong. I remember thinking - anyway even if it were wrong it did not matter, everybody would love it anyway! I suggested that we call the molecule Buckminsterfullerene - a bit of a long name, a bit of a mouthful too, but a smooth rolling mouthful and anyway it had a scientifically correct “- ene” ending. So, when we sent oﬀ the paper it was entitled C60 : Buckminsterfullerene. Rick did not like the name at first, perhaps because it was too long, and suggested some other possible names in the paper. Anyway for those people who don’t like the name there is an alternative - the correct IUPAC name· · · Fig. 15.9. Here is a picture of the football team [not available]: Bob Curl in the middle, captain of the team; Rick Smalley and Jim Heath and Sean O’Brien, the two grad students. Well, it turned out that C60 had a pre-history. There was a highly imaginative paper published in 1970 by Eiji Osawa. I hope your Japanese is up to reading this from the book by Yoshida and Osawa. Here is the football. “To cut a long story short because - it’s getting late, and I’ve got a number of other issues I wish to address - it was 1985 and we suggested that carbon could form a closed cage with a soccerball structure made up of 12 pentagons and 20 hexagons.”

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Then at Sussex from 1985 onwards we tried various approaches to make C60 and one we tried was by using a carbon arc - almost like an old movie projector which showed Charlie Chaplin films. Here is Jonathan Hare adjusting the carbon arc Fig. 15.10, and on a particular Monday he put phial with a red solution on my desk. I was very apprehensive and wondered whether this could be right - a red solution. Could this be C60 ? Soluble carbon! That was on the Monday. We tried to do a mass spectrometric analysis on the Thursday but it didn’t work. The next day I got a call from Nature· · · . That’s the journal· · · One gets lots of calls in one’s life but you know how it is, you never see the hurricane coming. They asked me whether I would be prepared to referee a paper on C60 and of course I said yes. THE FAX came at 12:05 and it was a bombshell. This was the manuscript of the fantastic paper by Wolfgang Kr¨aatchmer, Lowell Lamb, Kostas Fostiropoulos and Don Huﬀman Fig. 15.11. It is one of the great papers of the twentieth century - but it was bad for

Fig. 15.8 Buckminster Fuller’s dome design

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Fig. 15.9 The correct IUPAC name for the Buckminsterfullerene

us. As I read it I saw that they had a red (!!!!) solution as well - expletive deleted. I wondered: Should I commit suicide or· · · go for lunch. Well, anyone who has been to lunch at an English University knows that there’s not an awful lot of diﬀerence. But, anyway, in that paper there was also a picture of beautiful crystals Fig. 15.12. I think this is one of the most sublime scientific pictures of the century. If you had said, prior to 1990, that you could dissolve pure carbon in benzene and crystallize it, almost all chemists would have said you were crazy. Well, Kr¨atchmer, Lamb, Fostiropoulos and Huﬀman deserve a lot of credit and it’s a pity that they cannot share Nobel prize. Intellectually however they do. My colleague Roger Taylor then discovered that he could chromato-graphically separate the red solution into two, one magenta and the other red. This is C60 and that’s C70 . We also were able to conclusively prove the structure by showing that the NMR spectrum of C60 consists only of a single line Fig. 15.13. we can do chemistry with this compound now. This is one of my favourites. Behind here I brought one of these models along. We can now study the chemistry. We can put phenyl groups around this pentagon in C60 Fig. 15.14. The molecule has five legs and looks like a little bacterial creature that can walk. There are five phenyl groups and a hydrogen atom here. This is the male of the species· · · I shall pass the model around. You can have a look at its vital statistics. Now, there is a huge amount of chemistry which can be done with C60 but I do not have time to deal with it all. I shall just deal with just one aspect. This is my Star Wars image Fig. 15.15. This is the death star C60 chasing and this little ferrocene space ship across the sky. We are now creating nanocosmic structures. Well, that’s one thing, but what has really excited people a lot is the nanotechnology that has developed from the C60 discovery. Buckminster Fuller not only pro-

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duced the domes, he also designed these cylindrical structures Fig. 15 and they’re in his patents. We can make carbon ones too, and we call them nanotubes. This is basically a graphite tube with two half C60 hemispherical ends. I have brought a model of one along with me here. They are basically tubes of graphite. To get a feeling for the size of these materials we should note that the scale relationship of the C60 Structure to a soccer ball is about the same as the relationship of a soccer ball to the earth - each a factor of 100 million Fig. 15. These structures are something like fifty to a hundred times stronger than steel, and that strength and that tensile capability should be realizable. The materials conduct as well as copper at some one-sixth the weight, so the future possibilities in civil engineering materials all the way down to nano-scale electronic components is extremely exciting. That’s why scores of research projects are going on at the present time aimed at trying to make them. When I first made a model of one I called it a zeppelene - but my students had a somewhat ruder name for them. Pass this model of one around anyway. Not only that, we can make them out of boron nitride too. My favourite is this structure here. This is a nanotube which is about thirty angstroms in diameter and you can see one end of it here. There is a metal particle on the end which has spun this tube which has three walls. The walls are about 3.4 angstroms apart as in graphite. I’ve had some fantastic students working with me who never do what I tell them - they always do something slightly or radically diﬀerent - they are very inventive or innovative which I like. Indeed, the best thing is to have students who, when you tell them to do something, try something else which extends the original idea. That is the way one comes up with some amazing advances. One of the most recent advances is shown here Fig. 15.18. We see something that almost look like stars in the sky. As you look at these in more and more detail however, it turns out they are basically seeds for flower-like nano-structures so that filaments rods are just coming out of the central objects and there are literally hundreds of them. At the moment we have no idea what they are - as these results are only two or three weeks old and we really do not know what is going on at all - but one thing is certain they are truly beautiful. I do not basically care whether they are useful or not, they just look wonderful and the main intellectual drive is to learn exactly how these amazing structures were formed. That is the essence of the sort of science that I do.

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Fig. 15.10 Jonathan Hare adjusting a carbon arc

Fig. 15.11 A bombshell - one of the great papers of he 20th century

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Fig. 15.12 The paper had also a picture of crystals

Fig. 15.13 Conclusive proof of the structure: NMR spectrum

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Fig. 15.14 We can put phenyl groups around the pentagon in C60

Fig. 15.15 Star wars image of nanocosmic structure

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Fig. 15.16 Fuller’s cylinder, or nanotube

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Fig. 15.17 Scale factors of 108

Fig. 15.18 Flower-like nanostructures - one of the most recent advances

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4 The Public Understanding of Science I would like to come to the final parts of my talk and there are a number of things which I would like to address. The problems associated with science and its relationships with industry, the media and government. The problem with the media is epitomized by this image Fig. 15.19 where we see the headline, “Can scientists shake oﬀ their mad image?

Fig. 15.19 A nutty scientist in the Back to the Future movie

(By the way I had my hair cut specially for this presentation). This Fig. 15.20 is a portrait of Einstein by one of my favourite painters - the Swiss artist Hans Erni and it indicates who is responsible for our problem. Now I have a surprise for you - this is not the man responsible for the beautiful theories - of Relativity and the Photoelectric eﬀect etc. No, this is the man - it is the young, handsome Einstein with short hair· · ·. I am sure that if only Einstein had cut his hair in his old age many of the problems of the scientific community would not be so serious. The problem is further shown by my next example Fig. 15.21. This is a newspaper article which I put up on the notice board and someone wrote on it, ‘Fantastic likeness, Harry,’ This is the stereotypical clich´ed caricature of a scientist. Now, I’ve just been in Spain

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Fig. 15.20 Albert Einstein by Hans Erni

and they have a much greater respect for science as we can see from my picture in the newspaper in Cadiz Fig. 15.22. I was dancing the flamenco with Naomi Campbell but they have edited her out - they are more interested in the science in Spain. Scientists do not get this sort of treatment in the UK or in Canada. Anyway, let me show you another example, this time from the Brighton Evening Argus Fig. 15.23. There was an article about the fact that we had discovered the carbon molecules in space. It says, “Life’s Key May Lie Among The Stars”. I put this cutting up on the notice board too, and one of my students wrote, “That’s show biz” on it. I made him do an extra year for his Ph.D. for writing that. Anyway, just listen to this: “A new discovery by Sussex University boﬃns could make scientists change their minds about how life began. Their theory is that the very first forms of life could have been created in outer space.”

well, this is the Brighton Evening Argus. The best line however is this one:

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Fig. 15.21 It has taken us ages to get a tiny amount of money

“The chemicals were discovered thanks to Canadian radio-astrology.”

However I haven’t quite finished with the newspapers yet. This article was written by Simon Jenkins in The Times where in a major article he says: “· · · the national curriculum puts quite unrealistic emphasis on science and mathematics which few of us ever need.”

I wish for this guy, every time he switched the light switch, it would not go on and he would be forced to fix it himself. I wish this guy, that when he went into hospital for open heart surgery he would be prepared to undergo the operation without anaesthetics - one of the greatest humanitarian contributions of chemistry. People like this are dangerous because they perpetuate the philosophy that it is perfectly OK not to understand how the modern world functions or educate the next generation of scientists. A basic understanding of some aspects of science and mathematics is not that diﬃcult. Look at this [OH, not available]. Is there anyone here who thinks they can solve this equation? The point is that you can solve this almost without thinking because this is the equation you have to solve to cross the road - Even chickens can do it. To give you one true example of the problem: John Maynard-Smith, one of

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Fig. 15.22 A greater respect for science in Spain

our outstanding evolutionary biologists and a colleague at Sussex, wrote an article for a magazine and the editor said that there were to be no equations in the article. John however did put one in it, dx/dt = a and said that he really needed this equation. The editor however responded “Well, okay, I’ll let you have this one, but can you not at least simplify it by crossmultiplying the d’s.” well what about Science, C60 and Government? [OH, not available]. In the House of Lords this question was posed:

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Fig. 15.23 The best line in the newspaper was · · · · · ·

“What steps are the Government taking to encourage the use of Buckminster Fullerence in science and industry.”

This was the answer [OH upside down]. It makes a lot more sense that way. And then Load Williams of Elvel asked: “My lords, is the noble lord aware in supplementing his answer that the football shape carbon molecule is also known for some extraordinary reason as Buckyball?”

Baroness Seare went on to say, “My lords, forgive my ignorance, but can the noble lord say whether this thing is animal, vegetable or mineral.”

The answer: “My lords, I am glad the noble baroness asked that question. I can say that Buckminsterfullerene is a molecule composed of sixty carbon atoms and known to chemists as C60 , those atoms form a closed cage made up of twelve pentagons and twenty hexagons that fit together like the surface of a football”.

My favourite is Lord Renton: “My lords, is this the shape of a rugger football or a soccer football?”

Now, fortunately, there was someone in the visitor’s gallery who knew the answer to this question Fig. 15.24. Then came Lord Campbell of Alloway who asked: “My lords, what does it do?”

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Lord Reay said: “My lords, it is thought to have several possible uses, for batteries, as a lubricant, or as a semiconductor. All that is speculation. It may turn to have no uses at all.”

Earl Russell then commented: “My lords, can one say that it does nothing and does it very well.”

Well, in fact it does have a use because it turned out that a friend of mine discovered that in the Harvard Gazette personal column this set of ads appeared. One says: “Palm Beach professor seeks stylish lady for theatre evenings”

and a little further down we find “Fullerenes, fossils and fungi; Singles interested in such topics are meeting through the Science Connection!!!!”

Fig. 15.24 Who knew the answer? An Orang Utan studying a football

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5 Science Education Well, I now come to the last part of my presentation and I have a few things to say on the subject of language. I think that the main problems of science relate to the language of science. For example I think that if you really want to understand the culture of a country you really have to learn the language and you have to do some work. In particular if you want to understand Shakespeare and you are Japanese you have to learn some English to appreciate the essential cultural aspect. Now I hope that most of you have learned some Chinese characters. Basically this is Chinese equivalent of “Hear no evil, see no evil, speak no evil.” Fig. 15.25 In Chinese it is “If you hear evil, walk away etc. · · · ” In Japanese it is Misaru, Kikasaru, Iwasaru but it has an interesting double meaning in that saru in Japanese also means monkey. So in Japanese there is an elegant double meaning and to understand it you have to learn some Japanese. In Nikko this beautiful carving of the three monkeys is to be found at the site of the burial site of the First Shogun Fig. 15.26 - thus although this saying is to be found in many diﬀerent languages the flavour of its meaning in each one depends inherently on the way it is expressed in each culture. There is a similar problem to be found in the sciences. When I present this image [OH, not available], a chemist sees the molecule benzene. Or, if I simply write the formula C6 H6 a Chemist immediately visualises this beautiful molecular architecture, the history of the understanding of its structure and its pivotal role in chemistry. I would finally like to tell you that I have been involved with the Vega Science Trust for the last two years and details are to be found at the www.vega.drg.uk web site. We have been making TV programmes which focus on the cultural and

Fig. 15.25 If you want to understand culture, learn the language

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Fig. 15.26 Japanese version has an elegant double meaning

intellectual aspects of science. Many of the science programmes on television involve film of animals. We often see films for which the archetype is an eagle catching a gerbil, tearing it up and shoving the pieces down the throats of a little eaglets. That’s basically it and it is certainly fascinating to learn at first hand in colourful detail the plethora of ways that nature has invented for eating itself. However I do not consider that there is much science in this. In any case you can get a basic idea by going to a restaurant anytime - you don’t have to watch it on television. What Vega programmes try to do is present the cultural and intellectual aspects of all the sciences and in this way I hope that one day the vast majority of people will become truly educated suﬃciently well to appreciate the humour in my earlier anecdote about the editor who asked my colleague to simplify a diﬀerential equation by cross multiplying the d’s. In some ways it is not a joke, it is really a rather sad reflection on the fact that one of the great intellectual advances of all time, the invention of Calculus (by Newton and Leibnitz) is understood by so few people, many of whom consider themselves educated. So we have been making programmes and, just to give you an idea of what we have done: We have recorded Bill Klemperer’s, The Chemistry of Space, John Maynard-Smith on the Origin of Light, Akira Tonomura has actually taken images of a field of force inside a magnetic film. You know when you sprinkle iron filings around a magnet they line up and follow the lines of force. Tonomura has shown that you can see lines of force inside a magnet using a modern electron microscope.

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David Bomford spoke on Science and Fine Art and we also have recorded Jocelyn Bell, who with Anthony Hewish discovered the pulsar. The most recent programme is one of the most important as it deals with long term induction diseases. It is by Roy Anderson and deals with the BSE epidemic in the UK. We have also started a new set of workshop programmes, the Reflection on Science series. I am very proud of these and in particular this one entitled How to be Right and Wrong is by Sir John Cornforth who won the Nobel prize in 1975. John has been deaf since the age of twenty but our programme has captured his genius, his humanity, his remarkable ability to communicate in a witty and informative manner. In these programmes we have found an excellent science communication approach. We have also recorded Susan Greenfield who describes her work on the brain. So, we are making a real eﬀort to put real science on TV. I think this has to be done, otherwise we are not going to solve the problem of public understanding of science or so I believe. Well, how can it be done. Last year in Yokohama I gave a workshop with young eight and nine year old kids and they just love science as you can see that by the faces of these kids. I have given similar workshops in Santa Barbara with Hispanic youngsters who just loved making C60 models. We can go through real science, we can do Euler’s Law, C + F − E = 2, i.e. the number of corners plus the number of faces minus the number of edges is equal to 2 Fig. 15.27. We can discuss Leonardo’s drawing of the structures. At the end of this, if you want to know what is useful, we managed to keep this set of kids quiet for thirty minutes making C60 . There is not a single teacher who does not accept that this is the most useful molecule ever made - That’s got to be good. I think we also see the development of creativity, because this kid has found a new use for C60 - as a hat! He’s obviously auditioning for a part in ’Silence of the Buckyball’. This is a cartoon story that we got from two young girls at Angmering School in Sussex: “New Kid in Town. Hi, I’m diamond. I’m a kind of carbon. So am I. I’m graphite. We’re the only types of carbon there are around. Wrong. There’s a new carbon in town - ’Buckminster Fullerene.’ Okay? Bucky, to my friends. I’m carbon, too, you know. Can’t be! He’s round. He looks like a football. We’re better than him, but then can you do this? Bucky bounces.”

So kids can get enthusiastic about chemistry. I’ve got a couple of things I want to add before to finish. One is this prescient and superbly crafted observation by John Cornforth made to the Australian Chemical Society in 1985: “· · · But scientists are a small minority and people conversant with science, let alone scientists, are a small minority in administration, government and, in most countries including this one, business. The perspective of the politicians does not usually extend beyond the next election. The unborn have no vote, whereas the easiest way to get votes of the majority is to promise them increases in their power to consume. The average citizen’s reaction is, “What did posterity ever do for me?” The Administrator seldom has a scientific background or any remit to consider an extended future. The businessman wants to make a profit, the quicker the better for himself and his shareholders. Among all these people there seems to be a general vague expectation, if they think of the matter at all, that scientists are sure

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Fig. 15.27 Children can go through real science

to find some way to rescue future generations from the shit into which the present one is dropping them.”

My main passion is for art - in particular graphic art. Most of my books at home are art books and I would like to share this page from one of my recent acquisitions -. I have never presented it before, but I think this is one of the most humane comments I have ever come across Fig. 15.28. It is by Stine: “I am an alien creature. I was sent from another planet with a message of goodwill from my people to you Earth people. Dear Earth people, when you finally, at last, destroy your planet and have no place to live you can come and live with us and we will teach you how to live in peace and harmony and we will give you a coupon good for 10% oﬀ all deep dish pizzas, too. - Sincerely Bob.”

For me this witty, humanitarian sentence sums up much of the way I feel. It is a wonderful piece of writing and a comment on modern life. Finally I would like to finish up with this last image Fig. 15.29. It is of a little boy - Ellis - and comment that if C60 can make a kid as exuberantly happy as this it just has to be good.

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Fig. 15.28 when you destroy the Earth, you can come and live with us

Fig. 15.29 C60 can make a kid exuberantly happy

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16

Are We Really Made of Quarks? Jerome I. Friedman

Abstract This address was presented by Jerome I. Friedman at the Nishina Memorial Lecture at Osaka International Center, on July 30, 2000.

Thank you for your kind introduction. It is a great honor and pleasure to present the Nishina Memorial Lecture to an audience in the city of Osaka, and I want to thank the Nishina Foundation for inviting me. I consider this a very special honor because Professor Nishina was one of the great pioneers of modern physics. As you see, the title of this talk is - Are We Really Made of Quarks? We physicists believe we are. And the question is - Why do we believe this? This is the story I want to tell you today. If you look at the stable matter in our world and in the Jerome I. Friedman c stars and planets beyond us, it’s made of 3 objects: elec- NMF trons, UP quarks and DOWN quarks. This is a surprisingly simple picture. But we didn’t come to this conclusion very easily. There was enormous controversy about the quark model and its relevance. The quark model violated cherished points of view; and it was not accepted until a great deal of experimental evidence came in., overcoming the arguments of skeptics. Let me first start by giving an introduction to the hierarchy of the structure of matter. Looking at the top of the view graph we see just ordinary matter, consisting of atoms and molecules. Everything here is made up of such matter, this table, us and everything around us. If we increase the magnification a 100 million times, we see the atom. The atom consists of electrons going around a positively charged Jerome I. Friedman (1930 – ). Nobel Laureate in Physics (1990) Massachusetts Institute of Technology (USA) at the time of this address J. I. Friedman: Are We Really Made of Quarks?, Lect. Notes Phys. 746, 349–370 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 16

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small object in the center called the nucleus. That picture was proposed in 1903 by Hantaro Nagaoka, who later became President of Osaka University. In 1911 this model was confirmed by Rutherford in a famous series of experiments using the scattering of alpha particles. If we now increase the magnification another 100,000 times, we see the nucleus , which is composed of neutrons and protons. That picture started unfolding in 1919 and culminated with the discovery of neutrons in 1932 by Chadwick. If we increase the magnification further, we see that the proton and neutron are composed of other particles called quarks. That story started unfolding in 1968 and goes on to the present. That’s the story I want to tell you. What particles existed in 1946? The electron was discovered by J.J. Thompson in 1897; and we have the positron, which is its anti-particle, that was discovered by Anderson in the cosmic rays in 1932.

Fig. 16.1

In 1936, another particle was discovered called the muon. This was a great surprise because it has all the properties of an electron except that it is 200 times heavier. Nobody understood what role it played in nature. In fact when it was discovered, the physicist I.I. Rabi asked, “Who ordered that?”, and it was not understood for many years. There were the proton, neutron, and the photon, which basically is just a quantum of energy of electromagnetic radiation, such as gamma rays, x-rays, light, and radio waves. There was also the neutrino - it’s another interesting particle. In the early experiments on beta decay, that is radioactive decay of unstable nuclei, it was observed that energy was not conserved. Since physicists don’t like to give up a cherished conservation principle, it was hypothesized by Pauli in 1931 that particles were being emitted in beta decay which could not be detected. These par-

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ticles were called neutrinos. It wasn’t until 1956 that the neutrino was discovered. The pion was proposed in 1935 by the famous Japanese physicist, Hideki Yukawa. This was an interesting prediction. By looking at the behavior of the nuclear forces, that is the forces between the neutron and proton, the proton and proton, and the neutron and neutron, and by using the observations of how far these forces extend in space, Yukawa predicted the existence of a new particle. He predicted its approximate mass, and physicists started searching for it because the argument was very compelling. Yukawa, who was a Professor at the University of Osaka, was awarded the Nobel Prize in 1949 for this pioneering theoretical work. In 1947 this particle was discovered, and it was called the 7c meson. This was the famous photograph in which its discovery was announced. This particle was first seen in nuclear emulsion, which is just a thick photographic plate that you look at with a microscope. Here’s the it coming in, and as it’s coming in it slows down and then stops. It then decays into a muon which goes on here and then finally stops and decays.

Fig. 16.2

This was a great triumph and there was enormous elation in the community. The newly discovered particle had the right mass, which could be determined by various methods. There was a feeling that perhaps there was some understanding of what was going on. But that enthusiasm was very short-lived because what happened after the pion discovery was that great complexity developed very rapidly in this field. This complexity was driven by new technology in the form of new accelerators called synchrotrons and new types of detectors, primarily the bubble chamber. These were important instruments in the story of how quarks were proposed and discovered. I will say a few words about the bubble chamber. Basically, it’s a pot of liquid in a so-called super-heated state. The liquid is just about ready to boil. There is a piston

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which you raise very rapidly and this decreases the pressure. It’s like opening up a bottle of carbonated water. When you open a bottle carbonated water, you release the pressure and you see bubbling. In the same way, the liquid in the bubble chamber has the tendency to bubble when the piston is raised. Now what happens during that time is that a beam of particles comes in and the particles interact, producing all kinds of particles. Each track seen in the chamber is the result of a charged particle going along, ionizing the atoms in the liquid. And how does this work? The charged particles knock out electrons from the atoms and because these atoms are damaged and emit low energy electrons, they become the centers for bubble formation. So bubbles form along the paths of the particles and just at that point, you strobe a light on, causing the camera here to take a picture. Then you lower the piston which stops the boiling and you’re ready to start all over again and take another picture. There is one other element that you should be aware of - that you put the bubble chamber in a magnetic field, because when a charged particle moves in a magnetic field it goes around in a circular orbit and the radius of curvature is equal to the particle’s momentum divided by the charge of the particle times the magnitude of the magnetic field. And so if you measure the radius of curvature you can tell what the momentum is. The momentum is just the mass times the velocity and you can therefore determine the energy of the particle. So you can measure everything that is required to resolve some of the issues in the identification of particles. Here is, for example, a bubble chamber picture. You see here how a low energy proton hits another proton in this bubble chamber and these particles are produced. You can see the track curvature here caused by the magnetic field and you see these are diﬀerent charges. This is one charge and this is another charge of the opposite sign, as you can see from the opposite signs of the radius of curvature. And so that’s what a low energy interaction looks like. Then you have a high energy interaction which can be seen in the next view graph. You see this very high energy particle coming in and it has this catastrophic collision, producing many, many particles. You see all of these particles being made in this collision. And here’s another picture that I always like to show because it shows two features that are very nice. This is a picture of high energy photons, producing electronpositron pairs. This is actually a confirmation of the fact that you can convert the energy of the photon, which has no rest mass, into the rest masses of the positron and the electron. So this is a verification that E = mc2 . Another thing you see here - the spirals. What are the spirals? Remember I told you that charged particles going through material ionizes atoms in the material. Well when a particle ionizes material, it has to lose energy. Losing energy, it has to spiral in because the radius of curvature is proportional to its momentum which is decreasing with its energy. Now let’s get down to what the significance of the development of the bubble chamber was. What you see in the next view graph is a bubble chamber picture which has been cleaned up from a hydrogen bubble chamber that operated at the Lawrence Berkeley Laboratory. The point to see here is that you could actually reconstruct the entire event. You can identify the exotic particles in this event by knowing the identity of some of the particles and by using energy and momentum

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Fig. 16.3

Fig. 16.4

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conservation. Because you could calculate the masses of new kinds of particles, you could discover the existence of these particles. You can reconstruct everything, using the things you know about physics, namely energy conservation, momentum conservation, and charge conservation. And this is what was done.

Fig. 16.5

As a result of this experimental technique, many new particles were discovered. There was a particle of the month club in those days. By 1966 about 60 diﬀerent particles were discovered. We called them elementary particles, but the question is If you have 60 of anything, can they be truly elementary? People started wondering about that. This was the genesis of the quark model. What happened then was that in 1961 Gell-Mann and Ne’eman independently developed a classification scheme for these many newly discovered particles. It was like the periodic table of the elements except that it was for particles. It was based upon having particles organized into families of the same spin and parity. Don’t worry about parity, a quantum mechanics concept we don’t have to discuss. Spin is a concept that is somewhat more accessible. Particles have the properties of a spinning top, described in terms of quantum

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mechanics. Then in 1964 Gell-Mann and Zweig independently proposed quarks as the building blocks of these families. I will explain these ideas now. Here for example is one of the families for a certain spin - spin 3/2. The thing about this scheme which made it useful was that it was predictive as well as descriptive. If it was just descriptive, it would have been of no use- it would just be numerology. But it was very much like the periodic table of the elements. It was predictive. In the early 60’s most of the particles in the spin 3/2 family had been discovered. But the heaviest particle of this family was missing. Physicists who worked on this problem believed that this particle, the so-called omega-minus, had to exist. It was a very unusual particle. In addition to being very heavy, it has unusual quantum numbers, but I don’t want to go into this because it’s not important for this discussion. As a result of these considerations, everybody in the world who could search for this particle started searching for it. If this particle were not found, this classification scheme would not be viable. In 1964, after looking through 100,000 bubble chamber pictures, physicists at Brookhaven National Laboratory found one such event. And this is the picture that includes the event. You have to really admire the people who found this because it’s hard to see the event in the picture. It was a real tour de force to find it. Because everything could be reconstructed on the basis of energy and momentum conservation, the mass of this particle, the omega minus, was measured. The particle was discovered with just this one event. There was tremendous elation because it meant that the classification scheme had validity, and of course other predictions started coming in too. Then in 1964, the quark model was proposed. Initially, it had three types: the UP quark, the DOWN quark and the STRANGE quark. Strangeness was a new quantum number that had been independently proposed by Kazuhiko Nishijima and Murray Gell-Mann to resolve some experimental paradoxes. All of the quarks had a spin 1/2. But they had a very peculiar property which was very surprising and very troubling. They all have fractional charges and no particle in nature had ever been found with a fractional charge. The UP quark has a charge +2/3, the DOWN quark is −1/3 and the STRANGE quark is −1/3. Now the proton, you see, is made up of 2 UP quarks and a DOWN quark, giving the proton a charge +1; and the neutron is made up 2 DOWN quarks and an UP quark, giving a charge 0. You see that’s how it was put together. There were some other features that were put in, but that was the basic idea. You see the thing that is really beautiful about it and why the quark model had relevance was that these families now were believed to be composed of quarks in patterns with a beautiful symmetry. That is, the symmetries of the families were generated by the quarks. For example, this particle here furthest to the left is composed of 3 DOWN quarks, the one furthest to the right is 3 UP quarks, and the particle at the top, the omega minus, is 3 STRANGE quarks. Every particle in between is a mixture of the three kinds of quarks in a very well defined way. So it was a nice picture, but the question was Are quarks real? What do physicists do to find out if something is real? They will look for it. After all, that’s how you find out if something is real. Can I really find it somewhere?

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Fig. 16.6

Fig. 16.7

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Fig. 16.8

Well, there were many attempts to find these quarks. There were attempts to find them at accelerators, in the cosmic rays, and in the terrestrial environment - in mud, seawater, anywhere. Not a quark was found. To many physicists this was not surprising. Fractional charges were considered to be a really strange and unacceptable concept, and the general point of view in 1966 was that quarks were most likely just mathematical representations - useful but not real. But what did physicists think the proton and neutron looked like? What was the picture of the structure of the proton and neutron in that era? Well, it actually was equally strange, and in a certain sense even stranger. There was a point of view at that time called nuclear democracy, that is the bootstrap model. The idea was that the proton was made up of the neutron plus a positive π meson plus any other particle that will give the proper quantum numbers. A neutron was made up of a proton plus a negative π meson plus other appropriate particles. So all particles were made up of other particles. It’s as if somebody said each of you in this auditorium is a composite of everybody else in this auditorium. Now that is a very strange point of view, but in quantum mechanics that is something you can propose for particles. So that was the point of view at that time; and when you look at the structure of such particles, they will have diﬀuse sub-structures with no elementary building blocks. They are a blob of charge that is very smooth and diﬀuse. That was the picture of the proton and the neutron and all other particles in those days. What did Gell-Mann, who is the father of the quark model, say about quarks at that time? He said the .... “idea that mesons and such particles are made up primarily of quarks is diﬃcult to believe.... The probability that the meson consists of a real quark pair rather than two mesons or a baryon and anti-baryon must be quite

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small...... Thus it seems to me that whether or not real quarks exist, the quark and anti-quark we have been talking about are mathematical. “And then he goes on to say,... “if the mesons and baryons (that is, the protons and neutrons) are made up of mathematical quarks, then the quark model may perfectly well be compatible with the bootstrap hypothesis, that hadrons (that is, all the strongly interacting particles) are made up out of one another.” That is the nuclear democracy point of view. So there was not great confidence about the quark model at that time. There was a physicist at CERN who wrote a book about quarks and ended up with this conclusion:.... “Of course the whole quark idea is ill-founded. So far, quarks have escaped detection.” Then he says at the end:.... “The quark model should, therefore, at least for the moment, not be taken for more than what it is, namely, the tentative and simplistic expression of an as yet obscure dynamics underlying the hadronic world. As such, however, the model is of great heuristic value.” There were, however, a few physicists who were real believers. They would not give up the quark model. They persisted in making calculations of applications of the quark model, but few physicists paid attention to them. So that was the situation at the time. In 1966 there was an important development. The Stanford Linear Accelerator at SLAC was completed and brought into operation. This is a very long high energy linear accelerator for accelerating electrons. Inelastic electron-proton scattering experiments were started in 1967 and continued until 1974 by an MIT-SLAC collaboration, which included Henry Kendall, Richard Taylor, and myself along with other physicists. Conceptually this was a very simple experiment. You would shoot electrons at protons. Electrons would scatter oﬀ and many other particles would be produced. You would only detect the electrons and this provided the first direct evidence for quarks. Let me explain how, because the scientific methodology is really quite simple. I will explain it by an analogy. I give you a fish bowl with a certain number of fish in it and put it in a dark room. I ask you: How many fish are in the bowl? I also ask that you not put your hand in the fish bowl. But I give you a flashlight. Well, what you would do is turn on the flashlight and look, right? You would see how many fish there are in the fishbowl. That would be the obvious thing to do. Well, you see, the experiment was basically the same idea. Instead of having a light beam, you have an electron beam. Instead of using your eyes, you use particle detectors. Instead of having a brain to reconstruct the images, you do that with a computer, programmed by human intelligence. And, of course, instead of looking for fish inside the fishbowl, you are looking for what is inside the proton. So it’s basically that idea. You are looking inside the proton with the equivalent of a very powerful electron microscope. To see a small object of size D clearly in a microscope, you must use light that has a wavelength that is considerably smaller than D. The wavelength is the distance between two successive crests of the wave. You can think of the wavelength as being equivalent to the separation of lines on a ruler. If you want to use a ruler to measure the size of an object with reasonable precision, the separation of these lines should be much smaller than the size of the object.

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According to quantum mechanics, electrons, as well as other particles, have a wavelength and this wavelength decreases as the energy of the particle increases. In an electron microscope, electrons are accelerated to suﬃcient energy to have much shorter wavelengths than ordinary light. This is why electron microscopes can be used to “see” much smaller objects than optical microscopes. So the MIT-SLAG experiments utilized the equivalent of a very powerful electron microscope. The Stanford Linear Accelerator delivered a high intensity beam of 20 billion electronvolt electrons, which provided an eﬀective magnification 60 billion times greater than that with ordinary light. One could measure a size that was about 1120 the size of a proton. This was necessary because otherwise you couldn’t see what is inside the proton. The proton is about a hundred thousand times smaller than the atom, having a radius of about 10−13 cm. This is the picture of the Stanford Linear Accelerator. It is two miles long and you can see there’s a road going over it. The electrons are bent into three beam lines. These are the two experimental halls. The experiment was done in the larger of the two halls. The electron beam is bent and it enters this hall which houses the experimental apparatus, which consisted of two large magnetic spectrometers. Here is a picture of the spectrometers . This is the 20 GeV spectrometer (a GeV is one billion electron-volts). Here is where the beam comes in, here is the target, here is the 8 GeV spectrometer and here are the rails that run around the pivot, on which the spectrometers can be rotated. These were large and very heavy devices. The 20 GeV spectrometer weighed over 3000 tons.

Fig. 16.9

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Fig. 16.10

Now what are the characteristics of scattering that you would expect on the basis of these two models, the quark model and nuclear democracy? In a certain sense, this is really the crux of the matter from a physical point of view. If you had the old physics where the charge was quite diﬀuse ( you see the upper image of the model of the proton in the 60’s) you would expect the particle to come in and not be deviated too much because the charge is smeared out and there’s nothing hard inside to really scatter it very much. The incoming particle comes in and goes through the proton without too much deviation. But if you have constituents inside the proton, then occasionally a particle comes in and scatters with a large angle from one of the constituents, as you can see in the lower image. The observation of a large amount of large angle scattering would imply much smaller objects inside the proton. So you look for the scattering distribution to see what the structure in the proton is, and this is how the experiments were analyzed. I want to show you what was found. Here in this view graph we show the dependence of the probability of scattering on a quantity that is proportional to the square of the scattering angle. The top curves here are the measurements. This rapidly falling curve is the type of distribution you would expect from the old physics. And you see the diﬀerence, about a factor of a thousand, between what the old physics would have predicted in scattering probability and what the experiment found at larger angles.

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Fig. 16.11 Scattering

Basically what these measurements showed was that copious large angle scattering was observed. Now, the experimenters went on to try to analyze and reconstruct the images in terms of what was known. How big were the objects inside? The results indicated that they were point-like. They were smaller than could be measured with the resolution of the system. And when we first did this analysis we concluded that, if it behaves in this way, it implies point-like objects inside. But this was a very strange point of view. It was so diﬀerent from what was thought at the time that we were reluctant to discuss it publicly. In fact when I gave the first presentation of these results in Vienna in 1968, my colleagues asked me not to report that the proton looks like it has point-like objects inside. To say such a thing would have made us all look as if we were somewhat deranged, and so I didn’t say it. It turned out that Professor Panofsky who was the Director of the Stanford Linear Accelerator gave the plenary talk and he inserted the statement that “....theoretical speculations are focused on the possibility that these data might give evidence on the behavior of point-like structures in the nucleon.” (Nucleon is the generic name for the proton and neutron.) So he made this surprising assertion. But we, as young assistant professors at that time, felt we could not. So that’s how it was first announced to the world, but nobody really believed it. It was considered a very bizarre point of view. Theorists were very enterprising and they produced in a short time a large stack of theoretical papers trying to explain these new results in terms of models that employed the old physics.

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Fig. 16.12

None of them really worked, and that was a problem because you see many attempts were made. If this were a physics seminar, I would tell you all about these old models but it is not important for today’s talk. These models were ultimately tested experimentally and they all failed in one aspect or another. None of the traditional points of view explained the surprising electron scattering results. However, the quark model was not generally accepted. So what could explain these results? That was really a puzzle. It was a big puzzle. But there was one theoretical contribution which helped resolve the whole controversy. It was made by Richard Feynman with his development of the Parton Model. I want to say something about this approach because it played such a crucial role. When he came to SLAC in August of 1968 he was already working on the Parton Model. What was this model? He was working on the problem of protons scattering from protons. He described the proton as being made up of parts, which he called partons. He did not know what the parts were, but he analyzed the scattering in terms of the parts of one proton hitting those of the other. When he came to SLAG, he heard about the electron scattering results. He talked to a number of people there. He became excited about these results and he quickly concluded that

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these experiments provided the perfect test of the Parton Model. Overnight he wrote down a set of equations which became the basis of resolving this problem, establishing a framework for analyzing the electron scattering results and all subsequent measurements. He came back to SLAG the very next day with the results. It was a very exciting weekend and I was fortunate to have been there at the time. And what is the Parton Model as applied to electron scattering? Well you know, it’s really not all that diﬀerent from what I mentioned earlier with regard to point-like constituents in the proton. But Feynman was a great and highly respected theorist who could get away with proposing such an unorthodox view. His idea was that there are point-like objects in the proton called partons. We didn’t know what they are but they are bound. The electrons scatter from them and the partons recoil and interact internally producing known particles. So the partons don’t come out, but they produce pions, K mesons and everything we’ve observed in the laboratory. If the partons are point-like, there is a large amount of large angle scattering, which I pointed out earlier in this talk. The Parton Model was also consistent with all the kinematic behavior that was observed in the experiment. There were some technical issues which I can’t discuss because they are too complicated. One such issue was a kinematic behavior called scaling, which had been proposed by Bjorken and was observed experimentally. This model explained scaling behavior and provided a physical interpretation of it. But the central question was: What are the partons? Are they quarks? At that time he wasn’t willing to say what they were. He just said that this is a way of looking at the problem. Now the question is: How do we show that these little objects inside the proton are quarks? Well, we have to show two things: They must be spin 1/2 particles and they must have fractional charges consistent with the quark model. Those are the requirements. If you don’t show those, you haven’t proven anything. Well we could actually show what the spin was in a very straightforward way early in the program. It was a hard experiment but we could do it. The idea is that you make a comparison of forward scattering and backward scattering. It turns out that backward scattering has a bigger component of magnetic scattering, which depends on the spin of the constituent from which the electron scatters. You could actually measure the spin of whatever is scattering electrons in the proton. In this view graph you see the predictions for spin zero constituents, and those for spin 1 would be way up here. Now obviously the errors on the experimental points are large. It was a hard experiment because of the radiative corrections, but the results are clearly consistent with spin 1/2. So if there were constituents in the proton, we knew at that time they were spin 1/2 particles. Half of the problem was over. But fractional charge was a much more diﬃcult problem; and to really resolve that problem another type of scattering had to be brought into the picture. Neutrino scattering had to provide the answer. And let me explain why. First of all, what are neutrinos? Let me say a few things about neutrinos. Neutrinos basically are particles which are almost ghost-like. They have no mass or a very small mass, they have no charge and they barely interact. A recent experiment in Japan, Super-Kamiokande has recently shown that at least one neutrino has a very

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Fig. 16.13

small mass. And the preliminary data of a second experiment in Japan, K2K, using a diﬀerent approach appear to confirm this result. Neutrinos interact so weakly that a 100 billion electron-volt neutrino, has a mean interaction length in iron of 2.5 million miles. So doing experiments with neutrinos means that you have to use lots of neutrinos, have a huge target and have a great deal of patience. Neutrinos are produced from particle decays but we won’t get into the details of that. The ironic thing is that the first results came from the Gargamelle bubble chamber at CERN which was able to make these measurements. The first thing the bubble chamber showed was that the scattering probability for neutrinos, as a function of energy, went up as a straight line. This demonstrated that the neutrino measurements were also finding pointlike structure in the protons. And comparisons of electron and neutrino scattering

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later confirmed that the point- like constituents of the neutron and proton have the fractional charges of the quark model. So how do you find out about the charges of the constituents by making such comparisons of the scattering? Now this is actually a simple argument although it may seem a little complicated. In this view graph you see here an electron scattering from a DOWN quark, and here from an UP quark. Now the force that causes the scattering of the electron by the quark has to depend upon the charge of the quark and the charge of the electron. So the force is proportional to the product of these two charges. If we have neutrino scattering, as shown below, the complication is that the neutrino turns into a muon and exchanges a particle called the W particle. But let’s not worry about that. The point is that the force between the neutrino and the quark in this scattering results from eﬀective charges associated with the so-called weak interaction. This eﬀective charge is not an electric charge. We call it a weak coupling constant, g. The force that causes the scattering here is proportional to g2 . Therefore, if you take the ratio of neutrino scattering to electron scattering, what you’re getting here is proportional to g4 divided by the square of the charge of the electron times the square of the charge of the quark. So the point here is that by measuring the ratio of these scattering probabilities and properly normalizing it, you can get information about the charge of the quark. And that’s all there is to it. That was done and the result comes out this way. The ratio of the scattering probabilities properly normalized comes out to be 2 over the square of the UP quark charge plus the square of the DOWN quark charge. And if you put the values of the quark charges into this, this ratio turns out to be 3.6. When the experimental value of this ratio was evaluated by comparing the MITSLAC scattering results with the CERN bubble chamber results, the answer turned out to be 3.4 + / − 0.7. Of course, the error was large because of the great diﬃculty of measuring neutrino scattering in a bubble chamber, but the agreement was remarkable. If quarks did not have these fractional charges, you would not get close to this number. It was a remarkable agreement and the idea that there were quarks inside the proton and neutron became something that one could not deny. Let’s keep a scorecard here, which is seen in the next transparency. If we look at the bootstrap- nuclear democracy model, we have spin 1 and spin 0, but for the quark model we have spin 1/2 and experiment gives spin 1/2. Fractional charges? For the bootstrap- nuclear democracy model, no; quark model, yes; experiment, yes. Point-like structure? For the bootstrap- nuclear democracy model, no; quark model, yes; experiment, yes. We cannot escape the quark model. There was no way that the old model satisfied the experimental results. What the picture of the proton becomes in this case is what is seen in the next view graph. This is the proton. Here are 3 quarks and there’s another feature present called color which I won’t go into. The term color represents the source of the strong force, which is responsible for holding the quarks together in the proton. There are 3 colors and each of the quarks in the proton has a diﬀerent color. And you see these wiggly lines here; these represent the forces which hold quarks together. The forces are due to the exchange of particles called gluons, and occasionally a gluon

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Fig. 16.14

Fig. 16.15

will actually make a quark, anti-quark pair and they will come together and form a gluon again. All of these together constitute the proton. One of the interesting features about gluons is that they interact with one another. A gluon will attach itself to another gluon. You see a photon will not attach itself to another photon but a gluon has this feature and this results in some very unusual behavior of the strong force. So this is what a proton looks like. The nuclear democracy model faded away between 1974 and 1980. There were some die-hards who didn’t want to give up but by 1980 they constituted a very small minority. By that time all theory and experiments were based on the quark model.

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Fig. 16.16

Fig. 16.17 for anti-quarks

Baryon Number→−B SIZE OF QUARK 1× 10−17 cm Charge→−Q

So far all the experiments that have been done up to the present time are consistent with the quark model, so let’s talk about the properties of quarks as we know them now. It turns out we now have six diﬀerent kinds of quarks. Stable matter is made up of only two of these, the UP and DOWN quarks; but in addition there are the STRANGE, CHARM, BOTTOM, and TOP quarks. The TOP quark was discovered only a few years ago. As you can see the UP and DOWN masses are quite small, just a few MeV. The STRANGE quark mass is about 150 MeV, the CHARM quark 1.5 GeV and the BOTTOM 5 GeV. The TOP quark is enormously heavy. It’s about 174 GeV which means that it’s heavier than about 185 protons. This is a great mystery. Nobody understands why there is this tremendous variation in quark masses. All the quarks have fractional charges, 2/3 or −1/3. All have spin 1/2 and all have baryon number 1/3, which means that it takes 3 of them to make up a proton or any proton-like particle. One question remains - What is the size of the quark? Well, the size of the quark is still smaller than we can measure. We presently measure it to be smaller that 10−17 cm in size. So we say it’s point-like.

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We don’t necessarily believe that it’s a point, but as far as our tools of measure1 ment can go, we only see points. Now 10 7 cm is an upper limit of what its size could be. Let’s think about what that means. That’s an exceedingly small size. If we took a carbon atom and expanded it to the size of the earth, a quark would be less than a quarter of an inch in comparison. And that’s the upper limit of its size. Now the size of electrons has been measured and they have the same upper limit for their size. So there’s a very strange point of view that’s emerging from these results. The little nuggets of matter, the quarks and the electrons, that make up matter essentially occupy no space. We’re all empty space. Sorry to tell you that. Because you know if you look at the total volume of an atom and you compare the volumes of all the quarks and electrons in the atom calculated from the upper limit of their sizes, the quarks and electrons occupy an unbelievably small fraction of volume of the atom. It is only about one part in 1026. So the question is, if that’s the case, why can’t I put my hand through this table? Because after all, these infinitesimal nuggets won’t collide when the probability is so small for collision. Well, the reason you can’t do that is because of the force fields. The force fields basically give us the sense of continuous matter. They occupy all of that empty space. And therefore if I try to put my hand through the table, it’s repelled by the force fields in this table. The nuggets in my hand are being repelled by the force fields of the nuggets in the table and vice-versa. So that’s the concept of matter in the modern view. Now you might say to me that I am trying to fool you in a certain sense, because one of the reasons we didn’t believe in quarks in the first place was that a quark had never been found. So you might ask me, Has a quark been found? If you ask me that, I have to say no. So why do I believe in quarks? Well it turns out there was a theory called quantum chromodynamics proposed in 1973, which showed that because of the strange properties of the gluon field, quarks are most likely permanently confined inside the proton and other particles. Remember I said gluon fields connect to one another, unlike photon fields. That property produces a very unusual force, a force which actually tends to get somewhat larger or at least remains constant as you pull 2 quarks apart. So you realize what that means. It’s like a spring. When I try to pull a spring apart, the force increases. If this is truly the force field, the quarks are permanently confined. If I try to pull one quark to infinity, which is where the quark can be free, I have to supply an infinite amount of energy, which is clearly impossible. This means that the quark is not free and can never be free. Now this is not proved mathematically; but every indication from experiment and theory indicates that this is the case, and theorists are trying to develop mathematical proofs. Now if you have two quarks sitting side by side separated by 10−13 cm the force between them is roughly of the order of 15 tons. This gives you an idea of the strength of the forces between two quarks. If I try to pull two quarks 1 cm apart, I’ve got to expend an energy of 1013 GeV. If I try to make an accelerator capable of putting that amount of energy into this system of two quarks, that accelerator, if built on the basis of current technology, would have to be comparable in size to our solar system. So I can’t do that.

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But what happens if you take a quark and anti-quark and you try to pull them apart? After you have separated them by an infinitesimal distance the force field breaks and an anti-quark and quark form at the broken ends of the force field. The original quark pair constituted one meson and after the break occurs you have two mesons. If you keep on doing that, you have three mesons and so on. This is the way particle production occurs in this theory. So it’s a very unusual theory, a very interesting theory. There are many questions still to be answered. Do quarks have finite size and if so, how big are they? Now if they have a finite size they most likely have an internal structure of some kind. This structure would mean that maybe something else is inside of them. So there could be another layer of matter inside quarks; but there’s one problem with that and I’ll tell you what the problem is. This problem doesn’t mean it’s impossible, but it makes it seem very unlikely or unreasonable. The problem arises because the quark is so small. Quantum mechanics says that all particles have an associated wave length that is related to the particle’s momentum. The larger the momentum, the smaller the wave length; and if you want to confine a particle within a certain volume, the wavelength of the particle has to be comparable to the size of the volume. The smaller the volume, the smaller the wavelength, and the higher the kinetic energy of that particle inside. So if you look at how small the upper limit of the size of a quark is, any smaller particle inside of it would have to have an immense kinetic energy, actually more than 10,000 times greater than the kinetic energy of a quark in the proton. And the greater the kinetic energy of the particle inside the stronger the force has to be to hold the smaller particle inside. If you estimate the force required to hold a particle within the volume of a quark, if the quark were as large as the upper limit of its size, it turns out you get a force that is about 100 million times greater than the strong force. And the strong force is the strongest fundamental force that we know of in nature. So the forces inside would be absolutely immense if you had something inside in the quark. This doesn’t mean that this internal structure of the quark doesn’t exist, but that it would be mind boggling if it did. But there is a possibility that it does, and that there are new types of forces and particles in nature of which we have no knowledge. The only way to search for this structure is to have higher energy available for further studies; because as I said before, in experiments probing the structure of particles, the eﬀective magnification grows with energy. Fortunately, there is a new collider being built at CERN called the Large Hadron Collider, which will be completed in 2005. It will produce a total energy of 14 trillion electron volts. The highest energy we have now is about 2 trillion electron volts. Given the increase in beam energy and intensity, the Large Hadron Collider will increase the eﬀective magnification by a factor of 10 or greater. So one will be able to push the limit of the size of the quark down to about 10−8 cm or lower - or find new structure - with this future collider. But you see there is a problem here. For every factor of 10 smaller in size that you probe, you must have a factor of 10 more in energy, which makes it very diﬃcult to continue the probe beyond the Large Hadron Collider without the development of new types of accelerator technology.

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But who knows? Maybe something unexpected will be found and maybe in the year 2007 somebody will report that there is a new layer in the structure of matter. That would be very exciting. In concluding this lecture, I would like to make a few personal remarks. What attracted me to physics was a deep curiosity about the wonders of nature and a desire to learn as much as I could about how the world works at its most basic level. So I want to say to the students in the audience, if you have a deep curiosity about nature, if you have a sense of awe about the magnificent wonders of the universe, I strongly recommend a career in science. You will find, as I have, that there is great pleasure in learning about how the world works - that phenomena which seem like magic can be understood on the basis of fundamental laws and principles. And exploring the unknown is a very exciting challenge. There is immense joy in finding out something new, something that no one else has ever known before. So study science, nurture your curiosity, follow your imagination, and perhaps someday you will be standing here talking about a new discovery. Thank you.

Fig. 16.18 Scene of the lecture of Professor Jerome Friedman at Osaaka International Center (2000)

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Very Elementary Particle Physics Martinus J.G. Veltman

Abstract This address was presented by Martinus J.G. Veltman as the Nishina Memorial Lecture at the High Energy Accelerator Research Organization on April 4, 2003, and at the University of Tokyo on April 11, 2003

Introduction Today we believe that everything, matter, radiation, gravitational fields, is made up from elementary particles. The object of particle physics is to study the properties of these elementary particles. Knowing all about them in principle implies knowing all about everything. That is a long way oﬀ, we do not know if our knowledge is complete, and also the way from elementary particles to the very complicated Universe around us is very very diﬃcult. Yet one might think that at least everything can be explained once we know all about the elementary particles. Of course, when we look to Martinus J.G. Veltman such complicated things as living matter, an animal or a hu- NMF c man being, it is really hard to see how one could understand all that. And of course, there may be specific properties of particles that elude the finest detection instruments and are yet crucial to complex systems such as a human being. In the second half of the twentieth century the field of elementary particle physics came into existence and much progress has been made. Since 1948 about 25 Nobel prizes have been given to some 42 physicists working in this field, and this can be seen as a measure of the amount of ingenuity involved and the results achieved. Relatively little of this is known to the general public. Martinus J.G. Veltman (1931 – ). Nobel Laureate in Physics (1999) University of Michigan (USA) at the time of this address M. J. G. Veltman: Very Elementary Particle Physics, Lect. Notes Phys. 746, 371–392 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 17

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In this short account a most elementary introduction to the subject is presented. It may be a small step to help bridging the gap between the scientific knowledge achieved and the general understanding of the subject.

Photons and Electrons Photons are very familiar to us all: all radiation consists of photons. This includes radio waves, visible light (from red to dark blue), X-rays, gamma rays. The first physics Nobel prize, in 1901, was given to R¨ontgen, for his discovery of X-rays or r¨ontgen rays. The 1921 physics Nobel prize was awarded to Einstein for his discovery that light is made up from particles, photons. Einstein is most famous for his theory of relativity, but it is his discovery of photons that is mentioned by the Swedish Academy. Indeed, many think that this is perhaps his most daring and revolutionary discovery! The diﬀerence between all these types of photons is their energy. The photons of radio waves have lower energy than those of visible light (of which red light photons are less energetic than blue light photons), those of X-rays are of still higher energy, and the gamma rays contain photons that are even more energetic than those in X-rays. In particle physics experiments the photon energies are usually very high, and then one deals with individual photons. The energy of those photons starts at 100,000,000,000 times that of the photons emitted by portable phones.

Fig. 17.1

Especially at lower energies the number of photons involved is staggering. To give an idea: a 1 watt portable phone, when sending, emits roughly 10,000,000,000,000,000,000,000 photons per second. Together these photons make the wave pattern of radio waves. Also in visible light the number of photons is generally very large. Interestingly, there exist devices, called photo-multipliers that are so sensitive that they can detect single photons of visible light. The photons of visible light are one million times as energetic as those emitted by a portable phone, and while the number of photons emitted is correspondingly lower the amount is still enormous.

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Electrons are all around us. They move in wires in your house, make light, and function in complicated ways in your computer. They also make the pictures on your TV or computer screen. In the tube displaying the picture electrons are accelerated and deflected, to hit the screen thereby emitting light.

Fig. 17.2

In the tube, on the left in the picture, a piece of material called the cathode is heated. As a consequence electrons jump out of the material, and if nothing were done they would fall back. However, applying an electric field of several thousand volt they are pulled away and accelerated. Then they are deflected, usually by means of magnetic fields generated by coils, deflection coils. They make the beam of electrons move about the screen. There they paint the picture that you can watch if you have nothing better to do. Thus inside your TV tube there is an accelerator, although of rather low energy as accelerators go. The energy of the electrons is expressed in electron-Volts. An electron has an energy of one electron-Volt (abbreviated to eV) after it has been accelerated by an electric field of 1 Volt. In a television tube the field may be something like 5000 V, thus the electrons in the beam, when they hit the screen, have an energy of 5000 eV. In particle physics the energies reached are much higher, and one uses the unit MeV. One MeV is one million eV. Thus the electrons inside the TV tube have an energy of 0.005 MeV. Try to remember that unit, because it is used everywhere in particle physics. Related units are GeV (1 GigaeV = 1000 MeV) and TeV (1 Tera eV = 1000 GeV).

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Making New Particles In order to make particles one must first make an energetic beam of electrons or protons. Protons can be found in the nucleus of an atom together with neutrons. The simplest nucleus is that of hydrogen, it contains only one proton. The picture shows a hydrogen atom, one proton with one electron circling around it. The electron is negatively charged, the proton has exactly the same charge but of the opposite sign. The total charge of a hydrogen atom is the sum of these two and Is thus zero, it is electrically neutral.

Fig. 17.3

The first step then is to take a box filled with hydrogen. Subsequently a strong spark, an electric discharge, is produced in that box. This amounts to a beam of electrons moving through the hydrogen. When it meets a hydrogen atom on its way the electron is knocked out of the atom, and there results an electron and a proton drifting in that box. Ionization is the name given to the process of stripping electrons from an atom.

Fig. 17.4

The next step is to apply an electric field. If the field is positive on the left then the electrons are pulled to the left and the protons, having the opposite charge, are pulled to the right. Making a little window (of some thin material) the protons emerge on the right hand side and one has a proton beam. Likewise one has en electron beam on the left hand side, but this is not an eﬃcient way to make electron beams. One can do it better as shown by the TV tube.

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To produce new particles one must create a minuscule bubble of concentrated energy. From Einstein’s equation E = mc2 we know that matter is a form of energy, and in order to make a particle of some mass one must have an energy bubble of at least that much energy. The bubble will decay into whatever is possible, sometimes this, sometimes that. But always, the energy equivalent to the sum of the masses of the particles that it decays into is less than the initial energy of the bubble. That is why particle physicists want forever bigger accelerators. Those bigger machines create ever more energetic bubbles, and very heavy particles, not seen before, may appear among the decay products of those bubbles. To create a bubble of high energy the beam of protons coming out of the ionization chamber is accelerated to high energy, and then the protons are smashed into other particles, for example particles in an atomic nucleus. Thus one simply shoots the beam into a suitable material, a target. Whenever there is a collision of a particle in the beam with a nucleus a bubble will form and that bubble will decay into all kinds of particles. In this way new particles can be found. Those particles, themselves little bubbles of energy, are usually unstable and they decay after a little while and that is why they are not seen in the matter around us. There are only a few stable particles, mainly photons, electrons, protons and neutrinos.

Fig. 17.5

The new particles found are given names, and their properties are studied. In the early days these particles were called mesons. For example one finds copiously π-mesons, or briefly pions, particles with a mass about 260 times bigger than the electron mass. Those pions decay mostly into a muon (a μ-meson, a particle whose mass is about 200 times that of the electron) and a neutrino (ν, mass 0). The muon, while relatively long-lived, decays in an electron, a neutrino and an anti-neutrino. Anti-particles have almost the same properties as particles (they have the same mass, but opposite charge), but that will be discussed later. Often they are designated by placing a bar above the symbol, for example one writes ν¯ for an anti-neutrino.

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Those things can already be seen using accelerators producing beams of moderate energy. Let us quote some numbers. The electron mass has an energy equivalent of 0.5 MeV, and a π (pion) has a mass of 135 MeV. The μ (muon) has a mass of 105 MeV. Accelerators with beams of protons with an energy of 1 GeV = 1000 MeV have no trouble creating those particles. These particles are often electrically charged, positive or negative. The charge is usually measured in units equal to minus the charge of the electron, thus the electron has charge −1. The pion for example occurs in three varieties: π+ , π− and π0 , with charges +1, −1 and 0. The charged pions decay into a muon and a neutrino: π+ → μ+ + ν and π− → μ− + ν. As indicated, the muons appear in two varieties, the μ+ and the μ− . There is no neutral muon. In every process seen up to now charge is always strictly conserved, so a negative pion decays into a negative muon (and a neutral neutrino), while a positive pion will always decay into a positive muon. So let us now consider the whole situation such as can be found at CERN, Geneva. In 1959 an accelerator of 30 GeV = 30,000 MeV was switched on. See the figure further down. First there is an ionization chamber, producing a beam of protons. With electric fields of moderate value those protons are accelerated slightly and focussed into a tight beam. This beam is let into a big circular pipe, diameter 200 m. All around that pipe magnets are placed, and magnetic fields are made such that the beam is curved and remains inside the pipe. At certain points along the beam pipe there are segments with an electric field, and when the beam passes through such a segment the particles receive a kick and their energy increases. The beam goes around many times, and the magnetic fields are increased gradually to keep the ever higher energy protons inside the beam pipe. At some point the magnetic fields reach their limit, and then no more acceleration is possible. At that point the beam is extracted from the beam pipe and directed to a target. In the resulting collisions many particles will be produced. With various methods (magnetic fields, shielding with certain openings) those particles that one wants to study are selected, focussed into beams (called secondary beams) and directed into detectors for further study. Of course, this can only be done with particles that live suﬃciently long and do not decay halfway in the process. There are several such particles, among them pions. Thus at CERN there were secondary pion beams with which experiments could be done. In this way the precise properties of pions were established. At that time the detectors used mostly were bubble chambers and spark chambers, each with their advantages and disadvantages. They are described in the next chapter.

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Fig. 17.6 Particle physics accelerators. The diameter of the machine constructed at CERN (called PS) in 1959 is 200 m. The energy reached is 30 GeV = 30,000 MeV. At Fermilab near Chicago: diameter 2 km, energy 1 TeV = 1000 GeV

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Detectors The invention of the bubble chamber by Glaser (Nobel prize 1960) marked the beginning of modern experimental particle physics. In a bubble chamber some liquid is kept near the boiling point, and (charged) particles moving through the liquid ionize atoms or molecules (knocking oﬀ electrons) on their path. As a consequence of these disturbances small boiling bubbles form along the track. Next a picture is taken, and the particle reactions can be studied in detail. To identify the sign of the charge of the particles passing through the bubble chamber a magnetic field is generated by means of coils near the chamber. The particle tracks will be curved due to this magnetic field, and positively charged particles will curve in the opposite way compared to negatively charged particles. Also, from the degree of curvature of the tracks one obtains information about the velocity of the particles. It should be emphasized that electrically neutral particles make no tracks, they are observed only indirectly. In using the bubble chamber the material of the bubble chamber functions as a target. A beam of particles coming from an accelerator is sent into the bubble chamber, and the particles in the beam may collide with the atoms in the fluid. Usually these collisions are with the nuclei. The figure shows an example of a simple bubble chamber picture.

Fig. 17.7

Bubble chambers have a big disadvantage: they are slow. The process of bringing the fluid to the boiling point, taking a picture and then moving away from the boiling point is relatively slow (a few seconds). On the other hand the pictures are quite detailed, and allow a rather precise analysis. Spark chambers consist of a number of metal plates, mounted parallel to each other with some well chosen gas in between. Particles passing through the gas result in ionization, and if one supplies a high voltage between the plates there will be sparks precisely at the place where the particle passed. Usually there is no magnetic field, so the tracks are not curved.

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Fig. 17.8

The location of the track is also much less precisely defined. In the picture an event analogous to the above bubble chamber event is depicted. In this case the material in the plates functions as a target; events originating in the gas are much less likely simply because the gas has little density compared to the metal. There are two advantages to the spark chamber over the bubble chamber. First, by using heavy metal plates (that are functioning as a target) one may have a really massive target, which is of advantage if one wants to study particles that react only rarely. Neutrinos are such particles, they interact so rarely that for example neutrinos from the sun usually have no trouble passing through the earth.

The 1963 Cern Neutrino Experiment The second advantage of spark chambers is that they can be triggered. By means of various techniques, involving other types of detectors, one may first establish that some event is of interest and only put voltage on the plates for those cases. In other words, one may make a selection in the type of events and concentrate on those of interest. The introduction of spark chambers made neutrino physics possible. One could then have so much target material that the possibility of a neutrino interacting with the material became large enough to make experiments possible. The basic idea for such an experiment was due to Schwartz, who then together with Lederman and Steinberger did the very first experiment (Nobel prize 1988) at the Brookhaven National Laboratory, Long Island, USA. In 1963 a neutrino experiment was done at Cern and the figure shows the general layout. A big improvement compared to the earlier Brookhaven experiment was a horn, invented by van der Meer (he did get a Nobel prize later but not for this invention). That horn focussed the pions coming from the target, and that increased greatly the intensity of the pion beam coming out of the horn. Pions decay, principally into a muon and a neutrino, and letting them

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Fig. 17.9

pass some distance many will decay. Gradually the pion beam changes in a mixture of muons and neutrinos (plus other stuﬀ coming from the target). The subsequent massive amount of shielding (some 25 m of steel) stopped all particles except the neutrinos. Thus almost exclusively neutrinos passed through the bubble chamber and the spark chamber positioned behind that shielding. From time to time one of them would interact with the material in either bubble chamber or spark chamber.

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The bubble chamber was installed although one had little hope of seeing any neutrino induced events. In the first run 460,000 pictures were taken and luckily, about 240 events were seen. Without the horn one would very likely have had only few events, if any. The spark chambers did better, as there was so much more material. Also, one did not have to scan many pictures, the spark chambers were triggered only if one knew, through other type detectors, that some charged particles came out of the chamber. Some 2000 events were seen on that many pictures. The numbers mentioned here are for the first run, the experiment ran for extended periods over many years. One of the bubble chamber pictures generated much interest for reasons that cannot be explained here. The following figure shows the event, faithfully copied from the actual picture. The neutrino beam entered from the right. After the collision several particles came out, and there was also a recoiling nucleus (or whatever remained of it after the collision). One of the particles produced was a negatively charged muon; it can be recognized by the fact that muons are charged particles that interact relatively rarely. In this picture the muon actually leaves the chamber without interacting. The remaining tracks are from electrons and positrons. A positron is precisely like an electron, however it has a positive charge. It is the anti-particle from the electron, one could thus also speak of an anti-electron. Except for what seems to be just one positron (in the middle, below) and one single electron (perhaps an electron kicked out of an atom, see arrow) one observes only pairs, electron-positron pairs. Such pairs are created by energetic photons as will be discussed in the next chapter.

Fig. 17.10

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Feynman Rules In 1948 great progress was made in the theory of elementary particles. Feynman introduced his diagram technique, and without that technique the theory would not have advanced to the point that it is today. Here is the idea. In the antenna of a radio (or television) emitter electrons move back and forth inside the antenna. While doing so they emit photons, making the radio waves. The figure (called a vertex) depicts this process. An electron comes in from the left, emits a photon and continues.

Now the details of the process of emitting radiation by an electron are known since a long time, and they can be calculated in all precision. Thus corresponding to this picture there is a precise mathematical expression giving the numerical value for this process. Feynman made this into a very neat package. He gave a simple recipe whereby, given a diagram, one could write down very easily the corresponding mathematical expression from which the amount of radiation by the electron could be computed. The arrow in the electron lines gives the flow of (negative) charge. The beautiful thing about these diagrams is that they have a strong intuitive appeal. Here is the next situation. On the receiver side, photons interact with the electrons in the antenna and make them move, thus generating currents. This is depicted by the diagram shown. It is very much like the previous diagram, except the photon is now incoming rather than outgoing. And again, there exists a mathematical expression that can be written down easily and that gives the precise strength for this process. Just looking at it one observes that the second diagram can be obtained from the first by moving the photon from out to in. This procedure is called crossing, a property of Feynman diagrams. Moving a line from in to out or the other way around gives another process that then indeed exists. This leads to remarkable things. Taking the last diagram and moving the incoming electron to be outgoing one obtains the diagram shown here. In this diagram one incoming photon becomes a pair of an electron and something else that must be very close to an electron, except the arrow points the opposite way. There is a flow of negative charge inwards, which must be interpreted as a flow of positive charge outwards. Thus the charge of that particle is opposite to that of the electron. This particle is a positron, the anti-particle of the electron. With this interpretation there is agreement with another fact of nature: charge is always conserved. If one starts with zero (the charge of the

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Fig. 17.11

Fig. 17.12

Fig. 17.13

photon) then one must end with zero (the charge of the electron plus that of the positron). In the bubble chamber picture shown in the previous chapter several positrons appear. The photons, being neutral, are invisible, but they become electron-positron pairs that can be seen. They need not be symmetrical, one of the particles may come out faster than the other. The bubble chamber picture was taken in 1963, the positron was seen for the first time in 1930, by Anderson working at the California Institute of Technology (Nobel Prize 1936). The diagrams shown above can be seen as elements that can be used to depict more complicate processes. For example, an electron can emit a photon that is then absorbed by another electron. In this way electrons can exchange a photon. In the process they deflect. Some innovative person has coined the example of two iceskaters where one of them throws a sack of sand to the other. You can imagine the path of the skaters, they will deflect at the point were the exchange is made. This process, exchange of a photon, is represented by the diagram shown. One speaks of Coulomb scattering. As always, having the diagram it is quite simple to write the corresponding mathematical equation, and there is no diﬃculty in calcu-

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Fig. 17.14

lating all details. In our analogy all depends on the amount of sand in the sack; in the electron case the properties of the photon exchanged varies from case to case according to some probability pattern. One can also compute this, which then gives the relative probability of this or that photon exchanged. Another observed process is Compton scattering (Nobel prize 1927). A photon may hit an electron and then subsequently that electron may emit a photon. That second photon needs not be of the same energy as the incoming photon. For example, a blue light photon could come in and the outgoing photon could be a red one. There are actually two diagrams here, because it is also possible that the electron first emits a photon and then later absorbs the incoming photon.

Weak Interactions In 1896 Bequerel discovered strange radiation, which was later understood as due to the decay of the neutron (Nobel prize 1903): neutron → proton + electron + anti-neutrino

(17.1)

Today this is called β-decay. In shorter notation this can be written as: N → P + e− + ν¯

(17.2)

The bar above the ν denotes the anti-particle. It took a long time, till about 1957, to understand this process in detail. Now we can write a diagram corresponding to this process, and we also know the corresponding equations. So we can say precisely how often the neutron decays with the electron going in some definite direction with respect to the proton. For example, starting with a neutron at rest, we can give the probability that after the decay the electron moves away opposite to the proton. Or that they come out at right angles. Looking to just one decay nothing can be said, but looking to, say, 100,000 decays we can pick out those cases that have the requested configuration (proton and electron opposite for example). If the probability for that to happen is 0.2$, then we will see that happen in roughly 200 cases. That is the way these things work, and for β-decay we can compute it all. So, here is the diagram. There is one new element in this: the arrow for the neutrino is pointing inwards, like for a positron. The neutrino has no charge, thus

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Fig. 17.15

Fig. 17.16

there is no charge flow associated with this. Here the arrow is eﬀectively used to indicate that we are dealing with an anti-particle. From this process another may be obtained by means of crossing. Moving the anti-neutrino to the incoming side, whereby it becomes a neutrino, we find the process: ν + N → P + e− (17.3) This is something that can be seen in a neutrino experiment as that at CERN in 1963. An incoming neutrino may hit a neutron in some nucleus, and then an electron and proton should come out. The electron is easy to recognize so this type of event should be recognized without diﬃculty. Moreover, since we know all about the mathematical expression corresponding to this diagram we can even predict how often this should happen. Indeed, events like this have been observed in the neutrino experiment in the amount predicted. So far, so good. There is a serious theoretical diﬃculty however with this process. In a neutrino experiment the energy of the incoming neutrino is below 10 GeV = 10,000 MeV. This is a relatively low energy as these things go. But theoretically one can also compute this process for higher and higher energy, and then things go wrong. As the energy of the neutrino is made larger the probability for this process to happen increases fast (on paper), to grow to impossible values. By impossible we mean that the probability exceeds one. That would imply, idiotically, that one would see more of these events than neutrinos in the beam. One must go to very high energy neutrinos before this happens, but it does. There is (theoretically) trouble. We may look at the analogous case for electrons and photons. The diagram for scattering of an electron from an electron has been given before (Coulomb scattering) and there is no problem. Let us therefore try something similar. We invent a new (hypothetical) particle to make a diagram that looks like the Coulomb scattering diagram. There is one big diﬀerence. Since charge must be conserved always the

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Fig. 17.17

new particle, called a vector-boson and denoted by W, must have a positive charge. This can be seen at the neutrino side: the neutrino chages into a negatively charged electron and a W, thus the charge of the W must be the opposite of that of the electron, i.e. positive, like the positron charge. This positive W then combines with the neutron (no charge) to become a proton (positive charge). The way we have done it the arrow in the W line denotes the flow of positive charge. Indeed, considering now the mathematical expression corresponding to this diagram there is no diﬃculty at high energy. And for low energy the diagram gives practically the same as the original diagram (without W) provided this W is suﬃciently heavy. A heavy W is something that will not move very much at low energies, and the eﬀect is that the whole behaves then as if the W line is contracted to a point. Well, that W has been found experimentally at CERN in 1983 (1984 Nobel prize to Rubbia and vander Meer). Its mass is considerable: it is 85 times heavier than the proton. You need a lot of energy to make such a particle. Its mass represents an energy equivalent to 80 GeV = 80,000 Mev (compare the electron mass, 0.5 MeV!). But in 1983 a machine was available that produced energy bubbles of about 900 GeV and that was enough. That is not immediately obvious, because the energy bubbles were produced colliding protons, and protons themselves tend to be somewhat extended objects. The energy was therefore not too well concentrated. Anyway, it worked, and since then we are sure about the existence of the vector-bosons. Theoretically the existence of the W was guessed on the basis of the high energy behaviour of diagrams. That principle is really on the basis of the theory developed in the early seventies, and for which the 1999 Nobel prize was given (’t Hooft and V.). That theory goes a lot further, through the study of hypothetical processes and considering the high energy behaviour of such processes. Even if those reactions cannot be reproduced in the laboratory, the theory should never really produce idiotic behaviour as discussed above. So let us go on. Here a generalization of the anti-particle idea must be introduced. The new rule is: given a vertex then also the vertex with all arrows reversed must exist. Thus in the figure the left diagram implies the existence of the one on the right. The first process that we will consider is the scattering of a W from and electron. It is a hypothetical reaction, because there is no way that we can produce beams of

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Fig. 17.18

Fig. 17.19

Fig. 17.20

vector-bosons. They are actually quite unstable, once produced they decay swiftly into lower mass particles. Here are two diagrams for W-e scattering. We used for the left diagram only the ν-W-e couplings (one of them completely crossed) that occur in the figures above. Thus the left diagram should exist. But its behaviour is bad at high energies. Peeking at the corresponding diagrams for photons and electrons, namely Compton scattering, we invented another diagram where a W is emitted before the incoming W is absorbed. Indeed, that would repair things, but unfortunately that would require a particle X−− with a double negative charge. Nature is very strict about charge conservation, so starting with an electron and emitting a positively charged W requires that the third particle has a double negative charge. And that is bad, because there is no such particle. Is there another solution? This requires some creative thinking, and the figure shows the solution. It involves a new particle that must be electrically neutral. It is called the Z0 , and we must ask the experimentalists if it exists. The Z0 was seen also by Rubbia and van der Meer, in the above mentioned 1983 experiment. Actually the nicest and cleanest way of producing such a Z0 is through another reaction, obtained from the one abouve by crossing. The reaction corresponding to this pictures,

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Fig. 17.21

Fig. 17.22

Fig. 17.23

e− + e+ → W+ W−

(17.4)

was observed at the largest machine available at CERN (called LEP, for Large Electron Positron collider), where 100 GeV electrons were collided with 100 GeV positrons. Many such events have been seen, and the Z0 has been studied in great detail and with great precision. There is perfect agreement with the theory. Let us summarize the rules that we have learned. Crossing. Moving for an existing process incoming lines to become outgoing and vice-versa produces new processes that must exist as well. This implies the existence of anti-particles. As mentioned before, the rule for anti-particles goes a little further: whenever there is some vertex also the vertex with all arrows reversed must also exist. Good high energy behaviour. This requires that for any process, if there is one diagram of a type as shown below, at least one of the others must exist as well.

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Fig. 17.24

Fig. 17.25

Fig. 17.26

Fig. 17.27

Top-Quark Let us finally discuss how the top-quark came into the picture. At CERN when producing the Z0 various decay modes were observed. Among them a decay mode of the Z0 involving a new particle, called the bottom-quark. This was not the way the bottom-quark was originally discovered, it was first seen in another reaction. The bottom-quark has a mass of about 4.3 GeV and a fractional charge, namely − 13 . Following by now familiar methods we consider W+ -bottom scattering. That is a purely hypothetical reaction, there is no way that we can produce a beam of vetorbosons (W’s). Actually, there are some bottom-quarks present in protons and neutrons, so as a target we could use protons. That would still be diﬃcult, because the amount of bottom-quarks in a proton is very small.

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Fig. 17.28

Fig. 17.29

The diagram shown must exist. However, that diagram by itself produces a bad result with respect to high energy behaviour, as discussed before. According to our rules there must exist some other diagram and there are two possibilities. The first possibility is shown in the figure. It involves a new particle. We have indicated the electric charges, and from conservation of charge we deduce that this new particle must have a charge of + 23 . And indeed, such a particle has been observed at Fermilab near Chicago. It is called the top-quark. Before it was found the theoretical knowledge using precision results from LEP was perfected to the point that the mass of this top-quark could be predicted quite accurately. This of course greatly facilitated the experimental search for that particle. To be precise, the prediction for the top-quark mass was 177 ± 7 GeV, the value found at Fermilab is 174 ± 5 GeV. The fact that the theoretical prediction for the top mass agreed so well with the experimental result was quoted by the Nobel Committee on the occasion of the 1999 Nobel prize. To be complete, there are some uncertainties related to another particle called the Higgs particle, whose existence can be deduced by considering W+ − W+ scattering. We will not discuss that here.

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Fig. 17.30

Concluding Remarks It will be obvious to the reader that this text only scratches the surface of the subject matter. One can do only so much in a note as short as this. On the next page an overview of the known elementary particles is given. Matter around us is build up from electrons, protons and neutrons. The proton contains a down and two up quarks, the neutron an up and two down quarks. The quarks come in three kinds, coded using the colors red, green and blue. These quarks together with the electron and the electron-neutrino constitute the first family. There are however two more families, diﬀering from the first mainly because the particles are much heavier. Otherwise they have the same properties. Nobody knows why there are three families. The known particles and their names, masses and charges. Every ball corresponds to a particle. There are three families with largely identical properties. The particles with non-integer charge are called quarks, the last two in every family are called leptons. Every quark comes in three varieties, indicated by means of the colors red, green and blue. There is thus a red, green and blue charm quark, with a mass of 1300 MeV and with charge 23 . The neutrino’s have possibly a very small mass, subject of further experimentation. To each of these particles corresponds an anti-particle with the same mass, but with the opposite charge. For example, there is an anti-muon with charge +1 and an anti-τ-neutrino with charge 0. In addition there is the W+ (charge +1, mass 80330 MeV), the W− (−l, mass 80330), the Z0 (0, mass 91187), eight gluons (0, 0), the photon (0, 0) and the graviton (0, 0). The sofar hypothethical Higgs particle has a mass of at least 114000 MeV and charge 0.

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Fig. 17.31 Professor Martinus Veltman during the lecture at University of Tokyo (2003)

18

The Klein-Nishina Formula & Quantum Electrodynamics Chen Ning Yang

Abstract This address was presented by Chen Ning Yang at the Nishina Memorial Lecture at Okayama Institute for Quantum Physics on October 13, 2005

One of the greatest scientific revolutions in the history of mankind was the development of Quantum Mechanics. Its birth was a very diﬃcult process, extending from Planck’s paper of 1900 to the papers of Einstein, Bohr, Heisenberg, Schr¨odinger, Dirac and many others. After 1925-1927, a successful theory was in place, explaining many complicated phenomena in atomic spectra. Then attention moved to higher energy phenomena. It was in this period, 19281932, full of great new ideas and equally great confusions, that the Klein-Nishina Formula played a crucial role. The Chen Ning Yang formula was published in 1929, in the journals Nature and NMF c Z. Physik. It dealt with the famous classical problem of the scattering of light waves by a charged particle. This classical problem had been studied by J. J. Thomson. Conceptually in classical theory, the scattered wave’s frequency must be the same as the incoming frequency, resulting in a total cross-section:

σ=

8π e4 . 3 m2 c 4

Chen Ning Yang (1922 – ). Nobel Laureate in Physics (1957) Tsinghua University (China) and Chinese University (Hong Kong) at the time of this address C. N. Yang: The Klein-Nishina Formula & Quantum Electrodynamics, Lect. Notes Phys. 746, 393–397 (2008) c Nishina Memorial Foundation 2008 DOI 10.1007/978-4-431-77056-5 18

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But in 1923 in an epoch making experiment, Compton found that the scattered waves had a lower frequency than the incoming waves. He further showed that if one adopts Einstein’s ideas about the light quanta, then conservation laws of energy and of momenta in fact led quantitatively to the lower frequency of the scattered waves. Compton also tried to guesstimate the scattering cross-section, using a half-baked classical picture with ad hoc ideas about the frequency change, obtaining: 8π e4 1 , 3 m2 c4 1 + 2α α = hν/mc2 .

σ=

Now, when hν is very small compared to mc2 , this formula reduces to Thomson’s. This Compton theory was one of those magic guess works so typical of the 1920’s, He knew his theory cannot be entirely correct, so he made the best guess possible. Later on, in 1926, Dirac and Gordon used Quantum Mechanics in diﬀerent ways, but obtained the same formula:

σ=

2πe4 1 + α 2(1 + α) 1 − ln(1 + 2α) . 1 + 2α α m2 c4 α2

This formula is very much like the Compton formula, only more complicated. It is also not entirely correct, because it doesn’t have the electron spin. Then came Dirac’s relativistic equation of 1928 which led to great success but greater confusion. Some forty years later, Oppenheimer in his interview by T. S. Kuhn, used the metaphor: Magic and Sickness to describe Dirac’s equation. Why Magic? Because 1. Before Dirac’s equation, the spin was a hypothesis, but with Dirac’s equation the spin was natural. 2. It had the correct spin-orbit coupling, 3. It had the correct magnetic momenta for the electron. Yet there is also Sickness because of the “negative energy states”, which led to great contradictions. Sickness led to confusion, sometimes even to madness. To give one example: Eddington entered the picture, saying that Dirac’s equation is 4 × 4, and 4 is 2 × 2. But (8 × 8 + 2 × 2) × 2 = 136, so he claimed the fine structure constant should be 1/136. One year later he modified the theory, and said “no, you should

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add one to it”, so it should be 1/137. A few months before he died, Eddington said I am continually trying to find out why people find the procedure obscure. But I would point out that even Einstein was considered obscure, and hundreds of people have thought it necessary to explain him. I cannot seriously believe that I ever attain the obscurity that Dirac does. But in the case of Einstein and Dirac people have thought it worthwhile to penetrate the obscurity. I believe they will understand me all right when they realize they have got to do so ? and when it becomes the fashion “to explain Eddington.” Thus Dirac’s magic and sickness did in a way influence Eddington. The dominant question in physics in 1928-1930 was: Was Dirac’s equation correct? In this atmosphere Klein and Nishina arrived at their formula in September 1928: 2πe4 1 + α 2(1 + α) 1 − ln(1 + 2α) σ= 2 4 2 1 + 2α α m c α 1 + 3α 2πe4 1 ln(1 + 2α) − . + 2 4 m c 2α (1 + 2α)2 This was a remarkable formula for two reasons: (a) It turned out to be correct, and (b) it however was based on a wrong theory, i.e. Dirac’s 1928 paper which had the sickly negative energy states. Soon after the K-N paper, people found the Klein-Nishina formula to be in rough agreement with the data about the absorption of x-rays by matter, which was taken as additional support for Dirac’s equation. But still the negative energy states remained a fundamental sickness and caused great agonies. Oppenheimer later remembered that Pauli’s opinions then was “Any theory that had such a sickness must agree with experience only by accident.” That was the typical attitude of the theoretical physicists around that time. Then came the hole theory of Dirac. Dirac said: Okay, there are many negative states, but this sea of negative states is usually fully occupied. Once in a while, there is a hole in the sea and that would appeared as a positively charged particle. That was the hole theory. He first proposed the idea in a letter to Niels Bohr dated Nov. 26, 1929, and later published it in 1930. This revolutionary idea of Dirac’s introduced the subtle modern view of the complexity of the vacuum. Thus began the modern quantum field theory of electromagnetism: which today we call QED. In a speech of 1959 at Bryn Mawr, I had likened

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Chen Ning Yang

Dirac’s bold proposal of the hole theory to the first introduction of negative numbers. How about the K-N formula in the new hole theory? It was then shown by Dirac, and by Waller independently, that the Klein-Nishina formula, derived without the infinite sea of holes, was nevertheless magically correct. Thus the Klein-Nishina formula became the first correct formula of QED discovered by physicists. Its agreement with experiments was, e.g. reported by Rutherford in his Presidential address to the Royal Society. Despite this, most theorists still refused to believe the hole theory. It was deemed too revolutionary. Pauli, Bohr, Landau and Peierls all argued against it. The negative energy states were dubbed “donkey electrons” and ridiculed. Why “donkey electrons”? Because with a negative energy state, if you apply force on it, the more force you apply, the more it resists, like the behavior of a donkey. Adding to the confusion was Dirac’s original proposal to have protons as the holes. His 1930 paper had the title “A Theory of Elections and Protons”. This particular confusion was later resolved through the theoretical papers of Oppenheimer, Tamm and Dirac, all in 1930. In these papers they proved that a hole cannot be a proton, because if the hole were a proton, then an electron would jump into it, in approximately 10−10 seconds, making the hydrogen atom unstable. The conclusion was: there has to be 2 seas, one for the electron and one for the proton. Thus by the end of 1930 the main theoretical framework for QED was complete. But a new experimental confusion arose, also in 1930, delaying the general acceptance of QED for another 2 years. The experiment was the absorption of γ rays by heavy elements. Earlier work with lower energy photons had produced agreement with the K-N formula. Now higher energy γ-rays became available at about 2.6 MeV, from thorium C. People began to check with the new γ-ray the validity of the KleinNishina formula. In a 1983 article by C. D. Anderson, reminiscing about 1930-1932: At that time it was generally believed that the absorption of ’high energy’ γrays was almost wholly by Compton scattering, as governed by the Klein-Nishina formula. Anderson was a graduate student of Millikan, who had assigned another graduate student, C. Y. Chao, to study with counters this absorption process, to see whether for γ-rays it also agrees with the K-N formula. In a beautifully simple experiment, Chao found that for heavy targets at 2.6 MeV there is more absorption than predicted by the K-N formula. He called these “anomalous absorption”. Furthermore, in a second experiment, also in 1930, Chao found what he called “additional scattered rays” in the scattering.

18 The Klein-Nishina Formula & Quantum Electrodynamics

397

These discoveries were not understood theoretically, and were thought to be nuclear phenomena, unrelated to QED. Adding to the confusion was the unfortunate situation that two other experimental groups did not agree with Chao’s findings. As we shall mention below, Chao’s findings were in fact correct, and “anomalous absorption” and “additional scattered rays” were essential QED phenomena required by the hole theory. But that understanding came only after Anderson’s discovery in 1932 of the positron with his cloud chamber pictures, vividly showing the correctness of the hole theory. People then looked back at the Chao experiment and found that in fact “Anomalous absorption” was pair creation, and “Additional scattered rays” was pair annihilation. Both essential phenomena in QED! Thus by 1932 the theoretical framework of QED was complete, and was in agreement with all experiments. The next chapter in the history of QED opened with the theoretical discovery in the mid-1930s of higher-order divergences, which led eventually to the renormalization program of 1947-1949. But that is not the subject of my talk today.

Appendix A

List of Nishina Memorial Lectures

Year Speaker

Title

1955 Sin-itiro Tomonaga Takeo Hatanaka 1956 Cecil F. Powell Oskar B. Klein

Cosmic Rays Changing Universe Cosmic Rays Problems related to Small and Big Numbers of Physics Gravitation Interaction between Dirac Particles Structure of Matter Experiments on Atomic Nuclei Norikura Observatory and Cosmic-Ray Observation by Balloon Relation between the Sun and the Earth My Twenty Years of Cosmic-Ray Research Non-Linear Theory of Field Strong Coupling Theory Biological Action of Radiation and the Order The Status of the Theory of Superconductivity Development of the Atomism Elementary Particles Theory of Thermoelectric Refrigeration and its Applications The Sun and the Ionosphere Discovery of Nuclear Power Nuclear Power Generation New Developments in Elementary Particle Theory Foundation of the Quantum Mechnics The Atomism in Modern Physics The Radioactivity Radiation Belt Observed by Rockets and Artificial Satellites in the Soviet Union

Oskar B. Klein Seishi Kikuchi Hiroo Kumagai 1957 Chihiro Ishii Yuji Hagiwara Chihiro Ishi 1958 Jean L. Destouches Robert Serber Shoten Oka 1959 John M. Blatt Sin-itiro Tomonaga Victor F. Weisskopf Yoshio Suga Yuichiro Aono 1960 Sin-itiro Tomonaga Ryoukiti Sagane J. Robert Oppenheimer L. Rosenfeld M. A. Markov Sin-itiro Tomonaga 1961 S.N. Vernov

399

400

1962 1963 1965 1966

A List of Nishina Memorial Lectures

Donald A. Glaser Minoru Oda E. W. Muller Moriso Hirata Mitio Hatoyama Noboru Takagi Isidol I. Rabi Hideki Yukawa Sin-itiro Tomonaga

Satio Hayakawa 1967 Werner C. Heisenberg Juntaro Kamahora 1968 Kodi Husimi 1969 Eiichi Goto 1970 Sin-itiro Tomonaga Kouichi Shimoda 1971 Hideki Yukawa 1972 Itaru Watanabe 1973 Chuji Tsuboi 1974 Sin-itiro Tomonaga 1975 1976 1977 1978

1979 1980 1981

1982

Minoru Oda Sin-itiro Tomonaga Kodi Husimi Felix Bloch Felix Bloch Norimune Aida Satoshi Watanabe Julian Schwinger Morikazu Toda R. E. Peierls Tetsuji Nishikawa W.K.H. Panofsky Hiroichi Hasegawa Sadao Nakajima Tasuku Honjo

1983 H. Schopper Chien-Shiung Wu Gerard ’t Hooft John Bardeen

Bubble Chambers and Elementary Particle Physics The Archeology of the Cosmos Field Ion Microscope Physics of Cracks Electronics Age and Transistors Observation Rocket and Cosmic Science Social Responsibility of Scientists Dr. Nishina, Mr. Tomonaga and I Development of Quantum Electrodynamics: Personal Recollection Radiation Reveals the Universe Abstraction in Modern Science (→ p. 1) Early Days of Cancer Research Early Days of Nuclear Fusion and Plasma Research Forte and Weak of Computer Reminiscences of Nuclear Physics Advancement of Laser Science Character of Physicists Life Science and Human’s Futures The Earth which is Alive Changing visions of the Universe : from the Copernicus to Einstein X-ray Stars and Black Holes Introduction to Atomic Physics Dream and Reality of Fusion Energy History of NMR Early Days of Quantum Mechanics New Research of Friction Phenomena Cooperation Phenomenon and Pattern Recognition Two Shakers of Physics (→ p. 27) Natural Phenomenon and Nonlinear Mathematics Model-making in Physics Search for Quarks - Ultimate Elementary Particles From Linear Accelerators to Linear Colliders Cosmic Dusts and the Birth of Planets World of Extremely Low Temperature Moving Genes : Molecular Genetics Basis of Immunological Phenomenon CERN and LEP The Discovery of the Parity Violation in Weak Interaction and its Recent Development (→ p. 43) Is Quantum Field Theory a Theory ? Evidence for Quantum Tunneling in Quasi-OneDimensional Metals

A List of Nishina Memorial Lectures

1984 E. M. Lifshitz Humitaka Sato Freeman J. Dyson Yasuo Tanaka 1985 Carlo Rubbia Yoichiro Nambu Richard P. Feynman Ben R. Mottelson Mikio Namiki 1986 Aaron Klug Masaki Morimoto 1987 Ken Kikuchi Nikolai G. Basov Toshimitsu Yamazaki 1988 Kai Siegbahn Masaki Morimoto Masatoshi Koshiba 1989 Philip W. Anderson Philip W. Anderson Humitaka Sato Kunihiko Kigoshi 1990 Leon V. Hove Nobuhiko Saito ** see footnote ** 1991 Daiichiro Sugimoto 1992 Mikio Namiki

Charles H. Townes Yutaka Toyosawa 1993 Heinrich Rohrer Heinrich Rohrer James W. Cronin Jun Kondo 1994 Kinichiro Miura 1995 Joseph H. Taylor

401

L.D. Landau – His Life and Work Birth of the Universe Origins of Life (→ p. 71) X-ray Astronomy in Japan Discovery of Weak Bosons Is ”the Elementary Particle” a particle? The Computing Machines in the Future (→ p. 99) Niels Bohr and Modern Physics (→ p. 115) Quantum Mechanics and Observation Problems Hierarchies in Chromosome Structure Radio Waves Reveal the Universe Searches for Elementary Particles by Large Accelerators Physical and Chemical Processes in Electroionization Discharge Plasma Muon Spin: Rotation, Relaxation, and Resonance From Atomic Physics to Surface Science (→ p. 137) Ten Years in Radio Astrophysics Neutrino Astrophysics: Birth and the Future Theoretical Paradigms for the Sciences of Complexity (→ p. 229) Some Ideas on the Aesthetics of Science (→ p. 235) Birth of the Universe Radiometric Dating Particle Physics and Cosmology (→ p. 245) Protein: Reading and Decoding the Language of Amino Acid Yoshio Nishina Centennial Symposium – Evolutional Trends in the Physical Sciences New Method in Computer Physics: From Cosmos to Protein Mystery in Modern Science: Quantum Phenomenon, Character of Microscopic World in NonDaily Life What’s Going on in the Center of our Galaxy Paradox and Truth of Quantum Mechanics The New World of the Nanometer (→ p. 281) Challenge for Proximal Probe Methods (→ p. 281) The Experimemtal Discovery of CP Violation (→ p. 261) Peculiar Behavior of Conduction Electrons Road to Protein Design Binary Pulsers and Relativistic Gravity

402

A List of Nishina Memorial Lectures

Keiichi Maeda

Black Hole and Gravitational Wave: New Eyes for Observing the Universe in the 21st Century 1996 Eiji Hirota Science of Free Radical: Current Status and the Future 1997 Ilya Prigogine Is Future Given? Makoto Inoue Observing a Huge Back Hole 1998 Pierre-Gilles de Gennes From Rice to Snow (→ p. 297) Pierre-Gilles de Gennes Artificial Muscle Harold W. Kroto Science: A Round Peg in a Square World (→ p. 319) Shuji Nakamura Progress of Blue Luminescence Device : LED that Replaces Light Bulb 1999 Norio Kaifu SUBARU Telescope and New Space Observation 2000 Claude Cohen-Tannoudji Manuplating Atoms with Light Jerome Isaac Friedman Are we Really made of Quarks ? (→ p. 349) Akira Tonomura Look into the Quantum world 2001 Sumio Iijima Basis and Application of Carbon Nanotubes 2002 Yoji Totsuka Investigation of the Mystery of the Neutrino 2003 Martinus J.G. Veltman Very Elementary Particle Physics (→ p. 371) Atsuto Suzuki Investigating the Depth of the Elementary Particle, the Earth, and the Sun with the Neutrino 2004 Yasunobu Nakamura Superconducting Quantum Bit : Quantum Mechanics in the Electric Circuit 2005 Chen Ning Yang My Life as a Physicist and Teacher Chen Ning Yang The Klein-Nishina Formula and Quantum Electrodynamics (→ p. 393) Muneyuki Date Progress of Condensed Matter Science as Seen in Nishina Memorial Prizes Kazuhiko Nishijima Yoshio Nishina and the Origin of Elementary Particle Physics in Japan 2006 Makoto Kobayashi Whereabouts of Elementary Particle Physics 2007 Kosuke Morita Search for New Superheavy Elements

∗

R. Kubo (→ p. 17), J. Kondo, M. Kotani, A. Bohr, G. Ekspong, R. Peierls, L.M. Ledreman, Y. Nambu, B. Mottelson, P. Kienle, S. Nagamiya, M. Oda, L.P. Kadanoﬀ, M. Suzuki, B.B. Kadomtsev, J. Schwinger, V.L. Ginzburg, C.N. Yang, Yu.A. Ossipyan, H. Haken, J.J. Hopfield, and A. Klug, published as Springer Proceedings in Physics 57 ”Evolutional Trends in the Physical Sciences”, M. Suzuki and R. Kubo, eds.,1991, Springer Verlag.