Seminar on
FISSION Pont d'OyeV
This page intentionally left blank
Seminar on
FISSION Pont d'OyeV Castle of Pont d'Oye, Habay-la-Neuve, Belgium I 6 - I 9 September 2003
Editors
Cyriel Wagemans University of Gent, Belgium
JanWagemans SCK*C€N, Mol, Belgium
Pierre D'hondt SCK-CEN,Mol, Belgium
r pWorld Scientific N E W JERSEY * LONDON
-
SINGAPORE
.
SHANGHAI * HONG KONG * TAIPEI
BANGALORE
Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224
USA once: Suite 202, 1060 Main Street, River Edge, NJ 07661
UK once: 57 Shelton Street, Covent Garden, London WC2H 9HE
British Library Cataloguing-in-PublicationData A catalogue record for this book is available from the British Library
SEMINAR ON FISSION Copyright 0 2004 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereoj may not be reproduced in any form or by any means, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher.
For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher.
ISBN 981-238-792-7
Printed in Singapore by World Scientific Printers (S) Pte Ltd
Fonds voor Wetenschappelijk Onderzoek - Vlaanderen
1
I Fund for scientific research - Flanders (Belgium) I
Institute for Referenee Materials and Measurements
UNIVERSITEIT GENT
This page intentionally left blank
ORGANISING COMMITTEE P. D’hondt SCK-CEN Mol Belgium
M. Huyse University of Leuven Belgium C. Wagemans University of Gent Belgium
SCIENTIFIC ADVISORY COMMITTEE N. CIrjan University of Bordeaux France F. Gonnenwein University of Tubingen
Germany F.-J. Hambsch IRMM Gee1 Belgium
E. Jacobs University of Gent Belgium 0. Serot CEA Cadarache France
vii
This page intentionally left blank
PREFACE This Seminar is the fifth of a series started in 1986, being organised in the historical castle of Pont d’Oye (Habay-la-Neuve). The dimensions of this nice castle constitute a boundary condition resulting in a natural limitation of the number of participants. The experience of previous meetings indeed confirms our point of view that a small-size meeting like the present one creates a much better and more relaxed working atmosphere than a mega-conference, which is even intensified by the peaceful nature surrounding the castle. During this meeting, recent achievements in fission physics were discussed, giving special attention to low-energy fission and its traditional topics such as fission fragment characteristics, ternary fission, fission neutrons and fission cross sections (for various specific applications). Also the importance of fission for nuclear astrophysics was highlighted, especially how fission barriers affect the r-process. Furthermore, due attention was given to new facilities as well as to new results in the region of the heavy and superheavy nuclei. This Seminar is strongly supported by four organisations: the Nuclear Research Centre in Mol (SCKCEN), the Fund for Scientific Research Flanders (FWO), the Institute for Reference Materials and Measurements in Gee1 (IRMM) and the University of Gent (UG). The organising committee is very grateful to these sponsors. Also the valuable help of the International Advisory Committee and of the Chairmen of the Sessions is gratefully acknowledged. Cyriel Wagemans Conference chair
IX
This page intentionally left blank
CONTENTS
Organizations
V
Organising and Scientific Advisory Committees Preface
VII
1x
Fission in Nuclear Astrophysics Fission barriers: How do they affect the r-process? I. V: Panov, B. Pfeiffer, K.-L. Kratz, E. Kolbe, T Rauscher and F.-K. Thielemann
3
Large-scale Skyrme-Hartree-Fock calculations of fission barriers in a multi-dimensional space M Samyn and S. Goriely
13
Microscopic calculations of spontaneous fission half-lives and neutron-induced fission cross sections P.Demetriou, M Samyn and S. Goriely
21
Neutron-induced nucleosynthesis in the r-process B. Pfeifer and K.-L. Kratz
29
Fission Fragment Characteristics Microscopic and dynamical study of fiagment mass distributions in 2 3 8 fission ~ H. Goutte, P. Casoli and J.F. Berger
39
Prediction of fission mass yield distributions based on cross section evaluations 47 F.-J. Hambsch, S. Oberstedt, G. Vladuca andA. Tudora Mass yields and kinetic energies &om symmetric fission of 23%* and 240Pu* I. Tsekhanovich, G. Simpson, R Orlandi, A. Scherillo, D. Rochman and V: Sokolov
Xi
55
xii
Study of the mass and charge distribution of fragments from fission induced by intermediate energy neutrons on 238U P. Casoli, i? Ethvignot, i? Granier, R. 0.Nelson, N. Fotiades, M Devlin, D. Drake, K Younes, P.E. Garrel andJ.A. Becker
65
Observation of the structures in the mass-TKE distributions of fission fragments in spontaneous fission V.A. Kalinin, V.N. Dushin, V.A. Jakolev, B.F. Petrov, A S . Vorobyev, A.B. Laptev, O.A. Shcherbakov and F.-J. Hambsch
73
Fission yield measurements with the ISOL method U Koster for the ISOLDE Collaboration and the AlcaPARRNe Collaboration
83
Fragment excitation and moments of kinetic energy distributions in nuclear fission H.R. Faust
92
Evidence for collinear cluster tripartition W.H. Trzaska, Yu V. Pyatkov, D. V. Kamanin, S.R. Yamaletdinov, E.A. Sokol, A.A. Alexandrov, I.A. Alexandrova, E.A. Kuznetsova, S. V. Mitrofanov, Yu E. Penionzhkevich, V.G. Tishchenko, A.N. Tjukavkin, B. V. Florko, S. V. Khlebnikov and Yu V. Ryabov
102
Talks of General Interest
Neutrons from fission F. Gonnenwein
113
Ternary Fission
Recent experiments on particle-accompaniedfission M. Mutterer
135
The ternary alpha energy distribution revisited C. Wagemans, P. Janssens, J. Heyse, 0.Serot, P. Geltenbort and i? Soldner
142
New results on the ternary fission of Cm and Cf isotopes 0. Serot, C. Wagemans, J. Heyse, J. Wagemans and P. Geltenbort
151
...
Xlll
Fission in the Superheavy Region Multimodal fission in heavy ions induced reactions I. V. Pokrovsb For collaboration)
167
The role of the quasifission process in reactions for the synthesis of superheavy elements G. Giardina, G. Fazio, A. Lamberto, R. Palamara, A.K. Nasirov, A.I. Muminov, K. V. Pavliy, A. V. Khugaev, 2. Kanokov, F. Hanappe, 7: Materna and L. Stuttgt!
181
Tracking dissipation in capture reactions in the superheavy region T. Materna, V. Bouchat, F. Hanappe, 0. Dorvaux, C. Schmitt, L. Stuttgt5, Y. Aritomo, A. Bogatchev, I. Itkis, M. Itkis, M Jandel, G. Knyajeva, J. Kliman, E. Kozulin, N. Kondratiev, L. Krupa, E. Prokhorova, I. Pokrovski, V. Voskresenski, N. Amar, S. Grkvy, J. Pt!ter and G. Giardina
191
New Facilities Planned photofission experiments at the new Elbe accelerator in Rossendorf H. Sharma, K.M. Kosev, S. Fan, E. Grosse, A. Hartmann, A.R. Junghans, K.D. Schilling, M. Sobiella andA. Wagner
20 1
MYRRHA, a multipurpose accelerator driven system for R&D - Present status P. D’hondt, H. Ait Abderrahim, P. Kupschus, P. Benoit, E. Malambu, V. Sobolev, T. Aoust, K. Van Tichelen, B. Arien, F. Vermeersch, D. De Bruyn, D. Maes, W. ffaeck, Y. Jongen and D. Vandeplassche
209
Various Aspects of Nuclear Fission Fission of a 1 A GeV 238U-ionson a hydrogen-target M Bernas, P. Napolitani, F. Rejmund, C. Stephan, J. Taieb, L. Tassan-Got, P. Armbruster, T. Enqvist, M.-V. Ricciardi, K.-H. Schmidt, J. Benlliure, E. Casajeros, J. Pereira, A. Boudard, R. Legrain, S. Lerqy, C. Volant and S. Czajkowski
223
XIV
Fission dynamics with the “neutron clock” technique using demon neutron array at the Louvain-La-Neuve cyclotron facility Y. El Masri, J. Cabrera, T Keutgen, C.H. Dufauquez, V. Roberfoid, I. Tilquin, J. Van Mol, R.J. Charity, J.B. Natowitz, K. Hagel andR. Wada
232
Fission Cross Sections Study of proton induced fission of actinide nuclei between 20 and 80 MeV bombarding energies D. Belge, C. Dufauquez, T Keutgen, R. Prieels, A. Ninane, J. Van Mol, Y. El Masri and R. Charity
245
High resolution measurements of the 234U(n,f)cross section J. Heyse, C. Wagemans, K.W. Chou, L. DeSmet, J. Wagemans and 0.Serot
255
The 233Pafission cross section measurement and evaluation A. Oberstedt, F. Tovesson, F.-J. Hambsch, S. Oberstedt, V. Fritsch, B. Fogelberg, E. Ramstrom, G. Vladuca and A. Tudora
262
Determination of the 233Pa(n,f)reaction cross section from 0.5 to 10 MeV using the transfer reaction 232Th(3He,p)234Pa M. Petit, M. Aiche, G. Barreau, S. Boyer, S. Czajkowski, D. Dassi, C. Grosjean, A. Guiral, B. Haas, D. Karamanis, C. Rizea, F. Saintamon, E. Bouchez, F. Gunsing, A. Hurstel, C. Theisen, A. Billebaud, L. Perrot and S. Fortier
270
List of Participants
283
Author Index
289
Chapter 1
Fission in Nuclear Astrophysics
This page intentionally left blank
FISSION BARRIERS: HOW DO THEY AFFECT THE R-PROCESS? *
I.V. PANOV+ Institute for Theoretical a n d Experimental Physics, B. Cheremushkinskaya 25, Moscow, 117259, Russia. E-mail: Zgor.PanovQitep.ru
B. PFEIFFER, K.-L. KRATZ Instatute f u r Kernchemie, 0-55128 Mainz, Germany E-mail: KL. KratzOuni-mainz.de
E. KOLBE, T. RAUSCHER, F.-K. THIELEMANN University of Basel, Klingelbergstr. 82, CH-4056 Basel, Switzerland E-mail: fktQquasar.physik.unibas.ch
Fission is an important process which is responsible not only for the yields of transuranium isotopes, but may have a strong influence on the formation of the majority of heavy nuclei due to fission recycling in the r-process. Calculations of beta-delayed and neutron-induced fission rates were performed taking into account different fission barriers and mass formulae were done. It is shown that an increase of fission barriers results in naturally changes of fission rates, but that the absolute values of fission rates are nevertheless sufficiently high and lead to the termination of the r-process. Furthermore it is discussed, that the probability of triple fission could be high for A > 260 and have an affect on the formation on the heaviest nuclei.
1. Introduction Fission is a n important process which is responsible not only for the yields of the transuranium isotopes, but also for the formation of the majority of heavy nuclei due t o recycling. For the consistent treatment of r-process nucleosynthesis we need to consider fission on the basis of the same mass 'This work supported by grant 20-68031.02 of the Swiss National Science Foundation. tWork is partially supported by grants 04-02-16840-a and 04-02-16793-a of RFBR.
3
4
formulae used for for the calculation of other reaction rates and decay properties and have to evaluate all the fission branches - neutron-induced fission, beta-delayed fission and spontaneous fission. In addition one should analyze the importance of each of the fission branches for the termination of r-process, nuclear abundance yields and the related age determination from chronometer nuclei abundances. The fission barriers, used usually for fission rate c a l c ~ l a t i o n swere ~~ probably underestimated. Recent calculations20 l 5 predict higher fission barriers, sometimes significantly. Therefore, a recalculation of fission rates is important as well as an evaluation of their sensitivity on nuclear data. We consider all fission channels, but discuss first the beta-delayed and neutron-induced fission. When the first extended calculation of beta-delayed fission for the majority of r-process nuclei was done' it turned out that the fission probability could reach 100% and beta-delayed fission affects strongly the transuranium yields, especially on the yields of cosmochronometer nuclei. Their yields are used t o determine stellar age or the age of our galaxy as a lower limit on the age of the universe. For r-process conditions with long durations of high neutron densities also neutron-induced fission could play an important role. That can be seen from the comparison of neutron-induced fission rates for uranium isotopes' employing the old barrier estimates" and extended calculations for variety of fission barrier modelsz2 Recent extended calculations of fission barriers 16v20 require that all fission rates are recalculated for the inclusion in r-process calculations. Observations of metal-poor stars emphasize the importance of the mass region 110 < A < 130 for understanding of the role of fission in the rprocess. One notices that these nuclei are underabundant and the solar system r-process must have at least two components, one which dominates for A<130 and a second one which dominates for A>1306. The observation of the second component in low metallicity stars and the observed abundances for A<130 might give strong clues to fission properties, if the explanation of the second component is related to an r-process site with a high neutron supply which leads to fission cycling. This should be investigated as the site of the r-process is still uncertain. We want to emphasis here in advance, that besides neutron-induced fission and beta-delayed fission rates, the mass-distribution of fission yields should be important, as mention earlier14. Although the mass distribution of fission products is known rather well for long-lived transactinide nuclei,
5
the mass distribution after fission of neutron rich heavy elements is an open question. The r-process yields in the mass region of 80 < A < 120 can be affected by the mass distribution of fissioning nuclei - triple or ternary30 fission plays an important role. 2. Different fission treatment barriers In the past fission rate calculations were based on the Gross theory of betadecay" or statistical Hauser-Feshbach formalism for reactions. For beta-delayed fission also the beta-strength function should be known. Calculations of beta-strength function made use of different microscopic modelsz9. Below we will compare different calculations of fission probabilities and present results of new calculations. Two different fission barrier predictions were developed during recent years, showing that the fission barriers by Howard and MOllerI7 were systematically underestimated. The new calculations by Mamdouh et a1.16 and Myers, Swiatecki2Odiffer in some cases very strongly from the previously employed rates used. We make the comparison of barrier heights calculated in different approaches are made for isotopes of U and Cm. As it can be seen from the Figure 1 (the common features are the same for all actinides), the change of barriers hights as a function of neutron number is very similar for the different approaches, but differs strongly, especially for N x 184, where Mamdouh et a1.l6 show the absence of deformation and increasing barriers up t o 10 MeV and more. In Fig. 1 the neutron separation energies, as well as fission barriers for isotopes of U and Cm, calculated on the base of different mass relations, are shown. The mass formula of Hilf et al.' predicts significantly smaller mass numbers for the position of neutron drip line than This has important implications, because the r-process path can shift it strongly. For the region of interest, A > 250, the differences in B, values can be larger than 1 MeV. For the calculations of beta-delayed fission rates on the base of statistical model, in which double-hump formalism of nuclear fission is considered, we need the values for both barriers, while Myers and Swiateski2' only provide the maximum barrier height. In that case we derived the value of the second barrier due t o barrier differences from former calculation^^^:
Bfz = B f (Mysw) - ( B f l(HoMo8O) - B f 2(Homo8O)), Before applying the new fission rates t o nucleosynthesis, we will evaluate the
6
10
10
25
0 140
160
180
zm
140
220
N
160
180
2w
220
N
Figure 1. The neutron separation energies (line) and fission barriers (dashed line) for Cf isotopes on the base of ref.20 (left figure) and ref.15 (right figure).
calculation accuracy of fission rates as well as the importance of individual contribution from different fission processes, i.e. beta-delayed fission versus neutron-induced fission. 2.1. Calculation of fission rates
When the r-process approaches the actinide region, additional reaction channels appear. At first, this is beta-delayed fission, proposed by Berlovich and NovikovZ1, which competes with beta-delayed neutron emission and, depending to nuclear data, could reach 100%. If both are negligible, the rprocess could reach these nuclei and experience spontaneous fission mostly after r-process event. Last, but not least, the well known process of neutron induced fission has to be included. This last process, although its rates were calculated for uranium isotopes earlier5 has not been included in r-process calculations. However, neutron-induced fission rates can be very high, especially for isotopes of transuranium elements. These rates can exceed beta-decay rates by orders of magnitude even near the neutron drip-line. For very high neutron densities n, the product < onfv > n, can exceed beta-delayed fission rates X p d f and the recycling time until the neutron capture on fission products leads again t o the formation of actinides can be significantly less than the duration time of the r-process. In Fig.2 we compare of different rates for U and Cm isotopes. In order t o calculate fission rates for neutron-induced fission and betadelayed fission we made use of the statistical model code SMOKER, extended by including fission channel’ As astrophysical applications include unstable nuclei, not attained by experiment, all physical quantities need to be calculated according to the 15.
7
let08
l&
:
5
ai
3 1-
lC+%
f
6:
laM0
;1
4
Imo
4
1W 240
2W
250
A
Figure 2. isotopes.
270
240
250
260
270
280
A
The values of (n,y)-, (n,f)- and P-decay rates for U (left) and Cm (right)
prescriptions mentioned above. Additional information, which needs to be employed for the calculation of neutron-induced and beta-delayed fission, includes only the reaction Q-values and the fission barrier heights. For stable nuclei this information can come from the experiment, but for unstable nuclei one has to make use of a mass formula and theoretical predictions of fission barrier heights.
Figure 3. Fission probabilities p p d f (thin lines) and fission probability after neutron emission (bold lines) for U and Cf isotopes for different strength-functions: Thielemann et al.’ (lines) and Staudt and Klapdor’(dashed lines). Mass formula - ref’, Bf from ref”.
In addition the Q-values and fission barriers involved. One need to know neutron optical potentials and neutron-induced beta strength functions. The accuracy of all these quantities influence the probabilities of beta-delayed fission ~ t r o n g l y ~ ~ Several - ~ , ~ - attempts ~. to calculate these quantities were made, but their results differ strongly due to uncertainties
8
for beta-strength functions and fission barriers of very neutron-rich and especially deformed nuclei. The set of calculations16, while have been done in self-consistent way, show unexpectedly high values of fission barriers near the neutron drip-line, although the agreement for experimentally known isotopes is quite reasonable. In Fig. 3 different calculations of the beta-delayed fission probabilities with the same fission barriers17 are ~ o m p a r e d ~The ~ ~ strength-function . dependence and the high values of Ppdf are easily seen. For the transactinide region, neutron-induced fission could also be important branch of fission. The comparison of different rates for U-isotopes can be found in Fig. 2, where the rates are given for n,, = 1.2 . and 9'7 = 1. We should emphasis, that in the Fig.2 the beta-decay rates muland tiplied by lo5. It is clear that for the conditions when pY, > for nuclei with A > 250 neutron-induced fission should be more important than beta-delayed fission and radiative neutron-capture. In a scenario of neutron-star mergersl0,'' or polar jets in supernova 35 such conditions are maintained for a long time ( 1s). But it is very likely, if the fission barriers used in our calculations (Howard and Mo11erI7) are underestimated. Spontaneous fission in r-process calculations has been considered recently26 while the role of the beta-delayed fission and neutron-induced fission was neglected because of the high ETFSI fission barriers15. In our calculations, even for high fission barriers15 the neutron-induced fission rates are sufficiently high to terminate or at least significantly reduce the build-up of r-process elements of higher Z. Even the higher barriers" used for r-process calculationsz6 (see Fig.3 therein) confirm our conclusion (see below) about role of neutron-induced fission. However, for a consistent consideration of fission, spontaneous fission should also be included in the r-process. The beta-delayed fission in our calculation and the spontaneous fission in other approachesz6 will lead practically to the same result (see section Conclusions), at least within the calculation accuracy. However, without any doubt, neutron-induced and beta-delayed fission are more important in the r-process than spontaneous fission, which can play an important role only during cooling in the final decay of the r-process products.
9
3. Results for U and Cf The new fission-induced rates were calculated with different fission barriers as well as beta-delayed fission probabilities for all U and Cf isotopes. The strength functions of beta-decay were calculated as follows
with the reduced transition probabilities obtained from ref.g. From the presented results (Fig.3,5) we can conclude, that for the U isotopes the beta-delayed fission rates are significantly lower, when the new sets of Thomas-Fermi barriers2' and another barrier set based on the ETFSI mass f o r m ~ l a are ' ~ used in comparison to previously used barrier set17. For Cf isotopes the new data of P&f are also close to 100% (Fig.3,6). Neutron-induced fission rates (< uv >nf N A ) for uranium and curium isotopes are shownzz in comparison to rates utilizing different fission barriers and mass formulae Fig. 4.
A
Figure 4. Neutron-induced fission rates for and Cf isotopes for different fission barriers as well as for different mass formulae.
Neutron-induced fission can be of the significant importance in recycling of r-process if the density of free neutrons is rather high. The rates of induced fission are so large5.", that even for higher fission barriers16 this
10
I .o
1
.o
1.o
1 .o
0.5
0.5
0.5
0.5
0.0
0.0
0.0
00
A
A
Figure 5. Fission probabilities P p d f for U isotopes for consequent mass models of Myers, Swiatecki" (left) and Mamdouh et al.I5 (right).
branch of fission is still important. The preliminary calculations will be discussed in last section. 255
265
275
285
295
305
315
2%
265
275
285
295
305
1.0
10
I .o
0.5
05
0.5
0.0
00 255
265
275
285
A
295
305
00
315
A
Figure 6. The same as in Fig.5, but for for Cf isotopes.
4. Discussion on r-process application and conclusions
A preliminary comparative analysis of the influence of fission modes upon the results of nucleosynthesis was made in r-process calculation^^^ in the highly neutroniszd matter of neutron star merger eventsll. The Y(A) for 120 < A < 240 practically coincide with the calculations making use of the simplified assumption that for A=240 instantaneous fission will take place4, but differs strongly for the mass numbers 100 < A < 120 and A > 240 (see figures in ref18). In case of asymmetric fission yields, nuclei with A=100-120 were formed. Due to the significant difference between symmetric and asymmetric
11
fission upon the r-process, we applied a schematic model for the mass distributionla, including both symmetric and asymmetric13 fission. According to classical model of r-process, the r-process path proceeds close to nuclei with a neutron separation energy S,, M 2MeV, for which in the transuranium region the values of beta-delayed fission are the highest ones. According to P p d f of Thielemann et al.' the r-process would stop in the transuranium region a t A M 250-260. In that case' the approximation of 100% instantaneous fission in the vicinity of A-260 (for simplicity A=260) would be rather g o 0 d ~ 7 ~ J ~ . When using a full network in dynamical calculations without the assumption of the waiting point approximation ((n,y)- (7, n) approximation , the path of r-process changes with time and the efficiency of beta-delayed fission can strongly changes. In particular, for the model of neutron star mergers (Fkeiburghaus et al. 199911,Rosswog et a1.l') r-process nucleosynthesis proceeds mainly along neutron d r i ~ - l i n edue ~ ~ to very high neutron densities. In this case, when using the new fission rates the main flux could circumvent nuclei with high probabilities of beta-delayed fission and could form nuclei with Z up to 100 and masses A > 300. For realistic fission barrier^'^,'^ the nuclei with such masses could be formed, especially when r-process passes on along the neutron drip line in very high neutron density environments. In this case the predicted abundance curve be affected strongly by the inclusion of triple (ternary) fission. The probability of triple(ternary) f i ~ s i o n ~is~highly , ~ ' uncertain, but for Afis > 260, the fission into 3 fragments is possible and should occur. And early31, present32 and f o r t h ~ o m i n gexperiments ~~ should clarify the probabilities of such a processes. All these questions: probabilities of ternary and triple fission and mass distribution of fragments should be investigated soon. The strong r-process component for A>130 requires the detailed analysis of fission properties. Except for neutron-induced fission and &delayed fission also neutrino-induced fission was proposed recentlyz3. And in this connection one should notice that also neutrino ratesz5 can have great importance. Precise fission rates and mass fragment distributions after fission have need to be elaborated and included in r-process calculations. References
1. F.-K. Thielemann, J. Metzinger, H.V. Klapdor-Kleingrothaus, Zt. Phys. A309, 301 (1983). 2. J.J. Cowan, F.-K. Thielemann, J.W. Truran, Phys. Reports, 208,267 (1991).
12 3. I.V. Panov, Yu.S. Lyutostansky, V.I. Ljashuk, Bull. Acad. Sci. Ussr, Phys. ser. (USA) 54,2137 (1990). 4. J.J. Cowan et al., Astrophys. J . 521,194 (1999). 5. F.-K. Thielemann, A.G.W. Cameron, J.J. Cowan, 1989, Int. Conf. 50 years with Nuclear Fission, ed. J . Behrens, A.D. Carlson, p. 592. 6. C. Sneden, J.J. Cowan, 1.1. Ivans et al. Astrophys. J. 533,L139 (2000). 7. A. Staudt, H.V. Klapdor-Kleingrothaus. Nucl. Phys. A549,254 (1992). 8. E.R. Hilf, H.V. Groote, K. Takahashi. Proc. 3 Int. Conf. on Nucl. far from Stability, 1976, CERN-76-13, 142. 9. K.-L. Kratz et al. Astrophys. J . 403,216 (1993). 10. S. Rosswog, F.-K. Thielemann, M.B. Davis et al. Astron. Astrophys. 341, 499 (1999). 11. C. Freiburghaus, S. Rosswog, F.-K. Thielemann. Astrophys. J. 525, L121 (1999). 12. T. Rauscher, et al. Astrophys. J. 429,499 (1994). 13. M.G. Itkis, V.N. Okolovich, G.N. Smirenkin. Nucl. Phys. A502,243c (1989).
14. I.V. Panov, C. Freiburghaus, F.-K. Thielemann. Workshop on Nuclear Astrophysics, Ringberg, 2000, p. 73. 15. A. Mamdouh, J.M. Pearson, M. Rayet, F. Tondeur Nucl. Phys. A644, 389 (1998). 16. A. Mamdouh, J.M. Pearson, M. Rayet, F. Tondeur Nucl. Phys. A679, 337 (2001). 17. W.M. Howard, P. Moller. ADNDT. 25,219 (1980). 18. I.V. Panov, C. Freiburghaus, F.-K. Thielemann. Nucl. Phys. A688, 587c (2001). 19. B.S. Meyer et al. Phys.Rev. C. 39,39 (1989). 20. W.D. Myers, W.J.Swiatecki. Phys. Rev. C. 60,014606-1 (1999). 21. E.E. Berlovich, Yu.P. Novikov. Reports Academy of Science USSR. 185,1025 (1969). 22. I.V. Panov, F.-K. Thielemann. Astronomy Letters. 29,510 (2003). 23. Y.-Z. Qian. Astrophys. J. 569,L103 (2002). 24. T. Rauscher, F.-K. Thielemann. ADNDT 79, 47(2001). 25. K. Langanke, G. Martinez-Pinedo. Rev. Mod. Phys. 75,819 (2003). 26. S. Goriely, B. Clerbaux. Astron. Astrophys. 346,798 (1999). 27. I.V. Panov, F.-K. Thielemann. Nucl. Phys. A718,647 (2003). 28. T . Kodama, K. Takahashi. Nucl. Phys. A239,489 (1975). 29. Moller, P., Randrup, J . Nucl. Phys. A514, 1 (1990). 30. H Diehl, W. Greiner. Nucl. Pnys. A229,29 (1974). 31. Perelygin V.P. et al. Nucl. Phys. A127, 577 (1969). 32. Tsekhanovich I., et al. Phys.Rev. C67,034610 (2003); C.-M. Herbach et al. Nucl. Phys. A712,207 (2002). 33. Kopach Yu.N. et al. Phys.Rev. C65,04461 (2002). 34. I.V. Panov. Astronomy Letters. 29,163 (2003). 35. A.G.W. Cameron. Astrophys. J. 587,327 (2002).
LARGE-SCALE SKYRME-HARTREE-FOCK CALCULATIONS OF FISSION BARRIERS IN A MULTI-DIMENSIONAL SPACE
M. SAMYN AND S. GORIELY Znstitut d’tlstronomie et d’dstrophysique, CP-I26 ULB, Bud du IPriomphe, 8-1050 Brussels, Belgium E-mail: msamynOastro.ulb.ac. be We calculate fission barriers with the Skyrme-Hartree-Fock-Bogoliubov plus particle number projection (SHFB+PLN) method, using a Skyrme force fitted to essentially all the nuclear mass data with the same method. The reflection asymmetry is introduced to study the lowering of the outer barrier of three selected nuclei. We discuss the feasability of performing large-scale SHFB+PLN fissionbarrier calculations, i.e. for about 2000 nuclei of astrophysical interest
1. Introduction
Under certain hydrodynamical conditions, the r-process of nucleosynthesis may produce very neutron-rich fissioning nuclei for which no experimental data are known. The need for an accurate and reliable theoretical prediction of the various properties entering the reaction rates of relevance for the r-process has led us to consider the Skyrme-Hartree-Fock-Bogoliubov (SHFB) approach. We recently studied the impact of different Skyrme parametrizations. More specifically, various aspects of the contact pairing as well as the effective mass4 have been analyzed, the Skyrme force being derived by a fit to all experimental nuclear masses of the Audi and Wapstra c ~ m p i l a t i o n Very . ~ ~ ~recently, the SHFB approach has been corrected for the particle-number symmetry breaking inherent to the model. Based on that approach, a Skyrme force has been refitted and labelled BSk€L7 Here we will describe the present state of our efforts to extend the HFB calculations to the prediction of fission barriers. There have been several HFBCS and HFB calculations of the fission barriers for given selected nuclei in the past, but none of these models were so far applied to the calculation of nearly 2000 barriers required for astro-
13
14
physical applications. In fact, at present the only microscopic calculation of all these barriers was performed using the ETFSI (Extended Thomas-Fermi plus Strutinsky Integral) approximation to the HF method.8 With the much greater computer power at our disposal, we can now contemplate recalculating all these barriers with the HFB method. The calculations reported here are intended to show how the HFB method leads t o a satisfactory agreement with experiment. Since we aim at a unified treatment of all nuclear physics properties of relevance for the r-process, we adopt in this HFB+PLN barrier calculation the BSk8 force7 that emerged from the HFB+PLN mass formula. (In the same way, the ETFSI barriers were calculated with the SkSC4 force derived from the ETFSI-1 mass fit.8) Our calculational procedure is described in Sect. 2, and is illustrated in Sect. 3 by the cases of the double-humped barrier of 240Pu, 246Cm and 252Cf,where the influence of the reflection asymmetry is studied. An outlook for large-scale fission barriers calculations is finally given in Sect. 4. 2. The constrained HFB model and the calculation of barrier heights In the particle-hole ( p h ) channel, the interaction is chosen of the Skyrme type,
while in the particle-particle (pp) channel, a zero-range density-independent force is adopted,
w;; = V,,S(Tij)
,
(2)
which is assumed t o act in a restricted window up to a cutoff energy. In the above expressions, p p ( r ) is the local density. In the context of mass formulas, the pairing strength parameter V,, is allowed t o be different for neutrons and protons, and also to be slightly stronger for an odd number of nucleons (VG) than for an even number (V,',), i.e., the pairing force between neutrons, for example, depends on whether N is even or odd.
=
15
The derivation, with respect t o the HFB wave function, pkl-)
/*HFB)= k
with
pl
=x(UlkC?+%kC~)
,
(3)
1
(/3: is the creation operator of the kth quasi-particle and I -) is the vacuum with respect t o quasi-particles), of the expectation value of the Hamiltonian
leads t o the HFB equation^.^ Our method for solving these equations with the Skyrme interaction has been presented earlierl0>' and has now been improved and extended. The improvements concern the spurious centre-ofmass (cm) energy calculation, as well as the particle number symmetry and the parity symmetry restorations. We also consider a modified prescription for the rotational correction. These new modifications are detailed below. The HFB ground state is not an eigenstate of the total momentum operator. Thus, although the expectation value of the momentum operator P Cipi in the cm frame (HFBIPIHFB) vanishes, its dispersion (HFBlP21HFB) does not. Gaussian overlap approximation t o exact momentum projection gives for the spurious cm energy 1 E,, = -(HFBlP21HFB), (5) 2MA which has t o be subtracted from the calculated total energy. The cm correction is evaluated according to Eq. (5), doing so, however, perturbatively. That is, both the diagonal and off-diagonal terms of Eq.(5) are included only in the calculation of the converged total energy, not in the variational equation that leads t o the mean field in the HFB equation. The HFB ground state is not an eigenstate of the particle number operator. The average number of nucleons is imposed using a Lagrange parameter, the Fermi energy, but the HFB wave function of the nucleus under investigation includes components of wave functions of neighbouring nuclei. To recover the exact number of nucleons, projection techniques are used. The projection after variation (PAV) is easier t o implement and numericaly faster than the variation after projection (VAP) of the HFB wave function, and for this reason applied t o our calculations. However, t o avoid the known discontinuity in the pairing energy, the Lipkin-Nogami formalism, corresponding t o an approximate projection before variation, is included in the iterative process. The method is therefore labelled HFB+PLN.
16
The deformed HFB wave function also breaks the rotational invariance. Projection techniques should be used to restore the exact angular momentum of the wave function, and calculate all observable with the projected wave function. However, such prescription is computer time consuming, and the cranking approximation is used to evaluate the rotational correction energy given by
where j is the angular momentum operator and I c r a n k the Inglis-Belyaev cranking moment of inertia.g To avoid the spherical divergence, but also to reproduce accurately the mass of slightly deformed nuclei, it is necessary to introduce a damping of E:;tank that can be parametrized by
Erot = O.6E,C;tankth(4.7B2)
,
(7)
where the reduced quadrupole moment = e Q with 1 TO = l.2A1l3. This prescription is equivalent to introduce correlations beyond the meanfield of the form
The impact of such a rotational correction on the potential energy surface properties will be presented in Ref 'I. Since the reflection asymmetry is included in our HFB approach, the parity symmetry of the wave function is broken. To describe left-right asymmetric shapes coherently, we restore the parity symmetry on the basis of the generator coordinate method, extensively described in Ref 1 2 ; details of our procedure are explained in Ref ll. Finally, with such improvements, the Skyrme parameters are determined by a fit to all the 2135 (2 8 ) nuclear masses of the 2001 Audi and Wapstra compilation.6 The resulting parameters are given in Table 1 , and are refered to as the BSk8 Skyrme force, and lead to a final rms error of 660 keV. The HF states are expanded on an axially deformed oscillator basis. To closely follow the fission path, it is convenient to relate the deformation parameters of the basis to the so-called ( c , h , a ) parametrization used in the ETFSI calculations,* defined as the elongation, the necking and the left-right asymmetry parameters, respectively. It allows for the definition of a reference surface that more or less coincides with the actual surface of the fissioning nucleus.
>
17 Table 1. Parameters of the BSk8 Skyrme force
to (MeV.fm3) tl (MeV.fm5)
(MeV.fm5) (MeV.fm3('+7)) WO(MeV.fm5) V,$ (MeV.fm3) V$, (MeV.fm3) Cutoff (MeV)
t2
tg
-2035.5245 398.82080 -196.00319 12433.359 147.80967 -314.015 -293.019 CF f 17
I0 XI
x2 13
Y VPn (id.) V& (id.)
0.773828 -0.822006 -0.389640 0.130933 114 -329.780 -309.924
All information needed to calculate the fission probability and the fission fragments distribution are obtained from the analysis of the multidimensional energy surface in the deformation space. The only way t o obtain such a surface is t o constrain the HF calculation t o every possible deformation of the nucleus. We do not constrain on multipoles of higher order than four, as they are optimized by the HF self-consistency and believed not t o play a significant role. The multipole moments that must be constrained (we use the method of the quadratic constraint) are thus the quadrupole, the octupole and the hexadecapole moments, all being calculated in the frame of the centre of mass. For extreme deformations where the reference surface is split, the HF calculations are not constrained to ensure numerical convergence. A proper description of a system a t very large deformation would require a two-centre oscillator basis,13 so that our model is not able to describe the fission process beyond scission. The determination of barrier heights is relatively simple if there are just two deformation parameters, e.g, (c, h): with the total energy E of the given nucleus calculated at a sufficient number of deformations one just makes a contour plot of E in the (c, h ) plane. However, for more degrees of freedom, in particular admitting a left-right asymmetry, the fission path must be determined in the 3-dimensional space spanned by the variables (c, h, a ) . An ingenious solution t o this problem is provided by the "flooding model" of T o n d e ~ r . 'In ~ two dimensions we imagine water being slowly poured into the energy surface, and observe its depth, measured a t the lowest point, i.e., at the ground state, as it spills over the various barriers. The virtue of this method is that its algorithm can be easily generalized t o an arbitrary number of dimensions: see Ref for a detailed account. We stress that this model is applicable whether the energy E at each deformation is calculated in HF or ETFSI. In all cases we begin with a first HFB calculation of the energy surface, assuming left-right symmetry, a = 0. If the corresponding ETFSI calculation indicates that a particular barrier in this surface is asymmetric,
18
we calculate the HFB energy surface over the (c, h) plane in the vicinity of the concerned saddle point for each of the four values of a = n.6a, with n = 1, 2, 3, 4 and a suitable value bf 6a (note that a is never negative). When dynamical properties are c a l c ~ l a t e d , 'it~ is essential t o extend the asymmetric calculation at high enough deformations, in principle to an energy below the ground-state. The grid over the ( c ,h ) plane corresponds to 6 c = 6 h = 0.05. Before applying the flooding model, every surface is interpolated in the c and h directions using the cubic spline method, and with respect to a using Lagrange interpolation.
3. Three test cases: 240Pu,246Cm, and 252Cf
0.2 0.1
0.0 -0.1
-0.2
1 .o
1.2
1.4
1.6
1.8
2.0
2.2
C
Figure 1.
Contour plot of the left-right symmetric energy surface of 240Pu in the
( ~ , h ) ~ =plane. o The contour lines are spaced by 1 MeV. Small tick marks along each contour point in the downhill direction. Letters G, A, M, B, C refer to the ground-state (Pz = 0.276), the inner saddle-point (pz = 0.545), the isomeric state ( p 2 = 0.834), the left-right symmetric (pz = 1.515) and asymmetric outer saddle-point (pz = 1.267,@3= -0.199), respectively. The square centred on B shows the limits in the ( c , h) plane taken to calculate the local 3D energy surface with its saddle-point C. The upper right zone of the panel corresponds to the fission valley
19
We consider the 240Pu case in some detail in order to illustrate our general procedure, showing the energy surface for a = 0 in Fig. 1. The calculated (measured) energy of the ground-state (G) is -1812.61 (-1812.676) MeV, which is in agreement with the quality of the fit of BSk8 to the measured masses. The inner barrier height, measured to be of 5.8 ± 0.2 MeV,16 is predicted to be 5.9 MeV. The first shape isomeric state (M) is at 1.914 MeV above the ground-state (experimentally, about 2.25 ± 0.2 MeV17). The outer symmetric barrier B (at 9.6 MeV) has been recalculated by the method explained before, including the third dimension a within a local variation of c and h as shown by the square centred on B. The resulting asymmetric saddle-point (C) gives an outer barrier height of 5.9 MeV, while it is measured to be 5.45 ±0.2 MeV.17 The effect of the left-right asymmetry on the outer barrier is to lower it by 3.7 MeV. This procedure has been applied for two other cases: the results are summarized in Table 2 and compared to experimental data.16'17 Table 2. PES properties [MeV] predicted by the HFB+PLN(BSk8) model; the influence of reflection asymmetry is given for the outer barrier; experimented data are given between brackets (the uncertainty of the energy above ground state G of the shape isomer, ISO, and of the barrier heights Bj|0, is of the order of ±0.2MeV) M0pu 246
Cm
252 Cf
G -1812.61 (-1812.67) -1846.86 (-1846.97) -1880.41 (-1880.37)
Bi
5.9 (5.8) 6.0 (6.0) 6.7 (5.3)
ISO 1.91 (2.25) 1.71 (-) 1.06 (-)
ga=0
£fa>U
9.6 7.5 6.2
5.9 (5.45) 5.3 (4.8) 4.4 (3.5)
A word of caution should be given about the comparison between the calculated inner barrier heights and the experimental data. Triaxiality has been shown to lower the ETFSI(SkSC4) inner barrier of 240 Pu, 244Cm and the 252Cf by about .8, .9 and 1.3 MeV, respectively.18 This effect is however force dependent and expected to be smaller for the strong BSk8 pairing force, in a similar way as the pairing affects the asymmetric outer barrier.11 4. Outlook and conclusions
The present HFB+PLN calculation shows that microscopic models can compete with more phenomenological highly parametrized models in the reproduction of experimental data. The large-scale HFB calculation of the symmetric and asymmetric barriers for all the thousands nuclei of relevance for the r-process has now become feasible, although it still faces some technical difficulties, that are partly discussed in Ref u . A coherent and accu-
20
rate determination of nuclear masses and fission barriers within one unique mean field approach definitely represents one of t h e most challenging issues for nuclear astrophysics applications in the future. Work is in progress.
Acknowledgments
M.S. and S.G. are FNRS Research Fellow and Associate, respectively. We thank J.M. Pearson, P.-H. Heenen and M. Bender for stimulating and clarifying discussions. References 1. M. Samyn, S. Goriely, P.-H. Heenen, J. M. Pearson and F . Tondeur, Nucl. Phys. A700, 142 (2002). 2. S. Goriely, M. Samyn, P.-H. Heenen, J. M. Pearson and F. Tondeur, Phys. Rev. C66, 024326 (2002); (www-astro.uZb.ac.be). 3. M. Samyn, S. Goriely and J.M. Pearson, Nucl. Phys. A 7 2 5 (2003) 69. 4. S. Goriely, M. Samyn, M. Bender and J.M. Pearson, Phys. Rev. C (2003), in press. 5. G. Audi and A. H. Wapstra, Nucl. Phys. A595, 409 (1995). 6. A. H. Wapstra and G. Audi, private communication (2001). 7. M. Samyn, S. Goriely, M. Bender and J.M. Pearson, (2003) in preparation. 8. A. Mamdouh, J. M. Pearson, M. Rayet and F. Tondeur, Nucl. Phys. A644, 389 (1998); Nucl. Phys. A679, 337 (2001); (www-astro.ulb.ac.be). 9. P. Ring and P. Schuck, The nuclear many-body problem, Springer, New York (1980). 10. F. Tondeur, S. Goriely, J.M. Pearson and M. Onsi, Phys. Rev. C 6 2 , 024308 (2000) 11. M. Samyn, S. Goriely, (2003) in preparation. 12. P. Bonche, J. Dobaczewski, H. Flocard, P.-H. Heenen and J. Meyer, Nucl. Phys. A 5 1 0 (1990) 466. 13. J.F. Berger and D. Gogny, Nucl. Phys. A333, 302 (1980). 14. F. Tondeur, private communication. 15. P. Demetriou, this conference. 16. Reference Input Parameter Library - 2, IAEA-TecDoc (2003), in press; also available at www-nds.iaea.org. 17. M. Hunyadi et aZ., Phys. Lett. B 505 (2001) 27. 18. A. K. Dutta, J. M. Pearson, and F. Tondeur, Phys. Rev. C61, 054303 (2000).
MICROSCOPIC CALCULATIONS OF SPONTANEOUS FISSION HALF-LIVES AND NEUTRON-INDUCED FISSION CROSS SECTIONS
P. DEMETRIOU, M. SAMYN AND S. GORIELY Institut d 'Astronomae et d'Astrophysiqe, Universik! Libre d e Bruxelles, CP-226, Campus d e la Plaine, Bd. du Traomphe, B-1050 Brussels, Belgium E-mail:
[email protected] Fission potential-energy surfaces are calculated from a microscopic Hartree-FockBogoliubov description of the deformed nucleus, fully constrained in the three deformation coordinates c, h, a. The dynamical fission paths along the multidimensional deformation space are determined by applying the classical least action principle. The resulting dynamical fission barriers and spontaneous fission half-life are compared with static calculations and experimental values for 240Pu. Furthermore, microscopic calculations of fission barriers and nuclear level densities are used to obtain neutron-induced fission cross sections. The results for the actinides keV are compared with existing experimental data in the low energy region ~ 1 0 0 relevant to the r-process nucleosynthesis.
1. Introduction
Nuclear fission could play a crucial role in the r-process nucleosynthesis (for a general review see Ref.l). If under some conditions the nucleosynthesis reaches the transuranium region, then fission will prohibit the synthesis of the superheavy elements. Neutron-induced and beta-delayed fission in particular, in astrophysical environments where the neutron densities are sufficiently large t o produce fissile nuclei, may strongly influence the abundances in the lower mass region through the re-cycling of the r-process material, while spontaneous fission affects the final abundance pattern, especially the production of long-lived radiocosmochronometers Th and U. Of course all of these fission processes involve extremely neutron-rich nuclei that are unable t o be measured in the laboratory. It is therefore of paramount importance to be able t o make reliable predictions of the relevant beta-delayed and neutron-induced fission rates, as well as the spontaneous fission half-
21
22
lives, of all these unknown nuclides, starting from relatively close to the stability line and going out towards the drip line. In this respect, an attempt has been made to treat all aspects of fission on a microscopic basis, using a Skyrme-Hartree-Fock-Bogoliubov approach for the calculation of masses, fission barriers and fission level densities. In this work we present the results for the spontaneous fission properties of 240Puobtained with a Skyrme-Hartree-Fock-Bogoliubov method2 in a multidimensional deformation space. The fission paths and half-lives are calculated in a dynamical a p p r ~ a c h ~ In , ~ addition, ,~. we compare neutron-induced cross sections obtained with barrier heights and nuclear level densities from microscopic models with existing experimental data for nuclei in the actinide region. 2. Method of Calculations
The potential energy surface (PES) of the nucleus is calculated with the Hartree-Fock-Bogoliubov (HFB) approach with the appropriate restoration of broken symmetries. The calculations are constrained with respect to the multipole moments &, 0, H. The method is based on a Skyrme-type force and a 6-function pairing force. The parameters of the force are adjusted to reproduce the 2135 masses of stable nuclei with Z>8 and N>8, leading to a final deviation of 660 keV. The details of the PES calculations can be found in Ref.2 so in the following we limit ourselves to the points essential for the calculation of the fission properties. Assuming axially symmetrical deformations, the Q, 0, H deformation space is equivalent to the so-called c, h, a parametrization introduced in Ref.6. With this parametrization all deformed shapes of a given nucleus, including total break-up into two separated fragments, can be generated continuously from a spherical configuration. With the HFB potential energy calculated at a sufficient number of deformations c , h, a=O, we obtain the symmetric PES shown in Fig. 1. The ‘static’ barrier heights are then determined by the flooding method described in Ref.’. The results are given in Table 1. Table 1. Fission barriers B (inner, outer), action integrals (S) and half-lives T,f for 240Pu. static dynamic a=O
Binner (MeV) 5.9 6.2
Bouter(MeV) 9.6 12.4
S 74 49.7
Tsf(yr) 3~10”~ 1.9~10‘~
Apart from the PES, another important fission quantity is the inertia
23 0.25
0.2
0.15 0.1 0.05
0
h
-0.05 -0.1 -0.15
-0.2 -0.25
1
1.2
1.4
1.6
1.8
2
C
C Figure 1. The potential energy landscape in the two-dimensional deformation space c, h for a=O. The solid line is the dynamical path and the dashed line the static path.
tensor Bq,q,lwhere qz, qJ are the deformation parameters specifying the M-dimension deformation space, that describes the inertia of the nucleus with respect to changes in the deformation. It is calculated in the cranking approximation applied t o the Skyrme-ETF+BCS states as prescribed in Ref.6. In the case of the two-dimensional deformation space studied herein there are three components of the inertia tensor B,,, Bch,B h h . The inertia tensor varies strongly with the deformation coordinates as it is much more sensitive to the internal single-particle structure of the nucleus than the potential energy. The spontaneous fission half-life T,fis given by the formula
T
sf
ln2 1 -
71.
p’
where n is the number of assaults of the nucleus on the fission barrier in unit time and P is the probability of penetration through the barrier for a given assault. The number of assaults is given by the frequency w / 2 n of the vibration in the fission degree of freedom and thus by the zero-point
24
vibration energy of the nucleus in the fission degree of freedom E z p= 0.5tiW. The probability P is calculated in the one-dimensional semi-classical (WKB) approximation
+
P = [I exp(2S(Lmi,))]-l,
(2)
where the action integral S ( L ) along a one-dimensional trajectory L in a multidimensional deformation space is
S ( L )=
1;
/
m
d
s
.
(3)
Here, V ( s ) is the potential energy, B L ( s )is the effective inertia along the trajectory L and E is the energy of the fissioning nucleus. The parameter s specifies the position of a point on the trajectory and s1, s2 are the classical turning points determined by V(s1) = V ( s 2 ) = E . The effective inertia B ( s ) along the trajectory L is given by
where Bq,q,are the components of the inertia tensor and qa, qj the deformation coordinates c, h with a=O. In a dynamical calculation, the half-lives Tsfare determined by searching for the path that would minimize the action integral (3). This method has been applied extensively to the study of fission half-lives of actinide^^,^ and superheavy element^^,^>^ with considerable success. However, in all these previous calculations the potential energy surface and inertia parameters have been obtained in the macroscopic-microscopic approach. This is the first time a dynamical calculation of fission half-lives is performed on an entirely microscopic and fully constrained potential energy surface. The minimizat,ion of the action integral (3) is performed by means of a variational calculation following the prescription of Ref.3. In this method, smooth paths deviating from the straight line connecting the end points s l , sz, are expanded in Fourier series and are used as trial trajectories. The variation of the expansion coefficients turns out t o be a rapidly converging problem with respect to the number of terms in the expansion. The end points are determined as follows: the entry point s1 is taken to be the point of minimal energy (first minimum) before the entrance into the barrier, E,, = Vmzn(c~,ho,cr= 0) E z p ,where the zero-point energy in the fission degree of freedom is taken as E z p = 0.3 MeV6. The exit point corresponds to the same potential energy but is placed beyond the exit point out of the barrier.
+
25
As a first step, the dynamical calculations are performed for purely symmetric fission, i.e. a=O. The dynamical fission path is shown in Fig. 1. The static path, obtained by the method of steepest descent, is also plotted in the same figure for comparison. It crosses the static barriers through the saddle-points whereas the dynamical path prefers to go through higher barriers. The shape of the fission barriers along the static and dynamical paths are shown in Fig. 2. The dynamical barriers heights are larger than the static paths and are located at a different elongation c. The outer barrier height in particular is larger by 2.8 MeV. This is because the dynamic fission path depends on the effective inertia, as well as on the potential energy. A smaller effective inertia along a certain path would lead to a smaller a.ction integral and life-time so the path would be preferred despite its crossing larger potentia.1-energy barriers. On the other hand, the effective inertia along the static path turns out to be quite large which explains why the respective action integral S(L,i,)=74 is large compared to the dynaniical one (Table 1). The fission half-lives obtained from both static and dynaniical symmetric path are also shown in Table 1. The former leads to a rather large half-life while the latter dynamical calculations are in better 1 0If ~ the~ asymmeagreement with the experimental half-life of ~ 1 . 6 ~ ys. try degree of freedom is included a#O then it is expected that both static and dynamic outer barrier heights will be lower and in better agreement with the observed barrier heights. 3. Neutron-Induced Fission Cross Sections Neutron-induced fission cross sections can be of importance in the r-process nucleosynthesis calculations, particularly in environments of extremely high neutron densities leading to the production of superheavy fissile nuclei. The relevant quantities in the nucleosynthesis calculations are the Maxwellianaveraged cross sections (MACS) at temperatures around 1 . 5 ~ 1 0K.~ The fission cross sections that contribute to these MACS turn out to be in the energy range of M 100 keV. It is therefore necessary to predict neutroninduced fission cross sections at the above-mentioned energies, for extremely neutron-rich nuclei extending from the stability line out towards the dripline. Neutron-induced fission cross sections for excitation energies near or above the barrier heights, are normally calculated with the statistical Hauser-Feshbach (HF) theory of compound nucleus reactions. For excitation energies below the largest of the barriers, the non-negligible subbarrier effwts are taken into account by means of the picket-fence model". Impor-
26
1
C
Figure 2. Shape of the potential-energy barriers calculated along the static and dynamical fission paths with a=O.
tant ingredients in the HF calculations are the transmission coefficients for particle/photon emission and fission, and the nuclear level densities (NLDs) a t ground-state and saddle-point deformation. The fission transmission coefficients are based on the barrier heights of a large-scale calculation using the microscopic ETFSI method'. The widths of the barriers are taken from the systematics of Ref." for even-even, odd-even and odd-A nuclei. The NLDs are obtained from microscopic statistical calculations12. The NLDs at saddle-point deformation are calculated with the same microscopic model on the basis of the single-particle level scheme determined at the saddle-point deformation with constrained Hartree-Fock-BCS calculations (see Ref.13), but without taking into account the damping of collective effects. Transition states built on top of the fission barriers are taken into account where they are known14. To obtain an estimate of the reliability of this choice of input, the results for the actinide nuclei are compared with experimental data. The results are shown in Fig. 3 for 18 actinides for which experimental neutron-induced fission cross sections exist in the energy range from 50 to 200 keV. An estimate of the mean deviation of the theoretical calculations from experiment is given by the root-mean-square A similar accuracy is found when using the barriers deviation f,,,=8.3. and NLD systematics of Ref.14.
27
Figure 3. Ratio of theoretical Maxwellian-averaged cross sections over the corresponding experimental ones at T=1.5x10g K.
4. Conclusions
Dynamical calculations of fission half-lives have been performed for 240Pu based on the symmetric potential energy surface obtained from a fully constrained microscopic approach. The impact of the effective inertia is shown to be crucial in determining the fission path and the resulting fission barriers are found to be higher than the static ones. The outer static and dynamical barrier heights are expected to decrease when the asymmetry degree of freedom is included. Global microscopic predictions of barrier heights and nuclear level densities without any fine-tuning to individual nuclei, give rise to discrepancies of the order of f,,,=8.3 in average, in the experimentally well-explored actinide region. Improvements, in particular in the NLD predictions are foreseen before performing large-scale calculations of neutron-induced cross sections and estimating the impact of neutron-induced fission on the r-process nucleosynthesis.
Acknowledgements
P.D. holds a European TMR “Marie Curie” fellowship at the ULB. M.S and S.G are FNRS Research Fellow and Associate, respectively. References 1. J.J. Cowan, F.-K. Thielemann and J.W. Truran, Phys. R e p . 208, 267 (1991).
28 2. M. Samyn and S. Goriely, in these Proceedings. 3. A. Baran, K. Pomorski, A. Lukasiak and A. Sobiczewski, Nucl. Phys. A361, 81 (1981). 4. Z. Patyk, J. Skalski, A. Sobiczewski and S. Cwiok, Nucl. Phys. A502, 591c (1989). 5. R. Smolanczuk, J. Skalski and A. Sobiczewski, Phys. Rev. C52, 1871 (1995). 6. M. Brack, J. Damgaard, A.S. Jensen, H.C. Pauli, V.M. Strutinsky and C.Y. Wong, Rev. Mod. Phys 44, 320 (1972). 7 . A. Mamdouh, J.M. Pearson, M. Rayet and F. Tondeur, Nucl. Phys. A644, 389 (1998). 8. C.M. Reiss, PhD Thesis, Friedrich-Alexander-UniversitiitErlangen-Nirnberg, 2000. 9. T. Ledeberger and H.-C. Pauli, Nucl. Phys. A207,1 (1973). 10. J.E. Lynn and B.B. Back, J.Phys. A7,395 (1974). 11. S. Bjornholm and J.E. Lynn, Rev. Mod. Phys. 5 2 , 725 (1980). 12. P. Demetriou and S. Goriely, Nucl. Phys. 695,95 (2001). 13. Reference Input Parameter Library RIPLZ (2003) IAEA-TecDoc in press. (also available at www-nds.iaea.org) 14. S. Maslov, in Reference Input Parameter Library RIPLl (2001). (also available at www-nds.iaea.org)
NEUTRON-INDUCED NUCLEOSYNTHESIS IN THE R-PROCESS
B. PFEIFFER AND K.-L. KRATZ Znstitut fur Kernchemie, Universitat Mainz Fritz-Strassmann- Weg 2 0-55128 Mainz, Germany E-mail:Bernd.
[email protected] The astrophysical r-process is responsible for the synthesis of half the nuclear species beyond iron, including the heaviest elements in nature like Th, U and Pu. These long-lived elements are applied as cosmochronometers in determining the age of the Universe. Their relative abundances are strongly dependent on the processes terminating the r-process: spontaneous, neutron-induced and @delayed fission.
1. Introduction Approximately half of the nuclear species in nature beyond iron are produced via neutron captures on very short time scales in neutron-rich environments, i.e. the so-called r-process. Only under such conditions is it possible that highly unstable nuclei near the neutron dripline are produced, leading after decay back to stability also to the formation of the heaviest elements in nature like Th, U and Pu (see Fig. 1). But what terminates the r-process? Already B2FH1 postulated that the r-process would be terminated by fission. Indications to the location of the upper end of the r-process were obtained from the first large-scale thermonuclear experiment ("Mike") in 19522 and confirmed by the Plowshare programs underground explosions with maximized fluence of neutrons t o selected actinide targets3. In the later experiments, the neutron fluence exceeded that in Mike, but it was concluded that the yields of all the transuranium isotopes were significantly depleted by neutron-induced fission. It is notable that in none of these experiments was a measurable yield determined beyond A=257, which was recovered as a Fermium isotope. Despite its importance, the exact stellar site where the r-process occurs is still a mystery(see, e.g.*l5). However, two astrophysical settings are sug-
29
30
Figure 1. Schematic illustration of the r-process path (dark line on the neutron-rich side of 0-stability) and observed r-abundances (insert). Sharp peaks occur near A z8 0 , 130, and 195, where the r-process path crosses the N=50,82, and 126 magic neutron numbers. The chart of neutron-rich nuclides is shaded according to measured and predicted 0decay half-lives, Tl12.Grey scales for T1lzranges are explained in the legend bar. (From Ref. ' I )
gested most frequently, (i) type I1 supernovae (SN 11) with postulated highentropy ejecta (see, e.g.6), and (ii) neutron-star mergers or similar events (like axial jets in SN explosions) which eject matter with low entropies (see, e.g.'>'). The key of its understanding will probably only be obtained from a close interaction between astronomy, cosmochemistry, nuclear physics and astrophysical modelling of explosive scenarios. 2. Classical r-process model
As the site of the r-process has not been identified with certainty yet, we use the "classical r-process model", a largely model-independent, parametrized which has been used extensively before in r-process studies approach lo. The calculations are performed within the waiting-point approximation assuming complete (n,-y)w(T,n) equilibrium as shown e.g. in detail by Freiburghaus et a1.6. The abundance distribution within an isotopic chain is given by the Saha equation and is entirely determined by the neutron separation energies S, for a given temperature Tg and neutron density n,'. The nuclear-physics input needed for the classical r-process model com'i6
31
prises nuclear masses, &decay rates Tl/z and branchings for ,&delayed neutron emission P,. For the vast majority of these data no experimental information is available; hence, one has to rely mainly on theoretical predictions. The theoretical TI/z and P, values are based on QRPA calculations of the Gamow-Teller (GT) strength function for allowed transitions" and an estimate for the first-forbidden strength from the Gross Theory". Nuclear masses to calculate S, values have been taken from the ETFSI-Q model13, which takes into account the possible "quenching" of neutron shell gaps far from stability, initially predicted by Hartree-Fock Bogolyubov (HFB) calculati~nsl~. Applying these input data, a single r-process component is calculated assuming irradiation of an Fe seed with constant neutron density and temperature for a time 7. The total r-abundances are then calculated as a superposition of a multitude of components with neutron densities in the range 1020
3. Cosmochronometers Historically, nuclear chronometers have played an important role in the determination of the ages of our solar system and our Milky Way Galaxy. Particularly useful in this regard are the long-lived actinide radionuclides 232Th and 238U,which are exclusive products of the r-process. Early attempts of age dating were closely tied to theoretical models of star formation and Galactic chemical evolution. The boundary conditions for these studies were, of course, the primordial abundances of 232Th and 238U in solar-system matter. Spectroscopic studies of ultra-metall-poor (UMP) halo stars have, over the past decade, made possible a quite different approach: age determinations for individual field-halo and globular-cluster stars from nuclear chronometers. Since such stars were formed in the very earliest epoch of star formation and nucleosynthesis in our Galaxy, their ages are expected to provide a measure of the age of the Galaxy itself. And in contrast to the earlier attempts described above, one avoids the uncertainties of chemical
32
E lo2
0 0
rs U c 0
10'
T,=1.35;
n,=102'
- 10''
loo
I
aL
lo-'
tj
-w
%
10-2
v)
al
E
Q
c
2 a
60 80 100 120 140 160 180200220240260280300 Mass number A
ETFSI-Q CS 22892-052
Figure 2. Upper part: Fit to solar r-process isotopic abundances obtained as superposition of 16 equidistant Sn(n,,Ts) components. This result also shows a good fit to the r-process Pb and Bi contributions after summing the a-decay chains of heavier nuclei. Lower part: Observed neutron-capture element abundances in CS2298-052 (squares) compared to scaled N,,a values (dots) and our calculated r-abundances (full line). The upper limit on the U abundance is denoted by an arrow.
evolution as only one or a few nucleosynthesis events contributed to the interstellar matter from which the UMP stars formed. The approach has been to use the abundance of T h in the star relative to the abundance of the stable r-process (only) element Eu as the appropriate chronometer. The
33
original Th and Eu yields are obtained converting the isotopic abundances (see upper part of Fig. 2) to elemental ones. After scaling to the lower metallicities of the halo stars, the calculated r-yields are then compared to the observed yields (see lower part of Fig. 2). The observation of U and the determination of its abundance in several UMP stars now make it possible to use the U/Th pair as a chronometer. U/Th ages are in agreement with the Th/Eu ages as well as with other, independent age determinations for the Universe (see Ref. l6 and references therein).
4. Influence of fission on the r-process The high entropy supernova environments discussed so far have problems to reach the heaviest nuclei, thus fission is less important. Contrary, in very high neutron-density environments such as ejected neutron-star matter7 or axial jets from core collapse events with rotation ’, fission becomes a very important process responsible not only for the abundances of transuranium isotopes, but also influencing the majority of heavy nuclei via a cyclic sequence of neutron captures, fission of the heaviest nuclei and subsequent neutron capture on the fission products. Fission then has to be considered consistently in nucleosynthesis calculations, including all the aspects of fission - neutron-induced, P-delayed and spontaneous fission. For the formation of both the heaviest and also the light r-process nuclei and the termination of the r-process, the relative importance of each fission mode has to be determined. Spontaneous fission plays a secondary role, as fission via excitated states fed in neutron capture and P-decay is energetically favorable over ground-state decay. Extended calculations of P-delayed fission back in the 1980’s based on fission barrier calculations ofl7 had revealed that fission rates could reach 100% and may have a strong influence on the abundances of the transuanium nuclides feeding into the cosmochronornetersl8. Due to computational restrictions, the sophistication of the theoretical descriptions of nuclear masses and fission barriers was quite unsatisfactory until recently. The latest mass tables as FRDM l1 and ETFSIl’ cannot only reproduce measured masses satisfactorily but allow also reliable extrapolations to far unstable regions. Fast progress in computational power now allows to calculate nuclear fission modes and fragment mass asymmetries based on multi-dimensional potential-energy surfaces that guides the nuclear shape evolution up to the configuration of separated fission fragments
34
for all nuclei relevant to r-process nucleosynthesis (see, e.g."). Based on new mass models, fission barriers have been calculated recently by Mamdouh et al. 21 and Myers and Swiatecki22. These new values differ considerably from the older results 17; in general, the new barriers are predicted at higher energies. For the fission cycling time scale it is important to know whether fission in the r-process path begins at A = 230, 250 or 300, strongly depending on the barrier heigths. In addition, an r-process dominated by fission cycling is depleted in abundances below the A = 130 peak and fission yields for these lighter nuclei become highly imp~rtant~~>~~. It had been discussed why experimental constraints indicate that fission is not so important for ratios of chronometer nuclei like the T h and U isotopes25. Following the first detection of Th and U in an UMP star26, we have started a reevaluation of the influence of various nuclear physics input data on the predicted r-process production ratios of T h and U27. The branchings for neutron-capture-induced fission and @delayed fission have been estimated based on the fission barriers of 21 applying the rather simple method of Kodama and Takahashi28. It was found that neutron-induced fission does not influence the production of Th and U. However, ,&delayed fission is significant and might reduce the final U abundance by up to 10% and the final T h abundance by up to 25%27. This can change Th/X ages by up t o 4.6Gyr, U/X ages by up to 0.7 Gyr, and U/Th ages by up to 1 Gyr. This is in contrast to the previous study mentioned above suggesting that P-delayed fission can be neglected completely25. The influence of the competition between neutron-induced and ,Bdelayed fission modes on r-process abundances has been studied recently by Panov and Thielemann 29 based on the new sets of fisson barriers of21,22 (For the latest results, see3I). Freiburghaus et a1.6 had neglected fission modes in their network calculations. In a new parameter study based on this network fission is taken into account e ~ p l i c i t e l y ~ ~ .
5. Contributions related to the r-process
Recent results on fission barriers and fission life-times are presented at this conference. Beta-delayed fission rates are calculated with two sets of fission barrier predictions and ,&strength functions based on the finite range droplet model in Ref. 31. Fission barriers calculated using the constrained Skyrme-Hartree-Fock method (SHF) in a 3-dimensional deformation space
35
are compared to experimental ones in Ref. 32. Fission life-times and crosssections for astrophysical applications calculated in the frame of the SHF are compared to existing data and the sensitivity to input parameters such as fission barriers is discussed in Ref. 33.
References 1. E.M. Burbidge et al., Rev. Mod. Phys. 29, 547 (1957). 2. H. Diamond et al., Phys. Rev. 119, 2000 (1960). 3. G.I. Bell, Phys. Rev. 158, 1127 (1967). 4. G. Wallerstein et al., Rev. Mod. Phys. 69, 995 (1997). 5. D. Argast et al., A €4 A , in print; [astro-ph/0309237] 6. C. Freiburghaus et al., Ap. J. 516, 381 (1999). 7. S.K. .Rosswog et al., A €4 A 360, 171 (2000). 8. A.G.W. Cameron, Ap. J. 587, 327 (2003). 9. K.-L. Kratz et al., Ap. J. 403, 216 (1993). 10. B. Pfeiffer et al.,Nucl. Phys. A693, 282 (2001). 11. P. Moller et al., ADNDT66, 131 (1997). 12. P. Moller et al., Phys. Rev. C67, 055802 (2003). 13. J.M. Pearson et al., Phys. Lett. B387, 455 (1996). 14. J. Dobaczewski et al., Phys. Scrip. T56, 15 (1995). 15. J.J. Cowan et al., Ap. J . 521, 194 (1999). 16. C. Sneden et al., Ap. J . 591, 936 (2003). 17. W.M. Howard and P. Moller, ADNDT 25, 219 (1980). 18. F.-K. Thielemann et al., 2. Phys. A309, 301 (1983). 19. Y. Aboussir et al., ADNDT 61, 17 (1995). 20. P. Moller et al., Nature. 409, 785 (2001). 21. A. Mamdouh et al., Nucl. Phys. A679, 337 (2001). 22. W.D. Myers and W.J. Swiatecki, Phys. Rev. C60, 014606-1 (1999). 23. C. Freiburghaus et al., Ap. J. 525, L121 (1999). 24. I. Panov et al., Nucl. Phys A688, 587 (2001). 25. J.J. Cowan et al., Phsy. Rep. 208, 267 (1991). 26. R. Cayrel et al., Nature 409, 691 (2001). 27. H. Schatz et al., A p . J. 579, 626 (2002). 28. T. Kodama and K.Takahashi, Nucl. Phys. A239, 489 (1975). 29. I.V. Panov and F.-K. Thielemann, Nucl. Phys. A718, 647 (2003). 30. K. Farouqi, Ph.D. thesis, Mainz, in preparation 31. I.V. Panov et al., this conference 32. M. Samyn and S. Goriely, this conference 33. P. Demetriou et al., this conference
This page intentionally left blank
Chapter 2
Fission Fragment Characteristics
This page intentionally left blank
MICROSCOPIC AND DYNAMICAL STUDY OF FRAGMENT MASS DISTRIBUTIONS IN 238UFISSION
H. G O U T T E , P. CASOLI AND J. F. B E R G E R Commissariat ci I'Energie Atomique, Dkpartement de Physique Thkorique e t Appliquke, Service de Physique Nucle'aire, B. P. 12, 91680 Bruykres-Ie-Chdtel, France E-mail:
[email protected] A time dependent Generator Coordinate Method based on self-consistent intrinsic nuclear wave-function has been developed in order to derive fragment mass distribution in a completely microscopic way. Calculations are performed in the twodimensional space generated by the quadrupole and octupole collective variables. The basis set of wave functions is calculated using the Hartree-Fock-Bogoliubov method and the Gogny force. First calculations with selected initial states indicate that the main features of experimental mass distributions in 238U are reproduced. It appears that the peak-to-valley ratio significantly depends on the parity of the initial state and that dynamical effects are responsible for the spreading of the peak of the distributions.
1. Introduction In this work, a microscopic and time dependent approach is used to describe low energy fission dynamics in 238U. Calculations proceed in two steps : first the determination of both the potential energy surface and the inertia of the fissioning system from the first well to the exit points as functions of elongation and asymmetry degrees of freedom and second, the dynamical treatment of fission using the Time Dependent Generator Coordinate Method (TDGCM). This method was developped and validated in 1984 for the study of the most probable fission of 240Pu . It is generalized here to describe fragment mass distributions in fission. Compared with changes in the choice of collective coordinates but also in numerrefs ical methods have been made, because of the large domain of the studied deformations. In this work, static and dynamical mass distributions are first analyzed. It appears that the dynamics of the process is responsible for the large spread of mass distributions. Then the effect on the fragment
'
'i2,
39
40
mass distributions of the nodal structure of the initial state is analyzed. Calculations indicate that the peak-to-valley ratio is sensitive to the parity of the initial state.
2. Formalism In low energy fission the adiabatic hypothesis appears to be justified 3 , and collective and intrinsic degrees of freedom can be decoupled. Furthermore, assuming that the coherent motion of the system can be described by a few collective parameters, the dynamical evolution of the system is solved in the present work in a restricted space, generated by the quadrupole ( 0 2 0 ) and octupole ( 0 3 0 ) moments. These moments govern the overall deformation and the left-right asymmetry, respectively. The collective time-dependent states are defined according to the GCM theory as : *(Zl,z2, ...,zA,t)
where
=
J
d q 2 0 d q 3 0 f ( q 2 O , q 3 0 , t ) d ( ~ l , ~.Z. .,, z A , q Z O r q 3 0 ) ,
t ) are weight functions.
(1)
The deformed states the fissile system are obtained by means of the constrained Hartree-Fock-Bogoliubov (HFB) procedure using the D l S Gogny force '. Calculations are performed from the first well to the exit points for all asymmetries. The propagation of a given initial state is made by use of the time dependent Generator Coordinate Method with Gaussian Overlap Approximation. This leads to a Schrodinger-type equation : f(qzo,q30,
@("I, 1 2 ,
...,I A , q2orq3o) of
where g(q20, q 3 0 , t ) is defined as:
with
41
with Bij(q~o,q30) the inverse of the tensor of mass, V ( q 2 0 , 4 3 0 ) the HFB potential and ZPEij(q20, 430) the vibrational zerepoint energy corrections. All these quantities are determined from the HFB calculations. We notice that this collective hamiltonian has the same structure as the hamiltonians used in phenomenological approaches. However, in this work, the form and parameters of the collective hamiltonian follow from the time dependent GCM in a consistent manner. Eq. (2) is solved by discretization of q 2 0 and 430 on a mesh and an absorbing extra-area has been introduced to avoid reflexions on the edges of the box. The time evolution is determined using the unitary Crank-Nicholson for a given time step At : approach 516
As initial wave functions g(qZO,q30,0),quasi-stationnary vibrational states 420,430 first well - have been used Only the states lying between the top of the barrier and 2 MeV above have been considered in the present work.
- eigenstates of the modified two-dimensional .1'
3. Static results
3.1. Potential energy surface and pairing energy On figure 1 is displayed the HFB potential energy as a function of the quadrupole and octupole degrees of freedom in 238U.
Figure 1. HFB potential energy surface as a function of qzo and
q30
deformations in
238u.
As expected in this actinide nucleus, two valleys appear after the second
42
well. For well-elongated shapes, these valleys are separated by a ridge and lead either to symmetric or to the most probable asymmetric fragmentations. By working in the restricted space generated by q20 and 430 collective variables, we suppose implicitly that only one mode (the elongation) is responsible for fission for each asymmetry. There are some indications that it is not the case in all nuclei, as for instance in 258Fm,259-260Md ,2 5 8 and z60[104]where bimodal fission has been observed '. Nevertheless this hypothesis seems to be reasonnable in 238U,even if the existence of many fission modes as functions of nuclear elongation is still an open problem. On figure 2 is displayed the pairing energy Epair= ;Tr(An), with A and K the pairing field and the pairing tensor, respectively. This correlation energy characterizes the amount of superfluidity of the collective flow. We clearly see that pairing is the lowest in the asymetric valley (Epair m 6 MeV) and much larger in the symmetric one (Epoir > 15 MeV). As a consequence, collective inertia which is very sensitive to pairing correlations, is found to be larger in the asymmetric valley than in the symmetric one - up to a factor of two for a given elongation. This is an a posteriori justification of the fact that pairing correlations have to be introduced in dynamical studies of fission, which is done in a fully consistent way in the present HFB calculations using the finite-range effective Gogny force l o .
0
100
300
200 q20
400
500
(b)
Figure 2. Pairing energy as a function of qzo along the asymmetric (continuous curve) and the symmetric (dashed curve) fission paths in 238U.
~ ~
43
3.2. Total Kinetic Energy distribution
Microscopic properties of the almost separated fragments, such as the masses ( A H , A L )and the charges ( Z H , Z L )of the heavy and light fragments and the distance d between their centers of charge are calculated at the exit points for all octupole deformations. Many observables of fission fragment distributions can then be deduced. In this contribution we only display the total kinetic energy distribution. More complete results will be found in a forthcoming publication. The total kinetic energy of the fragments can be approximately estimated as the Coulomb repulsive interaction TII'E(AH)= with d the distance between the centers of charge of the fragments at scission. Theoretical values are shown on figure 3 as functions of AH the heavy fragment mass and compared to experimental data for 1.7 MeV neutron induced fission on 238U ll. We see that the general trend is reproduced, with a dip at AH = 119 and a peak for AH = 134. However the theoretical peak-to-valley ratio is over-estimated. This discrepancy can be explained by uncertainties in the precise values of the distance d or/and by the prescission kinetic energy not taken into account in the present estimate.
z$z:7a,
2ooc
120
128
136
144
152
160
Mass fragment Figure 3. Theoretical TKE distribution of 238Ufission fragments (continuous curve) compared to experimental data (dashed curve).
44
4. Dynamical results
4.1. Dynamical effects On figure 4 fragment mass distributions obtained from a static (dotted curve) and a dynamical calculation (continuous curve) are displayed and compared to evaluated data from the Wahl statistic for 4 MeV neutron induced fission on 237U (dashed curve) 1 2 . The static mass distribution has been obtained by solving a one-dimensional collective hamiltonian in the octupole variable at elongations following the scission line. The probability of having a given mass fragmentation is then given by the square of the ground-state wave function. This is similar to the fragmentation model of 13, where mass asymmetry vibrations were studied in the final stage of the fission process. Let us note that the elongation has not been fixed in the present work : it corresponds to the elongation of the exit points for each asymmetry. We clearly see that maxima have the same location around '10'
l0O0l
Mass Fragment Figure 4. Mass fragment distributions obtained from a dynamical calculation (continuous curve) and a static one (dotted curve) compared to the Wahl evaluation (dashed curve)
134 for the heavy fragment in both calculations. It means that the most probable fragmentation is just due to properties of the potential energy surface such as the well-known shell effects. On the contrary, the width of the dynamical distribution is found to be twice the static one. This is an indication that the spreading of the peaks is mostly due to dynamical effects. It appears that the dynamical mass distribution is in qualitative
45
agreement with experimental data, the peak being nevertheless too narrow and shifted toward symmetric fission.
4.2. Influence of the initial state on the mass distribution
The "dynamical" distribution shown in figure 4 has been obtained taking as an initial state a negative parity state located 2 MeV above the barrier. The effect of the initial state on the theoretical curves is analyzed in figure 5, where fragment mass distributions obtained for positive parity (dotted curve) and negative parity (dashed curve) initial states are plotted and compared with evaluated data (continuous curve). We see that the main difference between the theoretical results corresponds t o peakto-valley ratios varying between values of 10 for the positive parity initial state and infinity for negative one. Let us note that all positive initial parity states (resp. negative) in the interval of energy [ B f , B f+2 MeV] give results very similar to the typical dotted (resp. dashed) curve. Linear combinations of positive and negative parity basis states could be considered leading t o peak-to-valley ratios in between the two above values. An optimization of the initial state could even be considered in the future to get informations on the structure of this initial state such as the relative components of negative and positive states.
L 176
Mass Fragment Figure 5. Fragment maas distributions obtained for different initial states of the fissioning nucleus compared to evaluated data.
46
5. Conclusion
We have presented fragment mass and kinetic energy distributions for 238U fission calculated in the framework of a microscopic time dependent Generator Coordinate approach. Remarkably enough, an overall good agreement with experimental data is obtained. Results show that the large spread of mass yields cannot be reproduced without including the whole dynamics from the first well to scission. Also, the parity of the initial state chosen has been found to strongly influence symmetric fragmentation yields. Only part of the many results that can be derived from our microscopic approach has been mentioned in the present contribution ; details and further analyses will be developed in a forthcoming publication.
Acknowledgments
H . Goutte would like to thank N. Carjan and A . Rizea for useful advice concerning numerical methods and F. Goennenwein, D. Gogny and K.-H. Schmidt for enlightening discussions. References 1. J.-F. Berger et al., Nucl. Phys. A428 (1984) 23c. 2 . J.F. Berger M. Girod and D. Gogny, Comp. Phys. Comm. 63 (1991) 365. 3. J. Moreau and K. Heyde in "The nuclear fission process" C. Wagemans CRC Press (1991) 238. 4. J. Libert et al., Phys. Rev. C60 (1999) 054301. 5. W. H. Press et al., Numerical recipes : the art of scientific computing, Cambridge, Cambridge University Press (1986). 6. N. Carjan, M. Rizea and D. Strottman, Private communication (2003). 7. O.Serot, N.Carjan and D. Strottman, Nucl. Phys. A 569 (1994) 562. 8. P. Talou, N. Carjan and D. Strottman, Nucl. Phys. A647 (1999) 21. 9. E.K. Hulet et al., Phys. Rev. Lett. 56 (1986) 313. E.K. Hulet et al.,Phys. Rev. C 40 (1989) 770. 10. J. Decharge and D. Gogny, Phys. Rev. C21 (1980) 1568. 11. F. Vives et al., Nucl. Phys. A662 (2000) 63. 12. A. C. Wahl, Systematics of fission-product yields, LA-13928, Los Alamos. National Laboratory, (2002). 13. P.Lichtner et al. Phys. Lett. B45 (1973) 175.
PREDICTION OF FISSION MASS YIELD DISTRIBUTIONS BASED ON CROSS-SECTION EVALUATIONS F.-J. HAMBSCH AND S. OBERSTEDT EC-JRC-IRMM Retieseweg, B-2440 Geel, Belgium E-mail:
[email protected] G. VLADUCA AND A. TUDORA Bucharest University. Faculty of Physics, R-76900 Bucharest, Romania E-mail:
[email protected] The statistical model for fission cross-section evaluation is extended by the concept of multi-modality of the fission process. The three most dominant fission modes, the two asymmetric standard I (S 1) and standard I1 (S2) modes and the symmetric superlong (SL) mode are taken into account. Deconvoluted fission cross-sections for S1, S2 and SL modes for "5~238U(n, f) and 237Np(n,f), based on experimental branching ratios, were calculated for the first time in the incident neutron energy range from 0.01 to 5.5 MeV. Good agreement was found with the experimental fission cross-section data. Branching ratios were deduced for the different modes over the whole incident neutron energy region. Fission fragment mass yield distributions have been calculated at incident neutron energies, where no experimental data exist.
1. Introduction The concept of multi-modality in nuclear fission has been theoretically introduced in the eighties.' Here the Multi-Modal Random Neck-Rupture model (Mh4-RNR), has proven to be a good approximation to the fission process. This model pioneered fission research by giving also quantitative predictions for the typical observables as mean mass and mean total kinetic energy (TKE) of the fission fragments. The idea of multi-modal fission dates back to as early as 195 1. Bi-modal fission was used to interpret the mass distribution of the fissioning compound nucleus 233Th? This assumption worked in the region of light a ~ t i n i d e . ~ However, for heavier actinides, like e.g. 236U,the bi-modal approach turned out to be too simple. The MM-RNR model not limiting the number of possible fission modes, however, could explain the characteristic fission fragment properties over the whole actinide range from '13At to 258Fmquite successfully. The major part in this actinide mass range can be covered assuming three 47
48
dominant fission modes, the asymmetric standard I (Sl) and standard I1 (S2) modes and the symmetric superlong (SL) mode. Based on potential energy calculations, which have been performed for 238Np,4 239U,5and 252Cf,6it was found that the bifurcation point of the asymmetric fission modes lies in the second minimum of the double humped fission barrier. As a consequence separated outer barriers for each of the modes exist. For the symmetric superlong mode, this was already established since it is a well known experimental fact that the yield of symmetric masses is increasing with increasing incident neutron energy. In an effort to improve the fission cross-section evaluation, the multimodality of the fission process was included into the statistical model code. Based on experimental fission mode branching ratios measured at IJXMM, in the neutron energy range below the second chance fission threshold, and the ENDF/B-VI fission cross-section: the mode separated fission cross-sections are obtained for the reactions n + 235U,n + 238Uand n + 237Np.In these nuclei, compound nuclear fission is dominated by the above mentioned three fission modes. In this energy range the neutron interaction with the target nucleus takes place through direct and compound nuclear mechanisms. For these deformed heavy nuclei, the elastic channel is strongly coupled with the other possible channels in the process and the direct mechanism has to be treated with the coupled channel method. For the compound nucleus mechanism a statistical treatment is used for fission, neutron elastic and inelastic scattering and radiative capture cross-section calculations. For the direct mechanism the coupled channel method (ECIS-95 code ') is used and for the compound nucleus mechanism the STATIS code? The former provides the total cross-section, the direct contributions of the neutron elastic and inelastic cross-sections of the rotational levels coupled to the ground state and the neutron transmission coefficients T,,lJ needed in the compound nucleus calculations. The latter provides the fission cross-section, the radiative capture crosssection and the compound nuclear contributions of the neutron elastic and inelastic cross-sections of the rotational levels coupled to the ground-state as well as for the other inelastic levels (discrete and continuum) not coupled to the ground-state. The mode separated fission cross-section was described with the statistical model code STATIS"." taking into account the contribution of each fission
49
1 nabsorption .,/";t\"2' I -i \ I 1/ ': . C
\ -
J
I /
W
I
direct fission \
\
:1 :. Is1 I
indikct fission
isomeric fission
I
L
Deformation (4) Figure 1. Qualitative representation of the double humped fission barrier and the possible fission processes.
mode in competition with the other open channels. The inner barriers and the isomeric wells were taken the same for all modes, and the outer fission barrier for each fission mode was taken to be different (see Fig. 1). For each mode the sub-barrier effects, the direct, indirect and isomeric fission cross-sections are taken into account. Based on FUPL12 (Shell Correction Method calculations) the shape of 235U at the inner barrier, A, has axial and mass symmetry like at equilibrium deformation. At the outer barrier, B, in the case of the S1 and S2 modes mass asymmetry and axial symmetry is taken into account. The nuclear shape at the outer barrier of the SL mode is considered to have mass symmetry and axial asymmetry. In contrast to 235Ufor the nuclei 237Npand 238U,the shape of the nucleus at the inner barrier is mass symmetric and axial asymmetric. The outer barrier shape, however, is as mentioned above.
2. The statistical model For the neutron induced reactions of actinides in the incident energy range where only one CN is formed, the competitive processes are elastic (n) and inelastic (n;) scattering, radiative capture (y) and fission (f). In the frame of the modified statistical model, the CN formation cross-section and the decay of the CN are expressed by the following relations":
50
1044
10'
10.'
10.
. . .
10'
1
. , ..,
. . . . . ...,
I 0''
. .
, ,
I
10'
E (MeV)
E(MeV)
Figure 2. Total fission cross-section in comparison with mode separated fission cross-sections for 23SU(n,fl.
Figure 3. Total fission cross-section in comparison with mode separated fission cross-sections for 237Np(n,f).
. .
a'=n,n,,y, f,;
m = Sl,S2,SL
In these relations E is the incident neutron energy in the laboratory system (LS), J and II are the spin and parity of the compound nucleus. Vn,iJare the generalised neutron transmission coefficients and Pa'(E, Jn) is the CN decay probability for the exit channel a'. Details about the calculation of these quantities can be found in refs. 103L1.
3.
Results and discussions
For the studied reactions, the calculations are done in the incident energy range between 0.01 MeV and 5.5 MeV, where only the first fission chance is involved. The calculated fission cross-sections for the S1, S2 and SL modes and the total fission cross-section in comparison with the "experimental" modal crosssections (represented by different symbols) and available experimental data from EXFORI3 (open circles) are given in Figs. 2, 3 for 235Uand 237Np, respectively. Two observations can be made. First, concerning 23SU(n,f) the dataset named IRMM in Fig. 2 where the full two-dimensional Y(A, TKE) distribution has been used to deduced the branching ratios can be very well described by the statistical model (dotted lines in Fig. 2). For the data of Ref.I4, however, the agreement between the experimental modal cross-section and the calculated ones (dashed lines) is rather poor,
51
especially at incident neutron energies above 2 MeV. We trace this back to the fact that the branching ratios in ref.'4 were deduced from the mass
4 1a'
. . .
.....,
. . .
10.'
......
. .
.
.I
10'
E (MeV)
Figure 4. Fission mode branching ratios for 2'7Np(n, f )
distribution only and not taking into account the full information contained in the measured Y(A, TIE)-distribution. Again, a proof that it is important to use the full Y (A, TKE)-distribution for a reliable deduction of the branching ratios. Second, for threshold reactions like 237Npand 238U,to get reliable barrier parameters, it is very important that experimental information is available in the threshold region. Although some discrepancies are observed for the S1 mode, especially in the threshold region (0.6-1.3 MeV incident neutron energy, see Fig. 3), the overall agreement is convincingly good also for u7Np(n, f). Consequently, we assume that the calculated branching ratios in the entire incident energy range studied are good, too. The branching ratios for 237Np(n,f) as calculated with the
A,
Figure 5. Calculated mass-distribution based on the branching ratios deduced from Fig. 2 compared to experimental data for '"U(n, f) at thermal energy.
4 Figure 6. Calculated mass-distribution based on the branching ratios deduced from Fig. 2 compared to experimental data for 235U(n,f) at 5.5 MeV.
52
model and their comparison to the experimentally deduced branching ratios are given in Fig. 4. The deduced branching ratios in conjunction with the modal fission fragment properties permit to calculate the mass yield distributions convincingly well (see Figs. 5, 6 for thermal and 5.5 MeV incident neutron energy). However, concerning the behavior of the branching ratio of the SL mode, some caution is appropriate. Since the contribution of the SL mode to the total mass distribution is very small (only a few YOat maximum), the dependence as a function of incident neutron energy is very important. Since experimental investigations in the threshold region are very difficult, due to the low crosssection. Slight changes in the branching ratio of SL could have a large impact on the prediction of the energy dependent behavior. For the moment, since we do not know better, we remark the important contribution of the SL mode in the sub-barrier energy region for 237Np(n,f ) at incident neutron energy En< 0.02 MeV, where it becomes even dominant. For En < 0.1 MeV the contribution of the S1 and S2 modes are practically the same, and the SI mode dominates in the energy range 0.1 < En < 0.4 MeV. This can lead to hitherto unexpected fission fragment mass distributions in this energy range. The results for the modal fission cross-section for 238U(n, 0 are also remarkable (see Figs. 7, 8). First, this isotope has a very small sub-barrier crosssection of only b, which means that the isomeric contribution to the crosssection becomes important (actually amounts to about half of the cross-section in the sub-threshold region '). The calculations are, hence, very sensitive to the barrier parameters. Second, the cross-section shows structure at the fission 1001
.
,
.
, . , .
, . , . ,
,
E(MeV)
Figure 7 Total and mode separated fission crosssection for 23SU(n, f) together with the corresponding calculated mode separated fission cross-sections.
Figure 8. Calculated and experimental branching ratios for 238U(n,f).
53
threshold related to the existence of vibrational resonances at incident energies of about 0.9 MeV and 1.2 MeV. Around the second vibrational resonance at about En = 1.2 MeV, already very strong fluctuations in the fission fragment properties like mean TKE and angular distribution have been ~ b s e r v e d ' ~ - ' ~ . However, the observed fluctuations in the fission fragment branching ratios from ref." are much too strong to be parameterised by the model. It seems also, that the maximum of the observed fluctuations lies around En = 1.25 MeV, whereas the structure in the cross-section is more towards En = I .2 MeV. More experimental investigations around this vibrational resonance and the one at En = 0.9 MeV, where no experimental data exist today are necessary to verify the theoretical predictions. This is planned at IRMM for the coming years. The consequence of the drastic change on the mass distribution is obvious. In Figs. 9 and 10 two examples of predicted mass distributions are given. In Fig. 9 the mass distribution for "'Np at En = 0.4 MeV is plotted, showing a peak yield towards the position of the S1-mode, since the calculations predict that this mode is dominant at this incident energy (see Fig. 4). This should also have a consequence on the mean TKE, since the S1-mode has a more compact shape and hence a higher TKE. A similar conclusion can be drawn for 238U.Also here it is expected that the strength of the S1-mode is increasing for incident neutron energies smaller than 1.3 MeV. A verification should be in reach for state-ofthe-art experiments.
10
Fragmentmass
Figure 9. Predicted mass distribution for 237Np(n,f)at E ~ 0 . MeV. 4
4.
80
so
100
110
12n
130
i4n
150
160
170
A
Figure 10. Predicted mass distribution for '"U(n,f) at h 4 . 9 MeV.
Conclusions
For the first time fission mode deconvoluted fission cross-sections, based on branching ratios measured at IRMM, were calculated for incident neutron energies En = 0.01 to 5.5 MeV. For three different nuclei, 23s,238U and 237Np good agreement with experimental fission cross-section data has been achieved.
54
Reasonable values for the outer barrier heights and the corresponding curvatures of each mode are obtained. The possibility to calculate fission mass yield distributions at hitherto unmeasured neutron energies is supported by the excellent reproduction of mass yield distributions at measured neutron energies. References
U. Brosa, S. Grossmann, A. Muller, Phys. Rep. 197 167 (1990). A. Turkevich and J. B. Niday, Phys. Rev. 84 52 (1951). H. C. Britt, M. E. Wegner and J. C. Gursky, Phys. Rev. 129 2239 (1963). P. Siegler, F. -J. Hambsch, S. Oberstedt and J.P. Theobald, Nucl. Phys. A594 45 (1995). 5. S. Oberstedt, F.-J. Hambsch, F. Vivts, Nucl. Phys. A644 289 (1998). 6. F.-J. Hambsch, S. Oberstedt, J. Van Aarle, Proceedings of the International Conference on Nuclear Data for Science and Technology, May 19-24,1997, Trieste, Italy, Volume 59, Part 11, 1239. 7. ENDFB-VI; ZA92235,ZA92238,ZA93237, MF=3. 8. J. Raynal, 1994, Notes on ECIS94, CEA-N-2772. J. Raynal, private communication (1995). 9. G. Vladuca, M. Sin, C.C. Negoita, Annals of Nuclear EnergV 27 995 (2000). 10. G. Vladuca, A. Tudora, F.-J. Hambsch, S . Oberstedt, Nucl. Phys. A707 32 (2002). 11. G. Vladuca, A. Tudora, F. -J. Hambsch, S. Oberstedt, 1. Ruskov, Nucl. Phys. A720 274 (2003). 12. Reference Input Parameters Library RIPL Segment V.2 Fission level densities, recommended file (Maslov V.M.), 1998. 13. EXFOR Nuclear Data Library (2000), nucleus ZA93237, ZA93235, quantities CS, reactions (n,tot) (n,f) and (n,g). 14. Ch. Straede, C. Budtz-Jsrgensen, H.-H. Knitter, Nucl. Phys. A462 85 (1987). 15. F. Vivts, F. -J. Hambsch, H. Bax, S. Oberstedt, Nucl. Phys. A662 63 (2000). 16. D. L. Shpak, Sov. J. Nucl. Phys. 50 574 (1989). 17. A. A. Goverdovski, Lecture Notes at Workshop on Nuclear Reaction Data and Nuclear Reactors: Physics, Design and Safety, 25.2-28.3.2002, Abdus Salam Int. Centre for Theoretical Physics, Trieste Italy.
1. 2. 3. 4.
MASS YIELDS AND KINETIC ENERGIES FROM SYMMETRIC FISSION OF 236U* AND 240PU*
I. TSEKHANOVICH, G. SIMPSON, R. ORLANDI AND A. SCHERILLO Institut Laue-Langevin, 4 rue Jules Horowitz, B P 156, 38042 Grenoble Cedex 9, France E-mail:
[email protected]
D. ROCHMAN Los Alamos National Laboratory LANSCE-3, MS-H855, Los Alamos, NM 87545, USA E-mail:
[email protected]
V. SOKOLOV Petersburg Nuclear Physics Institute, Orlova Roscha, Gatchina, 188350 St Petersburg, Russia E-mail:
[email protected] We have precisely measured mass yields and kinetic-energy distributions of fission fragments from the thermal-neutron-induced fission of 235Uand 239Pu, in the symmetry region, with the Lohengrin mass separator at the Institut Laue-Langevin (Grenoble). The dip in the kinetic energy between asymmetric and symmetric fission regions amounts to 28 MeV for 235U and 23 MeV for 239Pu,which agrees with other experimental findings. A pronounced asymmetry in the yields was found for masses from A=119 t o A=125. For the 235Ucase, this asymmetry is at variance with the data given by libraries. An attempt has been made t o explain this asymmetry in the mass distribution as resulting from neutron evaporation. The presence of a five-mass structure found in the mass yields (235Unucleus) tentatively indicates the presence of a proton odd-even effect in the isotopic yields.
1. Introduction
At the present time, the demand for precise fission data is well established by the needs of both fundamental (models) and applied (reactor safety and waste management) physics. However, the experimental data set on
55
56
neutron-induced fission is still not complete. This is especially true for the valley of the mass-yield curve where, for most of the fissile isotopes, even the mass yields are poorly known. From the standpoint of the fission-process studies, the valley of the massyield curve is one of the most interesting regions. Here, the elongation of the fissioning compound nucleus and the deformation of nascent fragments vary on a big scale, from quite compact deformed-spherical (Mo-Sn) shape configurations to strongly elongated and deformed-deformed ones, as is the case for truly symmetric mass splits. This gives rise to a wide spectrum of fission-product kinetic and excitation energies. Thus, the information on the shape of the fission configuration is carried by the kinetic energy of the fission products, which is one of the observables at the mass separator Lohengrin. This paper presents and analyses the results (mass yields and kinetic energies of fission fragments) in the valley region from thermal-neutroninduced fission of 235U and 239Pu.
2. Experimental The measurements were performed at the Lohengrin mass separator' for unslowed fission fragments at the Institut Laue-Langevin (ILL) in Grenoble. The fission fragments separated with Lohengrin were detected in an ionisation chamber with a split anode (AE - E technique). Both the high efficiency and the good energy resolution of the ionisation chamber, combined with the excellent mass resolution of the Lohengrin mass separator, allowed accurate measurements in the low-yield symmetric-fission region to be performed. The thickness of targets used in experiments was of about 100 pglcm'. The targets were covered with thin nickel foils (thickness of 0.25 pm), to prevent sputtering of the fissile material into the separator. The experimental conditions as well as the measuring technique were similar to those from our previous studies; they have been published elsewhere (see, e g . , Ref. 2). Kinetic-energy distributions covering an energy interval of about 30 MeV (+15 MeV and -15 MeV from the most probable kinetic energy for each mass) were successively measured for 23 masses for the 236U* compound nucleus (from A=107 to A=129) and for 28 masses for the 240Pu* compound nucleus (from A=105 to A=132), each at the mean ionic-charge state. For each fragment mass, at least 8 ionic charge states, at the mean
57
kinetic energy, were measured. The evolution of the target intensity was followed as a function of exposure time, by daily measuring the reference spectra (kinetic-energy distribution of A=100). The mass A=100 intensity was further used also as a normalisation point for the data in symmetry. Its absolute yield value was taken from W. Lang et al.3 and C. Schmitt et al.4 for the 235Uand 239Pudata, respectively. The data obtained were corrected for the number of experimental parameters as explained in Refs. 2 and 5. Corrections applied to the total body of raw experimental data have provided a consistent set of independent yields ( Y )as a function of mass number ( A ) and kinetic energy (Ekin) of fission fragments studied. Their further integration over the kinetic energy parameter delivered the fission-fragment mass yield. However, it appeared that the mass yields obtained in such a way showed considerable disagreement with the library data, reaching a factor of two for the heaviest masses measured (i.e. around A=130). This effect could not be explained only from the data uncertainties. It is known that the kinetic energy of fission fragments is practically constant for all masses of the light peak of the mass-yield curve, and it decreases rapidly if one moves towards the region of symmetric fission. It was assumed that the change (decrease) of kinetic energy of fission fragments might affect their transmission into the correct solid angle' of the mass separator, due to the increased scattering of fission fragments into the non-isotropic target system (fissile material Ni foil). The correction for the fragment scattering will be proportional to the change in the kinetic energy parameter of fission fragments. To prove this assumption, a simplified Monte-Carlo simulation for the fragment scattering in the targets used in experiments was done using the SRIM code6. For each target, calculations were done for 82 coordinate points on the target surface; for each point, a discrete set of different incident angles (lo,2", 3" and so on) was considered. As the input data for SRIM, experimental values for the fragments' kinetic energies (corrected for the energy loss in the target) were used, and, for each mass, the most probable nuclear charge was taken from Ref. 7. The results of the simulation for the 239Pu target, integrated over all coordinate points and fragments' incident angles and normalised to mass A=105, are shown in Fig. 1, along with the fission fragments' kinetic energies. As appears from Fig. 1, the fragment scattering indeed may play a role in fragment yields when one goes to the symmetry region. For comparison, in Fig. 1, the experimental data on the fragments' kinetic energy are given.
+
l
o’6
.
l
105
I
,
I
,
110
,
I15
,
,
120
,
I
125
,
,
130
,
135
Mass ( m u )
Figure 1. Solid line: Calculated number of ions (fission fragments) transmitted into the correct solid angle (entrance slit of the mass separator) as a function of fragments’ mass number. Dotted line: Experimental data for fragments’ average kinetic energy. Both data sets are normalised on the corresponding values of mass A=105.
As seen, the curves show practically identical behaviour. It means that the correction on the fragment scattering in the target system can be derived with a reliable precision from the behaviour of the average kinetic energy parameter of secondary fragments. However, it should be noted that the correction on the scattering in the target system was derived from the simplified Monte-Carlo simulation and is of a preliminary nature; to define it in a correct way, all possible incident angles have to included in the simulation. The results on mass yields presented here were corrected on the fragments’ scattering. As seen from Fig. 1, this correction is not big. Moreover, it does not change abruptly when going from mass to mass. Hence, all effects found here in the mass yields would also have been present if no fragment scattering in the target system had been taken into consideration. 3. Results and Discussion
3.1. Kinetic energies of fission fragments The behaviour of fission fragments’ kinetic energy is similar for the two compound nuclei studied. For the 239Pu case, it can be traced from Fig. 1; the absolute values for energy can be recalculated from the value of A=105 (98.5 MeV). For the 235Unucleus, measured values of the kinetic energy in the symmetry region have been reported recently*. Figure 1 shows that the mean kinetic energy starts to decrease steeply
59
in the vicinity of mass A=110 and continues to decrease up to the true symmetry point. The average energy dip between asymmetric and symmetric fission amounts to approximately 23 MeV for 239Pu. For 235U,this value was found to be 28 MeV. These findings are in agreement with the literatureg. The sharp fall in the kinetic energy is associated with increasingly large deformations of initial primary fragments in this mass region. These deformations lead to high excitations of primary masses, which are observed as a large number of neutrons evaporated in this mass region (see e.g. Ref. 10). A local maximum when approaching the mass A=130, seen in Fig. 1, is well known. It is attributed t o a compact-scission configuration due to the two shell closures (2=50 and N=82), which give higher-than-average Coulomb repulsion for nascent fission fragments. 3.2. Mass yields
The absolute values for the mass yields for 235U were already presented in Ref. 8. The data from Ref. 8 had not been however corrected for the fragment scattering in the target system. The corrected values for 235Uare given in Fig. 2 (left picture) as well as those for 239Pu (right picture), along with the data sets given by A. Wahl’ and from European (JEF-2.2)l’ and American (ENDF/B-VI)” libraries.
-5
I
-
I
5
?i
2
01
s I
tm
tm
iio
115
Mass (mu)
tm
IU
no
001
m
110
IIJ
nu
II
110
Mass (a)
Figure 2. Absolute mass yields from the reactions 235U(nth, f ) (left) and 2 3 9 P ~ ( n t h , f ) (right) as a function of mass number: Comparison with libraries (ENDF/B-VI and JEF-2.2) and semi-empirical data by A. Wahl. The experimental data sets shown include previous Lohengrin data3-4 (A=100-106 for 235U and A=103 and 104 for 239Pu).
A striking feature in Fig. 2 is a quite large discrepancy between evaluated and experimental data for the masses between A=119 and A=125
60
for the 235U case. Yields of these masses significantly exceed values from libraries, making the mass-yield curve strongly asymmetric (relative to the true symmetry point). It is interesting to note that this asymmetry could be observed in uranium even at higher incident neutron energies (at least, up to 6 MeV)13. Nevertheless, as seen from Fig. 2, none of the libraries reproduces the yield asymmetry in a correct manner; their mass-yield data appears t o be symmetric rather than asymmetric. The discrepancy between experiment and libraries does not appear for the 239Pu nucleus, though the asymmetry is distinctly present: here, both experimental and library data agree rather well (right picture in Fig. 2). The local asymmetry in mass distributions in the valley region was also observed in experiments with 245Cm14and 241Am(2nth, f)15; it appears hence t o be a general feature of the mass-yield curve for thermal-neutroninduced fission. To understand the origin of this asymmetry, an estimate for the secondary mass yields was made based on the following equation: Ypost(A)=
C [Ypre(A +
n ) . Pn(A
+ n)]
(1)
n
Here, P,(A) is the probability of emitting n neutrons from the mass A , and Ypost(A) and YpTe(A)are secondary (after prompt neutron emission) and primary (before prompt neutron emission) mass yields. Since the P,(A)values are not known, to calculate them we assumed the following: 0
0
0
0
0
a normal distribution was taken for both the excitation energy of primary fragments and for the P,-values distribution; the P, distribution was centered at corresponding c(A)-values7, which are the average numbers of neutrons emitted by each mass; the neutron emission mechanism of fragment 1 was assumed to be independent of the state of the complementary specie (fragment 2). This determines the width of the neutron-multiplicity ntot distribution as
since ~ t " changes ,~ insignificantly with mass number16, we additionally supposed it to be constant for all mass splits; its numerical value was taken from Ref. 17; the width ~ 1 , of 2 the P,-distributions should be proportional to the fragments' excitation energy and the latter can be expressed via the
61
level density parameter, which, in first approximation, depends linearly on the mass number and the fragments' squared temperature. Then, having neglected the difference between the fragments' temperatures, the dependence of 01,z on mass was introduced in the following way
~i/A= i gz/A2
(3)
Ypre(A) was used as a fit parameter in calculations; its start values (initial estimate for primary mass yields) were taken from the JEF-2.2 library. The secondary yields were iteratively calculated with the P,-values determined in the way described and under the condition of symmetry for the primary-mass curve, until the difference between experimental and calculated data in the mass region of interest was minimised. The results are depicted in Fig. 3.
Figure 3. Absolute mass yields as a function of mass number: filled circles connected with a solid line - present data; dotted and dashed lines, respectively - calculated secondary and primary mass yields. Left: 235U; right: 239Pu.The data points for masses A=103-106 are taken from Refs. 3, 4;those for the heaviest masses (A=130-135for 235U and A=133-135 for 239Pu)come from the JEF-2.2 library.
As seen from Fig. 3, the experimental data are, in general, quite well reproduced. It is remarkable that for the asymmetric part of the mass-yield curve (A=119 to 125) the calculated primary and post-neutron mass yields practically coincide. It shows that the yield of the experimental secondary masses in this mass range correlates with that of the primary masses and does not stem from the mass transfer (due to neutron emission) from the heavy peak. On the contrary, for the light peak, the calculated primary and post-neutron curves are well separated. Thus, it is the neutron emission curve, which determines the asymmetry observed in the mass yields, by
62
diminishing yields of masses around A=ll2, whereas those of masses around A=125 remain practically unchanged. An overall view of Fig. 3 indicates a clear presence of the five-mass structure in the mass yields for 236U*(around masses A=125, 120 and 115, and perhaps A=110). It is known (see e.g. Ref. 18) that this structure in mass distributions is linked to the odd-even staggering in the yield of isotopic (charge) distributions. The odd-even effect in the charge distributions reflects the observation that, compared to fission fragments with odd charges, the yields for even charges are enhanced. In the case of uranium, the odd-even effect becomes distinctly visible in the symmetry region due to the low gradient of the mass-yield distribution (broad and flat valley). As neutron evaporation cannot be responsible for the observed mass-yield behaviour (it changes rather smoothly from mass to mass), the structure found is directly associated with a proton odd-even effect. This observation made for the first time for thermal-neutron-induced fission corroborates the GSI datalg and implies the necessity of taking into consideration odd-even modulations in the isotopic yield calculations for the symmetry region. The fact that the 5-mass structure does not appear in the case of 240Pu* may be interpreted as due to higher fragment excitations at this fissioning nucleus. Unfortunately, the method used in the present study does not allow us to resolve the nuclear charges in the mass region investigated, and no quantitative statements can be extracted from the present data, in terms of the element production (height of the odd-even effect). Finally, Fig. 4 is the updated picture (see Ref. 2) of the Lohengrin mass yields measured from the fission of different nuclei, induced by thermal neutrons (for each element, only one isotope was chosen). Two intersection regions are distinctly seen in Fig. 4. One of them covers a quite narrow range of yields (from 1% to 8%);it lies around mass A=130. The second one is to be found in the light peak, for masses A=7480; it extends across more than two orders of magnitude in the mass yield. The origin of these intersections is in proton and neutron shell effects as discussed in Ref. 2. The present systematics on the mass yield is of importance for the optimisation of production rates for the isotopes of interest in experiments aimed at studying the properties of fission fragments.
63
Mass ( m u ) Figure 4. Absolute mass yields from the neutron-induced fission of different nuclei: Data from the mass separator Lohengrin (connected symbols) completed with the ENDF/B-VI data (lines).
4. Conclusion
The mass-yield and kinetic-energy distributions of fragments from thermalneutron-induced fission of 235U and 239Pu have been studied in the symmetry region at the mass separator Lohengrin. The following statements summarise the main results of the study: (1) The data on the mass and kinetic-energy distributions were precisely measured in the mass range from A=107 to A=129 for 235U and from A=105 to A=132 for 239Pu,which considerably improved and extended previous experimental results. (2) The dip in the kinetic energy between asymmetric and symmetric fission regions amounts to 28 MeV for 235Uand 23 MeV for 239Pu. (3) A lack of symmetry in mass yields was found for both fissioning systems; for 235U, it is at variance with the recommended data. (4) The asymmetry in the mass yields could be qualitatively explained as a result of the prompt-neutron-evaporation process.
64 (5) The five-mass structure observed in the mass yields for 235Ugives an evidence for the presence of the proton odd-even effect in t h e isotopic yields in the symmetry mass region.
References 1. E. Moll, H. Schrader, G. Siegert, H. Hammers, M. Asghar, J.P. Bocquet, P. Armbruster, H. Ewald, H. Wollnik, Kemtechnik 19, 374 (1977). 2. I. Tsekhanovich, H.O. Denschlag, M. Davi, Z. Buyukmumcu, F. Gonnenwein, S. Oberstedt, H.R. Faust, Nucl. Phys. A688, 633 (2001). 3. W. Lang, H.G. Clerc, H. Wohlfarth, H. Schrader, K. H. Schmidt, Nucl Phys. A345, 34 (1980). 4. C. Schmitt, A. Guessow, J.P. Bocquet, N.G. Clerc, R. Brissot, D. Enhelhardt, H.R. Faust, F. Gonnenwein, M. Mutterer, H. Nifenecker, J. Pannicke, H. Ristori and J.P. Theobald, Nucl Phys. A430, 21 (1984). 5. I. Tsekhanovich, H.O. Denschlag, M. Davi, Z. Buyukmumcu, M. Wostheinrich, F. Gonnenwein, S. Oberstedt, H.R. Faust, Nucl. Phys. A 6 5 8 , 217 (1999). 6. J.P. Biersack and J.F. Ziegler. Computer code SRIM 2003, available from J.F. Ziegler, IBM Research, Yorktown Heights, NY 10598 and J.P. Biersack, Hahn-Meitner Institut, Berlin 39, Germany, see http://www.srim.org. 7. A.C. Wahl, At. Data Nucl. Data Tables 39, 1 (1988). 8. I. Tsekhanovich, H.R. Faust, D. Rochman, G. Simpson, A. Zhuk, in Proc. 5th Int. Conf. on Dynamical Aspects of Nuclear Fission, Casta-Papiernicka, Slovakia, 23.10-27.10 2001, p. 264. 9. D. Belhafaf, J.P. Bocquet, R. Brissot, Ch. Ristori, J. Cranqon, H. Nifeneker, J. Mougey, V.S. Ramamurthy, 2. Phys. A 309, 253 (1983). 10. M. Derengovski and E. Melkonian, Phys. Rev. C 2, 1554 (1970). 11. The JEF-2.2 nuclear data library. JEFF report 17, NEA data bank, April 2000. 12. ENDF/B-VI. Internet address http://ie.lbl.gov/fission.html. 13. Ch. Strade, C. Budtz-Jprrgensen and H.H. Knitter, Nucl. Phys. A 462, 85 (1987). 14. T. Friedrichs, H.R. Faust, G. Fioni, M. Gross, U. Koster, F. Munnich,
S. Oberstedt, in G. Fioni (ed.) Nuclear Fission and Fission-Product Spectroscopy. Proc. of the 2nd Intern. Workshop, Seyssins, France 1998, AIP Conference Proceedings 447, Woodbary, New York 1998, p. 231. 15. U. Guttler. Ph.D. thesis, Universitt Mainz, 1991. 16. A. Gavron and Z. Fraenkel, Phys. Rev. Lett. 27, 1148 (1971). 17. J. Terrel, Phys. Rev. 108, 783 (1957). 18. J.P. Bocquet, R. Brissot, H.R. Faust, M. Fowler, J. Wilhelmy, M. Asghar, and M. Djebara, 2.Phys. A 335, 41 (1990). 19. S. Steinhauser, J. Benlliure, C. Bockstiegel, H.-G. Clerc, A. Heinz, A. Grewe, M. de Jong, A.R. Junghans, J. Muller, M. Pfitzner and K.-H. Schmidt, Nucl. Phys. A 634, 89 (1998).
STUDY OF THE MASS AND CHARGE DISTRIBUTION OF FRAGMENTS FROM FISSION INDUCED B Y INTERMEDIATE ENERGY NEUTRONS ON URANIUM 238
P. CASOLI, T. ETHVIGNOT AND T. GRANIER Commissariat h 1'Energie Atomique, De'partement de Physique The'orique e t Applique'e, Service de Physique Nucle'aaire, B.P. 12, 91680 BruyBres-le Chcitel, France E-mail:
[email protected]
R. 0. NELSON, N. FOTIADES, M. DEVLIN AND D. DRAKE LANSCE-3, MS H855, Los Alamos National Laboratory, Los Alamos, NM 87545, USA E-mail: rnelson @lanl.gov
W. YOUNES, P. E. GARRETT AND J. A. BECKER P.O. Box 808, Lawrence Livermore National Laboratory, Livermore, CA 94551, USA E-mail:
[email protected] Prompt gamma-ray and x-ray spectroscopy techniques are being employed to study fission induced on 238U targets by neutrons of energy from 1MeV to 150 MeV. Data are acquired using the GEANIE high resolution gamma-ray spectrometer at the LANSCE/WNR unmoderated spallation neutron source. Information on the predecay yields (excitation functions and isotopic distributions) were extracted from gamma and gamma-gammacoincidence data for a wide range of nucleides. Charge yields were extracted by measuring prompt x-rays from a thin, fission-sensitive target using photovoltaic cells specially designed. The experimental results are presented and compared to model calculations.
1. Introduction Fragment production yields from neutron-induced fission of actinides have been extensiveIy studied using gamma-ray spectroscopy for many years. In particular it is well known that, for uranium isotopes, production yields
65
66
increase with the neutron energy in the symmetric fission region’. These measurements have mostly been conducted at incident-neutron energies below 15 MeV due to limitations of neutron sources. The majority of neutron-induced fission data comes from thermal neutrons, reactor fast-neutron spectra, 14-MeV neutrons, and some data taken with monoenergetic neutron sources typically below 10 MeV. Above 15 MeV, very few measurements have been made’. There is now renewed interest in neutron induced fission, in particular at intermediate energies (i.e. between 14 MeV and 1 GeV) due to the potential use of high-energy accelerators for nuclear waste transmutation and energy generation, for the production of beams of rare and radioactive ions, to test models of fission using the increased computational power available, and to learn more about the details of the fission process. In this perspective, a collaborative experimental program has been carried out by Bruyilres-le-Chatel and Los Alamos. This program takes advantage of the WNR facility4 at LANSCE (Los Alamos Neutron Science CEnter), a spallation source which provides a relatively large flux of fast neutrons in a broad energy range extending up to more than 150 MeV. Experiments utilizing the gamma-ray spectrometer GEANIE (GErmanium Array for Neutron-Induced excitation^)^ have provided new data on prompt gamma and x-ray emission. The fission process is described as elongation of the nucleus followed by scission in which two neutron-rich primary fragments are emitted. These fragments rapidly emit neutrons after which we refer to them as secondary fragments. These are produced in excited states and two processes participate in their electro-magnetic de-excitation: gamma emission and internal conversion. The latter is accompanied by the emission of K x-rays characteristic of the fragment’s atomic number. About 10% of the isotopes observed in gamma decay are stable, while 90% undergo beta decay on a time scale of ms to 100’s of seconds. It is the prompt gamma-rays emitted in less than 10 ns from the secondary fragments that are measured in our experiments. From the prompt gammaray yields we can infer fission secondary fragment yields for many product nuclides including the stable fragments that are not usually observed in radiochemical measurements of fission yields. At incident-neutron energies above the neutron binding energy (about 6 MeV for actinides) one or more pre-fission neutrons may be emitted. Thus the observed yields at higher incident energies are summed over several fissioning system: 239U, 2 3 8 ~ 2, 3 7 .~. .
67
In this report, we briefly describe the experiment and analysis, then results are presented for isotopic yield excitation functions, for the mass distribution of the barium isotopes and for inferred charge yields from the x-ray data.
2. Experiment
GEANIE is an array of 26 high-resolution germanium gamma-ray detectors. 11 of the detectors are LEPS dedicated to low energy photon spectroscopy, from 10 to 300 keV. The other 15 detectors are coaxial HPGe, more adapted to higher energy gamma-rays, typically from 300 to 2000 keV. BGO (bismuth germinate) background suppression shields are used on 20 of the detectors. GEANIE is located 20 meters from the WNR neutron production target at the end of a collimated flight path. The energies of the incident neutrons are determined by the time-of-flight technique, applied between the spallation target and GEANIE. Two types of experiments were done at GEANIE with 238U. The first one consisted of inclusive gamma-ray measurements and was performed with -400 mg/cm2 targets of 238U (99.8% enriched). GEANIE’s many detectors gave the opportunity for analysis of the recorded gammarays in both single-gamma and double-gamma-gamma-coincidence modes. The target’s relative thickness provided high gamma counting rates. However, the recorded gamma-rays originate not only from the fission fragments but also from other neutron-induced reactions occuring on the target or on the device, such as (n,n’) or (n,xn) on uranium. Background due to neutron scattering is particularly high for low energy photons and fission K x-ray can not be seen. For the x-ray measurements, it was necessary to detect the fission fragment in coincidence with the x-rays to get clean spectra in which the x-rays were observable. In a second class of experiment, we used solar cells as fission fragment detectors. We designed a thin, fission-sensitive target of 238U,consisting of eight 1 mg/cm2-layers deposited onto eight photovoltaic cells5. A coincidence with the detection of a fission fragment in a cell was required in the gamma and x-ray recording. Very thin solar cells were used to reduce x-ray attenuation. The active target was modeled with MCNP‘ to calculate the attenuation in the sample. The transmission average over the 8 cells ranged from about 15% for 10 keV x-rays (light fragments) to 70% for 35 keV x-rays (heavy fragments).
68
3. Analysis and Results 3.1. Identification of the fission fragments
Three different sets of data were used to identify the fission fragment: characteristic single-gamma-rays, gamma-gamma coincidences and fissiongamma coincidences. Thanks to a complementary analysis of the different types of measurement, we could identify about one hundred fission fragments. Elements from germanium to neodymium are seen. In some case up to ten isotopes of the same element are detected. The total number of created fragments is estimated at about one thousand. The fragment production yields range over several order of magnitude with a maximum being about 4% of the total yield. The observed fission fragments represent also about 10% of the estimated total number of created fragments, but account for almost 90% of the total fission yield.
L
I
Number of counts per 0.4 keV
Figure 1. Pure neutron-induced fission prompt-gammbrayspectrum obtained with a thin 238Utarget. All WNR neutron energies are included. A coincidence time of 50 ns between the fission fragment detectors and one of the 11 GEANIE LEPS was required.
As a part of the analysis, the figure 1 shows a portion of a pure-fission spectrum obtained with a thin 238U target. All the gamma-rays are produced by fission fragments and most of the intense gamma-rays are labelled by the symbols of the atoms that emit them.
69
3.2. Ezcitation functions and isotopic distributions For the extraction of the production cross sections of a fission fragment as a function of incident-neutron energy, i.e. the excitation function, the transitions of the ground state rotational band (GS) provide a good tool t o study even-even nuclei. It is known that in these nuclei the decay will feed the low-spin transitions (almost 100% for the 2+ t o O+ transition). Measuring the intensity of a gamma-ray from a low spin transition gives a good measurement of the yield of the fragment which emitted it.
i
1
10
lo2 Neutron Energy (MeV)
Figure 2. Excitation function of two GS transition ~ f ' ~ ~ XSingle e . and coincidence data are compared with Wahl systematics. Dotted lines indicate the error bars of the evaluations.
As an example, figure 2 displays the excitation function of the lowest two GS transitions of 138Xe and the measurement of the intensity of these two gamma-rays in coincidence. The three excitation functions are identical within errors, so we can assume that the gamma-rays are not contaminated: that means they are fed by the 13'Xe nucleus only, and that we can interpret these functions as production yields of the 138Xefragment. The excitation functions show the thresholds corresponding t o the different fission chances. The data are compared to the Wahl systematics7. The systematics values are calculated from a multi-gaussian fit t o mass and charge distributions of library data. The energy dependence is interpolated between data sets.
70
At energies above 14 MeV, Wahl used data from proton induced fission. The calculated values fit the data reasonably well. This method allows determination of the excitation function for about 30 even-even fission fragments. In our data set, we see that the shapes of the functions are very different from one fragment to the other, especially concerning the height of the thresholds. Then, we compare the production of different isotopes of the same element, obtaining isotopic distributions of the fragments
Figure 3. Mass distribution of barium isotopes, measured for 3 incident energy bins and compared with the values from Wahl systematics at the average energies of the bins.
As an example, figure 3 displays the production yields of five isotopes of barium, for three large incident-neutron energy bins. Results are compared with Wahl systematics. Both data and calculations show that at higher incident-neutron energies, the mean mass of the fragment goes down and the mass distribution is broader. Wahl calculations are consistent with our measurements at low incident energies but partially fail to reproduce them above 50 MeV. 3.3. Charge yields Coincidences between photon and fission fragment detection in the active target experiment permitted prompt K x-ray measurements'. Due to the large number of K x-ray lines, five per element, the x-ray energy spectrum is quite complex. Nevertheless, it has been possible, within the limits of the
71
recorded statistics, to deconvolute the contribution of the different elements for several groups of incident-neutron energy. This was done by fitting the data with a multigaussian function with one free parameter per element (see figure 4). Background was considered linear on successive energy ranges.
counts F
anne I-
-
"
--
100
Photon Energy (kev)
Figure 4. Low energy photon spectrum for fission on 238Uinduced by neutrons from 10 to 20 MeV. The 70 K x-ray lines correspond to 19 elements. The 15 most intense elements are labelled (Ka peaks except silver's Kp).
In the seventies, Reisdorf and collaborators measured the x-ray yields per fragment in spontaneus and low energy neutron induced fissiong. It appears that this depends only weakly on the nature of the fissioning system. By applying Reisdorf's prescription to our x-ray yields, we extract an estimate of the charge distribution of the fission fragments. These distributions are displayed in figure 5 for four incident-neutron energy bins. These results exhibit the expected increase in the probability for symmetric fission as one goes toward high incident-neutron energies. The values of Wahl systematics are consistent with our data for all incident energies.
4. Conclusion New data on prompt gamma and x-ray emission in intermediate energy neutron-induced fission on 238Uwere obtained. Gamma-ray measurements have enable the extraction of excitation functions for about 30 secondary fission fragments. An estimate of the charge distribution of the secondary fie sion fragments was obtained from x-ray measurements for several neutron-
72
Atomic Number
Atomic Number
Figure 5. Element yields per 100 fissions determined from the x-ray yield measurement for four incident-neutron energy bins (black dots): 1 ) threshold-6 MeV, 2) 11-20 MeV, 3) 20-50 MeV, 4) 50 MeV and up. Average energies are labelled. The histograms correspond to the Wahl systematics at the average energies.
energy bins. The comparison of these results with evaluated data (Wahl systematics) shows that the evaluations are consistent with measurements below 20 MeV but partially fail to reproduce the data at higher energies. References 1. S. Nagy e t ~ l Phys. , Rev. C17,163 (1978). 2. C. M. Zoller et al, Seminar on fission "Pont d'Oye III", Habay-la-Neuve (Be]), Report EUR16295EN, 56 (1995). 3. P. W. Lisowski et ~ l Nucl. , Sci. Eng. 106,208 (1971). 4. J. A. Becker and R. 0. Nelson, Nucl. Phys. News Int. 7,11 (1997). 5. T. Ethvignot et d, Nucl. Znstrum. Meth. A 490, 559 (2002). 6. J. Briesmeister, ed., "MCNP - A Monte-Carlo N-Particule Transport Code", LANL Report, LA-12625-M (1997). 7. A. C. Wahl, Systematics of fission-product yields, LANL Report, LA-13928 (2002). 8. T. Granier et a/, preprint (2003). 9. W. Reisdorf et d, Nucl. Phys. A 177, 337 (1971).
OBSERVATION OF STRUCTURES IN THE MASS-TKE DISTRIBUTIONS OF FISSION FRAGMENTS IN SPONTANEOUS FISSION * V.A. KALININ, V.N. DUSHIN, V.A. JAKOVLEV AND B.F. PETROV
V.G. Khlopin Radium Institute 2-nd Murinski Ave. 28, 194021, St. Petersburg, Russia A.S. VOROBYEV, A.B. LAPTEV AND O.A. SHCHERBAKOV Petersburg Nuclear Physics Institute 188350, Gatchina, Leningrad district, Russia F.-J. HAMBSCH EC-JRC-Institutefor Reference Materials and Measurements Retieseweg B-2440, Geel, Belgium
The number of prompt neutrons emitted in the fission event has been measured separately for each complementary fragment in coincidence with fragment mass and kinetic energies in spontaneous fission of 25ZCf and z48Cm.Two high efficient Gd-loaded liquid scintillator tanks were used for the neutron registration. Approximately 3. lo6 fission events coincident with prompt neutron emission have been accumulated for each isotope Two-dimensional neutron multiplicity distributions corrected for efficiency, background and pile-up have been reconstructed for each value of the fission fragment mass and total kinetic energy (TKE). Based on these unfolded multiplicity distributions fragment mass and TKE distributions for specific numbers of emitted neutrons from each of the complementary fragments have been obtained. These distributions exhibit pronounced structures reflecting the fine structures in the potential-energy surface. Structures showing a periodicity of two-masses at the edges of the mass-TKE distributions corresponding to the odd-even effect of the neutron pairing in the fissioning nucleus have been observed for the first time at large values of the fragment total excitation energy.
1. Introduction Information about neutron multiplicities is crucial for the better understanding of the fission process. Since an estimation of the energy dissipation at the scission point gives a value of about 10 MeV [1,2] for both fragments, which may be enough for the emission of only one neutron, the neutron multiplicity is a measure of the deformation of both fragments in the vicinity of the scission point. It also contains information on the energy partition released in the fission ~~
* This work is supported by ISTC, http://www.istc.ru.
73
74
process between different degrees of freedom, the distribution of the excitation energy between the fragments and on the neutron-y competition at the fission fragment de-excitation. Generally, this method is a powerful tool for the investigation of the dynamics of the strongly deformed fissioning system at the descent from saddle to scission. In the present report, some results of a recent advanced analysis of the data measured by the KRI-PNF'I-IRMM collaboration for spontaneous fission of 252Cfand 248Cmare presented. 2.
Experiment and Data Processing
Two large 200 1 Gd-loaded liquid scintillator tanks have been used for neutron detection in a 2x2x-geometry providing separate registration of the neutrons emitted from complementary fragments. The efficiency of the neutron registration was about 55% for each detector. A 16 cm thick iron shielding inserted between the tanks was used to decrease re-scattering of both fission neutrons and capture y-rays from one tank into the other (cross talk). The fission fragments were collimated towards the neutron detectors by means of a pin-hole collimator combined with a common cathode of the twin parallel plate gas-flow ionization chamber with Frisch grids. Approximately 3 . lo6 fission events have been accumulated for each of the nuclides under investigation. Mass and kinetic energy distributions of fission fragments have been obtained on the basis of reference values of the most probable mass and kinetic energies of the fission fragments. The first moment (mean multiplicity) and second moments (variance and co-variance) of the one-dimensional multiplicity distributions for both neutron detectors have been calculated for each fragment mass and total kinetic energy (TKE). These data have been corrected for neutron pile-up, background and detector efficiency, including cross talk effects. An iterative procedure was applied to introduce the correction for neutron emission based on the measured mass and TKE dependence of the mean neutron multiplicity. On the basis of the obtained moments a priory two-dimensional multiplicity distributions for the neutrons emitted from both complementary fragments have been modeled for each value of the fragment mass and TKE. The true shape of the distributions was found using an iterative procedure of minimization of the difference between the model distributions distorted by operators of efficiency, background, pile-up and the experimentally measured ones. A description of the experimental set-up and data processing as well as the first results can be found in Refs. [3-51. On the basis of the unfolded two-dimensional neutron
75
multiplicity distributions the fission fragment mass-TKE distributions for fixed pairs of emitted neutrons from complementary fragments have been formed. 3.
Results and discussion
All three observable measured in the present experiment - fragment masses, TKE and neutron multiplicity - generally should be strongly correlated since they represent the basic coordinates of the potential energy surface (PES) mass asymmetry and elongation. The evolution of the fissioning nucleus along the PES determines the fragment mass distribution in fission. This evolution as well as structures in the PES itself may also strongly depend for spontaneous fission on the initial potential energy of the fissioning system. In other words, it depends on the point of appearance of the system at the outer fission barrier after the tunneling transition. The results of this work partially presented below give examples of such correlations reflecting the structures on the potential energy surface. In Figs. 1, 2 the partial fission fragment mass distributions for fixed numbers of emitted neutrons in spontaneous fission of 248Cmand ’’’Cf are shown. vL/vH denotes the number of neutrons emitted from light and heavy fragments respectively. Two combinations of fission fragment deformation have been chosen for presentation. First, a compact heavy fragment with no neutron emission in combination with different deformations (number of emitted neutrons) of the light fragment (Fig. 1) and vise versa in Fig. 2. Such a choice may be explained by the fact that the structures of so called “cold deformed fission” observed for the first time by Alkhazov et.aZ. [6] are mostly appearing at high asymmetry in fragment deformation. Again, such combinations should be specific for the appearance of cluster phenomena in fission. The most interesting fact visible in the distributions in Fig. 1 is the dominating yield of the heavy mass 145 for 252Cfand 144 for 248Cmin case the light fragment is only slightly deformed (emission of one neutron only) with suppressed yield of the double magic mass 132. Drastic changes in the relative contribution of the yields of these masses emerge with increasing light fragment deformation corresponding to the emission of an additional neutron for 248Cm(two neutrons for 252Cf).A peak at A-I29 is appearing and even dominating in the case of 248Cmif the light fragment deformation is increased even further (emission of 6 neutrons or more). In Fig. 2 the mass distributions for a fixed compact configuration of the light fragment and different deformations of the heavy one are presented. The mass distributions look rather narrow and smooth up to the emission of two neutrons from the heavy fragment. With increasing deformation the distributions are becoming broader and structures with an approximate
76
period of 5 a.m.u, which may be related to the charge odd-even effect, are appearing. Starting from the emission of six neutrons by the heavy fragment for 252 Cf and four neutrons for 248Cma peak around A=84-86 (close to the N=50 shell) is appearing. The nature of the peaks in the symmetrical region is not hlly clear. Partially it may be explained by mixing of v ~ / v H and v,/vL cases due to the uncertainty in distinguishing between heavy and light fragments for symmetrical mass splits. For example the 0 6 distribution may have a contribution in this mass region of the 510 case, which has higher statistics. 18 16 14 12
s
s-
10 8
a,
5
6 4
2 0 90
100
110
120
130
140
150
160
Mass, a.m.u.
90
100
110
120
130
140
150
Mass, a.m.u. Figure 1. Partial fragment mass distributions for fixed numbers of emitted neutrons for *'*Cf (upper part) and 208Cm(lower part). VJVH denotes the number of neutrons emitted from the light and heavy fragments, respectively. The heavy fragment is compact.
77
12
10
8
s
6
4
2
0 80
90
100
110
120
130
140
150
160
Mass, a.m.u. Figure 2. Partial fragment mass distributions for fixed numbers of emitted neutrons for '"Cf (upper part) and 248Cm(lower part). v d v ~denotes the number of neutrons emitted from the light and heavy fragments, respectively. The light fragment is compact.
In Figs. 3, 4 the partial fission TKE distributions for fixed numbers of emitted neutrons of 248Cm(SF)are shown. Values of vL/vHcorrespond to those chosen for the mass distributions. In the case of an undeformed heavy fragment (Fig.3) the TKE distributions show an unusual behavior. The TKE distribution in the case of two neutron emission is not shifted towards lower TKE values as compare to the case of one neutron emission. A clear tendency of shifting the
78
TKE distribution towards lower TKE-values is observed above emission of 4 neutrons, which corresponds to a pronounced domination of the mass 132 in the corresponding mass distribution (c.f. Fig. 1). In Fig. 4 the same distributions are shown for larger deformation of the light fragment. A noticeable fact is the coincidence of different peaks in the distributions for different vL/vH.
150
160
170
180
190
200
210
220
TKE, MeV Figure 3. Partial TKE distributions for fixed numbers of emitted neutrons for 248Cm.v d v ~denotes the number of neutrons emitted from the light and heavy fragments, respectively.
8
9
6
a,
F
4
2
0
140
150
160
170 TKE, MeV
180
190
200
Figure 4. Partial TKE distributions for fixed numbers of emitted neutrons for 248Cm.VL/VH denotes the number of neutrons emitted from the light and heavy fragments, respectively.
79 230 220
-1157 -- 1350 - 1157 -9649 772 3 - 964 9 5797 - 772.3 387 1 - 579 7 194 6 - 387 1 2 000 -- 194 6
Cm-248
210
2
200
I
g 190 I-
180 170 160
I
-
80
,
100
.
,
120
’
,
140
220 -
.
,
160 -2058 - 2400 - 2058 -1715 1373 -- 1715 1031 -- 1373 6886 - 1031 346 3 - 688 6 4 000 - 346 3
Crn-248
210 -
2 200I
g 190-
I-
180 170 160!
I
I
80
100
120
140
,
160
Mass, a m u . Figure 5. Partial mass-TKE distribution for 248Cm for the cases v&= Part).
‘0 (upper part) an 210 (lower
In Fig. 5 partial mass-TKE distributions for spontaneous fission of 248Cm are shown in the cases vL/v$l10 and 210, respectively. These configurations have significantly different mass and TKE values for the maximum yield of fission fragments. In both cases the heavy fragment does not emit neutrons. This difference may be explained by the different deformation of the heavy fragment correlated with a different deformation energy of the light fragment. Compact configurations of the heavy fragment for two neutron emission from the light one can increase the TJSE due to a higher Coulomb repulsion. Also the different
80
mutual orientation of the fragments at the scission point might be considered as another explanation. It may be also assumed, that the vL/vel/O and 210 configurations contribute to the different fission modes in terms of the RNR model of Brosa [7], but this assumption needs hrther analysis. 220
Cm-248 2t2
210-
Vhh
200
>
-
190-
2 180F
170
-
160
-
.--.
I 80
.
I 100
.
, 120
,
,
140
.
I
.
160
Mass, a.rn.u. Figure 6. Partial mass-TKE distribution for "'Cm for the case vJv~=2/2.
Cm-248 v,/v, 312
zoo]
80
100
120
140
160
Mass, a.m.u. Figure 7. Partial mass-TKE distribution for 248Cmfor the case v & = 3 / 2 .
I 2 3 49
78.84 2646 8 879 2 980 1.000
--
700 0
--
78.84 26 46 8 879 2.980
_- 234 9 --
--
81 210 200 -
1159 4481 17 32 6 694 2587 1000
Cm-248 v/v, 313
190 180 -
2H
--
3000
-- 1159
-- 44 81 -- 17 32 -- 6694 - 2 587
170-
Mi
Y
+
160150 140 130:
I
1
I
I
I
I
I
.
Figure 8. Partial mass-TKE distribution for 248Cmfor the case vL/vH=3/3
In Figs. 6-8 mass-TKE distributions for different parity of number of emitted neutrons are presented. Nicely pronounced two-masse structures are seen at the edges of the distributions for the 212 and 313 cases, but not for the 312 combination of emitted neutrons. Such an effect has been earlier observed by Knitter et. al. [8] only in the cold compact fission. This effect appears only in the case when both fragments together or separately emit even number of neutrons. This means that the fission process is generally cold and part of the potential energy dissipated into intrinsic excitations on the descent to scission is not enough to fully break the neutron pairing. 4.
Conclusion
The data obtained in the present experiment with high efficient neutron detectors have been successfully used for the reconstruction of neutron multiplicity distributions. The set-up used is a very suitable tool for investigation of the basic properties of the fission process. A strong correlation between fragment masses, TKE and neutron multiplicity reflecting the structures of the potential energy surface has been observed. Unusual regular structures are visible at the edges of the mass-TKE distributions for even total numbers of emitted neutrons. It may be related to the conservation of the pairing effects in the fissioning system.
82
References
1 . Nifenecker H., Signarbieux C., Babinet R., Poitou J., Proc. 3 LA,% Symp. on Phys. and Chem. of Fission, Rochester, August. 13-17, 1973, vol I1 (1974) p.117 2. J.P.Bocquet and R. Brissot, Nucl. Phys., A502 (1989) 213-232 3. V. A. Kalinin, V. N. Dushin, B. F. Petrov, et. al., Proc. Seminar on Fission Pont d'Oye IV, Castle Pont d' Oye, Habay-la-Neuve, Belgium, 5 - 8 October 1999 ed. C. Wagemans et al., (1999) p.33 4. A.S. Vorobyev, V.N. Dushin, F.-J. Hambsch, et. al., Proc. "IX International Seminar on Interaction of Neutrons with Nuclei ", ISINN-9, Dubna, May 23-26, 2001". Dubna, JINR, E3-2001-192, 2001, p. 276-287; ibid. p. 288-295 5. V.N. Dushin, F.4. Harnbsch, V.A. Jakovlev, et. al., Nucl. Znstr. and Meth. A (in press) 6 . I.D. Alkhazov, A.V. Kuznetsov, S . S . Kovalenko, et al., Proc. ofInt. Con$ on Nucl. Data for Sci. and Technologv, Mito, Japan, May 30 - June 3, 1988, p.991 (1988) 7. U. Brosa, S. Grossman and A. Miiller, Phys. Rep., 197 (1990) 167 8. H.H. Knitter, F.-J. Hambsch and C. Budtz-Jerrgensen, Nucl. Phys., A536 (1992) 221.
FISSION YIELD MEASUREMENTS WITH THE ISOL METHOD
U. KOSTER, G. AUBOCK, U.C. BERGMANN, R. CATHERALL, J. CEDERKALL, L.M. FRAILE, s. FRANCHOO, H. FYNBO, u. GEORG, A. JOINET, O.C. JONSSON, J. LETTRY, K. PERAJARVI, L. WEISSMAN ISOLDE, CERN, CH-1211 Genkve 23 0. BAJEAT, R. BORCEA, C. BOURGEOIS, C. DONZAUD, M. DUCOURTIEUX, S. ESSABAA, D. GUILLEMAUD-MUELLER, F. HOSNI, F. IBRAHIM, C. LAU, H. LEFORT, J. OBERT, 0. PERRU, J.C. POTIER, B. ROUSSIERE Institut de Physique Nucle'aire d'Orsay, F-91406 Orsay Cedex
B. PFEIFFER Johannes- Gutenberg Universitat, Institut fur Kernchemie, 0-55128 Mainz E. FIORETTO, G. LHERSONNEAU, G. PRETE, L. STROE, L. TECCHIO Laboratori Nazionale d i Legnaro, INFN, I-35020 Padova C.AA. DIGET, H. JEPPESEN, K. RIISAGER Aarhus Universitet, Institut for Fysik og Astronomi, DK-8000 Aarhus H. GAUSEMEL, E. HAGEBB University of Oslo, Department of Chemistry, N-0315 Oslo
D. RIDIKAS CEA Saclay, DSM/DAPNIA/SPhN, F-91191 Gif-sur- Yvette Radioactive ion beam intensities have been measured at ISOL (isotope separation on-line) facilities from many different targets, but only rarely these intensities are converted into production cross-sections. Here we discuss the method and possible problems in this conversion at the examples of Kr and Xe produced by 1.4 GeV-proton-induced fission of 23sU at ISOLDE and Rb and Cs produced by x l 0 MeV-neutron-induced fission of 23sU at PARRNe.
83
84
1. Introduction Fission product yields are important observables of the fission process. Mass yields have been measured for many fissioning systems at various excitation energies and it is well known that, with increasing excitation energy of the system, the valley of symmetry will be filled and the yields in the wings of the mass distribution (i.e. in far asymmetric fission) will be enhanced. However, isotopic yields are more difficult t o obtain experimentally and are available for far fewer cases. An enlargement of our present knowledge of isotopic fission yields might not only help t o improve our understanding of the fission process, but has also important practical applications. Fission is the most promising process for the production of very neutron-rich medium mass isotopes. Many different, already operating or projected, facilities use fission to produce intense beams of neutron-rich isotopes. They employ different projectiles at different energies: 0 0
0
0 0
0 0 0
235U(nth,f):LOHENGRIN', OSIRIS2, M A F P 238U(p,f): ISOLDE (1.0-1.4 GeV P ) ~ LISOL , (30 MeV)', JYFLIGISOL (20 + 5 MeV)', HRIBF (42 MeV)7 Ta/W/Hg(p,~n..)_t~~'U(n,f): ISOLDE (1.4 GeV p)', IRIS (1.0 GeV)', ISAC-2 (0.5 GeV)lO, EURISOL (1.0 GeV)ll, R I A (0.9 GeV)12 13C(p,n)-+238U(n,f):SPES (10-100 MeV p)13 12C(d,n)+238U(n,f): PARRNe (26 MeV d)14, SPIRAL-II (40 MeV) l5 gBe(d,n)+238U(n,f): PARRNe (26 MeV d) W(e-, y)+23sU(y,f): DRIBS (25 MeV e-)16, ALTO (50 MeV)17 1H/6,7Li/gBe/20'Pb(238U,f):GSI-FRS (1 GeV/nucl.)", RIKEN (0.35 GeV/nucl.)", GSI-SIS200 (1.5 GeV/nucl.)20, R I A (0.4 GeV/nucl.)21
To select the optimum method for the production of the most neutron-rich nuclides we have to ask: (1) How do the fission yields of a given element drop towards very neutron-rich isotopes? (2) How depends the slope of the drop on the excitation energy of the fissioning system? In the following we will discuss recent experiments contributing to these questions.
85
2. Experimental method We have to choose a separation and identification method which enables us to reach the most neutron-rich isotopes. The yields of these rare isotopes will be very low ( 5 lop5), hence a clear isotope identification can only be reached via a good A and/or 2 separation. To study isotopes with a half-life of the order of 100 ms a rapid separation has to be performed online. For the study of fast-neutron-induced fission only the ISOL (isotope separation on-line) method provides sufficient luminosity. For 238U(p,f) either the ISOL method or in-flight separation in inverse kinematics (at the GSI-FRS) can be used. The ISOL method uses thick targets, which are not necessarily “thick” for the incident beam (protons, neutrons, etc.), but “thick” for the reaction products. The latter will be fully stopped in the target matrix. The target is kept at a high temperature to assure a fast out-diffusion of the reaction products which will subsequently effuse towards an ion source where they are ionized to singly charged ions, extracted and accelerated to several ten keV and then mass-separated by deflection in a magnetic field. The A separation is excellent (typically A/AA > 1000), but a 2 selectivity has to be introduced additionally. 3. From “yields” to “yields”
The mass-separated ion beam will be guided to a detection set-up to detect betas, beta-delayed gamma rays and/or beta-delayed neutrons. The event rate, corrected for the detection efficiency, the branching ratio and the transmission from the mass separator to the detection set-up gives the beam intensity. In the ISOL jargon the beam intensity normalized to the incident proton beam intensity is called “yield”. This “ISOL yield” has to be corrected for the ionization efficiency and the release efficiency to obtain the (normalized) in-target production rate. The latter can be translated directly into the production cross-section when knowing the target thickness. Comparing with the total fission cross-section finally allows to deduce the “real” fission yields. The ionization efficiency is element dependent, but to first order identical for isotopes of different mass. The release efficiency depends strongly on the half-life of the isotope in question. For a facility with dc primary beam and a known microstructure of the target, the release profile can be described by an analytical function. Fitting the latter to a release profile measured for one or several isotopes allows to calculate the release efficiency
86
for all isotopes of the same element. A detailed discussion of this procedure can be found in Refs. 14, 22. For a facility like ISOLDE which uses a strongly bunched primary beam ( 2 ps bunch length, duty cycle < 2 . the release profile gets more complicated: shortly after the proton impact the target will experience a thermal spike (briefly accelerating the diffusion),radiation-induced dislocations in the target material will affect the diffusion,a bunched release of gas might affect the effusion, etc. Thus, for practical reasons we use an empiric 4-parameter formula to fit the measured release p r o f i l e ~ ~Depending ~ r ~ ~ . on the used isotope, the measurement covers a dynamic range of some ms to many ten s. 4. Suitable elements
To avoid a biasing of the results from a steep change in mass yield we should choose nuclides close to the peaks of the fission distribution where the mass yield behaves rather smoothly, i.e. CB. 86 5 A <_ 104 (corresponding to the elements Br-Zr) and 132 5 A 5 150 (corresponding to Sn-Cs). Among these elements we should chose those which are released relatively quickly (to reach far out to short-lived isotopes) and which can be produced in a selective way (to assure a clear identification). In the following we will discuss recent results from two measurements: (1) Kr and Xe beams were produced at ISOLDE by 1.4 GeV protoninduced fission in a z38UC,/graphite targetz4. (2) At the PARRNe set-up at IPN Orsay fission was induced in a 238UC,/graphite target by neutrons created when stopping a 26 MeV deuteron beam in a 3 mm thick graphite converter. The forward directed fast neutron spectrum was centered around 10 MeV with a FWHM of 10 MeV25. Surface-ionized Rb and Cs isotopes have been measured26.
4.1. Noble gases Pure noble gas beams can be produced by isothermal chromatography, i.e. the target is connected via a water-cooled “distillation flask” to the ion source and only elements (or compounds) which are gaseous at room temperature will be able to reach the ion source. Noble gases have the advantage to give really cumulative cross-sections since the precursors (Br, Se, . . . ) are not released from the target and ion source unit, but decay
87
inside. Moreover, the ionization efficiency can be monitored on-line by injecting a suitable support gas containing Kr and Xe via a calibrated leak and measuring the stable isotope currents. However, for very neutron-rich Kr and Xe isotopes (e.g. "Kr, 9 mass units away from the stable ssKr and 143Xeljust 7 mass units away from the stable 136Xe)the branching ratios of the beta-delayed gamma rays are not well known or even no gamma ray energies are known at all. Hence these isotopes have to be identified and quantified by measuring the half-life of their beta decay with sufficient statistics. Figures 1 and 2 show the fission yields of 238U(p,f)with 1.4 GeV protons deduced from the ISOLDE yields in comparison to the independent yields of 238U(p,f)measured in inverse kinematics at 1.0 GeV at GSI-FRS18, the cumulative yields calculated from the former, the independent yields of 238U(n,f)measured with a reactor neutron the yields calculated with MCNPX29 (direct through proton-induced fission and total through proton- and neutron-induced fission) and the independent and cumulative recommended28 yields for a fast neutron spectrum.
0
o This experiment
*
10
5
d
10 7-
GSI independent GSI cumulative
OSlRlS MCNPX direct indep. A MCNPX total indep. A MCNPX total cumulative -Cumulative Independent T
Figure 1.
Measured and calculated fission yields of Kr isotopes.
--
0
0
-
88
I
F
10
'r
o0
-s
. T T T E @ ' T V T 0
5, ;
0 0
Y
9
0
Q
'5. 10
.m n LL
m B
0 0 0
T v T T ' T
o Thisexperiment
- 4 10 h 5-
10
r
10
6y 7-
OSlRlS
v MCNPX direct indep. MCNPX total indep. A MCNPX total cumul. -Cumulative - - - - - Independent A
i
; ;
0
:
Contribution of secondary reactions Since we are using rather thick ISOL targets (typically 20 cm long) one has to be aware of a possible contribution of secondary reactions. The incident beam of high-energy protons can produce secondary particles (protons, neutrons, light charged particles, pions, etc.) which in turn might induce fission. To estimate the contribution of such secondary reactions we performed two types of calculations:
(I) With the Monte Carlo code from JAER13' we simulated pencil beams of 2, 4 and 10 mm diameter and compared the relative production of fission fragments within the area of the incident beam to that in the laterally surrounding target area which is only intercepted by scattered protons and secondary particles. For a 4 mm diameter beam the outer target contributed at maximum 30%to the total production of slightly neutron-rich isotopes ( 135-140Xe),but far less for the neutron-deficient and more neutron-rich nuclides. (2) A second set of calculations was performed with the MCNPX code 29 simulating the full UCx/graphite target geometry including the enclosing graphite and tantalum containers. It was found that the secondary reactions contribute 21% of all fission events. However, since this is mainly low-energy fission the effect close to the fission peaks is more pronounced and can reach up to a factor five enhance-
89
ment. This calculation supports the explanation that the enhancement of the ISOLDE data compared to the GSI data is partly due to low-energy fission produced in secondary reactions and partly due to the difference of independent and cumulative cross-sections. The size of the incident proton beam is actually measured slightly upstream of the target and then extrapolated with the nominal beam optics to the target position. There it is supposed to be elliptical with qor, = 4 mm and overt. = 2.5
mm. An extremely conservative estimate of the uncertainty of the real beam size of f 2 5 % would, according to the MCNPX calculations translate into a change of the total fission rate by -13%0/ + 9%. The ratio of direct to secondary reactions is not significantly affected. 4.2. Alkalis Alkalis are another group of elements which is particularly favorable for the separation with the ISOL method. The heavier alkalis have very low ionization potentials (4.18 eV for Rb and 3.89 eV for Cs) which allows to ionize them efficiently and selectively on the hot surface of a metal with high work function (e.g. W). Isobars with higher ionization potential are ionized far less efficiently. Beta-delayed gamma rays of alkali isotopes are known far out (up to lo2Rb,15 mass units away from stable "Rb and 14'Cs, 16 mass units from stable 133Cs)and often also the branching ratios with sufficient precision. Moreover, the very neutron-rich isotopes of these elements have often high P, values which favors their identification via beta-delayed neutron detection. However, it is not easily possible to measure the ionization efficiency of alkalis on-line. Also, only a part of the precursors decays within the target, thereby populating the measured isotopes. Another part will leave the target and ion source unit as neutral atoms which will not reach the detection set-up. The released fraction will depend on the diffusion and effusion properties of the precursor elements, which in principle would need to be studied separately with a different ion source type where they can be ionized and detected after mass-separation. Hence, the measured yields are somewhere between independent and cumulative ones. For the very neutron-rich ones, the yield of the even more exotic precursor will be much smaller and can be safely neglected. Thus, for very neutron-rich isotopes the independent and cumulative yields will nearly coincide and are well represented by the measured yields. Since isotopic fission yields closer to stability can anyhow be measured more accurately with other methods the influence of the precursors is no principal drawback, but it remains a
90
problem to find a suitable isotope for the overall normalization. This could either be a sufficiently neutron-rich isotope where the independent yield gets close to the cumulative yield (i.e. Zg5Rb and 214%s) or, even better, Measurements of the latter from a shielded isotope, i.e. "Rb and 136Cs. the same target and ion source unit are planned. Figure 3 shows a preliminary evaluation for the fission yields measured at PARRNe in comparison to recommended28 values for the independent and cumulative yields with of 14 MeV-neutron-induced fission of 238U.The agreement looks satisfactory (in particular for the neutron-rich side), but the overall normalization factor for cesium was a factor two higher compared to rubidium. Since we do not expect such a big difference in the ionization efficiency this could indicate a systematic problem, possibly due to a very slow release component which remained unobserved.
5 . Conclusion
The transformation of ISOL beam intensities into production cross-sections requires a good understanding of the loss mechanisms in all steps from production to detection. This understanding is also required to reduce these losses and thus improve the intensity of existing radioactive ion beams. Hence a detailed study of this question can give a double benefit: more measured cross-sections and improved beams. The uncertainties of crosssections measured with the ISOL method will mostly remain dominated by systematic errors and rarely reach the accuracy of yields measured by in-flight facilities, but the much higher luminosity of ISOL facilities allows to reach far further out to exotic isotopes. Hence the driving force is the same as for all physics with exotic beams: A rough value measured far from stability may result in a much more stringent test of a model than a very precise measurement close to stability!
91
More than 1000 measured ISOLDE yields are “waiting to be converted” into experimental cross-sections of spallation, fragmentation and fission. Collaborators interested in this analysis are very welcome!
Acknowledgements Part of this work has been supported by the EU-RTD projects EURISOL (HPRI-CT-1999-50001) and TARGISOL (HPRI-CT-2001-50033).
References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24. 25. 26. 27.
P. Armbruster et al., Nucl. Instr. Meth. 139,213 (1976). B. Fogelberg et al., Nucl. Instr. Meth. B 70,137 (1992). T. von Egidy et al., Acta Phys. Slovaca 49,107 (1999). U. Georg et al., Nucl. Phys. A 701,137c (2002). K. Kruglov et al., Nucl. Phys. A 701,145c (2002). 3 . Aysto, Nucl. Phys. A 693,477 (2001). D. Stracener, Nucl. Instr. Meth. B 204,42 (2003). R. Catherall et al., Nucl. Instr. Meth. B 204,235 (2003). M. Portillo et al., Nucl. Instr. Meth. B 194,193 (2002). http://www.triumf.ca/isac/isac-home.htm1. http://www.ganil.fr/eurisol. B. Sherrill, Nucl. Instr. Meth. B 204,765 (2003). A. Andrighetto et al., Nucl. Instr. Meth. B 204,267 (2003). B. Roussihre et d., Nucl. Instr. Meth. B 194,151 (2002). http://www.ganil.fr/research/developments/spiral2/index.html. Y. Oganessian et al., Nucl. Phys. A 701,87c (2002). S. Essabaa et al., Nucl. Instr. Meth. B 204,780 (2003). M. Bernas et al., Nucl. Phys. A 725,213 (2003). T. Motobayashi, Nucl. Instr. Meth. B 204,736 (2003). H. Geissel et al., Nucl. Instr. Meth. B 204,71 (2003). J. Nolen et al., Nucl. Instr. Meth. B 204,293 (2003). C. Lau et al., to be published. J. Lettry et al., Nucl. Instr. Meth. B 126,130 (1997). U. Bergmann et al., Nucl. Instr. Meth. B 204,220 (2003). S. M6nard et al., Phys. Rev. ST Accel. Beams 2,033501 (1999). C. Lau et al., Nucl. Instr. Meth. B 204,257 (2003). G. Rudstam et al., in Proc. of the Int. Conf. on Nuclear Data for Science and Technology, ed. by J. Dickens (American Nuclear Society, La Grange Park, 11, 1994), pp. 977-980. 28. T. England and B. Rider, Report LA-UR-94-106, ENDF-349, Los Alamos National Laboratory, USA (1994). 29. L. Waters, MCNPX code, http://mcnpx.lanl.gov/. 30. H. Takada et al., Report JAERI-Data/Code 98-005, Japan Atomic Energy Research Institute (1998).
FRAGMENT EXCITATION AND MOMENTS OF KINETIC ENERGY DISTRIBUTIONS IN NUCLEAR FISSION
HERBERT R. FAUST Institut Laue-Langevin, 6, rue Jules Horowitz F-38042 Grenoble, France E-mail:faustOill.fr The Random Excitation Model (REX-M) in nuclear fission is formulated with the level density formula from the Fermi-gas model. It is assumed that excitation of fission fragments is totally determined by a temperature calculated from the reaction @value. From this assumption fragment excitation, moments of kinetic energy distributions, and neutron evaporation are calculated. It is shown that the measured distributions and the neutron evaporation characteristics are in good agreement with the model calculations. Finally we extend the REX-model to describe aspects of ternary fission.
1. Introduction
It was shown in ref. that the mean values for fragment excitation and fragment kinetic energies can be calculated on the basis of a statistical model which assumes that the temperature of the final fragments is strongly proportional to the reaction Q-value. In the above citation empirical distribution functions for fragment excitation were used, which led to the right mean values of the observables. It was outlined in the paper that the used exponential functions, however, do not give the right values for the variances of the kinetic energy distributions. In the present paper we replace the empirical exponential functions of paper by the thermodynamical expression from the Fermi-gas model, in order to get variances and higher moments of the distributions. 2. Fermi-Gas Distributions for the Level Densities of the
Fragments We start with the expression for the final temperature of the fission fragments from
92
93
T = ~ . Q
(1)
This equation states that the temperature in a fragment split is proportional to the available Q- value in spontaneous fission. In thermal neutron induced fission the contribution of the neutron binding energy has to be included, and we get
Here E , is the neutron binding energy of the compound nucleus, a1 and a2 are the level density parameter of fragment 1 and 2, respectively. The expression for the probability density of finding a system at a given temperature is according to 1 -E* P(E*)= - ' g ( E * ) .e x p ( T )
(3) Z The function g(E*) denotes the level density expression for the fragment, and 2 is the normalization constant bringing the integral over P ( E * ) t o unity. The last factor in eq. (3) is the usual Boltzmann term with its dependence on the temperature of the system. We will use further-on the Fermi-gas expression for the function of g(E*)
g(E*)= e z p ( 2 . m )
(4)
with a the level density parameter. Consequently eq. (3) becomes
for fragment 1, and
for fragment 2. We assume that in nuclear fission the excitation of the fragments is totally independent from each other. An example for the excitation function of a fragment pair in the reaction 233U(n,f ) is given in fig. (1).
94
dtalim~wM
d-energywM
Figure 1. Excitation functions for the fission fragment pair (A1,Zi),(A2,&)= (94,38), (140,54)from 2 3 3 U ( nf). ,
3. Monte-Carlo Procedure for finding TXE, TKE and Single Fragment Kinetic Energies The probability density for finding the combined system at an excitation energy E* cannot be given in closed form. Therefore we use a Monte-Carlo procedure which chooses randomly the fragment excitation in fragment 1 and 2, respectively, by obeying the distributions of eqs. (5) and (6). The probability distribution for the combined system P ( T X E ) is constructed from the Monte-Carlo events for the single fragments. This is exemplified in fig. (2).
0
I;' 0
, .?-. 25 50
,
,
.
.
,
.
,
I
75 100 125 150 175 '230
excitation energy [MeV
Figure 2. Distribution (un-normalized) for the total excitation energy T X E for the fragment pair shown in fig. 1.
From the distribution for T X E we construct the distribution for total kinetic energy TKE. Because of
95
TKE =Q -TXE
(7)
this distribution is just the mirror image of T X E , with the endpoint at the Q- value for the masslcharge split under consideration. The total kinetic energy is distributed onto the fragments according to energy and momentum conservation in binary reactions, which gives
for the light fragment with mass number
A1,
and
for the heavy fragment with mass number A z . Examples for the above reaction are given in fig. (3).
400
1001
,
,
,
,
,
,
,
,
j,;
0 0 2 0 4 0 6 0 8 0 1 0 0 1 2 0
ldneticenergy[MevI
L-
1:
200
100
0o
25
50
.. 75
100
kineticenergyFlevl
Figure 3. Kinetic energy distribution for the light (left) and heavy (right) fragment for the reaction shown in fig. (1).
4. Experimental Single Fragment Kinetic Energy Distributions We have performed high resolution measurements of selected fragments from thermal neutron induced fission of 2 3 3 U ( n , f at ) the LOHENGRIN spectrometer in Grenoble. An example for these distributions is shown in fig. (4), together with the calculations according to the above model. Mean
96
-
1
"01
k&energy[MeVl
kid
#neliCenergy[MeVl
Figure 4. Kinetic energy distributions (points) of mass A = 91 (left) and A = 148 (right), together with the calculations from the REX-model (lines). Calculations have been done for the most important contributions, which are A = 91,92 and A = 148,149,150,respectively.
kinetic energies calculated with the model are only a few per cent different from the ones derived from the empirical calculations shown in ref. '. In general the kinetic energy distributions show a tailing towards lower kinetic energies. This is a consequence of the asymmetric density distributions from eqs. (5) and (6). The variance of a distribution depends on the level density parameter of the fragment and the temperature, and increases if these values rise. The kinematics in binary reactions, eqs. (8) and ( S ) , modulates this effect, and causes a strong narrowing of the halfwidths of the energy distribution for the heavy fragment. Most of the widths of the kinetic energy distributions when approaching symmetry is, however, determined by the superposition of energy distributions of fragments with the same mass, but with different nuclear charge splits, and by the superposition of distributions with different neutron evaporation characteristics. Here, additionally, neutron emission shifts the distributions towards low kinetic energies.
5. Entry States and Neutron Evaporation from the Fragments The distribution functions for the excitation energy of the fragments given by eqs. ( 5) and (6) provide one of the input parameter for neutron evaporation calculations using the statistical model for compound nucleus deexcitation. The second quantity which has to be known in these calculations is the spin distribution for the fragments. This quantity is not known too precisely, but it is known that mean spin and widths of the distributions are
97
almost constant for all nuclear mass splits and for a wide range of actinides. Moreover, our calculations have shown that, in contrast to gamma emission characteristics, neutron emission is quite insensitive to the spin distribution function. Therefore we used a Gaussian distribution for the fragment spin, given by
( I - IOl2
1 u$&
P ( I ) = -.
expcp(-
202
1
where I0 was taken to be 6 h, and u was fixed to a value of 1.5. A typical entry state population is shown in fig. ( 5 ) for a fragment ( A ,2 ) = (94,38) from 233U(n, f).
0
2
4
6
8 1 0 1 2
spin Figure 5. Entry states in the plane excitation energy/spin for the fission product A = 94,Z = 38 from the reaction 233(1(n,f).
6. Neutron Multiplicities from the Statistical Decay of
Fragments We calculated neutron evaporation characteristics for neutron induced fission of 233U.For each possible mass/charge split the temperature has been calculated, and the excitation functions eqs. ( 5 ) , (6) established. Then for the given masslcharge split the entry states were constructed. These states were used as input into the 'PACE 11' statistical decay code '. The result for the neutron multiplicity M ( v ) is shown in fig. (6). In fig. (7) the probability for the emission for 1 to 8 neutrons is shown together with the data from 5 .
20,
02j
I 6
lbo
1%
lb
liro
160
mass Figure 6. Neutron multiplicities as function of mass number for 233U(n, f).
0.15 0.10
0.05
'@O
1
2
3
4
5
6
7
8
no. oflmllbms
Figure 7 . Neutron emission probabilities in 233U(n, f).
7. Extension of the Formalism to Ternary Fission It is straightforward to extend the above formalism to ternary fission. To eqs. (5) and (6) we have to add the probability function for the excitation of the third particle
This equation is added to the Monte-Carlo code t o find the excitation functions for T X E and T K E . For very light particles] where only a few levels are relevant] the excitation probability of each level can directly be calculated using the Boltzmann equation. The application of momentum and energy conservation in a 3-particle decay is Ekinl
-k
Ekin2
-k Ekin3 = T K E
for the kinetic energy, and for the linear momentum it is
(12)
99 ji+$+&=O
These considerations are most conveniently evaluated in the Dalitz-plot formalism
’.
Idn. energy(A=I30) [MeM
kh.energy (&IN)[ky
Mn. energy (A=IOO) [NleVl
Idn.energy(A=lOO) [thy
Figure 8. Available phase space in ternary fission. At the left the full phase space in the plane of the kinetic energy for A = 130 and A = 4 (upper part) as well as A = 130 and A = 4 (lower part) are shown. The right hand side show the correlation plots when the angles of emission are restricted to the observed values.
The reaction Q-value in ternary fission is in general lower than in binary mass splits. This leads to a lower temperature and subsequently to a reduced excitation of the fragments. We calculated the energetics of ternary splits into fission for the particular case, where the compound nucleus 236U fragments with masses A1 = 100 and A2 = 132 and an a particle. The available phase space according to energy and momentum conservation is shown in the (Ekin(132),Ekin(a))plane in fig. (8). It is seen in the left part of the figure that the whole available phase space is uniformly filled, and that all energies from zero to a maximum energy are permitted for A = 132, A = 100 and A = 4. On the left hand side of fig. (9) are shown the energy spectra of A = 130, A = 100 and A = 4. Clearly these spectra are at vari-
100
AT100
"1
01 0
.
, 50
.
, 100
.
, 150
.
A=1m
I
200
0
;,
,
,
50
100
150
200
50
100
150
200
,
10
2 . . 0
201 0 0
50
100
150
KnetiCenergYp!tWl
200
0
KdenergyFlev1
Figure 9. Spectra for the kinetic energies in ternary decay. At the left hand side the full phase space which is available from energy and momentum conservation is allowed. On the right hand side the emission angles have been restricted to the ones observed in the experiment.
ance with the observation in ternary fission. If we assume that, additionally to the energy and momentum conservation laws, angular momentum plays a prominent role in ternary splits, we have also to obey the angular momentum conservation. In order to test this hypothesis we limited the angles for emission to the ones observed in ternary decay. The result is shown on the right hand side of fig. (8) and (9). It is observed that in including angular momentum conservation laws the available phase spaces are severely cut,
101
and the kinetic energy spectra show the right behavior. 8. Conclusion
It has been shown that the present model, which is essentially parameter free, gives good agreement with data from binary fission. The only parameter which enters the model is the value of f which appears t o have a constant value of 0.045. The ternary fission process deserves additional attention with respect t o a further limitation of the phase space, in addition to limitations given by the energy and momentum conservation laws. Acknowledgments Discussions with F. Goennenwein are acknowledged.
References 1. H.R. Faust, Eur. Phys. J. A14,459 (2002) 2. Greiner, Neise, Stocker: Classical Theoretical Physics, Thermodynamics and Statistical Mechanics, Springer Verlag. 3. E. Segre, Nuclei and Particles, W.A. Benjamin, INC. (1965) 4. A. Gavron, Phys. Rev. C21, 230 (1980). 5. E.K. Hyde, The Nuclear Properties of the Heavy Elements, Prentice-Hall, INC. (1964).
EVIDENCE FOR COLLINEAR CLUSTER TRIPARTITION W.H.TRZASKA, YU.V.PYATKOVt, D.V. KAMANIN’, S.R.YAMALETDINOV Physics Department, University of Jyvaskyla, P. 0.Box 35 FIN-400 I4 Jyvaskyla, Finland E.A. SOKOL, A.A. ALEXANDROV, LA. ALEXANDROVA, E.A.KUZNETSOVA, S.V. MITROFANOV, YU.E. PENIONZHKEVICH, V.G. TISHCHENKO, A.N. TJUKAVKIN, B.V.FLORK0 Joint Institute for Nuclear Research, 141980 Dubna, Russia S.V. KHLEBNIKOV Khlopin-Radium-lnsntute,194021 St. Petersburg, Russia W.V.RYABOV Institute for Nuclear Research RAN, I 1 7312 Moscow, Russia
We present the latest experimental evidence for a new exotic decay mode - Collinear Cluster Tripartition. Among 2 million binary fission events from 252Cfdetected with FOBOS spectrometer we have found over 30 events with clear mass deficit of about 100 atomic mass units. 20 of these events form a distinct and well-separated rectangle in the mass-mass plot gated by velocities and momenta. The comers of the rectangle correspond to the masses of magic nuclei: “NNi and 84Se/86Kr.We thus interpret these events as originating from the three-fold decay of an elongated Cf nucleus dominated by the 3 clusters: “Ni, “Se and “Kr. Due to the collinear configuration at scission, most energy is carried out by the 2 external clusters leaving the central fragment nearly at rest
1.
Introduction
Manifestation of clustering in nuclear reactions has been the focus of interest of our collaboration for several years already. The K=130 cyclotron in Jyvaskyla is in many ways an ideal tool for this work. We have been pursuing these studies on several fronts simultaneously by investigating alpha resonance states in light and intermediate nuclei, by studying rainbow scattering, cluster radioactivity, and by systematic search for fine structure and other peculiarities in fusionfission reactions [I]. In our research a very wide range of experimental techniques is involved: from mica track detectors for searching for rare events Permanent address: MEPhI, 1 15409 Moscow, Russia.
’ Permanent address: Joint Institute for Nuclear Research, 141980 Dubna, Russia 102
103
of cluster decay akin to “Led radioactivity”, to big multi-detector arrays of gasfield, solid state and scintillator detectors for the study of neck fragmentation in superheavy nuclei. Our development work is not limited to the detector side. For instance, the new technique of processing 2-dimentional plots has produce a wealth of interesting results revealing fine structure (FS) in TKE-mass distributions of fission fragments [2-61. In our opinion, these structures are trajectories in the elongation-mass space preferred by fissioning nuclei. They reflect formation, evolution and decay of nuclear molecules consisting of and dominated by magic components (clusters). Using the opportunities offered by modern experimental techniques and computer methods we have made the next logical step in our research by returning to the classic and until now unsuccessful quest for the true ternary fission in which the nucleus would decay into 3 fragments of comparable mass. All our previous results indicate that clusters play a dominant role in nuclear processes at low excitations. We have expected a further confirmation of that experimental fact. Since our present search was restricted to 252Cf,one can say that we have set out to look for spontaneous multi-cluster decay of that nucleus. 1.1. Collinear cluster tripartition
Decay into 3 components can be realized in various ways [7]. One of the likely configurations would be an elongated nucleus consisting of three magic (or semi-magic) clusters. The elongated form would be maintained by Coulomb repulsion favoring co-linearity of such system while the closed shells of each cluster would enhance the probability of rupture of both necks as opposed to the fusion of one of the pair into a bigger cluster. Such process can be called Collinear Cluster Tripartition (CCT). Due to the collinear configuration at scission and accounting for the anticipated similarity in mass of all 3 participants, one should expect that most of the kinetic energy resulting from CCT would be carried out by the 2 external clusters leaving the central fragment nearly at rest. In this scenario CCT events would imitate closely regular binary fission events. They would preserve the proper folding angle (back to back emission) and have velocities similar to the other fission fragments. The clear distinction would be in mass. While for the binary fission of 252Cfthe sum of the two fragments is close to 252 and the symmetric mass division is unlikely, in CCT the sum would be only about 213 of the initial mass of the fissioning nucleus and the 2 registered fragments would be of similar masses, momenta and velocities. It is therefore obvious that direct mass measurement is the key requirement in experimental search for CCT.
104
Regrettably, HENDES [S] - the main experimental tool of our collaboration does not have this feature. Therefore, to carry out the intended measurement we had to use a device that in addition to time of flight would also register energies of the fragments.
2.
Experiment
The experiment was performed at the 47c spectrometer FOBOS [9] installed at the FLNR of the JINR. A multi-armed time-of-flight + energy (TOF-E) spectrometer was used to extract masses of FF from the decay of ''Cf. The details of the experiment were reported elsewhere [lo]. All in all 2 million events were processed from the measurement involving 6 pairs of FOBOS modules. The sketch of the setup is shown in Figure 1 .
Figure 1, Schematic drawing of the experimental setup. The start detector (with the source inside) is in the middle surrounded by 6 pairs of FOBOS modules (position sensitive, measuring TOF and Energy), and the ring of neutron detectors.
Since the main focus of the measurement was the search for exotic CCT events we have also tried to register neutrons using several 3He-based neutron counters placed in the plain perpendicular to the FF trajectories (see Figure 1). The results obtained in coincidence with neutrons and the discussion concerning the choice and use of neutron detectors will be reported separately [ll].
105
Nevertheless, due to the low overall efficiency of fragment-neutron coincidences and because of the low yield of the CCT mode discussed here, the collected neutron data have no impact on the results presented in this report. Otherwise, with the exception of a unique start detector with a build-in Cf source, the experiment was a typical off-beam FOBOS measurement.
2.1. Data analysis Detection of rare decay modes on the background of various strange events resulting from scattering on detector grids and other processes mimicking CCT is a big challenge. Data analysis alone took us already 2 years and it shall continue till all of the runs that we have collected are thoroughly processed. It would be impossible to report here on all the calibration procedures and cross checking that we have done in the analysis.
n
ul
c
\
EU
U
1,o
0.5
~
0.0 0.0
0.5
1,o
1.5
2 .o
Velocity [cmlnsf Figure 2. Velocity-velocity plot for all analyzed data. Only events inside the rectangle were used to construct the final mass-mass plot shown in Figure 4.
To simplify we can reduce this complex tusk to the generation of 3 matrices, each representing the number of events for the given pair of parameters characterizing each registered pair of fragments. Each pair of fragments was registered within the proper time gate and has fulfilled the folding angle requirement expected of ordinary binary fission events. Naturally,
106
the resulting matrices are linked and can be gated by the conditions set on the two others. The conditions required were those expected of CCT events: similar momenta and velocities for both registered fragments. Figure 2 shows the total velocity-velocity matrix. The velocity is expressed in cmhs and the intensity scale is logarithmic so that even a single event is visible. The rectangle indicates the gate that was applied. The width of this gate can be considered arbitrary, as it was not deduced from any specific model calculations. It roughly corresponds to the full width at half maximum of the velocity distribution of the light fragment. n
I
.
.
.
.
l
.
.
.
.
l . . .. ...- .. . -
.
.
I
.
c
t V
3
-
150
c13
100
E
3
4-J
50
0
Eo
I " " I " " l " " l "
0
50
100
150
2 00
Momentum [a,m.u. cm/ns] Figure 3. Momentum-momentum plot. Only events inside the rectangle were used to construct the final mass-mass plot shown in Figure 4.
In Figure 3 the total momentum-momentum matrix is presented. The gate that was used to look for CCT events in the final mass distribution is also marked. The momentum-momentum matrix was extracted from the velocityvelocity matrix by multiplying each coordinate by the relevant fragment mass derived from the energy and velocity information.
107
2.2. Results The final, gated mass-mass matrix is plotted in Figure 4. As expected, the requirement of similar velocities and momenta has made a considerable reduction in the number of events and has narrowed the mass asymmetry.
Figure 4 The final, velocity and momentum gated mass-mass spectrum.
The residual fission events stay symmetrically in a two-humped structure around the mass 126 and the remaining space is relatively background-free. However, around the mass 75 a distinct group of correlated events is visible. 20 of these events form a rectangle, symmetric along the mass-mass axis, with boarders at the mass values of about 68 and 85. The space around and inside the rectangle remains clear.
108
3.
Discussion
Is it possible that such a formation of events is completely random? The answer is no. The probability of generating a distinct, regular geometric figure on a clear background by statistics alone is next to nil. However, such a figure could be an instrumental effect or an artifact of data analysis. The only proper way to reject such eventuality is to make another, preferably different experiment and this is indeed our current goal. But, in the meantime, since all our efforts in finding a procedural or instrumental error have failed, we have to consider the possibility that the effect we have observed is real and reflect on the meaning and consequences of this - yet unconfirmed - discovery. Therefore, keeping in mind that this is only our working hypothesis, let’s assume that indeed some 20 events out of the analyzed 2 million binary decays of ”’Cf form a rectangle in the mass-mass plot with sides at masses about 68 and 85.
3.1. Clusteraziation of 2s2Cf nucleus There are many ways in which a larger nucleus may be subdivided into clusters so let’s see if there is a probable clusterization that would be consistent with our findings. By simply dividing the proton number of Cf (Z=98) into 3, and correcting the result for the influence of the nearest closed proton shell (Z=28), one gets 28 (Ni), 34 (Se) and 36 (Kr) as the likely atomic numbers for nuclei resulting form the possible CCT of 252Cf.The same procedure applied to the neutron number (N=l54) indicates that the closed shell of N=50 should manifest itself in at least 2 of the clusters involved in CCT scenario. Since neither Se nor Kr have a magic number of protons, to make them cluster-like one should require N=50 for both. To arrive at the most likely neutron number for the Ni cluster, one should consider the neutron to proton ratio ( d p ) of the involved nuclei. Since ofie would expect similarity between the 3 participants of CCT, it would be unreasonable to expect huge differences between them in the n/p ratio. 84 Se has n/p=1.47 while for 86Kr,n/p=1.39. The mean average of the two gives n/p=1.43. Taking this value for Ni we get 68Ni(N=40) as the “expected” third cluster participating in CCT. It should also be noted that N=40 is considered a semi-magic number which naturally strengthens the likelihood of its formation. There is a striking agreement between the prediction of this simple model and the masses defining the discussed rectangle in the measured mass-mass distribution shown in Figure 4. This agreement provides one more argument that our observation may be genuine. But, at this stage, instead of making further speculations, we prefer to wait for more experimental data.
109
Acknowledgments
This work was supported in part by CRDF (grant MO-0 1 1-0) and by grants from the Academy of Finland. One of us (S.R.Y.) wishes to thank CIMO for his 10-months scholarship grant. References
1. 2. 3. 4.
5. 6.
7. 8. 9. 10.
11.
W.H.Trzaska, Yad. Fiz. 65 (2002) 725. Yu.V.Pyatkov et al., Eur. Phys. J. A 10, (2001) 171-175. W.H.Trzaska et al., Proc. of EXON 2001, Lake Baikal, Russia, July 24 28,2001, World Scientific 2002 p.158. W.H.Trzaska et al., Proc. of DANF2001, 23-27 October 2001,CastaPapiernicka, Slovak Republic, World Scientific 2002. Yu.V.Pyatkov et al.. Nucl. Instr. and Meth. A 488 (2002) 381-399. W.H.Trzaska et al., Proc. of the Symposium on Nuclear Clusters (2002) 237-244, editors: R.Jolos and W.Scheid. H.Diehl and W.Greiner, Nucl.Phys. A 229 (1974) 29. W.H. Trzaska et al. In: Appl. of Accelerators in Research and Industry, AIP, N.Y. (1997) 1059. H.-G. Ortlepp et a]., Nucl. Instr. and Meth. A 403 (1998) 65. D.V. Kamanin et al., Physics of Atomic Nuclei, Vol. 66 (2003) 1655; see also httr,://fobos.iinr.ru/ . Yu.V.Pyatkov et al., Proc. XVI Fission Workshop in Obninsk, October 7- 10,2003 (in press).
This page intentionally left blank
Chapter 3
Talks of General Interest
This page intentionally left blank
NEUTRONS FROM FISSION F. GONNENWEIN Physikalisches Institut, Tiibingen , Auf der Morgenstelle D, Tiibingen, D 72076, Germany
Highlights from more than 60 years of research on neutron emission in fission reactions are surveyed. The emphasis is put on low energy fission. First, global average multiplicities, multiplicity distributions and neutron spectra are discussed. Next, angular distributions of neutrons relative to the fission axis are shown to point to the existence of neutrons emitted right at scission. Then the dependence of neutron emission on the masses and kinetic energies of fragments are considered , including correlations between neutrons emitted from complementary fragments. Finally heavy ion induced fission of compound nuclei with masses up to the region of superheavy nuclei is reviewed. Throughout the role neutron research has played in contributing to our understanding of fission is stressed.
1.
Introduction
Soon after the discovery of nuclear fission induced in U-isotopes by neutrons it was observed that almost invariably neutrons are again emitted in the course of the fission process. The possibility to run a chain reaction was realized and this gave neutron research in fission a first push. It also became evident that neutrons carry valuable and partly unique information on the process. Beyond global properties of neutrons it was interesting to study the correlation of neutrons with fission fragments and correlations of neutrons amongst themselves. Much was learned on deformation and excitation of fission fragments from these studies. By now the characteristics of neutron emission have become a tool to explore time scales in fission and, in very recent times, to assess different reaction mechanisms in the quest for superheavy elements. In the present survey of neutron emission in fission mostly low energy fission is discussed. A general question is where do neutrons in fission come from. One has to distinguish four different sources. There are first the “pre-scission neutrons”. They are evaporated from excited compound nuclei in competition with fission. Partly at least, they may also be evaporated from fission prone nuclei in the descent from the saddle to the scission point. Though there are strong indications for scission neutrons ejected right at scission to be a further source, direct and unequivocal proof for the existence of these “scission neutrons” is still open. By far most of the neutrons showing up in low energy fission are 113
114
evaporated after scission from the fragments. They may properly be called “fission neutrons”. At scission, however, only a minor fraction of the eventual excitation energy of fragments is already present as intrinsic excitation and available for evaporating neutrons. Most of the energy in question is stored as deformation energy and evaporation has to await the relaxation and equilibration of deformation energy into intrinsic excitation. This may take up to 5x10-2’s. By then the fragments are close to be fully accelerated. In most evaluations it is hence assumed that fission neutrons are emitted from fully accelerated fragments. Finally, emission of neutrons (and subsequently gammas) cool the primary fragments down to the ground states of the so-called secondary fragments. These latter fragments being in most cases P-unstable, they decay further and in propitious cases may lead to excited daughter nuclei with energies high enough to emit a neutron. These neutrons are named “delayed neutrons”, the delay being due to p-life times in the order of seconds and minutes. Delayed neutrons are linked to the fission process only in a very indirect way and will therefore not be discussed any further here. In the following we first explore global properties of neutrons in fission like their multiplicities and spectra. Next neutron angular distributions with respect to the fission axis, and emission probabilities as a hnction of fragment masses and energies are discussed. Finally the special role the study of neutron emission in heavy ion induced fission has played is outlined.
2.
Global Properties of Neutron Emission
For all technical applications of (n,f) reactions one of the most important properties of neutron emission is the number of neutrons available as a function of incoming neutron energy. An example is provided in Fig. 1 showing the average neutron multiplicity
versus incoming neutron energy En for the reaction 239Pu(n,f)[11. Not surprisingly the multiplicity increases for larger neutron energies En. In the range of energies studied the slope d/dEn is remarkably constant: d/dEn 1/8 MeV- 1. This tells that on average it takes some 8 MeV of excitation energy of the compound nucleus to emit one neutron. This energy is required to cover at least the neutron binding energy Bn and the kinetic energy q with which the neutron is emitted in the cm system of the fragment. Once the total excitation energy TXE of fragments has fallen behind the binding energy Bn the remaining energy is removed by gammas, Roughly the total y-energy <Ey> has to account for half the neutron binding energy per fragment. However, in experiment a sizable y-neutron competition is observed and <Ey> has to be parametrised as <Ey> = a + b with a = 1 MeV and b =: 1
-
115
MeV. Therefore, to the neutron contributions Bn and one has to add the aterm from y-competition to find the energy of roughly 8 MeV required for the emission of one additional neutron. A convenient rule of thumb for the average excitation energy of a fissioning nucleus in the actinides is
'a!'
'
"lb'
"
'2b'
'
'3b' ' '
'4'0'
'
"5b'
"
'$G
Incidence Energy [MeV1 Figure 1. Average neutron multiplicity versus energy of incoming neutron in the reaction 219 Pu(n,Q). From ref.[l]. With permission.
Besides the averages the distributions of neutron multiplicities P(v) are of interest. Typical examples of P(v) distributions for spontaneous fission in the actinides are plotted in Fig. 2. All shapes of the distributions are seen to be Gaussian-like. As well the averages as the widths of the distributions are getting larger for increasing mass and/or charge of the fissioning nucleus. The increase of tells that generally larger excitation energies are involved in the heavier compounds. It is therefore remarkable that neutron-less fission with v = 0 appears by contrast to have again a sizable probability for the heaviest nucleus shown, 2 5 2 N ~ ( ~Itf )should . be noted that neutron-less events are candidates for "cold fission" where all of the available energy ( the Q-value of the reaction) is exhausted by the kinetic energy of the fragments. A much more spectacular effect has been reported by J.F.Wild et al. [3] for 260Md(sf). There the multiplicity for v = 0 is P(v=O) = (9 f 1)% while it is only 0.2% for the much studied standard reaction 252Cf(sf).The surge of neutron-less fission events is observed in the mass region where "bimodal fission" obtains, i.e. for systems with nearly 2 x 50 protons and 2 x 82 neutrons. In bimodal fission two specific modes are superimposed, both leading to symmetric fission, but with one mode
116
exhibiting an exceptionally large and the other mode a smaller more standard total kinetic energy. The high energy mode is linked to the decay into two doubly magic fragments. This mode should have low neutron multiplicities and this is what is found in experiment.
c 2
P m P LI
z B E Y
NUMBER OF N E U T R O N S
Y
Figure 2. Neutron multiplicities for some (sf) reactions in the actinides. From [2]. With permission.
The kinetic energy spectra of fission neutrons are of importance for the design of nuclear reactors. For fissile target nuclei and for incoming neutron energies not exceeding some 5 MeV, only (n,f) reactions are feasible. With prescission neutrons being absent, and with scission neutrons being assumed to contribute only a minor fraction of alls neutrons, virtually all neutrons observed are evaporated from the fragments. As argued in the introduction, evaporation will effectively only set in after some 5 x lO-”s. In this time lapse the fragments have almost reached their final velocities. Since neutron evaporation at the low excitation energies in question has life times in excess of 10-’9s,it appears to be well justified to start from the conjecture that all neutrons are evaporated from full accelerated fragments. In the cm system of the moving fragments the neutron spectrum predicted by the evaporation theory of Weisskopf is approximated as (P(E)
- (E / T2 ) exp(-
E
/T)
(2)
with E the kinetic energy of neutrons in the fragment cm system and T the temperature of the residual nucleus. However, this formula is valid for the
117
evaporation of a single neutron only. In many if not most cases more than one neutron is emitted. For an emission cascade an approximate relation was derived in ref.[4]. It reads (P(E)
-
-
E‘
exp(-dT,e)
(3)
with h 5/11 for a cascade and Teff= (11112) T where T is the residual temperature after the first transition. More elaborate models follow in detail the evaporation cascade facing, however, a major difficulty: the initial distribution of excitation energies has to be known. For comparison with experiment, finally, the spectrum derived in the fragment cm system has to be transformed into the lab system where experiments take place. A simple relation from this transformation is immediately evident. The average neutron energy <En> in the lab system and = <E>
+ <Ef>
(4)
where Ef is the energy per nucleon of the moving fragment. Rather surprisingly, in the lab system a Maxwell distribution @(En)gives an excellent fit to the data
-
@(En) (En’” / T3”)exp(-En/ T)
(5)
with <En> = (3/2) T. A numerical example: for 252Cf(sf)one finds about <En> = 2.20 MeV, <E> = 1.45 MeV and <Ef> = 0.75 MeV [6].
Laboratory Neutron Energy E (MeV)
Figure 3 Laboratoly spectrum of neutrons from 235U(nh,9From [S] With permission
118
The lab spectrum from experiment and a fit to the data from a widely used model [5] is on display in Fig. 3 for the reaction 235U(n,f)induced by thermal neutrons. The fit looks perfect. It has to be said, however, that the question whether the contribution of scission neutrons to the spectrum should be taken into account has not yet found a generally accepted answer.
3.
Correlations between Neutrons and Fragments
More insight into the fission process is gained by measuring correlations between neutron emission and properties of fission fragments. Of prime interest is to investigate the angular distribution of neutrons relative to the fission axis, the latter being taken as the direction of flight of the light fragment by convention. The angular distribution of neutrons from 252Cf(sf)in the lab system is on display in Fig. 4 [7]. Neutron yields are plotted as a function of emission angle relative to the light fragment and as a function of neutron energy in the lab system. It is above all the anisotropy which catches the eye. This salient feature
Figure 4. Contour plot of neutron emission in lab system versus emission angle relative to light fragment and neutron energy. From [7]. With permission.
of preferential observation of neutrons along the direction of flight of the two fragments directly points to the fragments as two moving neutron sources. Whether in the cm systems of the respective fragments neutron emission is
119
isotropic, as expected for an evaporation process, or anisotropic, is still under debate. Arguments in favor of an anisotropic emission even in these cm systems underline the presence of quite large spins in the fragments which are oriented at right angles to the fission axis [S]. Taking into account this anisotropy indeed improves the quality of fits to the neutron spectrum [7,9]. However, as already indicated, an intriguing question is whether there are also neutrons emitted in the lab from a source at rest. Angular distributions give strong indications for their existence. This is shown in Fig. 5 for the reaction 235 U(n,,,f)[ lo]. The angular distribution W(0) with 0 the neutron-light fragment
Figure 5. Angular distributions of neutrons W(0) with 0 the angle between the neutron and the light fragment for the reaction 235U(n,,,,,f). See text for further details. From [lo]. With permission.
angle as measured and displayed as crosses [ 111 in the figure has been fitted either assuming no scission contribution at all (dashed line) or a contribution of 20% to the total neutron yield (histograms). Evidently, it is not possible to describe neutron angular distributions neglecting scission neutrons. In recent years similar large numbers of up to 0.5 scission neutrons / fission have been extracted from re-examining former experiments with more realistic schemes of evaporation for neutrons from the fragments [12]. As to theory, several models have been proposed, most of them invoking non-adiabatic potential changes with ejection of neutrons during rupture of the neck joining the two nascent fragments. A close connection between ternary fission with usually emission of charged particles and the appearance of scission neutrons has likewise been invoked [13]. From a systematics of ternary charged particle yields the scission neutron yields are extrapolated to be (0.18+0.04)/f in 252Cf(sf)and (0.55+0.09)/f
120
in 235U(n,h,f).By the way, ternary fission of particle unstable light nuclei like %e or 7He decaying by n-emission in times of some lO-”s are certainly a source of scission neutrons [14]. However, their yield is much too small to be relevant and observable in the spectra or angular distributions of neutrons. A spectacular discovery was made already in the early days of fission research when exploring the average neutron multiplicity as a function o f fragment mass number A [15]. Several more recent measurements of from 252Cf(sf)are compared in Fig.6 [16]. All authors agree that the graph for neutron multiplicity as a function of fragment mass resembles in shape a sawtooth. Most remarkable is the near-zero neutron multiplicity for heavy fragment masses in the vicinity of A = 132 and the large multiplicity for the
A
>
V
80
300
I20
140
160
Pre-neutron fragment mass, a. e. m Figure 6. Neutron multiplicity versus fragment mass A for the reaction 252Cf(sf).From [16]. With permission.
complementary fragment near A = 120. It was immediately recognised that this behaviour has to be traced to nuclear structure of the fragments. It is in fact the stiffness of the doubly magic ‘32Snwhich in contact with a soft Iz0Cd nucleus will remain at scission undeformed while the elongation of the scission configuration has to be brought about by the deformation of the complementary partner. The deformations and, in an equilibrium of forces, also the deformation energies are hence not shared equally by the two fragments. As outlined in the introduction, by far most of the eventual excitation energy of fragments is stored as deformation energy at scission. The unequal deformation energy then leads to the asymmetrical neutron multiplicity distribution seen in experiment. Detailed measurements of neutron-fragment correlations allow to evaluate beyond neutron multiplicities as well neutron spectra as a function of fragment
121
mass. An example, again for 252Cf(sf),is provided in Fig. 7 [17]. The left panel gives the average cm energy of neutrons , and the right panel the temperature T(A) of the spectra as a function of fragment mass. Compared to the neutron sawtooth in Fig. 6 , the average cm energy (left panel) is rather symmetric as a function of mass with larger neutron energies being observed near mass symmetry. By contrast, the behaviour of temperature (right panel) as a function of fragment mass retains at least some of the character of the multiplicity sawtooth. It should be stressed that measurements demonstrate that the temperatures of the final fragments are by no means equal. For theory it is a challenge to reproduce all of the mass-dependent details described [ 13.
A
100
120
140
mAss
1WJ
’
0
Figure 7 Average cm neutron energy (left panel) and temperature T(A) (right panel) of neutron spectra from 252Cf(sf)as a function of fragment mass A. From [ 171. With permission
The above detailed neutron studies give valuable information on nuclear structure as characterised by the level density parameter a. Indeed, approximating the nuclei as a Fermi gas the total excitation energy Ex is given as Ex = aTz. The excitation energy Ex is found from measured data: the neutron multiplicity , the neutron binding energy B, , the cm neutron energy and the energy carried away by gammas (see eq. (1)). On the other hand the temperature is obtained from fits to the neutron spectra (see Fig. 7). Thus level density parameters a for fission fragments, i.e. nuclei far away from the valley of stability, may be derived from experiment. The results bring to evidence that as a function of fragment mass A the level density parameters follow again the sawtooth behaviour of neutron multiplicity. Since level densities are linked to the deformability of nuclei, it is seen that the interpretation of the v-sawtooth in terms of mass-dependent deformabilities is consistent with mass-dependent features of nuclear structure.
122
4.
Correlations between Neutrons
Several important experiments have been performed where two detectors for the binary fragments were placed at the centre of two hemispheres filled with a liquid scintillator which intercepts the neutrons. The solid angle covered for the neutrons is 4x and thus data with good statistical accuracy can be obtained [18]. Due to the pronounced neutron-fragment correlation (see Fig. 4) the two hemispheres allow to disentangle neutrons being evaporated by either of the two fragments provided the registration of fragments is collimated in space. As an example results for the reaction 244Cm(sf)are on display in Fig. 8 [19]. Besides the sawtooth for (full points) similar to the one for 252Cf(sf)in Fig. 6 , the variance ozv(A) and the average total neutron multiplicity are shown by open triangles and crosses, respectively. For comparison the mass
O0W
*
8
var
90
*
t yield
~
100 310 1%
130 I40
150 1w:
Mass. a.m.u.
Figure 8 . Average neutron multiplicity +(A)>, variance crZv(,.,) , average total neutron multiplicity and mass yield Y(A) for the reaction "4Cm(sf). From [19]. With permission.
yield curve is given as a full line. Not surprisingly the variance follows in shape the average multiplicity sawtooth. The total neutron multiplicity, however, is rather constant, i.e. independent of fragment mass. Hence, in contrast to the excitation energies E,(A) of individual fragments, with multiplicity also the total excitation energy TXE is more or less constant over the full mass range. An intriguing observation is made when studying the correlation between the neutron numbers VI and vh from the light and heavy fragment, respectively, as a function of the total kinetic energy of fragments TKE. The correlation is quantified by the covariance COV(VI,V~) for the two random variables vI and vh. The definition for the covariance is
123
It is readily calculated from the variances measured. Experimental results for covariances averaged over fragment mass are plotted in Fig. 9 for "*Cf(sf), 24sCm(sf)and 244Cm(sf)as a function of TKE. From the figure it emerges that for all three spontaneous fission reactions studied the covariance is sizable for average kinetic energies TKE but vanishes for both, the largest and the smallest TKE seen in experiment. At large TKE the vanishing of the covariance is not surprising because for the largest TKE the available energy goes entirely into kinetic energy and therefore the excitation goes to zero. This means that all neutron multiplicities and hence also the neutron variances fade away and from eq. (6) it follows that the covariance has to become zero. Let us recall that this limiting situation in fission is called cold compact fission.
Figure 9. Covariance cov(v,,vi,) versus total kinetic fragment energy TKE for the reactions 252Cf(sf), 24"Cm(sf)and 244Cm(sf)averaged over fragment mass. From 11 91. With permission.
The vanishing of the covariance at the lowest TKE is, by contrast, not as easily understood. The interpretation starts from the notion that the characteristic features in Fig. 9 are found not only for the average over masses (as shown) but also for individual mass splits. It is then noticed that for given fragment masses and given TKE the total excitation energy TXE = Ex, + Exh is constant since from energy conservation the Q-value of the reaction (which is fixed once the masses are given) is equal to Q = TKE +TXE (the variance of Q due to the isobaric charge distributions of fragments of given mass is neglected here since it is small in comparison). The constancy of TXE entails on one hand
124
the TXE-variance to become zero, i.e. 02(TXE) = oZ(EXl+Exh) = 0, and on the other hand one deduces for the individual variances oZ(Ex~) and 02(Exh)that they must be equal since ExI= TXE - Exh= const - Exh.From the formula defining covariances in eq. ( 6 ) one arrives at
As the final step it is argued that a linear regression of the multiplicity v on the excitation energy Exis a sensible assumption (see eq. (1)) and therefore one has
The vanishing of the covariance at the highest and the lowest limits of TKE in Fig. 9 is thus seen to be equivalent to the vanishing of the variance of the excitation energies. It tells that at these limits the fission process has gone through a stage where no fluctuations and hence no temperature dependent intrinsic excitations of the fragments were present. Since the limiting cases of TKE correspond to limiting cases of the scission configuration, i.e. the most compact and the most elongated one, the particular stages have to be located at scission. At the lower TKE limit all of the eventual excitation energy of the fragments must have been tied up in deformation at scission. In analogy to cold compact fission at the high energy limit, cold fission at the lower TKE limit is called cold deformed fission. For future work on neutron correlations the scintillator hemispheres used so far in this type of studies should be replaced by granulated detectors covering the full solid angle. With such a detector assembly it would become feasible to look at correlations for small relative angles. This would allow to analyse not only correlations of neutrons emitted by complementary fragments but also correlations between neutrons from the same fragment. The combined analysis of neutron-neutron and neutron-fragment correlations should help to confirm the existence and contribution of scission neutrons and to settle the question whether neutrons are emitted isotropically or not in the cm-system of moving fragments. Of particular interest should be to explore the correlations between two neutrons evaporated by the fragments at small relative momenta. As predicted by theory [20] both, quantum-mechanical effects and final state interactions between the neutrons should come into view. For fission neutrons this could become a new field of research which has barely been discussed in the past.
125
5. Neutrons from Heavy Ion induced Fission Leaving the field of spontaneous and very low energy fission it is heavy ion induced fission where remarkable results from neutron studies have been obtained. At variance with the reactions discussed in the above, for the heavy ion
55
70 105 1 4 0 175 FRAGMENT MASS A
Figure 10. Total neutron multiplicity (tilled squares), pre-scission multiplicity (filled circles), postscission multiplicity (outlined squares and triangles) and the fragment distribution versus fragment mass for the reaction indicated in the insert. From [21]. With permission.
reactions the emission of neutrons prior to scission is one of the characteristic features. This is due to the fact that in order to overcome the Coulomb barrier between a heavy ion projectile and the target large incoming energies are required. The compound nucleus which is eventually formed has then a correspondingly high excitation energy. Therefore pre-scission neutron emission competes favourably with fission. The analysis of neutron data from heavy ion reactions starts from the assumption that neutrons may be evaporated from at least three sources. A first source which takes into account the pre-scission neutrons is supposed to be stationary in the cm system of the compound nucleus. It should be pointed out that in this neutron component also neutrons evaporated in the descent stage of a fissioning nucleus from saddle to scission are included. Two further sources, which are moving with the two fission fragments, respectively, take care of the post-scission neutrons emitted by the fragments. Typical results are shown in Fig. 10 for ''0 projectiles hitting a I9'Au target at a beam energy of 159 MeV. The mass distribution (continuous line) is symmetric. Filled circles represent the pre-scission multiplicities, open squares and triangles post-scission multiplicities and filled squares the total neutron
126
multiplicities. The pre-scission multiplicities exhibit a parabolic mass dependence while the post-scission multiplicities increase linearly with mass. As to the latter, the post-scission neutron sawtooth from low energy fission (see Fig. 6) has disappeared. This has simply to be ascribed to the fact that at large intrinsic excitation energies shell effects have molten away and that for a heated liquid drop the heat energy at given temperature is proportional to its mass. to-ia kn--r-,.
--
-*
I.
--.---
if fi-
~0-19
\
-7 ir
: I \ / LA ..I ^*
10-20
10-21
a
50
iaci
E,
150
(MeV)
Figure 11 Fission lifetimes derived from pre-scission neutron multiplicities (full circles) [22] and from y-measurements (open circle) [23] for nuclei with Z = 85 91 versm initial excitation energy of composite system With permission
Pre-scission neutrons carry valuable information on fission times because statistical model codes allow to calculate with good accuracy the times required for the evaporation of neutrons as a function of excitation energies. The number of neutrons observed therefore serve as a clock revealing when the last neutron before scission was emitted. The most impressive result from these studies is summarised in Fig.11. It shows the minimum time required to emit the number of pre-scission neutrons observed which is identified with fission life time. The solid line in the figure indicates fission life times calculated in a statistical model. What catches the eye are fission lifetimes that are much longer than expected from the model. The discrepancy points to a large viscosity of the nuclear fluid at the large excitation energies in question which is slowing down the fission process and which is not accounted for in the above calculations. In fact, as an alternative to the standard Bohr-Wheeler theory, very early in the history of fission it was proposed [24] to view fission as a diffusion process of a highly viscous liquid and where only fluctuations drive the system over the saddle point. Compared to standard theory this introduces a pre-saddle delay. In addition, at large viscosities also the descent times from saddle to scission should be slowed down [25]. For excitation energies in excess of about 50 MeV, both effects will give neutrons having evaporation times of to 10-20s a chance to overtake fission. It is a remarkable finding that even at high excitation
127
energies fission remains a slow process, never faster than some 10-20s.It should be stressed that at the low excitation energies of fissioning nuclei discussed in former chapters the fission times are much longer, attaining some lO-”s. But these long times are in a conventional statistical model due to the low level densities at the saddle point, dissipation at low excitation energies being rather small. With pre-scission neutrons serving as a fission clock, the mass dependence of their multiplicity evidenced in Fig. 10 can now be interpreted in physical terms. Compared to asymmetric fission the symmetric mass splits exhibit larger multiplicities which means that their time scale is longer [21,26]. Since according to theory at high excitations the majority of pre-scission neutrons are emitted on the way from saddle to scission, it appears that for mass symmetric splits the fission paths are longer. When moving to the study of heavier composite systems, i.e. heavier projectiles and/or heavier target nuclei, new phenomena appear where again neutron investigations are contributing to our understanding. In Fig. 10 results were shown for the reaction “0 + I9’Au where the fusion-fission mechanism is dominating. Figure 12 presents data obtained for a reaction with a much heavier projectile and heavier target, viz. 48Ca+ 248Cmwhich under the assumption of complete fusion without any neutron emission should yield the nucleus 296116. The top panel is a scatter plot of total kinetic energy (TKE ) and masses of fragments from fission-like decays and inelastic scatterings at a rather low excitation energy of only E* = 37 MeV. Events to the far left and the far right are centred around the masses of the incoming ions and correspond to inelastic scattering. Events inside the contour line are interpreted as a superposition of quasi-fission and possibly fusion-fission. In quasi-fission the iwo interacting ions form a composite system but without amalgamating to a compound nucleus with a fission barrier ensuring an extended lifetime. For quasi-fission it is typical that fragment masses are clustering around the doubly-magic ”‘Pb nucleus. This reaction contributes by far most of the events seen in the figure. The projection of the TKE-mass matrix on the mass axis is given in the lower panel of Fig. 12. Full points represent the mass yield. It is decomposed into a series of Gaussian distributions (dotted and full lines). The intriguing question is whether amongst these events, besides quasi-fission, there are also events from fusion-fission reactions. Only in case fusion-fission events can be identified with some confidence, there is evidence for the formation of a compound nucleus and hence the hope that with the reaction at hand the superheavy element 116 can be produced as an evaporation residue having managed to bypass fission.
128
Mass (u) Figure 12. Reaction “Ca + 24RCm-+ ’ ~ 6116. Upper panel: scatter plot of the (TKE, mass) matrix for fragments from fission and inelastic scattering. Lower panel: projection of the (TKE, mass) matrix onto the mass axis. For further details see text. From [27]. With permission.
A first hint that indeed fusion-fission events are hidden in the masssymmetric region is suggested by the three central Gaussians drawn as full lines. It is noteworthy that the leftmost of these Gaussians is centred near the fragment mass A = 132 which in fission usually signals the formation of the doublymagic I3’Sn nucleus typical for a compound fission reaction at low excitation energy. It should be underlined that the excitation energies in these studies were close to the Coulomb barrier, i.e. the smallest ones accessible to experiment. The deconvolution of yields in the central mass region into three Gaussians is then tentatively interpreted as the superposition of a symmetric and an asymmetric fission component. One should, by the way, not be disturbed by the fact that the magic I3’Sn nucleus is stabilising the light wing of asymmetric fission, and not the heavy wing as in the more familiar actinides. In a systematic analysis of mass distributions it could be shown [27] that for compound masses in excess of about 260 the stabilising influence of the I3’Sn nucleus in fact switches from the heavy to the light wing of asymmetric mass distributions. This is what is again observed in the present case. Of course, it is desirable to corroborate the above conjecture by more fingerprints from experiment. The idea to disentangle fusion-fission and quasi-
129
fission by neutron measurements was first proposed and tested for reactions induced by I8O for fusion-fission (see Fig. 10) and by 64Ni ions for quasifission, with targets ranging from the rare earths up to uranium [21]. The reaction under discussion in Fig. 12 is in the category of quasi-fission. Neutrons (gammas) were registered in coincidence with the fission fragments and the results for the neutron (gamma) multiplicity are indicated in Fig. 12 as stars (open circles; the gamma results are not further discussed here). It is quite evident that for quasi-fission less neutrons are found than for the symmetric mass region were fusion-fission events are suspected. The average total neutron numbers exceed = 9 in this mass region. They are very large and indicate that these events stem from a slow process, in contrast to the quasifission mass region which, because of the low neutron multiplicity, appears to be a much faster process. This is precisely what is expected for the relative lifetimes of fusion-fission and quasi-fission. Yet, from the average multiplicities alone it is still difficult to ascertain whether really all events described by the full line Gaussians in Fig. 12 near mass symmetry originate from fusion-fission. Could it not be that a certain fraction of these events stems from quasi-fission? To answer this question it has proven decisive to analyse the neutron data in more detail and to extract the distribution of neutron multiplicities, not only the averages. An analysis of this type has recently been performed for the reaction 48Ca + 244Pu+ 292114 at an excitation of the composite system of 40 MeV [28]. A remarkable result was obtained: the neutron distribution is split into two well separated groups, one with a mean neutron number comparable to the one observed for quasi-fission and a second one at larger mean neutron numbers. Quite naturally this latter group is considered to encompass neutron emission from fusion-fission reactions. For the reaction in question the two reaction mechanisms share the total yield in about equal weight. These findings are probably the most convincing evidence from fission studies that superheavy compound nuclei have been formed in the heavy ion reaction quoted. Of course, the most stringent proof for the formation of superheavy elements in the above reactions should come from the observation of the decay of evaporation residues and the comparison of the decay characteristics with theoretical predictions [29].
6 . Conclusions
In the present survey of neutron studies in nuclear fission the aim was to discuss the main ideas and achievements without attempting to ensure a complete coverage of all data. It emerges that a surprisingly large variety of fission
130
phenomena have been tackled and understood from the evaluation of neutron data though certainly not all questions having surfaced in the course of these analyses could be answered. Main results and open problems concern amongst others: neutron multiplicities as a function of fissility and excitation energy of the compound nucleus; neutron energy spectra and the issues how to describe the spectral shapes; neutron angular distributions relative to the fission axis and the attempts to identify the different sources contributing to neutron emission; the question whether scission neutrons exist and if yes how many there are; neutron multiplicities, excitation energies and temperatures of individual fragments giving insight into nuclear structure (the neutron sawtooth); correlations between neutrons bringing to evidence cold compact and cold deformed fission; neutrons serving as a clock in heavy ion induced fission with the discovery that fission is slow even at the highest excitation energies of compound nuclei; neutrons in heavy ion induced fission and how they can help to disentangle fusion-fission and quasi-fission mechanisms. Experimental and theoretical studies of neutron emission in fission are going on and it will be interesting to see which surprises this complex reaction has still to disclose.
References
1. A. Ruben, H. Marten and D. Seeliger, Z. f. Physik 338,67 (1991). 2. Yu. Ts. Oganessian and Yu.A.Lazarev, Treatise on Heavy-Ion Science, D.A. Bromley ed., Plenum Press 1985, Vo1.4, p3. 3. J. F. Wild, J. van Aarle, W. Westmeier et al., Phys. Rev. C41,640 (1990). 4. K. J. Le Couteur, D. W. Lang, Nucl. Phys. 13,32 (1959). 5 . D. G. Madland, Fission Neutron Spectra, 2003, to be published by IAEA. 6. J. Terrell, Physcis and Chemistry of Fission, IAEA Vienna, 1965, p3. 7. A. Ruben, H. Marten and D. Seeliger, INDC(GDR)-057, IAEA Vienna 1990, p5. 8. A. Gavron, Phys. Rev. C13,2562 (1976). 9. F.-J. Hambsch, S. Oberstedt, A. Tudora, G. Vladuca and I. Ruskov, Nucl. Phys. to be published 2003. 10. C. B. Franklyn, C. Hofmeyer and D.W. Mingay, Phys. Lett. 78B, 564 (1978). 1 1 . K. Skarsvag and K. Bergheim, Nucl. Phys. 45,72 (1963).
131
12. N.V. Kornilov, A. B. Kagalenko, S. V. Poupko et al., Nucl. Phys. A686, 187 (2001). 13. G. V. Val'ski, Int. Workshop on Physics of Nuclear Fission, IPPE Obninsk, Russia ,to be published. 14. Yu. N. Kopatch, M. Mutterer, D. Schwalm et al., Phys. Rev.C65, 044614 (2002). 15. S. L. Whetstone, Phys. Rev. 114, 581 (1959). 16. A. S. Vorobyev, V. N.Dushin, F.-J. Hambsch et al., ZX Znt. Sem. on Znteractions of Neutrons with Nuclei, Dubna 2001, p276. 17. C. Budtz-Jorgensen, and H. H. Knitter, Nucl. Phys. A490, 307 (1988). 18. C. Signarbieux, J. Poitou, M. Ribrag et al., Phys. Lett. 39B, 503 (1972). 19. V. A. Kalinin, V. N. Dushin, B. F. Petrov et al., VZZZ Znt. Sem. on Interactions of Neutrons with Nuclei, Dubna 2000, p26 1. 20. P. Lednicki and V.L. Lyuboshitz, Sov. J. Nucl. Phys. 35, 770 (1982). 21. D. J. Hinde, D. Hilscher, H. Rossner et al., Phys. Rev. C45, 1229 (1992). 22. D. J. Hinde, D. Hilscher and H. Rossner, Nucl Phys. A502,497c (1989). 23. P. Paul and M . Thoennessen, Ann. Rev. Nucl .Part. Sci 44,65 (1994). 24. H. A. Kramers, Physica 7,284 (1940). 25. H. Hofmann, J. R. Nix, Phys. Lett. 122B, 117 (1983). 26. D. Hilscher and H. Rossner, Ann. Phys. Fr. 17,471 (1992). 27. M. G. Itkis, A. A. Bogatchev, I. M. Itkis et al., Proc. ConJ: Nuclear Physics at Border Lines, World Scientific, eds. G. Fazio, G. Giardina, F. Hanappe et al., 2002, p146. 28. T. Materna, PHD thesis, ULB Brusssels, 2003, and these proceedings. 29. Yu. Ts. Oganessian, Nucl. Phys. A685, 17 (2001).
This page intentionally left blank
Chapter 4
Ternary Fission
This page intentionally left blank
RECENT EXPERIMENTS ON PARTICLE-ACCOMPANIED FISSION* M. MUTTERER Institutfur Kernphysik (IKP), Technische Universitat, 64289 Darmstadt, Germany
In the past, the rare ternary fission (TF) process was mainly studied either by inclusive measurements of the energies and fractional yields of the light charged particles (LCPs) from fission, or by experiments on the angular and energy correlation between LCPs and fission fragments (FF). These previous studies, although having revealed valuable insight into many aspects of the TF process, are inherently limited to the emission of stable or pradioactive LCP species. The present article describes a number of recent more elaborate correlation measurements that include either the registration of neutrons and y-rays with LCPs and FFs, or the coincident registration of two LCPs. These experimental approaches have permitted to identify the population of excited states in LCPs, the formation of neutron-unstable nuclei as short-lived intermediated LCPs, as well as the sequential decay of particle-unstable LCP species into charged particle pairs. "Quaternary" fission with an apparently independent emission of two charged particles has also been observed. These experimental studies, performed on either 252Cf(sf)or 233,235U(n,h,f), and the applied technologies are briefly summarized, and particular results are presented and discussed.
1.
Introduction
In ternary fission (TF) nucleons from the neck region, which develops right at scission between the fission fragments, cluster into particular light nuclei that are subsequently ejected at about right angles to the fission axis because of focusing in the strong Coulomb field from the nascent main fragments. In about 87% of ternary fission events a so-called long-range a-particle (LRA) is present, characterized by a continuous energy spectrum with z 16 MeV mean energy and =: 11 MeV width (fivhm). For the time being, a large variety of other rare LCP species, predominantly the neutron-rich isotopes from elements up to silicon, have been measured for various thermal-neutron induced fission reactions [ 1,2] mainly with the recoil spectrometer LOHENGRIN installed at the high-flux reactor of the ILL, Grenoble. For technical reasons, for spontaneous fission (e.g., "'Cf) no isotope yields of LCPs with Z > 3 have hitherto become accessible by the counting methods applied in that case.
*This work has been supported in parts by the BMBF (Contracts 06DA461 and 06TU669) and INTAS (No. 99-00229). 135
136
Another type of TF studies concerns angular and energy correlation experiments between the LCPs and FFs, which have aimed at achieving a complete kinematical description of the three-body break-up. Here, very detailed multiparameter studies were performed during the last 20 years. They were concentrated mainly on the relatively abundant a-TF mode and on a few fissioning systems 235U(n,h,f),239P~(n,h,f)) and, predominantly, '%f(sf) (see ref..[2] for an overview). These previous studies have revealed valuable insight into many aspects of the TF process. However, counting techniques of coincidence experiments naturally limit the registration of LCPs to a ns time scale, and even delays in the range of p between creation and detection are typical for the inclusive measurements with LOHENGRIN. These experiments are, thus, inherently limited to the detection of stable or P-radioactive LCP species. Hence, the TF process has hitherto been associated mainly with LCPs that are emitted in their respective (stable or P-radioactive) ground states. In the present paper, we are going to describe a number of recent more elaborate correlation experiments that either include the registration of neutrons and y-rays with LCPs and FFs, or the coincident registration of two LCPs. It will be shown that these measurements permit to identify several "uncommon" modes of particle-accompanied fission [3], such as the population of excited states in LCPs (eg., in "Be ), the formation of neutron-unstable nuclei (e.g., 5He) as short-lived intermediate LCPs, as well as the sequential decay of particle-unstable LCPs ( e g , 'Be). "Quaternary" fission (QF) with the simultaneous but apparently independent creation of two charged particles at scission has also been observed.
2.
Recent Experimental Studies
Recently, new correlation measurements on 252Cf(sf)TF have been performed that include registration of prompt fission neutrons and y-rays with LCPs and FFs: In the j r s t experiment at the MPI-K Heidelberg, the Darmstadt-Heidelberg 4x NaI (Tl) Crystal Ball Spectrometer was used as the neutron and y-ray detector, combined with the detection system CODIS for the FFs and LCPs [4,5]. This experimental approach has, e.g., permitted the excited state population in "Be LCPs to be investigated and the very short-lived neutronunstable nuclei 5He, 'He and *Li* to be identified as intermediate LCPs. The very short radioactive decay times of the neutron-unstable nuclei under study are comparable with the period of their acceleration (ca. lo-" s) in the timedependent Coulomb field of the fission fragments flying apart. The neutrons
137
from their decay are thus close probes of the conditions at a very short time after scission. In particular, the neutron angular distributions with respect to the residues are closely linked to the decay Q-values and the velocity distributions of the intermediate LCPs in the short period when they still experience a strong Coulomb repulsion. For the data analysis, the angular correlation between the neutrons and the charged residues has been modeled by a trajectory calculation for the precursor LCPs, taking into account the life-times and decay Q-values known from resonance spectroscopy. The measured neutron angular distributions could be well reproduced (see Fig. 1) and, hence, the fractional yields of the most abundant intermediate 5He and 'He LCPs, and the energy spectra of the corresponding 4He and 6He residues, were unambiguously determined. We note that the emission of intermediate 'He in 252Cffission has the second highest yield among all LCPs, being only superseded (by a factor of = 5 ) by 4He emission, but downgrading 3H (by a factor of =: 2 ) to the third most-abundant LCP.
Figure 1. Angular distribution of neutrons from the decay of intermediate 5He, 'He and 'Li* LCPs (from left to right) with respect to the direction of motion of 'He, 'He and 'Li residues. The data represent the projections of the measured angular distributions on the plane perpendicular to the fission axis. The solid lines are the corresponding distributions deduced from trajectory calculations of the intermediate LCPs decaying in the vicinity of fissioning nucleus. The angular distribution of prompt fission neutrons emanating from the accelerated fragments are already subtracted. For details see Ref. [5].
Since the energy distribution of the 4He residues was accurately determined, the TF a-spectrum of 252Cf ( s f ) could be reliably decomposed into the components from true ternary a -particles and 4He residues. It is important to note that the resulting mean energy of the true ternary a-particles, 16.4(3) MeV, is in fact 0.7(1) MeV higher than the 15.7(2) MeV mean energy of the composite spectrum usually quoted from measurements without identification of the intermediate 'He component. This is due to the lower mean energy of the 4He particles from 'He decay. On the other hand, the asymmetry in the TF a-
138
spectrum imposed by the 5He decay is rather weak, telling that the often discussed enhancement of the spectrum at the lowest energies E, < 10 MeV cannot be attributed to the emission of 5He alone (see also Ref. [6]). Furthermore the variation of total fragment excitation energies could be deduced for various ternary fission modes with LCPs up to carbon nuclei. Measured TF fragment mass spectra and neutron multiplicity distributions (A) indicate nuclear shells (mainly Z = 50, N = 82) to play an important role right at scission for pre-forming the fission fragment masses. In a second experiment performed at the GSI, Darmstadt in summer 2002, two segmented large-volume Super-clover Ge-detectors combined with the improved detection system “CODIS2” (see Fig. 2) have permitted highresolution ‘y-ray spectroscopy of FFs and LCPs in-flight after Doppler correction [7]. CODIS2 is the successor of CODIS, having a similar Frischgridded 4n twin ionization chamber (IC) with sectored cathode for measuring FF energies and emission angles, and two rings of LCP detectors with 12 AEEre, telescopes each. Compared to CODIS, several modifications have been made for the FF IC to accept the higher counting rate (2x lo4 fissionsh) and for the LCP telescopes to improve mass and nuclear charge resolution. Figure 3 demonstrates the high separation power achieved for the LCP registration. The GSI segmented Super Clover Ge detectors used in the experiment are among the largest Ge detectors in the world consisting of 4 Ge crystals, each one 14 cm in length and 6 cm in diameter. Double imization chamber with sectored cathode
,/)/li~co
anticomptoo shield
2 rings of 12 A L E telescopes
Figure 2. Sketch of the new experimental set-up for the study of 252Cf ternary fission. The central part is the FF and LCP detector system CODIS2, contained in a cylindrical vessel filled with 570 torr methane as the counting gas. The two big segmented Super Clover Ge detectors on both sides of CODIS2 are equipped with BGO anti-compton shields.
139
From this experiment angular distributions of individual y-rays in ternary (and binary) fission may be deduced for providing information on the fragment spins and their alignment. By studying y-rays from LCPs, the population of their excited states becomes more generally accessible. Furthermore, new data on isotopic LCP yields in ”’Cf fission are obtained due to the outstanding resolution of the LCP telescopes in CODIS2 (Fig. 3).
Figure 3 Sample plot for the separation of LCPs with the newly designed LCP telescopes in CODIS2 The plot shows AE-E,, patterns from He to C LCPs (bottom to top) Note that for the LI LCPs the three parallel lines for the 789Liisotopes are well separated from each other
Another type of recent experiments was devoted to the coincident registration of two LCPs in one fission event. So-called “quaternary” fission in 252Cf(sf)[3] and 233,235U(nth,f) [S] was studied with two different experimental set-ups. Figure 4 sketches the set-up for the 252Cf(sf)measurement. New data have been obtained on the sequential decay of particle-unstable LCP species (such as ‘Be) into charged particle pairs, and “true” quaternary fission with the simultaneous but apparently independent emission of two charged particles right at scission. In both cases angular distributions and correlations of two light charged particles accompanying the two main fission fragments were measured.
140
Likewise the energy spectra of the LCPs could be taken. Not surprisingly QF is still much rarer than ternary fission, and this is probably the reason why in 50 years of research into QF only some five experiments have been conducted.
380 pm,Si
252Cf
': pm si
fission source
\ Absorber foils
Figure 4: Experimental set-up for measuring of a - a and a - t coincidences in the fission of '"Cf ( Ref. [3] ).
Very similar to the particle-unstable LCPs like 'He decaying before detection into a charged particle and a neutron, there exist also unstable LCPs decaying with short lifetimes into two charged particles. The most prominent example for such an LCP is 8Be which is expected to have still a sizable yield as a ternary particle and which is disintegrating with = 0.07 fs into two aparticles. Besides this basically ternary decay which in a secondary process becomes quaternary, the question is whether true QF with the independent emission of two charged particles right at scission exists. The two varieties of QF have been differentiated from one another by exploiting the different patterns of angular correlations between the two charged LCPs. Yields and energy distributions of LCPs for each of the two processes were obtained here for the first time in one and the same experiment. As to the yields, it is first of all remarkable that for all types of QF the yields observed for 2332235U(nt,,,f) are roughly an order of magnitude lower than for the heavier 252Cfnucleus, error margins being, however, rather large. As to pseudo QF the *Be yield is at least one order of magnitude lower than the "Be yield. the yield ratios 8Be/ "Be in the two reactions under study are found to be very close to each other.
141
3.
Summary and Conclusions
The described experimental studies on 252Cf(sf) ternary fission, and 252Cf(sf) and 233,235U(nth,f) quaternary fission, have revealed new aspects of the process of particle-accompanied fission and, although not being yet fully exploited, may provide new insight into the exit channel of fission, more generally. Very similar to the particle-unstable LCPs as 'He, 'He and 'Li*, decaying before detection into a charged particle and a neutron, there exist also unstable LCPs decaying with short lifetimes into charged particle pairs. The most prominent example for such an LCP is 'Be disintegrating both, from its ground and excited state, into two a-particles. Besides this basically ternary decays turned quaternary in a sequential process, there is also true QF with the independent emission of two charged particles right at scission. References 1. C. Wagemans, The Nuclear Fission Process, C. Wagemans (Ed.), CRC Press, Boca Raton, Fl., USA (1991). Chapt. 12. 2. M. Mutterer and J.P. Theobald, Nuclear Decay Modes, D.N. Poenaru (Ed.), IOP Publ. LTD, Bristol, England (1996), Chapt. 12. 3. M. Mutterer, Yu.N. Kopatch, P. Jesinger, and F. Gonnenwein, Proc. gth Int. Conf. on Dynamical Aspects of Nuclear Fission (DANFOI), easta- PapierniEka, Slovak Republic, 200 1, World Scientific, Singapore (2002), p.326. 4. Yu.N. Kopatch, P. Singer, M. Mutterer, M. Klemens, A. Hotzel, D. Schwalm, P. Thirolf, M. Hesse, and F. Gonnenwein, Phys. Rev. Letters 82, 303 (1999). 5. Yu.N. Kopatch, M. Mutterer, D. Schwalm, P. Thirolf, and F. Gonnenwein, Phys. Rev. C65, 044614 (2002). 6. C. Wagemans et al., contribution to this conference. 7. Yu.N. Kopatch, M. Mutterer, P. Jesinger, J. von Kalben, I. Kojouharov, H. Schaffner, H.-J. Wollersheim, N. Kurz, E. Lubkiewicz, P. Aldrich, H. Scharma, A. Wagner, Z. Mezentseva, W.H. Trzaska, A. Krasznahorkay, and F. Gonnenwein, Proc. Symp. on Nuclear Clusters: from Light Exotic to Superheavy Nuclei, Rauischholzhausen, Germany, 2002, EP Systema Bt., Debrecen, Hungary (2002), p. 273. 8. F. Gonnenwein, P. Jesinger, M. Mutterer, A.M. Gagarski, G.A. Petrov, W.H. Trzaska, V. Nesvizhevsky, and 0. Zimmer, Proc. Int. Conf. Nuclear Physics at Border Lines, Lipari (Messina), Italy, 2001, World Scientific, Singapore (2002), p. 107.
THE TERNARY ALPHA ENERGY DISTRIBUTION REVISITED CYRIEL WAGEMANS AND PETER JANSSENS Department of Subatomic and Radiation Physics, University of Gent, Proeftuinstraat 86 8-9000 Gent, Belgium JAN HEYSE EC - JRC - Institute for Reference Materials and Measurements, B-2440 Geel, Belgium
OLIVIER SEROT CEA Cadarache, DEN/DER/SPRC/LEPh, F-13108 Saint-Paul-lez-Durance, France PETER GELTENBORT AND TORSTEN SOLDNER lnstitut Laue - Langevin, B.P. 156, F-38042 Grenoble, France
The shape of the energy distribution of the particles emitted in ternary fission has been studied since the discovery of the phenomenon for a large variety of fissioning systems. The general tendency of the observations is that most particles have a Gaussian-shaped energy distribution, except the a-particles, for which mostly an important non-Gaussian tailing on the low-energy side is reported. The origin of this tailing is generally ascribed to the decay of ternary ’He particles in an a-particle and a neutron. Since the experiments reported in the literature are rarely optimised for measuring the low-energy part of the aspectrum, we realised good experimental conditions for studying the 235U(nh,f)ternary a energy distribution at the High Flux Reactor of the ILL in Grenoble. Thanks to a very intense and clean neutron beam, a small, very thin sample of highly enriched U could be used, with an activity of only 1.6 Bq. So the measurements could be done without absorber in between the sample and the AE-E detector. With the resulting low detection limit of 6 MeV, a clearly asymmetric energy distribution was obtained, in agreement with most data in the literature.
1.
Introduction
A large variety of “light charged particles” going from protons to Ar, are emitted in ternary fission. Their energy distributions have been investigated with various detectors, from simple ionisation chambers or surface barrier AE-E detectors to telescopes coupled to electromagnetic spectrometers. The latter method has been used for a systematic study at the LOHENGRlN facility of the Institut Laue-Langevin (ILL) in Grenoble (see e.g. [1,2]). It appears that the energy distribution of all particles except the a ’ s is compatible with a Gaussian 142
143 distribution, but the experimental data are always truncated by the detection levels. From a literature study it appears that the Z=1 and Z=2 particles (being the most abundant) are the best studied ones, especially for the spontaneous fission of 252Cfand the thermal neutron induced fission of 235U.As an illustration, Figure 1 shows the 235U(n,h,f)data of D'hondt et a1.[3]. In this figure, the deviation from a Gaussian shape of the ternary a energy distribution can be clearly observed.
Figure 1. Energy distribution for Z=l and Z=2 ternary particles for 235U(n,4 [3]
This deviation becomes more pronounced if the results of D'hondt et al. [ 3 ] are combined with the low-energy data of CaYtucoli et al. [4] obtained at LOHENGRIN, as shown in Figure 2 . An even more pronounced deviation has been reported for 2s2Cf(SF)by W. Loveland [5], as shown in Figure 3 . Also in other cases a non-Gaussian low-energy tail has been observed, if the detection
144
limit was low enough, so the phenomenon seems to be present for all fissioning systems.
Energy (MeV) Figure 2. Energy distribution of the ternary a particles emitted in 235U(ne,f)obtained by combining the data of D'hondt et al. [3] and CaItucoli et al. [4]. The Gaussian fit takes into account the data points above 12.5 MeV.
The origin of this low-energy tailing in the ternary a energy distribution has been investigated by several authors. It appears to be caused by the decay of ternary 5He particles into an a-particle and a neutron. This is supported by estimations of the 5He emission yield, by 5He decay studies by Cheifetz et al. [6] and by a detailed investigation of 252Cf(SF)by Kopatch et al. [7]. 25
I "kf
0
Lowland
5
Energy (MeV) Figure 3. Energy distribution of the ternary a particles emitted in 252CF(SF)as reported by Loveland [5]. The Gaussian fit takes into account the data points above 12.5 MeV.
145
2.
Experimental conditions
Most experiments reported in the literature are not optimised for the detection of low-energy a’s, which are sensitive to energy losses, so we tried to realise good experimental conditions to study these particles for the thermal neutron induced ternary fission of 235U.First of all, the measurements were performed at the end of the PFI neutron guide at the High Flux Reactor of the ILL in Grenoble, where the neutron flux is very high (4x109neutrons/cm2.s) and the background very low. This made it possible to use only a small amount of 235 U , so the energy loss in the sample could be minimised. Since moreover highly enriched 235Uwas used, the total activity of the sample was only I .6 Bq, so no absorber foil was needed in between sample and detector to stop the radioactive decay a’s, hence suppressing another source of energy loss. The sample was a 10 pg/cm2 UF4 layer with a diameter of 15 mm, evaporated on a 20 pm A1 foil. The isotopic composition is given in Table 1. Table 1. Isotopic composition of the uranium sample
99.9724 0.0173 0.005
Figure 4. Energy distribution for the 252Cf(SF)ternary a’s, deconvoluted into “true a” (intermittent line) and residual a components.
146
3.
Measurements and results
The measurements were performed with a vacuum chamber, with the sample in its centre and a telescope detector mounted outside the neutron beam. This telescope consisted of a 15.4 pm thick silicon surface barrier AE detector and a 500 pm thick silicon surface barrier E detector. The detector area was 150 mm2 for the AE and 450 mm2 for the E detector, and the a-energy resolution was 50 keV and 19 keV, respectively. The detector signals were amplified and digitised, and coincident (AE,E) pairs were registered in a Labview-based data acquisition system. The energy calibration of the detectors was done using the well-known energies of the "B(t~,a)~Li,6Li(n,a)t, 143Nd(n,a)'40Cereactions and of the 234,235U radioactive decay a's. The measuring system was first tested with the spontaneous fission of 252Cf,using a source with an activity of 70 kBq. For this test, a 30 pm thick Al foil was placed in between the source and the telescope in order to stop the radioactive decay a's. As a consequence, the lower detection limit was 9.5 MeV and with the limited number of events (lo4) no low-energy tailing was observed. The energy distribution is shown in Figure 4; it is compatible with the results of Kopatch et al. [7]. 1200
'
ME) ,w(l
8w-
m4w
~
200 -
0 ,0
Energy (MeV)
Figure 5. Energy distribution for the * % ( n 4 ternary a's. The full line is a Gaussian fit to the data points above 12.5 MeV.
For the 235U(n,,,,f) measurements, the Al foil was removed, so the lower detection limit dropped to 6 MeV. The ternary a energy distribution obtained in this way is shown in Figure 5; the full line is a Gaussian fit to the data points
147
above 12.5 MeV. So for 235U(n,h,f)the low-energy tailing previously observed, e.g by D'hondt et a1.[3], is clearly confirmed.
4.
Discussion
4.1. The spontaneousfission of 252Cf
Figure 6 compares the data of Cosper et al. [S] and Loveland [5] with recent results of Hwang et al. [9] and Kopatch et al. [7]. This comparison shows that (a) only Loveland covers the region < 9 MeV which is most sensitive to lowenergy tailing and (b) the data of Hwang et al. [9] are completely discrepant. From a careful reading of their paper it becomes clear that their method for the energy calibration of a detector covered with mylar is wrong, since it does not take into account the non-linearity of energy loss with increasing energy of the particle. Also the thickness of the E detector used is at the limit.
Cosper (1967) Loveland(1974) b a n g (2000) Kapatch (2002)
**.
0
5
10
a
5
15
Energy (MeV) Figure 6 . Comparison of the (renormalised) energy distributions of "*Cf(SF) reported in literature.
Figure 4 shows a deconvolution of our 252Cf(SF)test data into a dominant component due to "true" ternary a's and a smaller one due to a's originating from the decay of ternary 'He particles. Table 2 gives the characteristics of both components, which are fully compatible with the results of Kopatch et al. [7]. This figure also demonstrates that the sum curve hardly deviates from a Gaussian shape on the low-energy side, in contrast to the results of Loveland [5] shown in Figure 3, but it should be repeated that our lower detection limit is 9.5 MeV.
148 Table 2. Characteristics of the energy distributions of the “true” and residual ternary a particles emitted in 252Cf(SF).
Particle “true” 4He residual 4He
<E> MeV 16.4 k 0.3 12.2 0.3
FWHM MeV 10.3 0.3 9.2 f 0.5
+
Yield % 83 k 5 17f5
4.2. The thermal neutron inducedfission of 23sU
Figure 7 shows a deconvolution of our 235U(n,h,f)data into a dominant component due to “true” ternary a’s and a smaller one due to a’s originating from the decay of ternary 5He particles. Table 3 gives the characteristics of both components. The average energy and the yield of the “true” ternary a’s are
>
Energy (MeV) Figure 7. Deconvolution of the 235U(nth,f) ternary a distribution in “true a’s” (intermittent line) and residual a’s (dotted line).
compatible with the corresponding ’”CF(SF) results of Kopatch et al. [7]; the somewhat smaller FWHM agrees with the observed decrease of this quantity with decreasing mass of the fissioning nucleus [lo]. For the residual a’s, the situation is somewhat different: the yield and the FWHM are compatible with the results of Kopatch et al. [7], but in order to obtain a good fit to the lowenergy tail the average energy had to be lowered by roughly 1 MeV. If we increase the average energy to 12 MeV, the sum of both components lies slightly below the experimental data. The remaining small fraction of the tail
149
could maybe be explained by the decay of excited 6He into an ct particle and two neutrons [ 111. A similar deconvolution of the present 235U(nth,f)data completed with those of Caitucoli et al. [4] yields comparable results. Table 3. Characteristics of the energy distributionsof the "true" and residual nary a particles
Particle “true” 4He residual 4He
<E> MeV 16.4 k 0.3 10.9 k 0.5
FWHM MeV 9.1 f 0.3 8.9 k 0.5
Yield % 85k6
15k6
5. Conclusions We have performed ternary a measurements for 235U(nth,f),optimised for the detection of low-energy a’s. With a lower detection limit of 6 MeV, the previously observed low-energy tailing has been clearly confirmed. This was not so for similar measurements on 252Cf(SF),but here the detection limit was 9.5 MeV. These measurements should be repeated with a lower detection limit to enable a better comparison.
Acknowledgments During the conference, Dr. M. Mutterer (T.U. Darmstadt) informed us that very recently 252Cf(SF)measurements were performed by V. Tishchenko [ 121 down to an a energy of about 2 MeV. A non-Gaussian low-energy tail was observed, however less pronounced than reported by Loveland [5].
References 1 . M. Wostheinrich, R. Pfister, F. Gonnenwein, H. Denschlag, H. Faust and S. Oberstedt, AIP Conf. Proc. 447,330 (1 998). 2. U. Koster, Ph. D. Thesis, T. U. Munich (2000). 3. P. D’hondt, C. Wagemans, A. De Clercq, G. Barreau and A. Deruytter, Nucl. Phys. A346,461 (1980) 4. F. CaYtucoli et al., Z. Phys. A 298, 219 (1980). 5. W. Loveland, Phys. Rev. 9, 395 (1974). 6. E. Cheifetz, B. Eylon and E. Fraenkel, Phys. Rev. Lett. 29, 805 (1972). 7. Y. Kopatch, M. Mutterer, D. Schwalm, P. Thirolf and F. Gonnenwein, Phys. Rev. C65,044614 (2002). 8. S. Cosper, J. Cerny and R. Gatti, Phys. Rev. 154, 1193 (1967). 9. J. Hwang et al., Phys. Rev. C61,047601 (2000).
150
10. The Nuclear Fission Process, C. Wagemans (Ed.), CRC Press, Boca Raton, USA (1991). 1 1 . A. Graevskii and G. Solyakin, Sov.J. Nucl. Phys. 18,369 (1974). 12. V. Tishchenko, Ph. D. Thesis, Dubna (2002).
NEW RESULTS ON THE TERNARY FISSION OF Cm AND Cf ISOTOPES 0. SEROT CEA-Cadarache, DEN/DER/SPRC/LEPh, Bat. 230, F-13108 Saint P a u l lez Durance, f i a n c e E-mail: olivier.serotOeea.fr
C. WAGEMANS Dept. of Subatomic and Radiation Physics, University of Gent, 8-9000 Gent, Belgium
J. HEYSE
EC- JRC-Institute for Reference Materials and Measurements, Retieseweg, B-2440 Geel, Belgium
J. WAGEMANS SCKeCEN, Boeretang 200, B-2400 Mol, Belgium
P. GELTENBORT Institut Laue Langeuin, BP 156, F-38042 Grenoble Ceder, f i a n c e
Recently, the influence of the excitation energy of the fissioning nucleus on the ternary triton emission probability (noted t/B) has been investigated for 248Cm. This was done by comparing the (t/B)-data obtained from the 24’Cm(nth,f) reaction (where the excitation energy of the fissioning nucleus corresponds to the neutron binding energy) and from 248Cm(sf)decay (where the excitation energy is zero). This study has revealed a slight increase of t / B with the excitation energy indicating that tritons do not behave in the same way as ternary alpha particles. The aim of this paper is to study this effect on the 246Cmcompound nucleus and on various Cf-isotopes. For that purpose, the energy distributions and yields of the ternary triton and alpha particles emitted from 246Cm(sf)have been measured, using a double telescope consisting of a twin ionization chamber coupled to two surface barrier detectors. The corresponding 245Cm(nth,f)data are available from a previous experiment. For the investigation of the Cf-isotopes, a 251Cf-samplealso containing 249Cf,250Cf and 252Cfhas been used. The measurement was performed at the high flux reactor of the Institute Laue Langevin in Grenoble (France), using a vacuum chamber with a single A E E telescope, consisting of two suited surface barrier detectors. This measurement was performed respectively with the neutron beam closed and opened in order to investigate contributions from (sf)-decays as well as (nth,f)reactions. For each fissioning nucleus studied, a comparison of the spontaneous and thermal neutron induced fission data confirms the previously observed behaviour for the 248Cmcompound nucleus, namely: a decrease of the ternary alpha emission probability and an increase of the triton emission probability with the excitation energy of the compound nucleus.
151
152
1. Introduction
The influence of the excitation energy of the fissioning nucleus on the ternary emission probability has already been studied in the past on 235U(n,f) and 239Pu(n,f)reactions, measuring the ternary fission probability (alpha and tritons) as a function of the incident neutron energy [l]. Due to the poor statistics, it was difficult to draw a clear conclusion of a possible effect of the internal excitation energy of the system on the ternary emission probability. Another way to study this effect is to compare the ternary emission probability for the same compound nucleus at zero excitation energy (spontaneous fission) and at neutron binding energy (thermal neutron induced fission). This approach was carried out for ternary alpha particles (see I21 and references therein). For the three compound nuclei studied (240Pu, 242Pu and 248Cm),an unexpected phenomenon was observed, namely a decrease of the ternary alpha particle emission probability with increasing excitation energy of the fissioning nucleus. In a recent work [3], the ternary triton emission probabilities were measured for 24sCm(sf)and 247Cm(nth,f) . A slight increase of this probability with increasing excitation energy could be observed, suggesting that ternary alpha particles behave in an opposite way as ternary triton particles. In order t o confirm the different behaviour of alpha and triton particles, the 246Cmcompound nucleus as well as Cf-isotopes were investigated. The present paper reports on these studies. 2. Investigation of the 24aCmcompound nucleus 2.1. 245Cm(wh,f)
The energy distributions and yields of ternary alpha and triton particles emitted during thermal neutron induced fission of 245Cm have been reported in ref. [4]. The results are summarised in Table 1. Note that the ternary alpha emission probability is in good agreement with the previous measurement reported by Koscon [5]. For the triton emission probability, no other data are available for comparison. 2.2. 24eCm(sf)
For this measurement a twin Frisch gridded ionisation chamber was used, which was coupled to two silicon surface barrier detectors. Our experimental setup was consisting of two AE-E telescopes placed on both sides of the
153 7000
.
, . ,
. , . , .
, . I
.
Channel Number
Figure 1. Binary fission measurement for 246Cm(sf).A clear separation between fission fragments and a-pile up events can be observed.
sample (where AE corresponds t o the energy deposited by the ternary particle in the ionisation chamber, E being the remaining energy). A similar system has been described in detail by Pommd et al. [S]. A spot of curium oxyde with a diameter of 15 mm was deposited on a 30 pm Al-foil using the electro-deposition technique. The thickness of the sample was 46.4 pg/cm2 and the enrichment in 246Cmwas 99.87 %. The measurement was performed in two steps: i) binary fission events were detected yielding the binary fission counting rate; ii) ternary particles were detected and identified allowing the determination of their energy distributions and their counting rates as well. Both steps were carried out in the same detection geometry. Making the ratio of both counting rates allows the determination of the ternary particle emission probabilities. Binary Fission measurement For the binary fission measurement, vacuum was installed in the chamber. The fission fragments were detected by the surface barrier detector placed on the sample side (on the other side of the sample, all the fission fragments were absorbed by the Al-backing foil). Thanks t o the thin sample
154 Right Telescope
Left Telescope 1
'
'
" " '
1
" '
15W 1200 8
900
8
600
:
3w
300
0 0
4
8
12
16
20
24
28
0
32
0
4
8
I2
16
20
24
28
32
600
600
450
450 8
8
U
8
5 300
300 150
150
0
0 0
2
4
8
6
10
I2
Enugy WeVI
14
16
I8
0
2
4
6
8
10
12
14
16
Energy
Figure 2. Measurement of the ternary alpha and triton energy distributions for 246Cm(sf). The spectra obtained from the two telescopes are shown: the right (left) telescope corresponds t o the sample side (backing side). The Gaussian fits performed on the experimental data are plotted and the number of detected events are given.
used, a clean separation between alpha pile-up and fission fragments could be obtained (see Fig. 1) allowing a clear determination of the binary fission counting rate (noted B). Ternary particle measurement For the detection of the ternary particles, the chamber was filled with methane gas kept a t a constant pressure (P=l bar for the ternary alpha detection and P=2 bar for the triton detection). The procedure used to identify ternary particles and separate them from the background was the one proposed by Goulding [7]. This method is based on the difference in energy loss of different particles in the same material, leading to the relawhere T is the effective thickness of tion: T / a = ( E AE)1.73 the AE-detector and a a specific constant of the detected particles. After the selection of the ternary particles in the T/a-spectrum, the total energy distribution ( A E E SE,where SE is the energy loss by the particle in
+
+ +
155 Table 1. Characteristics of the alpha and triton energy distributions for 246Cm(sf) and 245Cm(nth,f). Their emission probabilities are also given. Both statistical and systematic uncertainties are included.
<E> [MeV] FWHM [MeV] Emission Proba. x <E> [MeV] FWHM [MeV] Emission Proba. x lof4
246Crn(sf) (present work) 16.41f0.20 9.73f0.28 2.49f0.12 8.05f0.34 7.77-+0.47 1.72f0.24
245 Cm(nth,f)
Ref. [4] 16.35f0.15 10.10f0.20 2.15f0.12 8.40f0.25 7.76f0.38 1.85f0.21
the sample itself and in the Al-foil) could be obtained. In order to deduce the average energy and the Full Width at Half Maximum (FWHM) of the energy distribution, a Gaussian fit was performed on the experimental data. The ternary particle counting rate was calculated from the ratio between the integrated Gaussian fit and the measuring time. The energy distributions for both ternary alpha and triton particles obtained from the two telescopes are plotted in Fig. 2. The data obtained with both telescopes are in very nice agreement. The gaussian fits were performed from 14 MeV up to 40 MeV for the alpha particles. This 14 MeV threshold was chosen in order to reject events corresponding to the non gaussian part of the alpha spectrum since these events originate from the decay of 5He and/or 6He into 4He one or two neutrons (see Refs.[8], [9]for a detailed discussion of this point). A similar threshold was used for the analysis of the ternary alpha particles emitted from the 245Cm(nth,f)reaction, allowing a reliable comparison between 245Cm(nth,f)and 246Cm(sf)data. For the triton particles, the Gaussian fits were performed from 7.5 MeV (experimental threshold) up to 20 MeV. Average values (weighted by the uncertainties) deduced from the two telescope data are given in Table 1.
+
3. Investigation of Cf-isotopes
This measurement has been performed at the PFl cold neutron guide of the Institute Laue Langevin in Grenoble (France). A sample with a 4 mm diameter and containing 5 ,ug of Z5'Cf was used. The isotopic composition in May 2003 is given in Table 2. For the isotopes present in the sample only the thermal neutron induced fission cross sections of 251Cf(oiy=5322b) and 249Cf(u$'=l633b) are significant (values taken from the JEFF3.0 library). Taking into account the isotopic abundances, the ternary particles will predominantly come from
1 56 Table 2. Isotopic composition of the Cf-sample Isotope Abundance (%)
1 I
24YCf 18.940
I I
250 Cf 30.974
I 251 Cf 1 I 49.794 I
252Cf 0.292
251Cf(nth,f), but the contribution from 249Cf(nth,f) should be taken into account. In addition, considering the isotopic abundances of 250Cf and 252Cf,and their spontaneous fission decay constants, the ternary fission contributions from 250Cf(sf)and 252Cf(sf)have also to be taken into account. In this context, our measurement was carried out in two steps. Firstly, the experiment was performed with the neutron beam closed. In this way, the contributions from spontaneous fission decays could be determined. Secondly, the same experiment, but with the neutron beam opened was performed. After removing the spontaneous fission contribution previously measured, this step allows to investigate the contributions from the thermal neutron induced fission reactions. For both steps mentioned above, the same procedure as for the 246Cm(sf)measurement was applied. Ternary particles were detected using a vacuum chamber in which a AE-E telescope was placed (outside the neutron beam). The telescope was consisting of two silicon surface barrier detectors with an active area of 300 mm2 (for AE) and 450 mm2 (for E) and a depletion depth of 50 pm (for AE) and 1500 pm (for E), which is the best compromise found in order to detect simultaneously the ternary alpha and triton particles (we will see also that part of the ‘Hespectrum could be observed). The AE-detector was covered with a thin Al-foil (30 pm thick) in order to stop both fission fragments and a-particles coming from the radioactive decay of the sample. For the binary fission fragment detection, the Al-foil was removed and the AE-detector replaced by a ring with exactly the same geometric shape. In this way, binary fission fragments and ternary particles were detected in the same detection geometry. 3.1. Measu7trnent with the neutron beam closed
Binary fission measurement Due t o the high activity of the 251Cf sample, the separation between alpha pile-up and binary fission events was not so clean as for the 246Cmmeasurement (see left top of Fig. 3). Nevertheless, the binary fission counting rate could be deduced by making a cut at channel 1000 and extrapolating the binary fission tail down to channel 1. The ratio between the area of
1 57
Beam closed
-
i----l
OA-
. 0
4
Beam opened
03-
.
c" 02U '
g
U
0.1-
05
oa--
0.0
OA-
0.3
N F:
= 256.9 Is
-
H . . 3
03-
3 , I3 0.1-
0.0
0
500
1000 1500 2000 2500 3000 3500 4000
Channel Number
Channel Number
Figure 3. Binary fission measurements performed with the neutron beam closed (left part) and opened (right part). The binary fission counting rates were deduced after fitting the low energy tail (see bottom).
this new curve and the measuring time gives the binary fission counting rate (see left bottom of Fig. 3). Note that the measured number of binary 7.0 BF/s) can be expressed as fission events per second (NZF=256.9 follows: N
~
= ~
F
( ~ 2 5 0 ~ 2 5+0 ~ 2 5 2 ~ 2 5 2
sf
Aay
af
)
(1)
where and A?? are the 250Cf and 252Cf spontaneous fission decay constants, and NZ5O,NZ5' the numbers of atoms (known from the sample characteristics). The €-parameter is related to the detection geometry. It is found that the contributions from 250Cf and 252Cfare YZ5O=34.82 % and Y252=65.18 %, respectively.
158
Beam opened
Beam closed
-
. .
7ow
,
,
,
I
,
IMW
18.
0
.
,
,
,
. ,
,
,
4
8 U l 6 0 2 4 u l
0
I
8 1 2 1 6 L U 2 1
Figure 4. Ternary fission spectra measured with the neutron beam closed (left part) and opened (right part). Lines correspond to the Gaussian fits performed on the experimental data.
Ternary fission measurement A nice separation between background and ternary particles could be achieved from the T/a-spectrum. Therefore, the ternary 4He, 3H and could be properly identified and separated. Their energy distributions are shown in Fig. 4 (left part) and their characteristics (deduced from Gaussian fits) are given in Table 3. Again, a 14 MeV threshold was adopted for the Gaussian fit performed on the alpha particle spectrum. Note that for ‘He-
159 Table 3. Characteristics of the 4He, 3H and 6He spectra measured with the neutron beam closed and opened. Both statistical and systematic uncertainties are included.
4He 3H
6He
<E> FWHM [MeV] <E> [MeV] FWHM [MeV] <E> [MeV] FWHM [MeV]
Neutron beam closed 15.78f0.17 10.28f0.25 8.58f0.64 8.10&0.91 11.34 (fixed) 11.13f0.91
Neutron beam opened 15.71-+0.22 10.43f0.28 8.55f0.59 8.05f0.91 11.34 (fixed) 10.53f0.60
particles, the Gaussian fit was done fixing the average energy at 11.34 MeV (this value corresponds to the 6He average energy obtained from various fissioning nuclei [lo]). We obtained the following ternary particle counting rates:
N:fHe = (0.757 f 0.028) s-l N ::
= (0.055 f 0.008) s-l
N:re = (0.019 f 0.004) s-l The ratios between the ternary and binary fission counting rates are reported in Table 4. 3.2. Measurement with the neutron beam opened
Binary fission measurement The binary fission events measured with the beam opened are shown on the top right of Fig. 3. All fission events from both spontaneous fission decays and thermal neutron induced fission reactions were detected. In order to extract the binary fission counting rate, we used the same procedure as the one applied when the beam was closed (bottom right of Fig. 3). After removing the spontaneous fission contributions, we obtained: N,8,F=1346.2 f 10.0 BF/s, which can be written as:
: :N
= &,
( u 2 4 9 ~ 2 4 9+ , 2 5 1 ~ 2 5 1 nf nf
)
(2)
where ip is the neutron flux. Adopting ~ $ ~ = 1 6 3 3 band ui7=5322b, the 249Cf(nth,f) and 251Cf(nth,f) contributions are Y249=10.46 % and Y25’==89.54%, respectively.
Ternary fission measurement The energy distributions of the ternary particles detected are shown in the
160
Table 4. Ternary alpha and triton emission probabilities from z50Cf,z52Cf spontaneous fissions and from z4gCf(nth,f),251Cf(nth,f)reactions. Only statistical uncertainties are considered.
2 4 Y C f ( ~ , h ,4-f ) " ' C f ( ~ h ,f) 2 5 0 C f ( ~ f ) 252Cf(sf)
+
t/B 6He/B LRA/B x lo3 x lo4 x 105 2.72f0.02 2.35f0.04 7.06f0.15 2.95f0.08 2.14f0.10 7.39f0.44
right part of Fig. 4. The average energy and the full width at half maximum for each ternary particle are reported in Table 3 (again, for 'He-particles, the average energy was fixed a t 11.34 MeV). The corresponding counting rates (after removing the spontaneous fission contribution) arc:
N : p = (3.668f0.168) s-l N z y = (0.316 f 0.054) s-l N nf B H e= (0.095 f 0.020) s-' The ratios between the ternary and binary fission counting rates are reported in Table 4. In a first approximation, the 249Cf(nth,f)contribution can be neglected (Y249=10.46%). So, the ternary alpha and triton emission probabilities for the 251Cf(nth,f)reaction are (2.72f0.13) x lop3 and (2.35f0.40) x lop4, respectively, where both statistical and systematic uncertainties are included. 4. Discussion
The ternary alpha and triton emission probabilities discussed in this section are the following: from 229Th(nth,f) t o 243Am(nth,f),data were taken from Ref. [lo]. We completed these (nth,f)-data by: 245Cm(nth,f) [4], 247Cm(nth,f) [3] and 251Cf(nth,f) (present work, neglecting the u(sf) ~ 3 1 , 249Cf(nth,f) contribution). For (sf)-data, we used: 242y244Cm(~f) [14], 246Cm(sf) (present work), 248Crn(sf) [2], 250,252Cf(~f) [12] and 256-257Fm(~f) [12]. Note that the ternary alpha emission probability data (noted LRA/B, where LRA stands for Long Range Alpha) correspond to the 'pure' 4He emission, i.e. data were corrected in order to remove most of the 'residual' 5Hc contribution. 238124092421244P
4.1. Influence of the spectroscopic factor on the alpha emission probability It is well known that the ternary particle emission process is favored by the available deformation energy of the fissioning nucleus. Since the fissility
161
2.4-
9
2.0.
1.6,
36
31
38 Z'IA
39
'+ o
I
35
36
i
37 Z'IA
38
I
Figure 5 . Ternary alpha (top) and triton (bottom) emission probabilities from (sf)-data (left) and (nth,f)-data (right) as a function of the fissility parameter of the fissioning nucleus. The L U / B data corrected for the a-cluster preformation probability are plotted in the middle. Data obtained from the present work are indicated.
parameter Z2/A of the fissioning nucleus is a measure of the deformation, a positive correlation between the ternary particle emission probability and Z2/A is expected. This is illustrated in Fig. 5 where LRA/B (top) and t/B (bottom) are plotted as a function of Z2/A, separating (sf)-data (left part) and (nth,f)-data (right part). A rather good correlation for the triton particles can be observed, while for the ternary alpha particles, strong fluctuations are seen. In Carjan's model [15], the ternary alpha emission process is governed by the presence of an alpha cluster inside the nucleus which has to gain enough energy to overcome the coulomb barrier. This mechanism was suggested by the fact that all fissionable systems are alpha emitters and assuming
162 Table 5 . Ratio between ternary emission probabilities from (nth,f)-reactions and (sf)-decays. Only statistical uncertainties are considered. Compound Nuclei 240Pu 242Pu 246Cm 24SCm Average
I
4He
I
H
I 0.83f0.06 I 0.81f0.04 0.86f0.04 0.80f0.06 0.83f0.02
1.08f0.19 1.03f0.09 1.04f0.08
that this property was conserved by the nucleus during the fission process. In this context, the so-called experimental spectroscopic factor (S,) which correspond to the probability of an a-cluster preformation were calculated (see Refs. [16, 171 for details of the calculations) for all even-even fissioning nuclei. The ratio between the alpha emission probability and the spectroscopic factor (LRA/B)/S, is plotted in the middle part of Fig. 5 . It appears that the fluctuations of LRA/B are mainly due to the a-cluster preformation probability. Indeed, when LRA/B is corrected for S,, data vary in an almost smooth way as a function of Z2/A as triton particles do. This result confirms the great impact of S, on the LRA emission probability and is in line with Carjan’s theory.
4.2. Influence of the ezcitation energy on alpha and triton
emission probabilities In Table 5 , the ratio between LRA/B obtained from (nth,f)-reactions and (sf)-decays for a given compound nucleus is reported for two P u and two Cm isotopes. The same ratio is also given for ternary triton particles. As already mentioned in the introduction, this ratio reflects the influence of the excitation energy of the compound nucleus on the ternary emission probability. The new data clearly confirm the previously observed trend for 248Cm,namely: a decrease of the ternary alpha emission probability and an increase of the triton emission probability with the excitation energy of the compound nucleus. The same trend is clearly present in our measurement on Cf-isotopes (see Table 4). The weighted average ratios over all compound nuclei given in Table 5 are: < (nth,f)/(sf)>4He= 0.83 f 0.02 for alpha particles and < ( n t h , f ) / ( s f )> S H = 1.04 f 0.08 for triton particles. All these data confirm the differences already described in [18] on the emission mechanism of both ternary particles.
163
5. Conclusion
This paper presents new results on energy distributions and yields of ternary alpha and triton emission from 246Cm(sf).Comparing data from 2 4 6 C m ( ~ f ) and 245Cm(nth,f),we could show that the ternary alpha (triton) emission probability decreases (increases) with the excitation energy of the fissioning nucleus (see Table 1). The same trend could be observed from a similar experiment performed with a Cf-sample (see Table 4). In addition, it was shown that the different behaviour between ternary alpha and triton particles is probably due t o the influence of the cluster preformation in the case of a-particles.
Acknowledgments The authors are indebted for the use of the 251Cf-sampleto the Office Basic Energy Sciences, U.S. Department of Energy, through the transplutonium element production facilities at the Oak Ridge National Laboratory.
References 1. R. Ouasty, Ph.D. thesis, University of Bordeaux, CENBG-8801 (1988). 2. 0. Serot and C. Wagemans, Proc. Seminar on Fission Pont d’Oye IV, Habayla-Neuve, Belgium, 1999, World Scientific, Eds. C. Wagemans et al., p.45. 3. 0 . Serot and C. Wagemans, Proc. 3rd Int. Conf. on Fission and Properties of Neutron-Rich Nuclei, Sanibel Island, USA, Nov. 2002, in press. 4. 0. Serot et al., Proc. 5th Int. Conf. on Dynamical Aspects of Nuclear Fassion, Casta-Papiernicka, Slovak Republic, 2001, World Scientific, Eds. J. Kliman et al., p.319. 5. P. Kozcon, Technische Hochschule Darmstadt, Report IKDA 88/11 (1988). 6. S. Pomm6 et al., Nucl. Znstr. and Meth. A359, 587 (1995). 7. F. Goulding et al., Nucl. Instr. Meth. 31, 223 (1964). 8. C. Wagemans et al., these proceedings. 9. M. Mutterer et al., Proc. 5th Int. Conf. on Dynamical Aspects of Nuclear Fission, Casta-Papiernicka, Slovak Republic, 2001, World Scientific, Eds. J. Kliman et al., p.326. 10. C. Wagemans, in The Nuclear Fission Process, Ed. C. Wagemans, (CRC Press, Boca Raton, USA, 1991) Chapt.13. 11. M. Mutterer and J.P. Theobald, in Nuclear Decay Modes, Ed. D. Poenaru, (IOP Publ., Bristol, England, 1996) Chapt.12. 12. J.F. Wild et al., Phys. Rev. C 32 (1985) pp.488-495. 13. 0. Serot and C. Wagemans, Nucl. Phys. A 641 (1998) 34. 14. R.A. Nobles, Phys. Rev. 126 (1962) 1508. 15. N. Carjan, J. Phys. 37,1279 (1976). 16. 0. Serot, N. Carjan and C. Wagemans, Eur. Phys. J. A8, 187 (2000).
164
17. C. Wagemans and 0. Serot, Proc. 2nd Int. Conf. on Fission and Properties of Neutron-Rich Nuclei, St Andrews, Scotland, 1999, World Scientific, Eds. J.H. Hamilton et al., p.340. 18. C. Wagemans and 0. Serot, Proc. 5th Int. Conf. on Dynamical Aspects of Nuclear Fission, Casta-Papiernicka, Slovak Republic, 2001, World Scientific, Eds. J. Kliman et al., p.301.
Chapter 5
Fission in the Superheavy Region
This page intentionally left blank
MULTIMODAL FISSION IN HEAVY IONS INDUCED REACTIONS* I.V. POKROVSKY (FOR COLLABORATION) Flerov Laboratory of Nuclear Reaction, Joint Institutefor Nuclear Research, 6,Zholiot-Curie str., Dubna, 141980, Russia
The paper presents a review of the experimental works dedicated to the study of the multimodal fission phenomenon. These works were performed in a wide collaboration namely Flerov Laboratory of Nuclear Reaction (JINR, Russia), Institute of Nuclear Physics (National Nuclear Center, Kazakhstan), Institut de Recherches Subatomiques (France), Universite Libre de Bruxelles (Belgium), Laboratorio Nazionale del Sud (INFN, Italy), Laboratorio Nazionali di Legnaro (INFN, Italy) and The Cyclotron Institute (Texas A&M University, USA). Mass and energy distributions (MED) of the fission fragments from the fission of compound-nuclei 2'6,2'8,220Ra, 220,224.226Th , 270 Sg and 274Hs were measured and analyzed with relation to the fission modes presence. Neutron and y-quanta emissions accompanied the fission process of 226Thcompound-nucleus were measured and analyzed the same way.
1.
Introduction
The asymmetry of the fission fragments mass distributions was discovered practically at one time with the discovering of the fission phenomenon itself. After years a number of the experimental results clearly recognized the picture of the fission fragments mass and energy dependence onto the excitation energy and the nucleon composition of the compound-nucleus. At the same time, the statement about prevail of the symmetric fission for the hot nuclei have no exceptions, whereas the statement about prevail of the asymmetric fission in cold fission is true in the narrow region of actinide nuclei only. In the early 198O's, the asymmetric fission component was discovered in the fission of preactinide nuclei (lead region), produced in the reactions with light charge particles [l]. Its contribution into the total yield did not exceed 0.5%, and it was shown that in the framework of the hypothesis of two independent modes [2] it was quite easy to describe quantitatively the main trends in the fission fragment MED's behavior assuming that there were three independent modes instead of two, since two more independent modes could be distinguished in the asymmetric mode itself [3]. The calculations by Pashkevich became the theoretical basis for this approach. First for *08Pb [4], the existence of two * This work is supported by the Russian Foundation for Basic Research (Grant No 99-02-17891) and by INTAS (Grant No 97-11929,OO-655, YS-422). 167
168
valleys was predicted. Then for 'I3At by means of more complex calculations the existence of three valleys at the potential energy surfaces of those nuclei [5] was predicted in the dependence on the mass-asymmetric deformation. The properties of the fissioning nucleus and those of fission fragments formed this surface. The calculations agreed well with the experiment [I, 31. Brosa and coauthors [6] also calculated the fission modes for a large group of nuclei-actinides from '"Ac to element 108 and predicted the existence of three main valleys: the symmetric (S), the bottom of which was always at A,J2, and two asymmetric ones, namely, standard-one (S1) conditioned by the influence of the spherical shell in the heavy fission fragment with the mean mass 132- 134 (2 and N were close to the doubly magic 50 and 82, respectively) and standard-two (S2) appearing due to deformed shells also in the heavy fragment with a mean mass of -140. The study of MED's of spontaneous fission fragments of 236-244Pu isotopes performed by Wagemans' group [7 -91 demonstrated most clearly the existence of two independent asymmetric modes S1 and S2 for actinide nuclei. Until recently the region of nuclei with 213 < A < 226 remained practically unstudied regarding fission modes as the absence of the stable nuclei with atomic numbers Z = 84-87 makes the light charge particles beams useless. At the same time, in this region in particular the transition from predominantly symmetric to the predominantly asymmetric fission with increasing of compound nucleus mass number is predicted. Thus, it is expected that small changes in the excitation energy and nucleon composition of the compound nuclei would change dramatically all the fission characteristics such as mass and energy distributions, neutron and y-ray emission. The only way to study this region of nuclei is using heavy ions beams. Several years ago at the Flerov Laboratory of Nuclear Reactions (Dubna) experiments were started aimed at the study of the properties of the fission process in the intermediate region of nuclei at low excitation energies. We investigated MED's of fission fragments of 'I9Ac and 220-224Th nuclei in the subbarrier fusion reactions I6O + 203Tl,2043208 Pb [lo]. Significant yield of the asymmetric fission was observed. Detailed analysis of the data obtained shown the necessity of the study of neutron and gamma-quanta emissions accompanied the fission process of the mentioned above nuclei. It was also stated that TANDEM type accelerator should be used in such a kind of measurements.
169
2.
Experimental technique and results
'Yy7&kbj All the experiments were performed using well-known zoo technique of double-velocity s d 160 measurements. The first W- 140 experiments were performed Izo using '6~'0 8 ions beams 6 extracted from TANDEM accelerator of Laboratori Nazionali del Sud (LNS) 2 (INFN, Catania, Italy). 75 90 105 l2l 135 I50 Homogeneous lavers of 204,208Pb M (u) evaporated onto the carbon Figure 1. Two independent sets of the experimental +"%+%I
-
data obtained in reaction ''O(78MeV) + "'Pb
backings were used as targets. Time-of-flight spectrometer DEMAS [ 111 based on large area position-sensitive parallel plate avalanche counters (PPAC) was used in fission cross-section and fission fragments time-of-flights measurements. The y-ray multiplicities were measured with an array of six 3x3 inches NaI detectors arranged symmetrically around the target at the distance of 14 cm and at an angle of 55" out of the reaction plane. Fission of 220,224,226Th compound-nuclei was studied [ 12, 131. These experiments were further continued at higher energies on the K500 superconducting cyclotron at Texas A&M University Cyclotron Institute. New spectrometer CORSET [ 141 based on position-sensitive micro channel plate detectors was constructed for the neutron multiplicity measurements. Neutron emission and fission fragments MED from fission of 226Thcompoundnucleus were studied using "0 ions beams, extracted from VIVITRON accelerator of Institut de Recherches Subatomiques (Strasbourg, France) [ 151. Neutron multi-detector facility DEMON [161 together with CORSET spectrometer was used. The MED of 270Sg and 274Hs compound-nuclei, produced in reactions with "Ne and 26Mg ions beams, extracted from U400 accelerator of FLNR (JINR,Russia) were studied [17]. The fission cross-section and fission fragments MED of "ORa, produced in reactions with I2C ions beams, extracted from TANDEM accelerator of LNS were studied [18]. CORSET setup together with spectrometer PISOLO [19] were used in simultaneous fission and evaporation residues cross-sections measurements of 216,2'8,220 Ra compoundnuclei, produced in reactions with I2C and 48Caions [20], extracted from XTU Tandem + ALP1 accelerator of Laboratori Nazionali di Legnaro (Padova, INFN, Italy). MED of 216,2'8Racompound-nuclei were also measured and analyzed with relation to the reaction entrance channel [21].
170
3.
Experimental data treatment, analysis and discussion
3.1. Description of 226Thmass and energy distributions
Figure 1 presents two sets of experimental data obtained in reaction 20sPb('80,f) at the same energy of '*O ions (EM,= 78 MeV, EL,,, = 26 MeV), but using different spectrometers (CORSET and DEMAS) and even different accelerators (VIVITRON and TANDEM). At the top of the figure double-differential fission cross-sections a 2 0 / a M a E , are shown. To be shorter let's name this type of cross-section as matrix of fragments YexpdE).The bottom of the figure presents the first moments of that cross-sections, namely mass distributions, approximated with a series of Gaussians. Both sets of data are in accord with each other except that the width of the mass spectrum in case of DEMAS is a bit larger due to the fission fragments straggling in quite thick entrance windows of PPAC's. In any case, significant yield of the asymmetric fission is clearly visible in both cases. It is known, that experimentally observed distribution of the total kinetic energy of fission fragments with a given mass M[Yexp(M,Ek)] is a superposition of the fK(M, Ek)] distributions of three independent modes. Using the known expressions for the moments of composed distributions, experimental values of the yields Yexp(M),those of the mean kinetic energies zk,exp(M)and kinetic energy variance a&,,(M) can be expressed via characteristics of the independent fission modes [I, 31.
where the indices i and j correspond to the fission modes S1, S2 or S. It is obvious that for determining the values of Y,(M) from this system of equations it is necessary to set the dependences E k , , ( M ) and &,,(M) for all independent modes. The mode of setting those dependences was proposed in work [22]. Dependence of the average total kinetic energy on the fission fragment mass for each mode and the ratio between the squared average total kinetic energy and the variance of kinetic energy for each mode can be presented as follows: E , ( M ) = E k ( A / 2 ) ( 1 - ~ 2 ) ( 1 + a ~Ei(M)/oi(M) 2), =const, where p = 1 - M/A, and parameter a characterizes the degree of deviation of E , ( M ) from the parabolic dependence suggested by Nix and Swiatecki [23]. Distribution of the total kinetic energy of fission fragments with fixed masses for each mode can be described by the Sharlie function [22]:
171
where
y,(M) =)(Ek -i?k(M))3( /a: is the dissymmetry coefficient, y z ( M ) = )(E, - $ ( I V ) ) ~ 10;( 3 is the excess coefficient. Both coefficients
characterize the degree of deviation of the distribution from the normal one. At yl = y2 = 0 the Sharlie distribution identically turns into a normal one. In this work as well as in [22] it is assumed that y1 and y2 do not depend on the fission fragment mass. For the energy distribution of the symmetric mode, yl was equal to -0.1 and y2was equal to 0, in the case of asymmetric modes it was y2 = y2 = 0.2 [22].Parameter a was the same for all the fission modes. The procedure of the analysis was an iteration process realized within a standard computer code MINUIT [24]. In our analysis the following assumptions have been used. There are three independent modes, one symmetric and two asymmetric, which contribute to the fission fragment MED's of the indicated nuclei. In simple words, total kinetic energy spectra for each of the fragment mass were decomposed into three components. An example of decompositions is shown in Figure 2. Finally, integration of the curves shown with open circles gave us a yield of each of the fission modes at fixed mass. Mass distributions obtained as the results of decompositions are shown in the Figure 3 for both data sets. 1
10'
1 on
g
*
10"
80
FPY
Figure2. An example of the fixed mass total kinetic energy spectra decompositions
100
120 M (u)
140
160
Figure 3. Mass distributions obtained from the fixed mass TKE spectra decompositions. Triangles are for the lowest TKE fission mode (9,circles - for the intermediate TKE mode (S2), and squares - for the highest TKE mode (SZ). Black symbols are for the CORSET data and open symbols - for the DEMAS data. Exoerimental data are shown with lines.
The results of the decompositions are presented in [25] in full details. Here we only want to point out the fact that in the case of the fission mode (Sl) we obtained for both data sets a broad asymmetric and two-humped distribution with M- 137 instead of the narrow symmetric distribution Y,(M) with the mean
172
mass M - 133. This behavior of the (Sl) mode is caused by the peculiarities of the 226Thfission rather than by the experimental errors. This at first sight strange behavior of Yl(M) can be understood taking into account the results of [22].The authors managed to show convincingly that the fission mode (S3) exists as predicted by Brosa. In addition, it was established that in contrast to (Sl) and (S2), the (S3) mode is caused by the shell effects in the close-to-sphere neutron shell in the light fission fragment with N - 50. This is the reason why the high kinetic energies, which are close in values to Ek for mode (Sl), correspond to this mode. Proceeding from this, it becomes clear that in the three-component analysis mode (S3) would manifest itself as a distortion of the (S1) mode. Using a hypothesis on the unchanged charge density, one can easily obtain mass M - 144 of the heavy fission fragment complimentary to the light one with N = 5 0 . The expected positions of peaks for modes S1 (133), S2 (139) and S3 (144) are shown in Fig. 3 with arrows. As is seen, these values are close to the peak positions of yields of the corresponding modes obtained in this analysis. This fact allows us to make a conclusion about the significant role of mode S3 in the formation of the 226Thfission fragment MED. 3.2. Study of pray emissionfromflssion of 226Th
Figure 4 presents results obtained from the reaction 208Pb('80,f) with two energies of "0 projectile. Typical characteristics of the fission fragments are shown at the top part of figure 4. l&('0)=78 hkV LrO)=144 hkV For the energy Elab= 78 MeV the mentioned above descriptions of MED's are shown. For the energy El& = 144 MeV ( E,:,t. = 87 MeV) the MD has single Gaussian shape and shapes of Ek(hf) and &(hf) are parabolic, that testify to the 18 disappearance of shell effects. In 16 other words, only S mode is 14 realized in the fission of the heated nuclei. In figs. 4 g 4 j the ?c!i y-ray multiplicities My(M) and 75 100 125 150 75 100 125 150 their relative energies E y ( l as a M (amu) function of the fission fragment Figure 4. a-9 Fission fragments MED for two energies of I8O. masses are shown. In the g, h) -pray multiplicities vs. fragment mass My(M) presented distributions significant i .I)y-ray relative energies vs. fragment mass Ey(M)
& 1J - - ! :
173
differences may be noticed not only on the absolute values of My as a result of different temperatures T and angular momenta I of fissioning nuclei, but most important, in the structures of My(M) distributions at different beam energies. It is well known that the y-rays are emitted from the fission fragments after evaporation of post-scission neutrons vposlat the very last stage of their deexcitation. At this point the internal structure of fission fragments is very important. If the number of nucleons in the final fragment is close to the magic ones, the y-ray cascade will reflect the structure of the nuclear states peculiar to near magic, almost spherical nuclei. These nuclei have minimal densities of quasiparticle and rotational excited states and as a result the minimal value of My will be observed relative to the non-magic neighboring nuclei. This will take place even if the initial fragment is heated and strongly deformed [26]. On the other hand, during the spontaneous or low-energy fission at the scission point fragments can already be spherical, especially for the asymmetric modes S1 and S2. In this case the densities of quasiparticle and rotational excited states are already minimal; therefore for these fragments (modes) My will be minimal in comparison to the other modes. For the I?,:,,, = 87 MeV at the scission point all fission fragments are strongly heated and deformed, and their internal structure is insignificant. That is why the minima in My(M) at M H - 128-130 (and complementary to them) appears for all measured energies and might be associated with the structure of final stage fragments, which are around the magic numbers ZH- 50, NH - 80, and NL - 50. For all other masses there is no structure because they are far from the double-magic numbers. Another minimum around MH 128-130 at lower energy reflects the existence of close to spherical shapes in the heavy primary fragments near the scission point (5'2 mode) [13]. In this case the light fragment is deformed. Nevertheless, the total deformation of both fragments is significantly less than for the same mass range with higher excitation energies. In favor of this assumption is the fact that S2 mode is dominating during the fission of 226Thand has a yield almost one order of magnitude greater than the sum of S1+S3 modes (Fig. 1).
-
3.3. Study of neutron emission from fission of 226Th
As it was mentioned above, the neutrons from reaction 208Pb('80,f) were measured at two energies of "0 projectile (Elab= 78,90 MeV) using DEMON multi-detector facility [16] in the close to 4x geometry [15]. Neutron energy spectra were obtained measuring neutrons time-of-flights. Obtained spectra were fitted using well-known three moving sources fit [27] in order to extract from total neutron multiplicity (vbJ its pre-fission (vpre)and post-fission (vpos,)
174
components. The quantitative results are shown in figure 5 together with the results for reaction 208Pb('80,f) [28]. ,
220
. , . , . , . , .
,
.
200 -
9
-z"
a 4.a
180-
160-
w"
2-
.
140-
120-.
Figure 5. Total, pre-fission and post-fission neutron multiplicities from the reactions '08Pb(160,f) and zosPb(180,f)
.
,
. , . , . , .
I
.
Figure 6. Double-differential asymmetric fission cross-sections a z c / a M a E k of '"Th compound-nucleus
In order to obtain the neutron multiplicities for symmetric and asymmetric fission these processes should be separated. The central parts of MED were fitted basing on the statements [22]. The parameters obtained from fits were used to calculate the matrix of the fragments Y d E ) originated from the symmetric fission. Then this matrix was subtracted from the experimental one. The result of subtraction is shown in figure 6 for the energy Elob= 78 MeV ( E,Li,,= 26 MeV). In other words, figure 6 presents experimentally measured double- differential asymmetric fission cross-sections d2c/aMaEk of 226Th compound-nucleus. Basing on this matrix, the contours shown in fig. 6 with lines were created and applied to the experimental matrix. Finally we had three groups of events, namely two from the contours and one gated around A&2 f 10. Neutron spectra for each of the group were fitted independently and quantitative results are shown in Table 1. Table 1. Neutron multiplicities for different ranges of Y,(E) of 226Th AIL events
vpm vPtl vtOl
1.62 3.08 4.7
2.32 3.38 5.7
Li ht 1.85 2.19 4.04
2.53 2.51 5.04
Am/Zi10
1.52 3.11 4.63
2.59 3.21 5.8
1.94 2.13 4.07
2.24 2.78 5.02
175
The most interesting feature of the data from Table 1 is the dependence of pre-fission neutron multiplicity (vpre)on fragment mass. One can see that, on the contrary to the results of [29,30], for the lower energy the vprevalue for the asymmetric parts of YM(E) are about 0.35 neutrons larger than vpre for the symmetric one. But here we should note that the measurements in [29,30] were performed at the initial excitations of the compound-nuclei of Eli,, = 77 MeV and higher, when all the shell effects are washed out. Thus, the only way to explain such a strange behavior of vpre(M) dependence is the shell effects influence. Indeed, moving to the higher energy ( = 38 MeV) one can see that vprevalue for the asymmetric parts of Y d E ) becomes less than vprefor the symmetric one due to the higher contribution of the symmetric component into the contoured parts of YdE). So, the behavior of vpre(M)for the lower energy can be interpreted by saying that the time needed to follow the asymmetric valley is larger than that to follow the symmetric one. It may also mean that the time needed to emit one neutron is shorter. However, it seems unlikely that the consideration of the potential energy surface alone will be sufficient to understand the effect. First, the surface is modified by the emission of each prefission neutron, so the dynamical calculations are certainly required. Second, structure effects must obviously be taken into account. Because of the particular choice of the compound nucleus and of quite low excitation energy at which it is formed, the present study is the first in which it was demonstrated [15].
Eliil,
3.4. Fission modes and quasi-fusion in decay of Ra nuclei MED of 216,218.22%a nuclei produced in the reactions with I2C and 48Ca ions in wide range of the initial excitation energies ( = 22 - 57 MeV) were studied. The study of fission fragments MED of "%a at low excitations seems to be the most interesting task, as complimentary fragment to the double-magic 13'Sn (S1 mode) is "Sr, which has magic number of neutrons. This should significantly increase the relative yield of S1 mode. Experimentally this should be observed in total kinetic energy (Ek) spectrum, as this super-compact configuration should appear with very high Ek. Indeed, comparable yields of S1 and S2 modes have been observed experimentally in mass distributions as well as in Ek spectra [18, 311. From the comparison of the decomposition of the 226Thfission fragment MED with that of heavier nuclei [22] it follows that with increasing the mass of the fissioning nucleus the relative contribution of S1 mode into the asymmetric fission rapidly decreases. It agrees well with the results of [32 - 341 in which this mode was not called up for analyzing the MED's of fission fragments in the region of 2 2 7 A-~233Pa,and its contribution if any was very small. At the same
176 time, works [1,3] showed that in the fission of preactinide nuclei the contribution of the high energy and 52 modes were comparable. One possible explanation of the irregular behavior of the high-energy mode can be obtained from the systematic [22]. Indeed, if the far extrapolation is justified, in the vicinity of lead the location of the mode S3 peak will correspond to the heavy fission fragment mass M~ 130 and it will lead to an increase in the yield of high-energy mode. Finally, for compound nuclei 216~ 220 Ra we obtain ratios between the probabilities of the symmetric and asymmetric fission modes (Ys / Ya) as *«. a function of compound nucleus initial excitation energy and its nucleon composition [35]. Figure 7a presents the dependence of the Ys I Ya as a function of the mass number ACN 204 208 212 216 220 224 228 232 236 240 for the nuclei from 204Pb to 234U at £jP = 9-10MeV [36]. The results Figure 7. Ratio between the probabilities of the for 216"220Ra of the present study are symmetric and asymmetric fission modes (Y/Ya) shown with solid circles. They fit well as a function of compound nucleus mass. into the unified dependence. Figure 7b shows the experimentally found differences between the asymmetric and symmetric barriers E"} - Esf for 210Po, 213 At, nuclei in the region of heavy isotopes 226Ra-228Ac [36] and 233Pa-237Np from [37]. Thus in Figs. 7a and 7b we can observe a clear correlation between l "Pb("c,f) "Er("Ca,f) the ratio Ys I Ya and the difference of E = 40.5 M e V ) 200 the barrier height values and we ISO 160 160 expect that for 220Ra Eaf > E} and the ' 140 140 difference which is indicated in 120 120 6000 Fig. 7b will be 0.6-1.8 MeV [ 4500 dependency on the particular nucleus. ' 3000 1500 Very interesting effect was found 216 160 when Ra compound-nucleus is 155 formed in the reaction with 48Ca ions. 150 145 Figure 8 presents fission fragments 216 150 MED of Ra formed at the same 100 initial excitation E*nit ~ 40 MeV, but 50 in reactions with 12C and 48Ca ions. It 50 75 100 125 150 50 75 100 125 ] was found that the total yield of .M (u) „,M (u) „, ,,, Figures. Fission fragments MED of 216Ra asymmetric fission of Ra compound compound nucleus produced in reactions nucleus formed at this excitation with 12C and48Ca ions beams.
177
energy does not exceed the value of 1.5 % [35]. At the same, from the right part of Fig. 8 one can see that MED of the same nucleus produced in reaction with 48Cashows huge yield of the asymmetric component (-30 %). This effect can be only explained by the presence of the different process contribution, namely quasi-fission [21]. This preposition was confirmed analyzing the data on fission and evaporation residues cross-sections from the reactions z04Pb(1zC,f) and 168 Er(48Ca,f). The suppression of fission by quasi-fission was found for the reaction '68Er(48Ca,f) [20]. At the same time, only a small yield of the asymmetric component was observed for the reaction 208Pb(48Ca, f) while for the reactions 238U,244P~,248Cm(48Ca, f) asymmetric component dominates [38]. Summing up, we can assume that the nature of the quasi-fission process is closely connected with the nuclear shells [39]. Indeed, in decay of heaviest composite systems produced in reaction with 48Ca ions heavy peak of mass distribution is always centered around the mass M - 208, which is obviously due to very strong shells of double-magic "'Pb [38]. At the same time, in decay of 256N0 composite system only the light fragment can be close to the magic numbers (Z 28, N 50) and only a small yield of the asymmetric component is observed. In decay of 'I6Ra composite system heavy fragment as well as the light one are close to the spherical shells (Z - 28, N 50, Z 50, N 82) and the yield of the asymmetric component increased significantly [21]. Thus, we can conclude that the properties of quasi-fission process is very similar to the asymmetric fission and only one way to distinguish between them is to measure the decay times or the fragments angular correlations.
-
-
-
-
-
3.5. Fission modes and quasi-fission in decay of 270Sgand 2'4Hs nuclei
Finally we want to discuss the decay properties of heavy systems 270Sgand 274Hs, produced in the reactions with "Ne and "Mg ions beams correspondingly. The MED of 252-257Fm and 258Mdfission fragments at medium excitation energies (El 18 MeV) have been studied in Ref. [40]. It has been shown there that the complex structure of the fission fragment MED is observed at these excitation energies, though less distinctly. The interest in study of 270Sg and 2 7 4 H systems ~ was based upon three reasons. First, traditional ways of studying the properties of super-heavy elements, i.e., the study of the spontaneous fission of nuclei with 2 - 105, 106 and upper have evidently exhausted themselves since the accumulation of a large number of nuclei of these elements and subsequent investigation of their fission characteristics presents practically an impracticable experimental task. That is why an investigation of the fission fragments MED of super-heavy element using the sub-barrier fusion-fission reactions in which low excitation energies can be
-
178
available is the most acceptable and promising tool. Second, the 270Sgnucleus was chosen as it has 164 neutrons and since it undergoes fission into two equal parts the number of neutrons in both fission fragments is the magic one (without taking into account the pre-scission neutrons). At the same time, the 2 7 4 H ~ nucleus has 166 neutrons and since it undergoes fission the same way the number of neutrons in both fission fragments is again the magic one, but taking into account the pre-scission neutrons. EM= 102 MeV
E,&= 127 MeV
2000
1500 n
Nz
1000
HE:
D
500
40
80
120 I60 2W
40
80
125
120 160 200 240
M (u)
M (u)
150
175
ux) 225
250
275
300
325
E,. (MeV)
Figure 9. Fission fragments MED of 270Sg compound system at different TKE ranges
Figure 10. Variance of 274H~ fission fragments mass-distribution as a function of TKE.
Figure 9 shows fission fragment mass distributions of 270Sgfor specific TKE ranges. For Elab = 102 MeV ( E;,, 28 MeV) and TKE > 240 MeV, the sum of the two fission modes, the sharply narrow and the wide ones, is seen. For Elab = 127 MeV (El:,, 51 MeV) no structures can be seen as all the shell effects are washed out. We suppose that the narrow symmetric component is connected with the manifestation of the spherical neutron shell with N 82 in both fragments [18]. At the same time, enhanced yield of the masses in region A - 208 was observed and twofold interpretation (fission mode or quasi-fission) was done [IS]. Nearly the same situation is realized in the decay of 2 7 4 H compound ~ system, which was produced at three energies of 26Mg projectile @lab = 129, 143, 160 MeV; El:,, 31, 43, 59 MeV). At the lowest energy the yield of high-energy symmetric mode was observed in mass distribution as well as in TKE spectrum. Significantly higher yield of the masses in region of A 208 was observed at the energy Eiab= 143 MeV, comparing to the energy El& = 160 MeV and to 270Sgdecay. This fact is demonstrated in figure 10, where the mass variance is shown as a dependence on TKE. One can see, that the mass distribution for the lower energy is much wider in region of low TKE. Let us note, that in this case we deal with the heavier projectile comparing to
-
-
-
-
-
179 270
Sg. Thus, the assumption of quasi-fission component presence in decay of Sg and 274Hsbecomes preferable.
270
References 1. M. G. Itkis etal., 2. Phys. A320, 433 (1985); Sov. J. Part. Nucl. 19, 301 (1988); Nucl. Phys. A502,243 (1989). 2. A. Turkevich and J. B. Niday, Phys. Rev. 84, 52 (1951). 3. M. G. Itkis et al., Sov. J. Nucl. Phys. 41, 544 (1985); 41, 709 (1985). 4. V. V. Pashkevich, Nucl. Phys. A169,275 (1971). 5. V. V. Pashkevich, Proceedings of the XVIII International Symposium on Nuclear Physics and Phys. Chem. Fission, (Castle Gaussig, GDR, 1988), edited by H. Marten and D. Seeliger (Rossendorf, ZfK - 732, 1988), 120. 6. U. Brosa, S. Grossmann, and A. Muller, Phys. Rep. 197, 167 (1999). 7. C. Wagemans et al., Nucl. Phys. A502,283 (1989). 8. P. Schillebeeckx et al., Nucl. Phys. A545,623 (1992). 9. L. Dematte et al., Nucl. Phys. A617,331 (1997). 10. M. G. Itkis et al., Proceedings of the XV EPS Conference on Low Energy Nuclear Dynamics, (St. Petersburg, Russia, 1995), edited by Yu. Ts. Oganessian et al. (World Scientific, Singapore, 1995), 177. 11. M. G. Itkis et al., Heavy Ion Physics, Scientijic Report. JINR,179 (1994). 12. M.G. Itkis et al., JINRpreprint E7-96-414, Dubna, 1 (1997). 13. G.G. Chubarian et al., Phys. Rev. Lett. 87(5) 052701 (2001). 14. N.A. Kondratiev et al., Proceedings of the 4Ih Int. Con$ Dynamical Aspects of Nuclear Fission, (Casta-PaperniEka, Slovak Republic, 1998), edited by Yu.Ts. Oganessian et al. (World Scientific, Singapore, 1999) 43 1. 15. A. Kelic et al., Europhys. Lett. 47(5) 552 (1999). 16. S. Mouatassim et al., Nucl. Instr. andMeth. A359, 330 (1995). 17. M. G. Itkis et al., Phys. Rev. C59,3 172 (2003). 18. I. V. Pokrovsky et al., Phys. Rev. C60,041304 (1999). 19. G. Montagnoli et al., Nucl. Instr. andMeth. A454, 306 (2000). 20. R. N. Sagaidak et al,, Phys. Rev. C68,014603 (2003). 21. A. Yu. Chizhov et al., Phys. Rev. C67,011603 (2003). 22. S. I. Mulgin et al., Phys. Lett. B 462,29 (1999). 23. J. R. Nix and W. J . Swiatecki, Nucl. Phys. 71, 1 (1965). 24. CERN Computer 6600 series program Library Long-Write-UP MINUIT 25. I. V. Pokrovsky et al., Phys. Rev. C62,014615 (2000). 26. R.P. Schmitt et al., Z. Phys. A321,411 (1985). 27. D. Hilsher et al., Phys. Rev. C20, 576 (1979). 28. H. Rossner et al., Phys. Rev. C45, 719 (1992). 29. H. Rossner et al., Phys. Rev. C40,2629 (1989). 30. D. J. Hinde et al. // Phys. Rev. C45, 1229 (1992). 31. I. V. Pokrovsky et al., see Re$lS p.357. 32. E. Pfeiffer, Z. Phys. 240,403 (1970).
180
T. Ohtsuki et al., Phys. Rev. Lett. 66, 17 (1991). Y. Nagame et al., Phys. Lett. B387,26 (1996). M. G. Itkis et al., will be published H. J. Specht, Rev, Mod. Phys. 46,733 (1974). T. Ohtsuki et al., Phys. Rev. C48, 1667 (1993). M. G. Itkis et al., JINR Preprint EI5-2000-295, Dubna, 1 (2000) J. M. Itkis et al., Proceedings of Int. Symposium on New Projects and Lines of Research in Nuclear Physics (Messina, Italy, 2003), (World Scientific, Singapore, 2003), in press. 40. H. C. Britt et al., Phys. Rev. C30, 559 (1984).
33. 34. 35. 36. 37. 38. 39.
THE ROLE OF THE QUASIFISSION PROCESS IN REACTIONS FOR THE SYNTHESIS OF SUPERHEAW ELEMENTS G. GIARDINA, G. FAZIO, A. LAMBERTO Istituto Nazionale di Fisica Nucleare, Sezione di Catania, and Dipartimento di Fisica dell'llniversitci di Messina, Messina, Italy R. PALAMARA Dipartimento PAU dell'Universitd di Reggio Calabria, Reggio Calabria, Italy A.K. NASIROV +, A.I. MUMINOV, K.V. PAVLIY, A.V.KHUGAEV Heavy Ion Physics Department, INP, Tashkent, Uzbekistan Z. KANOKOV Physical Department of the National University of Uzbekistan, Tashkent, Uzbekistan F. HANAPPE, T. MATERNA Universiti Libre de Bruxelles, Bruxelles, Belgium L. STUTTGE Institut de Recherches Subatomiques, Strasbourg, France
We analyze the effect of entrance channels having very different mass asymmetries on the quasifission process in competition with the fusion, and on the fissility of the compound nucleus in competition with the evaporation residue production. According to the dinuclear system (DNS) concept, in reactions with massive nuclei, we estimate the capture and fusion cross sections. Using the calculated partial fusion cross section and the advanced statistical model, we also estimate the evaporation residue cross sections for the superheavy nucleus formation.
1. Introduction Quasifission reactions are binary processes which exhibit some of the characteristics of fusion-fission events, such as the full relaxation of the relative kinetic energy and considerable transfer of mass between the two fragments. The basic difference between the fusion-fission and quasifission processes is
Also at Bogoliubov Laboratory of Theoretical Physics, JINR, Dubna, Russia 181
182
that the compound nucleus formation is not achieved in the latter mechanism. In quasifission reactions, a dinuclear system, which is formed at the capture stage of heavy ion collisions, can evolve over the potential energy surface before reaching mass symmetry or decay by way of overcoming the quasifission barrier [1-6]. The latter decreases usually with an increase in the mass symmetry. The aim is to analyze the influence of the partial fusion cross section &"(E), which is sensitive to the competition between complete fusion and quasifission, on the GI& ratio providing information on the real fissility of the compound nucleus. Of course, the shape and yield of the evaporation residues are also strongly related to the o$F"(E) distribution caused by the dynamical effects in the entrance channel. The fusion-quasifission competition is determined by the fusion factor PCN which is calculated statistically, using intrinsic fusion and quasifission barriers (B>,s and Bd) [4-61. We calculate the capture, fusion and ER cross sections for the 48Ca+243Am and 48Ca+248Cm reactions leading to the "'1 15 and 296116 superheavy elements, respectively. Moreover, we consider a set of reactions with different mass asymmetry ( VA = (A2 - AJI(A1 + A 2 ) ) of the entrance channel, leading to the "'Th and 256Rfheavy compound nuclei. We compare our calculations with available experimental data [7,8] and discuss the effect of the entrance channel on the formation of evaporation residues for the '60+2""Pb and 96Zr+'24Sn reactions leading to the 220Th*compound nucleus, and for the 24Mg+232Uand 64Ni+'920sreactions leading to the 256Rfccompound nucleus.
2.
Method of calculation
According to the DNS concept [9], the evaporation residue production following a nuclear reaction is considered as a three-stage process. The first step is overcoming the Coulomb barrier by nuclei in the motion along the axis connecting nuclear centers at the in-coming stage of collision, and formation of a nuclear composite (the so-called molecular-like dinuclear system). This stage is called capture. The second stage is transformation of the DNS into a more compact compound nucleus in competition with the quasifission process. At this stage, the system must overcome the intrinsic barrier (BGJ at the potential energy surface [4-61 during the evolution on the mass (charge) asymmetry axis. At the third stage, the hot compound nucleus cools down by emission of neutrons and charged particles. There is a chance for the nucleus to undergo fission at each step of the de-excitation cascade. Therefore, the evaporation residue cross section is determined by the partial fusion cross sections and survival probabilities of the excited compound nucleus:
183
Id
g e r ( E )=
c (21+
e=o
I,U{~
(EIWsur
(
~
1) 2
(1)
Here, the effects connected with the entrance channel are included in the partial fusion cross section gp(E),which is determined by the product of partial capture cross sections and the related fusion factor (PcN) taking into account competition between complete fusion and quasifission processes: c{w( E )=
cyPture (E)PCN ( E ,1)
(2)
Here il is the de Broglie wavelength of the entrance channel; PPP'""(E) is the capture probability which depends on the collision dynamics and is determined by the number of partial waves (Q leading to capture. In (l), Wsur(E,t)is the survival probability against fission along the de-excitation cascade of CN. The intrinsic fusion barrier B>s is connected with mass (charge) asymmetry degrees of freedom of the dinuclear system and is determined by the total potential energy. At capture, the DNS is in the potential well. Thus, in order the quasifission could occur, it is necessary to overcome the barrier Bfl which is equal to the depth of the well of V(R). If the DNS excitation energy is not enough for overcoming B f l , it fluctuates on the charge asymmetry axis moving to a more symmetric configuration. The fusion probability PcdE,C) can be calculated using the level density and potential energy surface. The probability of realizing the complete fusion process is related to the ratio of the level densities, depending on the intrinsic fusion or quasifission barriers, by the expression:
where P(EIDNS- B * K ) is the DNS level density which is calculated on the quasifission and intrinsic fusion barriers (BK=B,, B*N). It should be stressed that Bdt) and B>@) depend on the orbital angular momentum: with an increase in 8, the quasifission barrier decreases while the intrinsic fusion barrier increases. Therefore, the factor PCN(4), being a function of these barriers B>.y and Bd and determining the competition between complete fusion and quasifission, decreases with increasing C at given values of the beam energy. A more detailed description of the model is given in Refs.[4-6].The survival probability Wsur(E,C)is related to the partial fusion cross section which affects the fission barrier and the rn which determines the evaporation residue
184
production along the de-excitation cascade of CN; vs,,,.(E,)is calculated with the use ofthe advanced statistical model (ASM) described in Refs.[ 10-121. 3.
Formation of heavy and superheavy elements
3.1. The reaction leading to 296116
In accordance with the above-mentioned consideration, our calculation of the capture cross section (solid line in Fig.1) for the 48Ca+248Cm reaction leading to the 296116compound nucleus is in complete agreement with the experimental data [13] for the production of all fragments (full squares), whereas the fusion cross section (dashed line) is not in agreement with the data (open squares) for the symmetric mass fragments ((Al+A2)/2) when a large mass interval of +20 amu is assumed. E' (MeV) 30 .
.
.
.
*
.
40 .
.
.
I
.
.
.
,
-^x
: "Ca + "%m
80
50
.
.
.
.
.
70
I
I
-> %116
"
- -.. - _ _ _ _
L-.---"-"
_----..______*
10' r
~
'a
10'
L,
220
,.J
,
230
240
,
,
,
,
250
, , I
260
, , I
.
270
,
,
, , ., , 280
290
E, (MeV)
Figure 1 The capture and fusion cross section calculation, in comparison with the experimental data [13,14], for the 48Ca+248Cm reaction leading to the 296116superheavy CN The difference between the fusion cross section and more symmetric fragment yield ((AI+A2)/2+10 amu) at a higher excitation energy is related to the contribution of the quasifission process yielding more symmetric fragments
Such disagreement is connected with the contribution of the quasifission process in the range of the more symmetric fragments in which the fusionfission process also contributes. If it is assumed that the experimental fusionfission events are in the (A1+A2)/2+10 amu interval (almost close to the -/, value), the calculated fusion cross sections (dashed line) will be closer to the new set of the experimental data (open triangles [14] in Fig.1). Indeed, in this case there is an appreciable contribution of the quasifission process (or a contribution which cannot be neglected), in addition to the fusionfission fragment formation. Therefore, the estimated experimental fusion cross section, connected with the new set of the experimental events of fission fragments, still appears to be a little larger than the calculated fusion excitation
185
function at higher excitation energies. A preliminary calculation of the mass distribution of quasifission fragments for a fixed reaction time treocof a DNS, performed in the framework of the model developed on the basis of the dinuclear system concept [15,16], indicates that the fragments of the quasifission process also appear in the mass-symmetric region and are mixed with the fragments coming from the fusion-fission process. In our calculation, the capture and fusion cross sections are characterized by the intrinsic fusion barrier B*hs=4.48 MeV and the quasifission barrier B,= 4.12 MeV. 3.2. The reaction leading to 291115 In this section we present the data on the reaction induced by the 48Ca beam (even-even nucleus with a double shell closure) on the 243Amtarget (odd-even nucleus) leading to the 29' 115 compound nucleus. In our calculation we find the intrinsic fusion barrier B*hS=1.8 MeV and the quasifission barrier B,= 4.2 MeV. These values lead to an appreciable ratio between fusion and quasifission. In Fig.2 we present the capture and fusion cross sections as well as the excitation functions of the evaporation residues after the emission of 2-5 neutrons from the 291115 excited compound nucleus. As one can see, the fusion cross section is about 1-2 mb for a wider beam energy range, the maximum for the ER3, is about 8 pb at E*=26 MeV and the maximum for E k , is about 1 pb at E*=35 MeV. E" (MeV) 10
20
SO
40
30
10' 10' 10 a
o^ r0J E
; io5 10 ' 10'
10''
210
220
23Q
2M
250
2M)
270
E,, (MeV)
Figure 2. The excitation functions for the evaporation residue nuclei obtained from the 29'115 CN after the (2-5) neutron emission in the 48Ca+243Am reaction. The figure also shows the capture and fusion cross sections.
3.3. The reactions leading to "OTh * and "'RP We investigate the '60+204Pband 96Zr+'24Snreactions leading to the 220Th* compound nucleus, and 24Mg+232Uand 64Ni+'920sreactions leading to the
186
256Rfc,in order to analyze the effect of the entrance channel on the CN fissility
GI& and formation of evaporation residues. In Fig.3 we present and compare the calculated capture, fusion and evaporation residue cross sections for the above-mentioned reactions. This figure shows the difference between the capture cross sections (panel a) for the two entrance channels with different mass asymmetries. As one can see, the capture for the two reactions occurs in two different energy ranges. 10 20 30 40 50 60 70 80 90 100110
_---
103[ a)
-I
_
_
_
_
_
-
-
A
-
a E
I0'
10 '
:I
10'
_ r _ _ _ _ _ - - - - - - -
/-
b,
?'''
i
+ "'Sn '"10
20 30 40 50 60 70 80 90 100110 100 110
E' (MeV)
Figure 3. Comparison of the capture (panels a) and fusion (panels b) cross sections for the '60+2"Pb and %Zr+'"Sn reactions leading to "'Th*, and the 24Mg+z3zU and 64Ni+'920sreactions leading to the
256RP.
Due to the large difference between Q-values of the reactions leading to the 220Th*and 2s6RPcompound nuclei, the subbarrier regions of fusion for the '60+204Pband 24Mg+232U reactions are respectively more wide in comparison with those for the 96Zr+'24Snand 6 ~ i + ' 9 2 0reactions s (see panels b of Fig.3). Moreover, since the competition between complete fusion and quasifission processes for these reactions depends on the orbital angular momentum of collisions, the partial fusion cross sections atfu(E)of the compound nucleus in different reactions are different. As a result, the evaporation residue cross sections depend on the entrance channel. Moreover, the yields of the fusion cross section for the 96Zr+'24Snand 24Mg+232U reactions are much lower than those for the '60+204Pband 64Ni+'920sreactions respectively.
187
Comparison of results obtained for different reactions leading to the same compound nucleus clarifies the reaction mechanism. Theoretical analysis shows that the choice of the beam energy for the production of the compound nucleus with the same excitation energy in different reactions does not allow one to reach the same partial fusion cross sections at the end of the fusion stage. In Fig.4 these dynamical effects are shown as a function of the partial fusion cross sections calculated for the reactions related to '"Th* and 2s6RP. As one can see from this figure, the crP(gfor the '60+204Pbreaction has a larger volume in comparison with the 96Zr+124Sn reaction. Generally, the partial fusion cross sections for the '60+204Pb reaction extend to higher angular momentum values, allowing for a larger number of geometrical configurations of reacting nuclei, whereas at excitation energies lower than about 45 MeV the partial fusion cross sections for the 96Zr+'24Snreaction extend to higher angular momentum values in comparison to those of the 160+204Pb reaction.
0 25i
Figure 4. Partial fusion cross sections up(@ for the '60+204Pband %Zr+'% reactions leading to "'Th*, and for the 24Mg+z3zU and 64Ni+'920s reactions leading to 256Rf*.
The structure and shape of cr$G"(E)for the same excited compound nucleus formed in different reactions are sensitive to dynamical effects in the entrance channel. Therefore, different entrance channels leading to the same excited compound nucleus do not generally produce the same evaporation residue cross section, due to the dependence of the survival probability (related to the rvlfio, values at all steps of the CN de-excitation cascade) on the angular momentum yields of CN. Since the '"Th* compound nucleus is formed with different
188
o$F"(E) distributions for the two reactions, its fissility is also dependent on the dynamical effect in the entrance channel. As Fig.4 shows, the yield and the angular momentum range increase for the 16 O+'04Pb reaction at excitation energies E* > 60 MeV. On the contrary, for the 96Zr+'24Snreaction, the angular momentum range of o&E) is larger than that of the 160+204Pb reaction at E* < 45 MeV. Table 1 shows the charge asymmetry parameter (772 = (2, - Zl)/(Zl + &)), the intrinsic fusion (B*&) and quasifission (Bd) barriers, and the fusion factor ( P C N ) for the reactions leading to "'Th* and '%P. Table 1. Charge asymmetry (qz), intrinsic fusion (Ek,)and quasifission barriers (Bd), and fusion factor (PcN)for the reactions I and I1 leading to the 220Th*CN, and for the reactions Ill and IV leading to z56Rf*,at E* = 55 MeV for both "OTh* and 256RPcompound nuclei. (MeV)
(MeV)
2.3 7.2
14.7 5.1
0.822 0.111 64
0.769 0.462
Ni+ 1920 s '
0.13 0.89 0.01
c/&o,
In Fig.5 we present the value against E* for the "'Th* CN obtained by the '60+204Pb and 96Zr+'24Snreactions. This figure shows that in the excitation energy range in which the two reactions lead to the formation of the "'Th* compound nucleus, the GIGo,values for the 160+204Pb reaction are about 1.1-1.2 times greater than those for the 96Zr+124Sn reaction, in the E* > 65 MeV energy region of the CN; whereas at lower excitation energies (E* < 50 MeV) the fissility of the CN for the 96Zr+'24Snreaction is about 1.3-4.6 times higher
1.0
0.5
20
30
40
50
60 70 E' (MeV)
89
90
100
- 00
13 20 25 Jo 35 40 65 D 5S 64 65 70 75
E' (MeV)
Figure 5 Comparison of the CN fissility values (q/fi0,) of the 2"Th* CN compound nucleus obtained by the 160+204Pb and %Zr+"'Sn reactions, and of the 256W CN obtained by the 24Mg+232U and 64Ni+1920s reactions
189
than that for the 160+204Pbreaction. This effect is due to different angular momentum values of op(E)for the 160+204Pband 96Zr+'24Snreactions, at lower and higher excitation energies E*, and it is also due to different ratios between quasifission and fusion for the reactions under discussion (see the PcN, B*f.3,B6values in Table 1). We calculated the rflr;o,ratio at each step along the de-excitation cascade of the compound nucleus as well as the excitation function of the evaporation residues. Of course, the production of ER is strongly related to the energy values at all dependence of the partial fusion cross section ap(E)and steps of the de-excitation cascade of the "OTh* CN. In Fig.6 our calculated total evaporation residues are compared with the experimental data [7,8] for the above-mentioned reactions leading to 220Th*.As one can see, the difference between the evaporation residue cross sections for the two reactions is related to the effects of the entrance channel leading to the same compound nucleus having different fusion cross sections and fissilities at each excitation energy of CN. In fact, in the E*> 60 MeV energy region of "'Th, the ratio between the fusion and the evaporation residue cross sections of the 160+204Pbreaction is about lo5, whereas the corresponding ratio for the 96Zr+124Sn reaction is about lo4; this result is due to bigger fissility of CN for the 160+204Pb reaction. Instead, in the E* < 45 MeV energy region of '"Th, the ratio between the fusion and the evaporation residue cross sections of the 160+204Pbreaction is about lo2, whereas the corresponding ratio for the 96 Zr+lZ4Snreaction is about lo3. Also in this case, the result is due to bigger fissility of CN for the 96Zr+'24Snreaction.
L/co,
m
30
40
50
80
E'
(MeV)
70
80
80
loo
Figure 6 Comparison of evaporation residues for the '60+204Pband 96Zr+'24Snreactions leading to the "'Th* CN The experimental data of the evaporation residues are taken from Refs [7,8]
The G/COl values against the excitation energy E* of the 256RPcompound nucleus are presented in Fig.5. Also in this case we find different fissility values for the compound nucleus 256Rfrproduced in the two 24Mg+232U and 64Ni+'920s reactions. We find that the GIGolvalues for the 24Mg+232U reaction are about
190
1.1-1.3 times greater than those for the 64Ni+'920sreaction, at the same excitation energy of the E* > 50 MeV range of CN produced in both reactions; whereas at lower excitation energies (E* < 46 MeV) the fissility of CN for the 64Ni+'920sreaction is about 1.l-1.3 times greater than that for 24Mg+232U reaction. The reason of this is that the 256RPCN is formed with different o - ( E )distributions in the two above-mentioned reactions, and the result is strongly sensitive to the dynamical effects of the entrance channel. References
1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 12. 12. 13. 14. 15. 16.
F. Hanappe et al., Phys. Rev. Lett. 32, 738 (1974). M. Lefort, Phys. Rev. C12,686 (1975). H. C. Britt et al., Phys. Rev. C13, 1483 (1976). G. Fazio et al., J. Phys. SOC. Jpn. 72,2509 (2003). G. Fazio et al., in press in Eur. Phys. J. A19 (2004). G. Fazio et al., Phys. At. Nucl. 66, 1071 (2003). D. J. Hinde et al., Phys. Rev. Lett. 89,282701 (2002). C.-C. Sahm et al., Nucl. Phys. A441,316 (1985). N. V. Antonenko et al., Phys. Lett. B319,425 (1993); Phys. Rev. (31,2635 (1995). A. D'Arrigo et al., Phys. Rev. C46, 1437 (1992). A. D'Arrigo et al., J. Phys. G20,365 (1994). R. N. Sagaidak et al., J. Phys. G24,611 (1998). M. G. Itkis et al., Proc. Int. Conf. Nuclear Physics at Border Lines, World Scientific (Singapore, 2002), p. 146. E. Kozulin, private communication. R. V. Dzholos et al., Sov. J. Nucl. Phys. 50 382 (1989). G. Fazio et al., Proc. Int. Symp. New Projects and Lines of Research in Nuclear Physics, World Scientific (Singapore, 2003), p.258.
TRACKING DISSIPATION IN CAPTURE REACTIONS IN THE SUPERHEAVY REGION
T. MATERNA: V. BOUCHAT AND F. HANAPPE Universite' Libre de Bruxelles CP 229, Bd du Triomphe 1050 Bruxelles, Belgium E-mail: [email protected] 0 . DORVAUX, c. SCHMITT AND L. STUTTGE IReS, Strasbourg, fiance
Y. ARITOMO, A. BOGATCHEV, I. ITKIS, M. ITKIS, M. JANDEL, G. KNYAJEVA, J. KLIMAN, E. KOZULIN, N. KONDRATIEV, L. KRUPA,
E. PROKHOROVA, I. POKROVSKI AND V. VOSKRESENSKI FLNR, JINR, Dubna, Russia N. AMAR, s. GREVY AND J. PETER LPC, Caen, France
G. GIARDINA Universitd d i Messina, Messina, Italy
The competition between fusion-fission and quasi-fission in the reactions 48Ca+zOs Pb and 48Ca+244 Pu (E' = 40 MeV) is investigated with the CORSET and DEMON detectors. The development of a new analysis method, W M A T E , enables us to obtain the pre-scission neutron multiplicity distributions ( P S N M D ) that allows to disentangle the contributions of fusion-fission and quasi-fission for the first time for a superheavy system at such a low excitation energy. The ratio of the fusion cross-section over the capture cross-section is found to be of the order of 10%.
*Aspirant fnrs.
191
192
1. Introduction In the reactions leading to superheavy elements, different processes compete: quasi-fission -when the system remains of a dinuclear type until separation of the fragments-, fusion-fission -when the system forms one unique nucleus that subsequently fissions-, and evaporation residue production -when, after fusion, the systems cools down by neutron and photon emission until it becomes stable against fission. This last process is the one one wants to favor in the experiments to synthesize superheavy nuclei. The production and the study of those elements is crucial to determine the number of protons and neutrons corresponding t o the spherical closed shell. The cross-sections for the synthesis of superheavy elements is extremely small (of the order of lpb), hence implying beam times of several weeks to observe one single atom. One therefore understands how important it is t o have a model predicting efficiently the best way t o achieve the evaporation residue production. The two data needed by the experimentalist are the target-projectile combination as well as the energy of the later. Several models try to answer these expectations by modeling the different steps of the process (capture, fusion, survival against fission). Each step is complex and the models can disagree by several orders of magnitude. If they generally agree on the available experimental data, i.e. capture and evaporation residue cross-sections, they show significant discrepancies about the fusion cross-section for which no experimental data could be obtained for such systems. The absence of data is due to the fact that both fusion-fission and quasi-fission can lead to similar fragments and hence these are not sufficient to evaluate the part of the events where fusion occurred before scission. One of the main ingredients of the models is the nuclear dissipation. The question of the dissipation in nuclear reactions is a long-standing problem. The theoretical values found in the literature cover three orders of magnitude and even when experimental data are used as constraints, the value are still spread over two orders of magnitude. The very nature of the dissipation is not yet fixed. Better constraints are hence necessary to extract the dissipation. The competition between fusion-fission and quasi-fission is very sensitive to the dissipation used in the model and hence could be an efficient way of tracking it. To constraint those models, we tried to obtained the fusion cross-section in the case of 48Ca+244 Pu a t 40 MeV of excitation. To achieve this, we identify this cross-section with the fusion-fission cross-section. This as-
193
sumption is justified by the fact that the survival probability for this kind of system is very small. We then only need to disentangle between the fusion-fission and the quasi-fission contributions within the capture reactions. This was done by the analysis of the pre-scission neutron multiplicity distributions (PSNMD) as will be detailed later, after the description of the experimental set-up and of the analysis method we used. 2. Experimental set-up Both reactions, 48Ca+208 Pb and 48Ca+244 Pu (E* = 40 MeV) were studied with the same set-up at the U400 cyclotron of the Flerov Laboratory of Nuclear Reactions (JINR, Dubna, Russia) during February and March 2001. The fragments were detected with the CORSET" two-arms timeof-flight spectrometer. Their masses and their energies were obtained from kinematic relations assuming a binary process. The neutrons were detected in coincidence with the fragments with the DEMONb neutron detector. DEMON is a composed of cylindric detectors (radius = 8 cm and depth = 20 cm) of NE213 liquid scintillator. 41 of those detectors were placed around the target at an distance of about 60 cm. The energy of the neutrons were calculated from their time of flight between the target and the detectors. 3. Pre-scission neutron multiplicity distributions (PSNMD)
We applied the method described in Appendix A using a very simple model of cascade evaporation of neutrons from the composite system (compound nucleus or di-nuclear system) and the two fully accelerated fragments. The emission is assumed to be isotropic in the rest frame of each source. The post-scission emission is divided between the fragments proportionally to their mass as is the excitation energy. The source parameters are the initial excitation energy, the pre- and post-scission multiplicities. The observable parameters to be fitted are the detected multiplicity, the number of the hit detector (equivalent to the angular distribution) and the energy of the neutron. For events with more than one neutron detected the number of the detector and the energy were determined by choosing a neutron randomly. Due to problems in evaluating the efficiency of the detectors, the absolute values of the multiplicities are questionable. They seem t o be too high aCORSET: CORrelation SET-up bDEMON: Ddtecteur MOdulaire de Neutrons (modular neutron detector)
194
compared to the systematics which however deals only with mean values. Nevertheless, the shape of the pre-scission neutron multiplicity distribution (PSNMD) were found to be very similar when the efficiency was changed within reasonable limits.
\ F
0.2
0.1
~~
0.0
\ i 7
i
Figure 1. Pre-scission neutron multiplicity distribution for 48Ca+208 Pb
In figure 1, we show the result obtained for the PSNMD for the system 48Ca+208 Pb where the mass of the fragments M was restricted t o be in a 60-mass-units-wide interval centered on symmetry: - 3 0 , g + 301 where A is the mass of the compound nucleus. The distribution exhibits only one component with around 2-3 neutrons emitted before scission. For such an asymmetric entrance channel, one expects fusion-fission to be dominant and hence to have only one process. The experimental results (including masstotal kinetic energy distribution as well) are coherent with that picture. For the 48Ga+244 Pu reaction, two analysis were made, one for scissions close to symmetry ( M E [$ f 301) and one for asymmetric scissions where the heavy fragment mass 'was close to 208 ( M H E [208 - 20,208 201). We know that the quasi-fission dominates in this asymmetric region'. The PSNMDs are given in figure 2. One can see that the distribution in the asymmetric region has two components: one identical to the quasi-fission distribution found for the asymmetric part, and one with more neutrons emitted, implying a much longer process that can be attributed to fusion-
[g
+
195
ate
1- -
-symmetric scissions asymmetricscissions
1
Figure 2. Pre-scission neutron multiplicity distributions for 48Ca+208Pufor symmetric and asymmetric scissions.
fission. The two processes seem to have contributions of the same order and we can therefore evaluate the contribution of fusion-fission to be 50% of the events in the interval A4 E [$ f301. Those events account for 20% of the total capture cross-section and hence the ratio of fusion cross-section over capture cross-section is found to be of the order of 10%. This value was confronted with the only model available treating the entrance channel and providing the neutron multiplicity distributions and the masses of the fragments: the model of Y. Aritomo2. The model uses a one-body dissipation. The agreement is good for the system 48Ca+'OS Pb but the model predicts only a very small fusion probability for 48Ca+244P~ and hence doesn't reproduce the second hump in the PSNMD. The reasons of this discrepancy are currently being investigated. Preliminary results show that the introduction of the temperature dependence of the dissipation as given by H. Hofamnn et aL3 could reconcile the model with the data. 4. Conclusion
A new analysis method has been developed that enabled us to see two components in the pre-scission neutron multiplicity distribution for fragments in the symmetric part of the mass distribution in the reaction 48Ca +244 Pu. The low-multiplicity component is attributed to quasi-fission and the other
196
one to fusion-fission. The fusion cross-section is then found to be of 10% of the capture cross-section. This is the first time that one can separate the contribution of fusionfission and quasi-fission in such a heavy system at low excitation energy. This is hence the first time that one has a proof that one observes true fission (after fusion) for a nucleus as heavy as Z=114.
Appendix A. !&?MATE:
a new analysis method
Appendix A.l. The problem to solve Let’s consider a model depending on ns source parameters ( S P ) S1, Sz, . . . ,,S , and let’s chose variables containing the experimental information: the observable parameters ( O P ) : 0 1 ’ 0 2 , . . . On,. For each set of values of the SP, the model provides us with the conditional probability (or correlation): C (01s) = C (Oi = oi with i = 1 , . . . ,120
1 Sj = sj with j
= 1,.. . , ns)
(A.1) using the notation S ( s ) and O(o) for the distributions of the SP and OP, we can write that, if the model is good, we must be able to find a S ( s ) reproducing the experimental distribution: Oexp(0) =
Omod(o) =
1
C(0lS) S ( S )
ds
(A4
Ds
The problem to solve is to invert (A.2), i.e. to obtain S ( s ) from the experimental results OexP(o). Since we use computers, the values of the variables over the domains DS and DO have to be discretized. Let each S j (Oi)take ds, (do,) values. The dimensions of the corresponding spaces are 6s =
n ds, (60 n do,).
ns
no
=
j=1
i=l
(A.2) can then be rewritten as
Appendix A.2. The existing method The backtracing method4 is a method that was already used t o obtain a solution in the case of neutron multiplicity di~tributions~3~. It approaches iteratively the solution minimizing the Kullback-Leibler coeffi-
197
60
cient ( K L = C O y P l n i=l
5).
This method has several drawbacks like the
fact that the procedure doesn't always convergence and even when it does, there is no way to be sure it is to a global minimum. But the major drawback is that the statistical fluctuations are not taken into account and one must therefore obtain a very high statistics in the experiment in order for the statistical error to be negligible. This is not easily achieved when dealing with superheavy systems, where the cross-sections are low. Appendix A.3. &OMATE
To address that problem, we developed a new method, '@@MATE7", where we simply minimize the x2 with respect to the Sj. Using (A.3), we have
x2(s') is a
parabolo'id (positive sum of squares), hence we have no local minimum which is not a global minimum. The minimum is unique provided that K e r C = 6, otherwise any two solutions differ only by a vector s' E Ker C. It looks like we just have to solve the linear set of equations = 0 VL = 1,.. . ,6s but the problem is actually more complicated. The following condition must hold:
$$
S j 2 0 v j = l , ...,&
(-4.5)
because one deals with distributions and a distribution cannot have negative values. For example, one cannot speak about -200 events emitting no neutrons. To solve the problem, i.e. to find the minimum of the parabolo'id with (A.5), one starts with a trial vector & and then follows the steepest descent with the restriction that one remains in the domain where (A.5) holds, until the solution is reached. Appendix A.4. Comparison of the methods
To evaluate the statistical error on the solution, one uses this solution as input to a simulation with the same number of events as in the experiment ~~
' w e Optimized Method Able to Treat the Errors
198
0.5
0.4
0.3 030
3 .2
02
0.15
>.
0.10 0.1
0.05 0.0 0
1
2
3
4 V
rn
5
6
7
0
2
3
4
5
6
7
vp.
Figure 3. PSNMD obtained for symmetric scissions of 48Ca+244 Pu with the backtracing (left) and W M A T E (right), (thick curves). The thin curves are the results of the qualification procedure repeated 5 times.
and uses the results as a new observable distribution to be fitted. If statistics had no influence, one should find back the distribution used as input to the ”simulated” experiment. The discrepancies can hence be attributed to the statistical fluctuations. This procedure, called qualzficatzon is done for various seeds of the random number generator. Figure 3 gives the results of the qualification procedure for the case with the least statistics available (symmetric scissions for 48Ca+244 Pu). The backtracing is clearly unstable and no conclusion can be made about the shape of the distribution. W M A T E behaves much better and enables us to identify unambiguously the presence of two separate components.
References M. G. Itkis et al., Nucl. Phys. A654, 870c (1999). Y. Aritomo et al., Phys. At. Nucl. 66, 1105 (2003). H. HofmannPhys. Rev. C64, 054316 (2001). P. DBsesquelles et al., Nucl. Phys. A604, 183-207 (1996). L. Donadille et al., Nucl. Phys. A656, 259 (1999). B. Benoit, Compitition entre les processus de fission-rapide et de fusion-fission dans la rigion des noyaux superlourds: 2669272,278110, These de l’Universit6 Libre de Bruxelles, anne acadkmique 2000-2001. 7. T. Materna, Capture et dissipation dans la rgion des noyaux superlourds, These de 1’Universitk Libre de Bruxelles, anne xad6mique 2002-2003.
1. 2. 3. 4. 5. 6.
Chapter 6
New Facilities
This page intentionally left blank
PLANNED PHOTOFISSION EXPERIMENTS AT THE NEW ELBE ACCELERATOR IN ROSSENDORF
H. SHARMA', K.M. KOSEV, s. FAN*, E. GROSSE, A. HARTMANN, A.R. JUNGHANS, K.D. SCHILLING, M. SOBIELLA, A. WAGNER Forschungszentrum Rossendorf e. V., Institut fur Kern- und Hadronenphysik, P. 0. Box 51 01 19,D-01314 Dresden, Germany
Spectroscopic beta-gamma investigations of neutron-rich nuclei close to the r-process path have been planned. These nuclei will be produced by photofission and their mass and charge numbers will be determined by time-of-flight (TOF) measurements. A novel time-of-flight spectrometer has been designed for this purpose. The coincidence spectra of the double-TOF measurements with the designed spectrometer have been simulated using a Monte Carlo method, which results in a mass and charge separation for the fission fragments (FF). The test of the spectrometer is under way by using a spontaneous fission source.
1.
Introduction
Most of the heavy elements are thought to be created by the rapid capture of a series of neutrons in the type-I1 supernovae where there is an enormous flux of neutrons for a short period, the process is known as r-process. The r-process pathway lies far from the line of stable nuclei. Once the neutron flux declines, the nuclei far away from the line of stability approach to the heavy nuclei on the line of stability by a series of beta decays. A quantitative understanding of the nucleosynthesis process requires the knowledge of the production rates, the masses and the beta-decay characteristics of the exotic nuclei. The shell structure of nuclei plays a vital role, since it determines the so-called waiting point on the r-process pathway. The beta-decay process plays a decisive role in the production rate of the nuclei in the universe. The spectroscopic data of exotic nuclei will provide valuable information on the structure of these nuclei, which is important for the various theoretical models applied for the precise estimate of the stellar processes of the nucleosynthesis. Such studies are planned at the superconducting electron linear accelerator ELBE at Rossendorf. The aim
' Now at Saha Institute of Nuclear Physics, Bidhan Nagar, Calcutta 700 064, India
* Now at China Institute of Atomic Energy, P.O.Box 275(41), Beijing 102413, China 20 1
202
of this report is to provide a detailed overview of the newly planned experimental facility to be applied for a beta-gamma spectroscopy of exotic neutron-rich nuclei. 2.
Experimental Setup
The electron beam of the ELBE accelerator has an excellent time structure (< 5 p s bunch width) and is used to produce - among other secondary beams - a
high-intensity bremsstrahlung beam. A typical bremsstrahlung spectrum produced by an electron beam of 16 MeV is shown in Fig. 1.
I
0
5
10 EYMW
15
Figure 1. GEANT simulation of a thin-target bremsstrahlung spectrum produced with 16 MeV electrons on a Nb radiator.
Neutron-rich exotic nuclei can be produced via photofission by using the bremsstrahlung photon beam from the ELBE accelerator. Production rates of exotic nuclei for the above mentioned beam parameters have been calculated in [l] for several fissioning nuclei. A typical isotopic distribution for the photoninduced fission of the 238Unucleus calculated in [l] is displayed in Fig. 2. The beta decay will be measured by an array of semiconductor or scintillation detectors. For the gamma-ray detection, an array of HPGe (cluster) detectors will be used. The most difficult task turns out to be the identification of the lowenergy fission fragments.
203
Figure 2. Calculated elemental mass distributions from the photofission of ’?J by 20WV bremsstrahlung photons compared with experimental data The latter are independent yields of long-lived fission products as measured via gamma-ray spectrometry with catcher foils [ I ] .
Generally, time-of-flight (TOF) measurements are used for the mass identifi- cation of fission fragments (FF). For the first time, a new method of charge identification of the FF’s by TOF measurements has been proposed by taking the advantage of the picosecond time structure of the electron beam from the ELBE accelerator. According to the proposed method, the TOF will be measured in two successive steps for each FF: The first TOF (tl) of each fragment will be measured with the start signal derived from the electron beam bunches and the stop signal deduced from a time-pickoff detector as mentioned ‘tl’ in Fig. 3. Furthermore, the fragments will pass through an optimized (in thickness) foil in order to reduce their velocities and, afterwards, the second TOF (t2) will be measured between the start signal from the first time-pickoff detector and the stop signal from the second time-pickoff detector as indicated in fig. 3. The coincidence measurements between t l and t2 will show a correlation according to the masses and charges of the fragments. In order to perform these measurements, a sophisticated TOF detector system has been constructed in Rossendorf.
204
Figure 3. Schematic layout of the proposed TOF spectrometer
The TOF spectrometer consists of four sets of position-sensitive timepickoff detectors as shown in Fig. 3. There are two arms for the simultaneous TOF measurement of the corresponding light and heavy fragments moving in opposite directions and each arm consists of a set of two time-pickoff detectors. The distances (flight paths) between the individual time-pickoff detectors can be varied, marked as ‘dl’ and ‘d2’ for arm1 in Fig. 3. Each time-pickoff detector consists of a stack of microchannel plates (MCP‘s) as signal amplifier, a twodimensional position-sensitive delay-line anode, a thin metallized polymer foil as electron emitter and an electrostatic mirror as shown in Fig. 4. The two sets of MCP‘s and delay-line anodes with active diameters of 0 = 40mm (DLD40) and 0 = 80mm (DLDSO), respectively, have been procured from the company RoentDek [2]. The two-dimensional position-sensitive anodes provide information about the polar and azimuthal emission angles of the fragments, which will be used for the Doppler correction of the prompt gamma rays as well as for the determination of the precise flight path of the fragments. The Doppler correction information will also be used for the cross verification of the measured TOF as a function of the fragment’s velocity. The secondary-electron (SE) emitters, the metallized thin foils of dimensions equivalent to the MCP detectors (i.e. with 0 = 40mm and 0 = SOmm, respectively), have been mounted in the detectors. Because of the large emittance angles and the broad energy distribution of the SE’s, a high accelerating electric field is required for a proper transportation of the SE’s to achieve a good time resolution. A high acceleration value can be achieved by mounting an accelerating grid near to the foil. But, this grid causes a curvature on the plane surface of the foil and deteriorates the overall time resolution of the spectrometer. Hence, in order to avoid this, two accelerating grids (one in front of the foil and the second in the back of the foil) have been
205
Figure 4. Setup of a time-pickoff detector, which shows such parts as the thin foil, the grids, the electrostatic mirror, the MCP stack and the two-dimensional position-sensitive anode.
designed for each MCP stack. For this purpose, a delicate mounting frame has been designed with combinations of ceramic (vitronit [3] ) and metal frames, which will hold the foil and the accelerating grids with sufficient mechanical tension and with the required high electric potential under high-vacuum conditions. The highly accelerated SE's will be transported towards the surface of the MCP isochronously by deflecting them by 90Owith respect to the beam axis using an electrostatic mirror. The mirror has been designed with metal and ceramic frames, which hold two accelerating grids with sufficient tension and with high electric potential in high-vacuum conditions. All accelerating grids included in the design of the spectrometer are made of tungsten wires with 0 = 3 1 p m diameter and separation distances between each other of 0.5 m m, which provide approximately 78 % transmittance for the fission fragments. The electric potential values for the foils, accelerating grids and mirrors have been optimized by simulation calculations for the electron trajectories using electrostatic Opera3D computer codes [4]. The mounting system of the TOF spectrometer has been designed by using standard beam line coupling flanges of standard dimensions in order to couple the spectrometer with the beam lines at the ELBE accelerator in Rossendorf or at the heavy-ion synchrotron at GSI.
206
3.
Monte Carlo Simulations
In order to understand the response of the proposed TOF spectrometer, the TOF spectra have been simulated using Monte Carlo techniques. The inputs of the simulation calculations were the distances between the time-pickoff detectors, information regarding the thickness distributions of the thin foils and the normalized yield distributions of the FF’s of a selected target nucleus for a given photon beam flux from the ELBE accelerator. The kinetic energies of the fragments, the corresponding energy losses of the fragments in the thin foils and the neutron emission from the excited fragments while in motion have been calculated. The calculated fragment yield distribution [ 11 was normalized to the experimental fragment yield distribution. The fragment’s kinetic energy was calculated using a standard procedure and corresponding liquid-drop parameters for the fissioning nucleus 238Uas described in Ref. [5]. The fragments with an excitation energy of about 8MeV (that is the average excitation energy for fragments produced in spontaneous or photon-induced fission) emit prompt neutrons at a time scale of less than 10-l6s [ S ] , which will affect the mass and charge resolution of the TOF spectrometer. The prompt neutron emission probability for each excited fragment was calculated using Fraser’s description [6] and the resulting effects on the TOF measurements were included in the simulation. The energy-loss values for the individual fragments in the foils were calculated on an event-by-event basis and the corresponding energy-straggling values were also estimated. The details of the simulation calculations can be found in ref. [7]. A typical time spectrum displayed in Fig. 5 shows the time correlation between t l and t2, which was calculated for the photon-induced fission of the 238Unucleus for the flight paths of dl = d2 = 300mm by using carbon foils of the thickness 500,ug/crn2.These correlation events show M and Z separation for the FF’s and indicate that the measurements should be carried out with time resolutions better than At1 = loops and At2 = 300ps for the unambiguous mass and charge separation, respectively. Currently, first laboratory test experiments of parts of the TOF spectrometer with a spontaneous fission source of 252Cfare in progress. The foil thickness distribution can be measured with an automatically processing alpha-source equipped setup that measures the energy-loss profile. The corresponding foil thickness profile will be included in the energy-loss calculation while analyzing the TOF spectra of the FF’s. The electronics setup has been designed with VME and CAMAC based modules. The data acquisition programs are also being developed for these investigations.
207
21.5
20
19.5
19
Figure 5. Correlation between ti and t2 calculated for the 23sU(y,f)reaction with an electron endpoint energy of 12 MeV, for distances dl = d2 =X)Omm and a carbon foll of 500 pg/cm2 thickness.
4.
Conclusions
A new experimental facility is being developed at the ELBE accelerator for the beta-gamma spectroscopy of neutron-rich nuclei close to the r-process path. These nuclei will be produced via photofission by using a secondary bremsstrahlung beam from the ELBE accelerator. The identification of the masses and charges of the FF's will be realized by sophisticated TOF measurements. A novel TOF spectrometer has been designed for this purpose. The Monte Carlo simulation calculations performed for this spectrometer have demonstrated that the simultaneous determination of masses and charges of the
208
FF’s is possible by TOF measurements, if a time resolution of better than l o o p can be achieved. References 1. Annual Report 2000, FZR-3 19 (2001) 39; http://www.fz-rossendorf.de /FWK/jb00tfan 1.htrnl. 2. RoentDek GmbH, http://www.roentdek.com. 3. Vitronit\copyright; httr,://www.vitron.de. 4. Vector Fields Ltd., Oxford OXSlJE, England. 5. The Nuclear Fission Process, Ed. C. Wagemans, CRC Press, 1991. 6. J. S. Fraser, Phys. Rev. 88 (1 952) 536. 7. Annual Report 2002, FZR-372 (2003) 36: http://www.fz-rossendorf.de /FWWjb02/sharmal .html.
MYRRHA, A MULTIPURPOSE ACCELERATOR DRIVEN SYSTEM FOR R&D - PRESENT STATUS P. D'HONDT, H. AIT ABDERRAHIM, P. KUPSCHUS, P. BENOIT, E. MALAMBU, V. SOBOLEV, T. AOUST, K. VAN TICHELEN, B. ARIEN, F. VERMEERSCH,
D. DE BRUYN, D. MAES, W. HAECK SCKCEN Boeretang 200, 2400 Mol (Belgium) Tel : t 3 2 14 332277 -Fax : +32 14 321529 E-mail :haitabde@sckcen. be
Y. JONGEN, D. VANDEPLASSCHE IBA Chemin du Cyclotron, rue J.E. Lenoir 6, 1348 Louvain-la-Neuve (Belgium),
Since 1998, SCK*CEN in partnership with IBA s.a., is designing a multipurpose ADS for R&D applications -MYRRHA - and is conducting an associated R&D support programme. MYRRHA is an Accelerator Driven System (ADS) under development at Mol in Belgium and aiming to serve as a basis for the European experimental ADS to provide protons and neutrons for various R&D applications It consists of a proton accelerator delivering a 350 MeV*5 mA proton beam to a liquid Pb-Bi spallation target that in turn couples to a Pb-Bi cooled, subcritical fast core. In a first stage, the project focuses mainly on demonstration of the ADS concept, safety research on sub-critical systems and nuclear waste transmutation studies. In a later stage, the device will also be dedicated to research on structural materials, nuclear fue1, liquid metal technology and associated aspects and on sub-critical reactor physics. Subsequently, it will be used for research on applications such as radioisotope production. The MYRRHA system is expected to become a major research infrastructure for the European partners involved in the P&T and ADS Demo development.
1. Introduction The ETWG (European Technical Working Group) on ADS concluded in April 2001 in its report "A European Roadmap for developing Accelerator Driven Systems (ADS) for Waste Incineration" that the P&T in association with the ADS in combination with the geological disposal can lead to an acceptable solution from the society acceptance point of view for the nuclear waste management problems. Therefore it concluded also that a heavy support in this field from the EC and the national programmes is needed to develop and build an experimental ADS demo facility in Europe. 209
210
One of SCK-CEN core competencies is and has at all times been the conception, design and realisation of large nuclear research facilities. One of the main SCK*CEN research facility, namely BR2 (a 100-MW Material Testing Reactor), is nowadays arriving at an age of 40 years just like the major MTRs in the world. The MYRRHA facility in planning has been conceived as potentially replacing BR2 and to be a fast spectrum facility complementary at European level to the thermal spectrum RJH (RCacteur Jules Horowitz) facility, in planning in France. This situation would give Europe a full research capability in terms of irradiation capabilities for nuclear R&D. Furthermore, the disposal of radioactive wastes has still to find a fully satisfactory solution, especially in terms of environmental and societal acceptability. Scientists are looking for ways to drastically reduce the radiotoxicity of the High Level Waste (HLW) to be stored in a deep geological repository as to reduce the time needed to reach the radiotoxicity level of the fuel ore originally used to produce energy. This can be achieved through the development of the Partitioning and Transmutation and burning Minor Actinides (MA) and to a less extent Long Lived Fission Products (LLFP) in dedicated waste burners such as Accelerator Driven Systems (ADS) or in critical reactors in combination with energy production. The MYRFWA project contribution will be to demonstrate the ADS concept at reasonable power level and the demonstration of the technological feasibility of MA and LLFP transmutation under realistic conditions and the economical assessment of this option as waste management option.
2. Principle features of the design of the MYRRHA facility The MYRRHA project is based on the coupling of a proton accelerator with a liquid Pb-Bi windowless spallation target, surrounded by a Pb-Bi cooled sub-critical neutron multiplying medium in a pool type configuration with a standing vessel (Fig. 1) [1,2]. The spallation target circuit is fully immersed in the reactor pool and interlinked with the core but its liquid metal contents is separated from the core coolant. This is a consequence of the windowless design presently favoured in order to use low energy protons on a very compact target at high beam power density in order not to loose on core performance. The core pool contains a fast-spectrum sub-critical core cooled with Pb-Bi eutectic (LBE) and several islands housing thermal spectrum regions located in in-pile sections (IPS) in the fast core. The core is fuelled with typical fast reactor fuel pins with an active length of 600 mm arranged in hexagonal assemblies. The three central hexagons are left free for housing the spallation module. The
21 1
core is made of fuel hexagonal assemblies of 85-mm flat-to-flat, composed of MOX typical fast reactor fuel (SuperphCnix like fuel rods) with total Pucontents of 30% and 20%. Since access from the top is very restricted and components introduced into the pool will be buoyant due to the high density of the LBE, the loading and unloading of fuel assemblies is foreseen to be carried out by force feed-back controlled robots in remote handling from underneath. The pool will also contain the liquid metal primary pumps, the heat exchangers using presently water as secondary fluid and the two fuel handling robots based on the well known rotating plug of fast reactors. The spallation circuit connects directly to the beam line and ultimately to the accelerator vacuum. It contains a mechanical impeller pump and a LWLM heat exchanger to the pool coolant (cold end). For regulation of the position of the free surface on which the proton beam impinges (whereby this defines the vacuum boundary of the spallation target), it comprises an auxiliary MHD pump. Further on, it contains services for the establishment of proper vacuum and corrosion limiting conditions. The device has a double-wall pool containment vessel (inner diameter of ca. 4 m and height close to 7 m), is surrounded by biological shield to limit the activation of the surrounding soil as the MYRRHA sub-critical reactor will be installed in an underground pit. This shield will be closed above the vessel lid by forming an a-compatible hot cell and handling area for all services to the machine. 3. Task profile Along the above design features, the MYRRHA project team is developing the MYRRHA project as a multipurpose irradiation facility for R&D applications on the basis of an Accelerator Driven System (ADS). The project is intended to fit into the European strategy towards an ADS Demo facility for nuclear waste transmutation. As such it should serve the following task catalogue: ADS concept demonstration: coupling of the 3 components at rather reasonable power level (few ten's of MWth) to allow operation with representative thermal feed-back and reactivity effects mitigation Safety studies for ADS: to allow beam trips mitigation, sub-criticality monitoring and control, optimisation of restart procedures after short or long stops, feedback to reactivity injection M transmutation studies: that need high fast flux level = 1015 n/cmz.s)
212
LLFP transmutation studies: that need high thermal flux level ( Q h = 1 to 2.10’~n/cm2.s) Medical radioisotopes: that need also high thermal flux level (Qth = -2.IOl5 n/cmz.s) Material research: that needs large irradiation volumes with high constant MeV= 1 - 5.10i4 n/cm2.s) fast flux level Fuel research: that needs irradiation rigs with adaptable flux spectrum and level loi4 to 1015n/cmZ.s) Initiation of medical and new technological applications such as proton therapy and proton material irradiation studies The present MYRRHA concept is driven by the flexibility and the versatility needed to serve the above applications. Some choices are also conditioned by the objectives of willing to make MYRRHA as demonstrative as possible for the final objective of having the means for assessing the feasibility of an industrial ADS prototype. The MYRRHA project team has favoured as much as possible mature or less demanding technologies in terms of research & development. Nevertheless, not all the components of MYRRHA are existing. Therefore, a thorough R&D support programme for the ‘risky’ points has been started since 1997 and has been updated since 2002.
4. Design features and parameters and their justification 4.1 The main design parameters of MYRRHA and MYRRHA spallation
target The performances of an ADS in terms of flux and power levels are dictated by the spallation source strength, which is proportional to the proton beam current at a particular energy and the sub-criticality level of the core. The sub-criticality level of 0.95 has been considered as an appropriate level for a first of kind medium-scale ADS. Indeed, this is the criticality level accepted by the safety authorities for fuel storage. Besides this aspect, we considered various incidental situations that can lead to reactivity variation and found that the majority of those effects would bring a negative reactivity injection or a limited positive reactivity injection not leading to criticality when starting at a Keff of 0.95. Fixing the sub-criticality level - determining the nuclear gain - and the desired neutron flux in the position of the irradiation location for MA transmutation determines the required strength of the neutron spallation source. In order to achieve the above-mentioned performances at the modest total power level aimed at, we have to limit the central hole diameter to a maximum diameter of 120 mm. As a consequence of this constraint and on the other hand
213
having the need of a minimum lateral Pb-Bi target volume for allowing an effective spallation process, the proton beam external diameter is limited to 72 mm whereby the beam profile will be shaped by time averaging of a scanned pencil beam. The required spallation source intensity to produce the desired neutron flux at this location is close to 2.lOI7 d s . At the chosen proton energy of 350 MeV, this requires 5 mA of proton beam intensity and this in turn would lead to a proton current density on an eventual beam-window of order 150 pA/cm2. This is by at least a factor of 3 exceeding the current density of other attempted window design for spallation sources which already have high uncertainties with regard to material properties suffering from swelling and radiation embrittlement. As a result, we favoured the windowless spallation target design in MYRRHA [3]. 4.2 The Required Accelerator
The proton beam characteristics of 350 MeV x 5 mA allow to reach a fast neutron flux of l.lO'Sdcmz.s(E,075MeV) at the MA irradiation position under the geometrical and spatial restrictions of the sub-critical core and the spallation source. These performances are regarded as being within the reach of the extrapolated cyclotron technology of IBA. Compared to the largest continuous wave (CW) neutron source - SINQ at PSI with its cyclotron generated proton beam of 590 MeV and 1.8 mA - it is a modest extrapolation. The MYRRHA normal conducting cyclotron would consist of 4 magnet segments of about 45" with 2 acceleration cavities at ca 20 MHz RF frequency. The diameter of the active field is of order of 10 m, the diameter of the physical magnets of order of 16 m with a total weight exceeding 5000 t. Due to these very large dimensions, a supra-conducting magnets cyclotron option has been evaluated by IBA and led to a reduction of the magnet diameter by a factor of 2. Nevertheless, taking into account the conclusions of an expert group related to the accelerator reliability to be achieved for the ADS application, the LINAC option is now the favoured solution for the MYRRHA accelerator. 4.3 Sub-critical Core Configuration
As already mentioned above due to the objective of obtaining a fast spectrum core and the criterion that no revolutionary options were to be considered, we started the neutronic design of the sub-critical core based on MOX classical fast reactor fuel technology. The fuel assembly design had to be adapted to the PbBi coolant characteristics especially for its higher density as compared to Na. A first core configuration with typical SuperphCnix hexagonal fuel assembly (122 mm flat-to-flat with 127 fuel pins per assembly) with a modified
214
cell pitch to answer the requested performances has been conceived. Nevertheless, this configuration is subject to the large radial bum-up and mechanical deformation stress gradients that will make fuel assemblies reshuffling difficult or even impossible. Therefore, we moved towards a smaller fuel assembly, 85 mm flat-to-flat, with 61 fuel pins per assembly allowing a larger flexibility in the core configuration design. Indeed, the reactivity worth in the M Y N A core of such a fuel assembly is ranging between -450 to 1600 pcm. The active core height is kept to 600 mm and the maximum core radius is 1000 mm with 99 hexagonal positions. Not all the positions are filled with fuel assemblies but could contain moderating material (to create thermal neutron flux trap with Dth = 2.10” n/cmz.s) or fast spectrum irradiation device. A typical MYRRHA configuration with Keff of 95 can be achieved by using 45 to 50 fuel assemblies. There are 19 core positions accessible through the reactor lid capable of housing experimental devices equipped with their own operating conditions control supplied by services above the reactor lid. All the other position can be housing either fuel assemblies or non-on-line serviced experimental rigs. The expected performances in terms of fast and thermal fluxes, linear power in the core and total power in MYFU2HA are summarised in Table 1. Two interim fuel storages are foreseen inside the vessel on the side of the core fixed to the diaphragm. They are dimensioned for housing the equivalent of two full core loadings ensuring this way that no time consuming operations must take place in the out-of-vessel transfer of fuel assemblies or waiting for the about 100 days of cool-down. The MYRRHA operation fuel cycle will be determined by the Keff drop as a function of the irradiation time or core bum-up. The targeted operating regime is 3 months of operations and 1 month for core re-shuffling, loading and maintenance. This will lead to a drop in Keff of about 1000 pcm at maximum (16 % drop in multiplication factor) which has only a minor effect at the locations for MA transmutation (18% flux reduction). Core reshuffling and partial core reloading with fresh fuel would allow compensating this loss of Keff.
-
4.4 Remote handling system
Due to the high activation dose on the top of the reactor and the high potential of a-contamination, the MYRRHA team has decided from the very beginning to design MYRRHA as to be operated remotely thanks to robots. The proposed MYRRHA project at SCKoCEN will be operated thanks to remote handling for all maintenance operations on the machine primary systems and associated
215
equipment. Experience from similar projects [4,5]has shown the importance of considering the implications of remote handling on the design of the plant from the earliest stage. Oxford Technologies Ltd (OTL) has been granted a contract for studying the implications of remote maintenance on the design of the MYRRHA machine and the overall project management. Table 1. MYRRHA facility performances Neutronic Parameters
I E
Units
I
H,O-Island
Core
Proton beam
l EI Pp
MeV 3.121
?
Intensity
1017n/s
Keff
Importance Factor
r V
:E
MF=l/(l-K,)
Av. Power density
w/cm3
6.14
6.01
1.92
1.88
0.9541
0.9359
0.9590
0.9414
1.13
1.10
24.40
17.07
51
34
290
165 705 0.57 0.74 1.17 3233
(*) Ef = 210 MeV/fission
1
The study includes an analysis of the remote handling requirements of MYRRHA, defines an approach to be used for ensuring the implementation of a plant suitable for remote handling and concludes with a concept proposal for a
216
system suitable for the fully remote maintenance of MYRRHA over its entire working life. In-Service Inspection & Repair (ISI&R) is also addressed by means of robotics based on In-Vessel Inspection Manipulator, periscopes or articulated arms equipped with ultrasonic cameras to be deployed when needed inside the MYRRHA vessel. The development of the ultrasonic sensors operating under LBE at temperatures up to 500°C and radioactive aggressive environment (gamma and neutrons) is going on in collaboration with the Kaunas University Ultrasonic Institute [6,7,S].
5. The complementary R&D programme Despite the fact that we intend to build this facility with a high degree of conventional technology there are a number of features which do not comply with this. Therefore, SCK*CEN has since 1997 started an ambitious support research programme and is developing it according to the requests coming from the progressing design. This R&D support programme has been updated last and particularly for what concerns the fuel development and qualification. The support R&D programme covers the following areas of highest uncertainties: The windowless spallation target design. Here we investigate the confluent flow pattern of the target formation co-axial with the proton beam on the one hand and the compatibility of the LM flow towards the accelerator vacuum on the other hand. For the first part, a number of the design activities have been and are being performed to study the flow behaviour and to obtain an adequate design. Successful experiments have been performed using water and mercury as simulating fluids. Optimisation experiments with water are currently going on. The results of these experiments will be carried over to experiments with the real fluid Pb-Bi. Computational Fluid Dynamics calculations are performed in parallel and are indispensable as it is impossible to experimentally simulate the heat deposition by the proton beam without actually having a beam. In summary, the results of these activities, although not yet totally conclusive, look very encouraging to yield the desired target configuration [ 3 ] . For the second part SCK*CEN presently carries out the Vacuum Interface Compatibility Experiment, in short VICE. In a large (ca. 6 m high) UHV vessel of spallation loop dimensions we attempt to quantify the emanation of ca 130 kg of Pb-Bi LM at 500°C in the vacuum pumping geometry relevant
217
0
for MYRRHA and try to assess the resulting vacuum conditions albeit without being able to provide the proton beam in this experiment. The LM corrosion aspects of the coolant are of high concem to us because MYRRHA would be the first facility in the western world to use the technology other than for experimental evaluation. By keeping close to present knowledge, mainly worked out in the Russian nuclear programs, and making use of the knowledge now being acquired by European laboratories with which we collaborate, the MYRRHA design uses moderate temperatures and controlled oxygen contents of the LM (the key to the corrosion issue). Nevertheless, for M Y M A the proposed choices have to be hardened by experimental evidence. A programme has been conceived and experimental results are under way. The third aspect concerns the handling operations under LM, i.e. the forcefeedback mechanical aspects as well as the sensors and the fact that the medium is opaque and monitoring under light visibility is not an option. We have started the development of ultra-sonic sensors with the required properties to work under LM though not in direct contact with it. The concentrated effort is directed to ensure in the first place the safe and controlled loading and unloading of the SC but will eventually be widened to all operations under LM. A test pool programme is in development in which key operations will be studied under LM in model form. As the remote handling approach is presently favoured for the operation and maintenance, it is clear that a R&D support programme should be launched in this area of robotics under liquid metal reduced visibility and hot condition. This programme is under preparation in collaboration with OTL Ltd and UI of Kaunas University of Lithuania. The R&D programme has been updated to include a fuel programme. Indeed, the choice of conventional MOX fuel does not lead immediately to a straight forward solution since the cladding needs to be compatible with the coolant LBE and so a minimum of fuel pin and assembly qualification is still required under these circumstances. Moreover, some back-up of fuel choice has still to be considered at this stage. It is considered mandatory that for the Licensing Authority the irradiation of fuel pin(s) to relevant levels of the order of 100 dpa for cladding damage and up 100 GWd/t for fuel bum-up needs to be successfully demonstrated before fuel manufacturing will be licensed. It is mandatory to generate an engineering design data base for the preselected structural materials (T91 and A316 L) for the different uses (fuel cladding, core structure and spallation target T91 and reactor vessel A316 L)
218
though different forms; thin tubes, plates, welded in MYRFWA irradiation and operation conditions. Therefore, we are considering to pay more attention to the selection and fabricability and weldability of the candidate materials. 6. Conclusion At mid-2002, the MYRRHA pre-design file has been submitted to an International Technical Guidance Committee for reviewing the pre-design phase as achieved for the MYRRHA project. This international panel consisted of expert from research reactor designers, reactor safety authorities, spallation target specialists. The conclusions and recommendations of this panel were as follow: No show stopper are identified in the project, Give more attention to safety case studies and iterate to the pre-design before entering the detailed engineering phase, Address some R&D topics that can lead to timing bottlenecks very soon such as fuel pin and assembly development and qualification, Make a decision on the accelerator option (cyclotron vs. Linac) and eventually revisit beam parameters. The MYRRHA team responded the worries expressed above by the ITGC and worked further the development of the project. MYRRHA is responding the objectives of the XADS Facility in terms of demonstration and performance, and responding by design to some key issues related to the LBE ADS such as: the LBE corrosion by leaving the major of the system at “cold” conditions and limiting the LBE velocity below 2.5 m/s, criticality control during core loading by leaving the spallation target in position and loading from underneath, avoiding spallation target window break by choosing the windowless design, addressing the ISI&R and the O&M from the conceptual design by means of robotics and ultrasonic visualisation. MYRRHA is a challenging facility from many point of views therefore we are convinced that it will trigger a renewal of R&D activities within the fission community. Its development will attract young talented researchers and engineers looking for challenges. It will be a new irradiation facility for research and development in Europe for future innovative energy systems.
219
References
-A Multipurpose Accelerator Driven System (ADS) for Research & Development. March 2002 Pre-Design Report", R-3595 (2002). H. Ait Abderrahim, P. Kupschus, E. Malambu, Ph. Benoit, K. Van Tichelen, B. Arien, F. Vermeersch, Y . Jongen, S. Ternier and D. Vandeplassche, "MYRRHA: A multipurpose accelerator driven system for research & development," Nuclear Instruments & Methods in Physics Research, A 463 (2001) 487-494. K. Van Tichelen, "MYRRHA: Design and Verification Experiments for the Windowless Spallation Target of the ADS Prototype MYRRHA," ADTTA'01, Reno, Nevada, November 11-15,2001. A.C. Rolfe, Remote Handling on fusion experiments, Fusion Engineering Design 36 (1997) 91-100. R. Haange, Overview of remote maintenance scenarios for the ITER machine. Fusion Engineering Design 27 (1 995) 69-82. R. Kazys, A.Voleisis, L.Mazeika, R. Sliteris, R. Van Nieuwenhove, P. Kupschus, H. Ait Abderrahim, "Investigation of ultrasonic properties of a liquid metal used as a coolant in accelerator driven reactors", 2001 IEEE International Ultrasonics Symposium, October 8- 1 1, 2002, Munich, Germany R. Kazys et al., "Ultrasonic Imaging Techniques for Visualisation in Hot Metals" 5th World Congress on Ultrasonics WCU2003, Paris, France, September 7-10,2003. R. Kazys et al., "Ultrasonic transducers for high temperature applications in accelerator driven reactors", 5th World Congress on Ultrasonics WCU2003, Paris, France, September 7-10,2003.
1. H. Ait Abderrahim, P. Kupschus & MYRRHA-team, "MYRRHA
2.
3.
4.
5. 6.
7.
8.
This page intentionally left blank
Chapter 7
Various Aspects of Nuclear Fission
This page intentionally left blank
FISSION OF 1 A GEV 238U-IONSON A HYDROGEN-TARGET
M. BERNAS, P. NAPOLITANI, F. REJMUND, C. STEPHAN, J. TAIEB, L. TASSAN-GOT I.P.N. d’Orsay, F-91406 Orsay Cedex, France E-mail: [email protected] r
P. ARMBRUSTER, T. ENQVIST, M.-V. RICCIARDI, K.-H. SCHMIDT G.S.I. Dannstadt, D-6&291 Darmstadt, Germany J. BENLLIURE, E. CASAJEROS, J. PEREIRA Univ. of Santiago de Composteela, E-15706 Santiago, Spain
A. BOUDARD, R. LEGRAIN, S. LERAY, C. VOLANT DAPNIA/SPhN CEA/Saclay F-91191 Gif-sur-Yvette Cedex, France S. CZAJKOWSKI DAPNIA/SPhN CENBG, IN2P3 F-33175 Gradignan, France The production cross sections and the kinematical properties of fission fragment residues have been studied in the reaction 238U (1 A.GeV) p. Isotopic distributions were measured for all elements from 0 (Z = 8) to Gd (Z= 64). The distribution of fission velocities and of production cross sections as function of Z of the fragments, provide relevant informations on the intermediate fissioning nuclei.
+
1. Introduction
The spallation and fission of the excited nuclei produced in collisions of 1 A.GeV U on a hydrogen target has been investigated in order to extend the p132 domain of data already obtained by our collaboration, namely Au and P b + p3 to a fissile projectile. These studies are part of an experimental program to collect nuclear data relevant for ADS4>5 , RNB and spallation neutron sources. For technical applications, reliable and accurate cross sections are needed and a special care was devoted to the experiment in order
+
223
224
to fulfill these requirements. We report here on the measurement of fission residues left after the cascade of nucleon-nucleon collisions induced by the proton in the U-nucleus. The excited fragments produced cool down by evaporation of nucleons or light particles and may undergo fission. Evaporation residues have been analysed in a parallel work6. The experimental set up used at GSI is briefly described and the main results are presented. We show how from the kinematical properties and the isotopic distribution of fission fragments (f.f), the intermediate fissioning parent nucleus can be inferred. The balance between evaporation residues and f.f. provides a test of the energy dissipation of the excited intermediate system. 2. Experiment Using inverse kinematics at relativistic energy, the f.f. are totally stripped of their electrons and forward focused. They can be separated by the FRagment Separator (FRS)' and identified by the associated detection system i.e. an ionisation chamber and a time of flight for Z and A determination, respectively. The performances of the equipment were demonstrated by the identification of 117 new n-rich fission fragments in U (0.75 GeV) Be c~llisions~~~. The systematic scanning of the FRS magnetic rigidity allows to reconstruct the center of mass velocity spectra, truncated by the FRS angular acceptance a,as shown in Fig. l b. Note that 4 to 5 isotopes of all of the 36 elements populated by fission are scanned simultaneously. It reduces the relative uncertainties due to beam intensity calibration or dead time corrections. The laboratory velocity of f.f. results from the Lorentz addition of the projectile velocity with the fission velocity. From the gap between the first momenta of the two peaks, that is twice the apparent velocity Vapp, knowing a and its variance oa,we calculate the angular transmission and the fission velocity Vf for each isotope, see''.
+
3. Kinematics
Fission velocities varies as the inverse of the atomic number Z due to momentum conservation in fission. For each element, velocities of 15 to 25 isotopes are investigated. They decrease slightly with the mass of the isotope (1 to 2 %) except for the 4 lightest isotopes where they drop by 10 to 20%. This fall confirms that the 4 lightest isotopes are produced by secondary break-up of heavier fission fragments". A mean value of the velocity per element is presented on Fig. 2, to-
225
-2
-1
0
1
2
V (cdns) Figure 1. a) Schematic view of the experimental parameters shaping the measured velocity spectrum in the frame of the fissioning system. Vf is the fission-fragment velocity, a is the angular acceptance of the FRS, and o m its variance. b) Velocity spectrum of lz8Te in the frame of the fissioning system. The velocity V = 0 refers to the projectile frame. VaPp is the apparent fission velocity defined in the text.
gether with the 3 straight lines expected in case of fission of U, Rn and Hg. The paramerization ofl23l3 and a deformation of p = 0.65 is assumed for
226
2.0 1.8
1.6
cn
C 1.1 \ E 1.2 0 Y
z 1.0 0.8
0.6 0.b
10
20
30
b0
50
60
70
Z Figure 2. Fission fragment velocities as a function of 2. The lines are obtained using the calculation of velocity for fissioning parent nuclei of 20 = 80 (full line), 20 = 86 (dashed line) and 20 = 92 (dotted line) with the parametrisation of ref. 12 and 13 and a deformation of p = 0.65 for both fragments.
calculating the three distributions of velocity as a function of Z of the f.f.. A small decrease of the measured values relative to the expected slope for decreasing Z is found. The data are compatible with 84 < Z < 90 for the fissioning nuclei.
4. Isotopic Yields: Symmetric and asymmetric fission Isotopic cross sections have been obtained for all isotopes of the 36 elements produced by U p fission, down to a threshold value of 0.1 mb. They cover a range of 0.1 to 14 mb. The measurements can be extended further for neutron-rich isotopes since they are not contaminated by secondary break-up, contrary to cross sections on the neutron-deficient side. Three distributions are shown here on Fig. 3 to illustrate our results. A systematic uncertainty of 10% is calculated, mostly due to the beam monitoring. The error bars reported on Fig. 3 correspond to the relative uncertainties. The isotopic cross section distributions show a bell shape with a shoulder on the neutron-rich side, more prominent in case of isotopes strongly
+
227 c
3
A = 100
A = 134
-
E l Z
V
'
0.1
-
52
zmc
Z = 30
0.1
0.1
+
Figure 3. Isotopic cross sections for fission-fragments in the reaction 238U 1 AGeV p for elements soZn, 4oZr and 52Te. The arrows indicate a pair of isotopes, the production of which is enhanced in asymmetric fission.
populated in asymmetric fission. The "asymmetric" regime of fission, has Pb been analysed in various experiments. In our previous study of U fission for example14, it was enhanced due to the strong Coulomb - excitation of the giant resonance. The mean value of the mass A, A ( 2 ) and the width OA(Z) were determined coherently with previous works. The isotopic distributions presently measured are decomposed into contributions of symmetric and asymmetric fissions. As a result the element distribution shown on Fig. 4a can be shared into both components, as shown on the figure. The mean value of Z, = 45 , is calculated for the total of the distribution shown on Fig.4a, down to Z = 28. For Z < 28, the binary break-up is still observed, and assigned by the FRS kinematical selection15. The occurence of the very asymmetric break-up with rising cross sections was already observed and discussed in other systems at similar excitation energies16. The region populated by the two fission regimes are characterized on the Fig. 4b. Asymmetric fission populates a narrow corridor (& = 1.8) in the neutron-rich region, @/Z = 1.52). The symmetric process drives in a region of less neutron-rich isotopes, towards the valley of stability, where N / Z ( ~ 1 . 3 increases ) slowly with Z, crossing the valley at Z = 57, as shown on Fig. 4b and increases from 2 for 2 = 30 to 4 for Z = 60. From the mean values of the atomic numbers of f.f. = 45 and from the = 63 the most probable symmetric fission leads mean neutron number to two f.f. of losRh. A mean fissioning parent nucleus can be recontructed
+
z
06
z
228
.
1
.
1
-
I
z
,:ti'* qD
b*
*I
-cI
*a
P
10 r
v)
***
.+ **** +*+*+*t*+
0
1 -
(a)
*
*
<>oa i'
t++++ +t
*'
<,bO
~
<,coo
1
'%
I .
1
O3: 6
" '?
++
t
t
1
+
tt
'* *\+
c
1: I
1.8
1.6 N
cI
I
.-0
eu
... ..
-
I
9%.
C
g
-
I
*.
€100 : v
u
.
- lb
.
1
'
$0
.
I
3b
.
I
bb
-
I
I
.
5b
+t
1
6b
.
I .
7b-
(b)
ti*+*+++
L
+
Figure 4. a) Distribution of f.f. integrated over N for 238U p at 1 A.GeV (Full points or squares). Light circles: symmetric fission, and dashes: asymmetric component (with large error bars). In order to single out the symmetric component, the related values have been divided by a factor of 2. b)Mean neutron number divided by Z as a function of Z for the total distribution and for symmetric and asymmetric fission.
using the conservation of protons and neutrons in the spallation process and the energy balance between the cascade and the evaporation chain ending in fission. The mean cascade in 238Uinduced by the protons leads to a 232Thexcited at E" = 183 MeV after 3 protons and 4 neutrons have been torn away from the incident system. Then a mean number of 11 neutrons are evaporated to reach a '"Th at E* = 149 MeV. With a mean number of 5 post fission neutrons emitted, the two symmetric f.f. of lo8Rh
229
are obtained. This estimation is based on known energies required to free neutrons and protons in the cascade and on binding energies of neutrons in the evaporation process. The simulations to be done still, will substantiate the result. The fission cross section is calculated by summing elemental cross sections a ( 2 ) over the whole fission area. For symmetric and asymmetric fission, cross sections of (1.42 f0.15) b and of (0.105 f 0.01) b are found, respectively. The total fission cross section amounts to (1.53 f 0.15) b, a value which compares well with the results of direct measurements of fission cross sections (1.46f0.07) b and (1.48f0.06) b17,18,respectively. 100 50
.
2
10
.-v) &
5
fl!
l
20
rJ
%
\
1 *a!
8
% .)
2
*
i
* *
1
x
c
0.5
?
0
20
40
60
80
100
120
140
160
, 180
*
-y#P 200
220
Mass Loss, AA Figure 5. Comparison of cross-sections for evaporation and fission residues as a function of the mass-loss AA for the two collision systems Pb p (triangles) and U p (full points) at 1 A GeV.
+
5.
+
Mass Yields: Comparison with the Pb (1 A GeV)+ p system
The mass distribution a(A ) is built by summing isotopic cross sections for A fixed. It shows a roughly symmetric Gaussian shape except for the shoulders of asymmetric fission. We have plotted on Fig. 5 cross sections as function of the mass loss for spallation residues and f.f.. The P b p results3 are reported also to illustrate the importance of the fissility in case of U. Total cross sections are almost the same within 10 %, (see the
+
230
U +p Pb + D
238
(barn) 1.99f 0.17 1.84f 0.23
(barn) 1.53 f 0.13 0.16 f 0.07
(barn) 0.46f0.08 1.68f0.22
U ( l A GeV) + p
126
0
25 mb 5 mb 1 mb
02mb 40 pb
=
8 pb 1 pb
2 8
Figure 6. Two-dimensional plot of the isotopic cross sections for fission fragments (ref 10 et 15) and evaporation residues (ref 6) obtained in 1 A GeV 238U p shown on the chart of isotopes with indication of the stable isotopes. Increasing dark level correspond to decreasing cross sections according to the logarithmic scale indicated.
+
Table) but the dominant contribution of the fission for U is inhibited in case of Pb, whereas for Pb, excited fragments cool down mainly by neutron evaporation. Simulations have been performed by our collaboration to reproduce the measured f.f. cross sections. The best result is obtained by using a calculation of the cascade with a new version of INCLl’, the statistical deexcitation code ABLA20v21, and a fission parametrization PROF122 The cross sections for (U p)-evaporation residues6 cannot be reproduced by the Bohr and Weeler model and dissipation has to be included in the calculation. The reproduction of measured data is optimum with a dissipation constant /3 = 2*1021 s-lZ3.
+
23 1
6. Conclusion
The isotopic cross sections are determined for 1300 isotopes produced in the reaction U (1 AGeV) p see Fig. 6. The fission fragments, separated kinematically from the spallation residues are investigated and production cross-sections are determined within a range of 2 to 3 orders of magnitude down to 10 to 100 pb with an accuracy better than 15 %. The kinetic energy of each fragment is determined. Of a total cross section of 2 barns, 77 % is attributed to fission and 23 % to evaporation residues. Multifragmentation can be neglected. The mean element number and the mean neutron number of the f.f. .allow to reconstruct 221Th as the mean parent fissioning nucleus.
+
References 1. 2. 3. 4.
F. Rejmund et al. Nucl. Phys.A683 481 (2001) J. Benlliure et al. Seminar on fission, Pont d'Oye
Iv 223 (1999)
T. Enqvist et al. Nucl. Phys.A686 481 (2001) F. Carminati, R. Klapisch, J. P. Revol, Ch. Roche, J. A. Rubio, C. Rubbia.
CERN Report CERN/AT/93-47(ET), (1993). 5. G. Fioni, see the contribution therein. 6. J. Taieb, PhD Thesis Univ. Paris XI (2000) IPNO-T-00-10 and J. Taieb et al. Nucl. Phys. A724 413 (2003) 7. H. Geissel et al. Nucl. Instrum. MethodsB70 286 (1992). 8. M. Bernas et al. Phys. Lett.415B 111 (1997) 9. Ch. Engelmann, Thesis Univ. Tubingen (1998), GSI Rep. Diss. 1998-15, and Zeit. Phys.A352 351 (1995) 10. M. Bernas et al. Nucl. Phys.725A 213 (2003) 11. P. Napolitani et al. Nucl. Phys.727A 120 (2003) 12. B.D. Wilkins, E.P. Steinberg, R.R. Chasman, Phys. Rev.Cl4 1832 (1976) 13. C. Bockstiegel et al. Phys. Lett.398B 259 (1997) 14. C. Donzaud Eur. Phys. J.Al 407 (1998) 15. M. V. Ricciardi et al. proceedings of the XXXIX Int. Winter Meeting on Nucl. Phys., Bormio, Italy (2001). M. V. Ricciardi, PhD Thesis in progress, GSI-Darmstadt. 16. D.G. Sarantites et al. Phys. Lett.218B 427 (1989) 17. B. A. Bochagov et al. Sov. J. Nucl. Phys.28-2 291 (1978) 18. L. A. Vaishnene et al.2. Phys.302A 143 (1981) 19. A. Boudard, J. Cugnon, S. Leray and C. Volant, Phys. Rev.66C 044615 (2002) 20. J.-J. Gaimard and K.-H. Schmidt Nucl. Phys.531A 709 (1991) 21. A. R. Junghans et al. Nucl. Phys.629A 635 (1998) 22. J. Benlliure et al. Nucl. Phys.628A 458 (1998) 23. B. Jurado, PhD Thesis, Univ. Compostela (2002) and GSI Rep. 2002-10, t o be published
FISSION DYNAMICS WITH THE “NEUTRON CLOCK” TECHNIQUE USING DEMON NEUTRON ARRAY AT THE LOUVAIN-LA-NEUVE CYCLOTRON FACILITY.
Y. EL MASRI, J. CABRERA, TH. KEUTGEN, CH. DUFAUQUEZ, V ROBERFROID, I. TILQUIN AND J . VAN MOL F N R S and Institute of Nuclear Physics, Catholic University of Louvain, B-1348 Louvain-la-Neuve, Belgium.
R.J. CHARITY Department of Chemistry, Washington University, St. Louis, Missouri 63130, USA.
J.B. NATOWITZ, K. HAGEL AND R.WADA Cyclotron Institute, Texas A B M University, College Station, Texas 77845, USA.
In this work,the particle evaporation “clock” method has been applied with success to the interpretation of p r e and postscission neutron and light charged particle multiplicities extracted from the fusion-fission reactions; 8 to 16 MeV/A 20Ne+’5gTb and zoNe+’6gTm. The neutron properties were established with the DEMON neutron array. The experimental observables were compared with statistical model calculations using a new version of GEMINI Monte-Carlo code. These simulations,incorporatingsimple aspects of the fission dynamics (time-dependent fission width and deformation-dependent transmission coefficients) predicted by the HICOL dynamical code,have enabled us to estimate the ranges of conventionalfission and fast-fission timescales at different compound-nucleus excitation energies. The additional fission dynamical delay times which were required to reproduce our data were found to decrease as the initial excitation energy of the fissioning nucleus increases from 108 to 254 MeV (or for nuclear temperature (T) from 1.3 to 2.3 MeV). This method is shown in simulations, to give times closer to the median lifetime (halflife). The time distributions have extremely long tails covering more than SEVEN orders of magnitude, consistent with previous results obtained with other techniques (crystal blocking, KX-rays and GDR ^(-rays). The decrease of median fission lifetimes and subsequent fission transient times with increasing the excitation energies may suggest a decrease in nuclear viscosity above T N 2 MeV, consistent with the onset of two-body dissipation mechanism.
232
233
1. Introduction The timescale of the fission process has been addressed using a number of experimental techniques’-6. However, the largest number of studies have been based on the neutron LLclock’’ technique’ which essentially comprises measurements of the pre- and postscission multiplicities of the emitIn order ted neutrons by the fissioning nucleus before and after fission to understand these multiplicities it would be useful to perform full reaction trajectory calculations in the multiparameter space of all the fission degrees of freedom. The simulations should follow the fission trajectory to thermal equilibration and to the scission configuration. It should also include the evaporation of all types of light particle emissions (LP=neutron (n) and light charged particles (LCP) such as p, d, ... and a ) which compete statistically with fission. In the absence of such extremely difficult simulations, nuclear fission dynamics ( timescales,nuclear viscosity ...) have been usually deduced following two steps: i) In the first step,one relates the measured experimental observables (LP, y-pre-scission multiplicities, fission (F) and evaporation residues (ER) cross-sections for different set of possible entrance channel conditions) to the fission timescales or lifetimes using the most complete and sophisticated statistical and/or dynamical model calculations available; ii) In the second step, one relates these timescales and all the extracted physical parameters derived from the first step,to the essential characteristics of nuclear viscosity for fission in particular, and to the energy-dissipation dynamics in general. The main contributions to the dissipation come from either the nucleon-nuclear surface (one-body di~sipation)~ or the nucleon-nucleon collisions (two-body dissipation)’. This second step is very hard since it is not even clear what form the nuclear viscosity takes in the fission process. Due to practical reasons,many of the experimental techniques used to address fission dynamics,are coupled to statistical-model calculations (SMC) (with or without incorporating aspects of the fission dynamics) to give a time for fission. This makes all these techniques rely on the accuracy of the SMC and even on the basic question of its applicability knowing the complex features of the fission collective dynamics and its coupling with the particle degrees of freedomg. Therefore, in the absence of another approach, the authors of LP or gamma ‘Lclock”techniques typically present their results in term of ) is introduced into the some extra-dynamical fission time delay ( ~ d which SMC to reproduce the experimental LP prescission multiplicities. These sec). This fission delay time studies obtain values for ~d of 10-100 zs
’.
234 can comprise a contribution from a presaddle fission delay ( T ~ associ~ ~ ated with a transient fission decay rate which is initially suppressed due to the non-equilibration of the compound nucleus (CN) collective degree of freedom (difision description),and a contribution from the time ( T S S C ) required from the fissioning nucleus to move from the saddle-point to the scission-point (SSC) configuration.
2. Experimental set-up and results In this paper we report on the determination of fission lifetimes using measurements of pre- and postscission neutron, proton and alpha multiplicities. The fissioning CN with excitation energies of 108 to 254 MeV, were produced in the reactions of 8, 10, 13 and 16 MeV/A ‘ONe beams,delivered by the Louvain-la-Neuve cyclotron on lS9Tb and 169Tm targets. An earlier accounts of the experimental and data analysis are available in Refs.lo. Fission fragments (FF) were detected in coincidence in two, 20x20cm2, X and Y position sensitive, multi-wire proportional counters arranged on both sides of the beam axis. ER were detected and identified in two microchannel plate-Si-diode assemblies. Neutrons and LCP were detected in coincidence with FF and ER. The 96 DEMON liquid-scintillation counters were used to detect and characterize neutron emission with an angular coverage both in- and out-of-the reaction plane (47r geometry)ll. LCP were detected with a set of triple-Si-telescopes. In our studies,neutrons were assumed to originate from up to four moving sources. In temporal order, first there were preequilibrium (PE) neutrons resulting from incompletefusion reactions (not a thermalized source), secondly are the prescission neutrons evaporated prior to scission from the thermally equilibrated CN with a multiplicity and last are the postscission neutrons evapoThe energy rated from the fission fragments with multiplicities spectra of the last three sources were assumed to be thermal-like in their respective reference frames. Evaporation and fission cross sections ( U E R and O F ) were determined from measured FF and ER angular distributions over a wide angular range. Table 1 lists the estimated residual excitation energies Ei*,PEof the composite system after P E emission and its intrinsic A.M.(Jg:). Also are mentioned the A.M. values where the fission barriers are predicted to vanish (JBF=o)in order to explore the possible presence of FAST FISSION processes”. They are also known as fission without barrier processes. Usually conventional-fission (CoF) and fast-fission (FaF) processes can be, to some extend, isolated in the A.M. space of the fissioning
(.re),
(urst).
~
~
)
235 nucleus. Within the sharp-cut-off approximation, CoF can be associated with the A.M. range between JER and JBF=O (where J E R is the upper limit of A.M. contributing t o the ER formation) with a cross-section oCoF. (1) On the other hand FaF is dominating in the range of JBF=Oto JZZ with a cross-section ogiF. Table 1 also lists the excitation energies at scission
(E:c)taking into account the total energies (Q-values and kinetic energies) removed by all the prescission emitted particles. Table 1. For both reactions studied, are listed (with their uncertainties) respectively, the estimated initial CN excitation energy after preequilibrium emission, its corresponding A.M., ER cross-section, ER-fission cross-section ratio, the pre- and postscission neutron multiplicities for symmetric mass partition, the extracted CN mean nuclear temperature, its excitation energy at scission. With JBF=O= 78 and 77 A respectively.
103 f 3 133f 1 173 f 3 207f6
72 84 93 99
711 f 4 6 743f48 796 f 4 5 924f53
99f3 132fl 172f3 211f6
74 87 95 100
351f59 359f31 414f25 478f20
1.11 f 0 . 0 8 3.5 f 0 . 2 0.89f0.07 4.8f0.1 0.99f0.07 5.9f0.2 1 . 2 2 f 0 . 0 9 7.1 5 0 . 2 ZoNe + l j 9 T m 0 . 3 3 f 0 . 0 6 3.2410.2 0.29f0.03 4.7f0.1 0 . 3 4 f 0 . 0 2 6.2 f 0.1 0.41f0.03 7.1f0.2
2.0f0.1 1.8f0.1 2.3 f O . l 2.5f0.2
1.38 1.75 2.04 2.25
56 f 70 f 80 f 90 f
2 2 4 4
2.4f0.1 2.2f0.1 2.3f0.1 2.5f0.1
1.33 1.66 1.93 2.11
52f2 72f2 82 f 4 89f4
3. Statistical-model Simulations using GEMINI code
In this study we have performed SMC incorporating simplistic aspects of the dynamics of FaF and statistical fission using a recently modified version of the GEMINI Monte-Carlo code13. In these calculations we have subdivided the A.M. space J into two regions such as discussed in the previous section. A) In region (1) or J<JBF=o,a standard statistical decay of the CN is modelled to account for CoF events. Standard spherical transmission coefficients for LP emissions are assumed. In order to reproduce the experimental values of v r " , we introduce an initial time period ,$), where fission decay is "hindered" (see below). Consequently T:') may be interpreted as also including the saddle-to-scission time TSSC. In practice in the new version of GEMINI code,if one defines ,rip,the total LP emission width at the step j of the CN decay (summed over of all LP types such as
236
n,p,d...a ) and I?$ the total fission width (summed over all possible fission mass and charge partitions), then riot= rip+I'+becomes the total decay width of the nucleus at the step j . Thus: a) If the elapsed time tj-1 up to the step j is 7:') then, the fission probability is given by the standard statistical expression : Pj = l?$/l?iot and tj=tj-1 At, =tj-1 fi/riot;
>
+
+
b) If ti-1 < T:'), one must take into account the fission hindrance and the probability for fission increases with the difference 6 =(T:" - tj-l) following expression:
pi - yj f
-
f/
rjtot * ezPcp(-J/Tj)
(1)
where rf is the asymptotic value of the fission width a t S= 0,calculated with the the A.M.-dependent fission barriers from Sierk'* and ~j = fi/I'ip. The exponential factor expresses the probability for not evaporating a particle during the initial period when fission is suppressed. Equation 2 means that ~j increases exponentially from a very small value (- zero) for tj-1 << Td(1) and reaches I$/!&
at tj-l = T:') as expected if one accounts for nuclear
+
viscosity. However in this case , t j = fi/rf,,. Moreover instead of adding mean times ( ~ = j fi/I'iot) to determine t j , the effective decay times At, t o be really added to tj-1, are distributed following a time-dependent exponential law such as: f(Atj) = l . / ~*j exp(-Atj/Tj). Thus,the total probability of a nucleus decay within the time interval [0, Atj] is u = 1.exp(-Atj/rj) where u can be considered as a uniform random variable in the interval [0, I]. After inverting this function one can show that: a) If tj-1 T:'); then t j = tj-1 - fi/I'iot* ln(1-u) (one simply adds the *In(1-u) real statistical time); b) If tj-1 < T ! ) ; then t j = ( where one displaces the fission lifetime to at least 7:') and then adds the statistical time). In practice the available thermal excitation energy for the system becomes drastically reduced with time due to LP emissions and thus the fission and LP emission widths become smaller and smaller as the nucleus approaches the saddle point. Then the CN statistical decay times (Atj) becomes longer and longer at the final steps. So the time for the last fission step ,(At,), will'dominate the fission characteristic lifetimes and thus cannot be neglected in the build-up time. B) In region (2), we have followed a simple scheme which we believe captures the most important aspects of fast fission that relates t o pre- and postscission evaporation. The evaporation from the composite system was treated as being from a deformed system of CONSTANT deformation which
>
~i')
237
is meant to represent the mean shape of the system prior to scission. Based on the dynamical code HICOL15, this shape was taken as prolate with T , / T , = 1.5, the ratio of major to minor axes of the system assumed to rotate about an axis perpendicular to its major axis. Particle evaporation was considered for a time period of which was meant to represent the duration of the FaF interaction. Deformation energies, rotational energies and particle transmission coefficients appropriate for the assumed deformation were used in our GEMINI calculations. For both regions (1) and (2), the postscission evaporation is simulated using spherical transmission coefficients. As FaF was not observed in the E/A=8 MeV reaction data, the values of 7:') and the level-density parameter^'^ a, and a f were adjusted to reproduce the pre- and postscission multiplicities of n, p and a particles and the cross- section ratios U E R / U F . The fitted values of the level-density parameters are a,=AcN/S MeV-' and a f / a , = 1.05. These values were assumed independent of excitation energy and used in the simulations for the higher beam energies (E/A= 10, 13 and 16 MeV). The fitted value of 7:'' = 45f5zs at E/A= 8 MeV, and its values at the higher bombarding energies were adjusted to fit the experimental ratios U E R / U F . Once $) was adjusted, the FaF delay time was then varied in order to fit the multiplicities of all the LP at the higher E*. For both pre- and postscission multiplicities, the simulated values are calculated as a weighted average:
~f'
$'
$4
where and vpi are the simulated multiplicities for region (1) and (2), each being a function of its corresponding dynamical time delay T:') and $) respectively and ,&) and d2)are the fission cross-sections associated with these two regions with a(') d 2 )= U F . As shown in Ref. 10 all the experimental multiplicities and cross-section ratios were very well reproduced by the adjustment of only the two fission delay times 7:') and ~ f ) .Their evolutions are displayed in Fig. 1as a function of the CN initial excitation energies E:EE. The fission delay 7:') associated with CoF process decreases with increasing E:EE from 45f5zs to the quasi-constant 15f5zs for the two highest energies. The value of T:) N 452s value of extracted from the two lowest E:EE agrees very well with the systematics of Hinde et a1.l6. The values extracted from the highest bombarding energies are also approximately 15f5zs, about equal to the corresponding T:') values. The similarity of the two dynamical times suggests they may have similar origins
+
-
N
$'
238
Figure 1. Evolution of the dynamical times T:’) and T:” extracted from the statisticalmodel calculations using the GEMINI code with the initial excitation energies E,*TE for the 20Ne 159Tbreaction (see text for details). The lines are to guide the eye.
+
(for example the evolution from a compact composite system t o a dinuclear shape). 4. Fission timescales
Figure 2 illustrates the predicted two-dimensional distributions of the logarithm of fission times (tf) as a function of the prescission neutron multiplicities ( v r “ )for the reaction “Ne+15’Tb at 8 and 16 MeV/A. The most striking difference in the data sets from the two targets is the ER probability (see Table 1). But the properties of the fission fragments appeared to be very similar for the two targets (see Table 1) as they are not different in mass. Therefore in the following,we will only concentrate the discussion on the data from the 20Ne 15’Tb reaction. All the conclusions drawn in this case were shown t o be identical for the 16’Tm target”. Figures 2a and 2c, show the time distributions associated with CoF decay with their characteristic time r,f’ and mean multiplicities. The plotted prescission multiplicities are assumed t o cover pre- and postsaddle neutron emissions ~ .2d shows for ,E/A=16 MeV reaction, the and thus tf rtrans 7 ~ sFig. time distribution for FaF events (JBF=O J JL:) with its characteristic rf’ and v?’ values. No predictions are shown for the beam energy E/A=8 MeV as no FaF was experimentally observed at this energy. As discussed above all these time distributions are zero up until the appropriate value of rp’. At 16 MeV/A the FaF events fission immediately at tf = r f ’ by assumption as they correspond to fission process without barrier. Conserf’ rssc as the quently one can easily assume that in this case tf ~ ~ region ~ transient time T (2’~ , in. this is zero. From these time distributions
+
vt’
-
+
< <
- -
239 -I4
=: Q .=
2
-16
-18
-20
-20
-19
-18
-17
-16
-15
-14
-
0
5
10
Yo
5
LO
15
y
Figure 2. Two-dimensional distributions of the logarithm of fission lifetimes (tf ), as a function of the prescission neutron multiplicities for the CoF and FaF processes in the reaction 2oNe '"Tb at 8 and 16 MeV/A, as predicted by the GEMINI code (see text for details). Open circles designate < T f > ( j ) evolutions and full points T:)'"'
ure
+
evolutions. Their global values < T f > g ' and are also designated. b) shows the projection, on the time-axis, of the log(tf) distribution as predicted at 8 MeV/A. The dynamical time T : ' ) and the median scission time ~ ~ fare~indicated. ' / ~
and from those similar at 10 and 13 MeV/A reactions'O, one can conclude that the range of CoF timescales is quite large, covering roughly up to SEVEN orders of magnitude. Given such a wide distribution of times, there are a number of characteristic times that can be associated with such distributions. For example the average or mean time < T f > . These times in region (1) (<~f>(')) are orders of magnitude larger than their corresponding T:') as shown in Figs. 2a and 2c by the calculated values indicated for each v r e (open points). Their calculated over all the predicted events global mean fission times were found to be 31.4 lo3, 15.3 lo3, 28.9 lo3 and 12.2 lo3 zs for E/A= 8, 10, 13 and 16 MeV 20Ne+159Tbreactions respectively. The fluctuation in times is related to the limited statistics in the long tails as single event,at large time, can make sizable change to the mean time. In any case, such long times are, in line with the results of the mean lifetime measurements by the crystal blocking technique. In fact, early measurements with that technique reported a significant tail to the fission time distribution at times greater
<~f>g)
240
than 30.103 zs for fission induced in 19F+1siTa fusion reaction’. More recently,measurements3 for E/A= 24 MeV ’38U+’8Si found mean fission lifetimes greater than 100 zs for excitation energies up to 250 MeV. One must recall that the range of sensitivity of the crystal blocking technique is limited by the velocity of the fissioning system. The importance of fission events with long times (>lo00 zs) has also been confirmed using KX-rays to time the fission of target and projectile-like fragments in the reaction E/A= 7.5 MeV 238U+238U. Another characteristic time of a distribution is the median or halftime, r;I2, the time by which half of the scission has already occurred. As illustrated in Figs. 2a and 2c (full points), these times ( r ~ ) ’ ” ’ ) , are less
*
dispersed and quite well defined as a function of v;) multiplicities and are much more similar in magnitude to the dynamical times. Their global over all the predicted events, are displayed in Fig. 3 as a values function of Ei*,PE. These times, like the dynamical times, decrease from 116.4, 102.2, 42.6 to 38.5 zs with Ei*,PEincreasing from 101 t o 216 MeV. Fig. 2b shows that practically half of the CN have fissioned with fission lifetimes near rji) and the other half are dispersed over 4 to 5 orders of magnitude. For FaF events, Fig. 2d shows that rj~k”’ is around 15 zs for the 16 MeV/A reaction. Their values are also displayed in Fig. 3 as a function of E:rE. They decrease from 20 to 15 zs for the two highest excitation energies (180 and 216 MeV) practically equal to r f ’ . In general the fission lifetimes reported by other authors’>” using neutron clock technique were found t o range between 5 and 200 zs. Our present work shows how complex is fission lifetime extraction and how difficult is to characterize it in a single value. In fact the calculated global mean lifetime values show that there is no a simple relationship between $) and vflre values. The few long- lived fissioning nuclei strongly contribute in the important increase of the fission lifetime. Similarly these values seem to be less sensitive to T:’) variations. In principle,in region (2) one accounts for only the FaF events so, T;:&’/~ ry’ 15f5 zs and is practically constant for the two
,rj:ki”,
N
N
ri1)
highest EtZE. This time must also correspond to T S S Q . As takes into account the mean times (rtrans) and ( T S S C ) , then one can speculate that may be attributed t o the difference in time between rjtk’/2 and the median fission time for nucleus to evolve from the equilibrium point With the assumption of a constant value t o the saddle point time. These of rssc over in the entire E* range, one can extract -r$~~S/’
(r$,!i$’).
24 1
0J
80
1W
120
140
IMI
180
200
’
0
E;~(M~v)
Figure 3. Variations of the simulated global median scission lifetimes and T ~ ~with ~ the ~ initial , / excitation ~ energies E,’nPE for the ‘ONe (see text for details). The lines are to guide the eye .
~jfk””-rj:k1/’
+ 159Tb reaction
values are also displayed in Fig. 3. They vary slowly between 101 and 87 zs for E;ZE increasing from 101 t o 139 MeV but they rapidly decrease t o a constant value around 25 zs at the two highest E:ZE i.e. 180 and 216 MeV or their corresponding mean nuclear temperatures (TTe= 2.04 and 2.25 MeV respectively see Table 1). One should notice that at low J values JER <J< JBF=O,the CN equilibrium configuration must not have changed for the four Ei*,PE.Nevertheless for these nuclei, T;:&’” values remain greater than
7-i’) and
they decrease with increasing E*.
5 . Conclusion
Even though it is extremely difficult t o evaluate the uncertainties associated with all these fission lifetimes due t o the large number of theoretical approximations applied in the SMC in order t o simulate the experimental physical observables , and ( C T E R / C T Fratios), the general decreasing behavior of r ~ ~with ~ increasing ~ / 2 E* remains too significant t o be ignored. This behavior is also associated with the decreasing the dynamical fission delay times 7:’’ in the specific region of conventional fission, where no FaF contribution could be held responsible for the observed behavior. Such a clear dependence of $) and was not seen in previous results, usually confined t o lower excitation energy regimes E* < 100 MeV. Our data imply a decrease of these characteristic fission lifetimes for E* above 100 MeV while the excitation energies of the nucleus at the scission point (E&)are perceptibly increasing (more than 30 MeV (see Table 1)). This observation would imply a decrease in the friction or nuclear viscosity with nuclear temperature (above T 2 MeV) as such it may illuminate the
Tit)
N
242
nature of the dissipation mechanism. One-body dissipation is predicted t o increase or remains constant with temperature' whilst two-body dissipation is expected t o decreaseE. The fission dynamical timescales are supposed t o follow, as a function of T, the behavior of the subsequent dissipation mechanism. In conclusion the results of our study seem t o favor two-body as the dominant dissipation mechanism for T 3 2 MeV. J.Wilczynski et a1.l' have applied a deterministic model of nuclear dynamics to extract friction coefficients from analyses of deep-inelastic or fast-fission reactions. Their results suggested a possible decrease in dissipation (a l/T2) above T = 2.2 MeV which they also interpreted as evidence for the onset of strong two-body dissipation. Anyway, more theoretical and experimental studies are still in order to confirm this conclusion.
References 1. D. Hilscher and H. Rossner, Ann. Phys. I+. 17,471 (1992). 2. J.S. Foster et al., Nucl. Phys. A464, 497 (1987). 3. F. Goldenbaum et al, Phys. Rev. Lett. 82, 5012 (1999. 4. J.D. Molitoris et al., Phys. Rev. Lett. 70,537 (1993). 5. P. Paul and M. Thoennessen, Ann. Rev. Nucl. Part. Sci. 44,65 (1994). 6. Gert van't Hof, Ph.D. Thesis, Rijksuniversiteit Groningen (1995). 7. H. Hofman et al., Nucl. Phys. A598, 187 (1996)and J. Blocki et al., Ann. Phys. 113,330 (1978). 8. G. Wegmann, Phys. Lett. 50B,327 (1974)and J.R. Nix and A.J. Sierk, Phys. Rev. C21,396 (1980)and references therein. 9. P. Grange et al., Phys. Lett. 96B,26 (1980),P. Grange et al., Phys.Rev. C27, 2063 (1983),P. Grange et al.,Phys. Rev. C34,209 (1986),H.A. Weidenmuller et al., Phys. Rev. C29, 879 (1984) and K.H. Bhatt et al., Phys. Rev. C33, 954 (1986). 10. Th. Keutgen, Ph.D. Thesis, Catholic University of Louvain (1999) and J.B. Cabrera, Ph.D. Thesis, Catholic University of Louvain (2002); J. Cabrera et al., Phys. Rev. C68, 034613 (2003)and references therein. 11. I. Tilquin et al., Nucl. Instrum. Methods Phys. Res. A365, 446 (1995)and I. Tilquin, Ph.D. Thesis, Catholic University of Louvain (1997). 12. C. Gregoire et al., Nucl. Phys. A387, 37c (1982). 13. R.J. Charity et al., Nucl. Phys. A483,371 (1988)and R.J. Charity, computer code GEMINI (unpublished) http://wunmr.wustl.edu/Nrc. 14. A.J. Sierk, Phys. Rev. C33, 2039 (1986). 15. H. Felmeier, Rep. Prog. Phys. 50,915 (1987)and references therein. 16. D.J. Hinde et al., Phys. Rev. C45, 1229 (1992)and references therein. 17. D.J. Hinde et al., Phys. Rev. C39, 2268 (1989). 18. J. Wilczynski et al., Phys. Rev. C54, 325 (1996).
Chapter 8
Fission Cross Sections
This page intentionally left blank
STUDY OF PROTON-INDUCED FISSION OF ACTINIDE NUCLEI BETWEEN 20 AND 80 MEV BOMBARDING ENERGIES
D. BELGE, CH. DUFAUQUEZ, TH. KEUTGEN, R. PRIEELS, A. NINANE, J. VAN MOL AND Y. EL MASRI FNRS and Institut de Physique Nuclaire, UCL, Louuain-la-Neuue, Belgium E-mail: [email protected]. ac. be R. CHARITY University of Washington, St Louis, USA, E-mail: CharityQwuchem.wustl. edu Neutron and proton-induced fission studies on actinide nuclei, a t low and intermediate energies, are of great interest for fundamental understanding of the fission processes and especially for applied nuclear research such as transmutation of long-lived radioactive wastes. As a first step of a long-range research program at Louvain-la-Neuve cyclotron facility, we have recently performed the measurements on the proton-induced fission reactions with 238Uand 239Putargets at 26.5 and 62.9 MeV bombarding energies. Some preliminary results are presented. Future measurements on other actinides are foreseen.
1. Introduction Nuclear waste originating from nuclear power plants have been a source of concern to the general population for a long time. A first solution to this problem, consisting of deep geological disposal with or without reprocessing, has been studied (see the contribution of G. Fioni to this conference). However, this solution will not attenuate the radiotoxic inventory which is still growing. Meanwhile, the proposition has been raised that the radiotoxicity should be reduced over time by burning the long-lived actinides waste in a nuclear-reaction process. Some people have also suggested that after the Chernobyl accident, the security at reactors needs to be increased. Moreover on a medium time range of 50 up to 100 years, the world community may suffer from lack of energy due to the reduction in the fossil matter from which we presently obtain 80 % of our energy needs. 245
246
The energy supply must then be obtained from new technologies: fusion, renewable processes, reactors with 232Thas the main fuel, high-energy fission reactors burning 238U,etc... This latter option is appealing since it also gives a possibility of burning the nuclear waste. This supports the concept of accelerator driven systems (ADS) which are subcritical reactors driven by extra neutrons produced in a spallation target irradiated with energetic protons. However many aspects of such a concept must be kept under control: the accelerator, the spallation target, the partitioning, the fuel, etc... Important programs related to neutron production from spallation targets have already started Concerning both the target and the fuel, a large number of proton 6,7,8,9and neutron induced fission experiments have been carried out at energies above 10 MeV. Most of these concern fission of sub-actinides (i.e., W, P b and Bi) and actinides (i.e., T h and U). A recent compilation and systematic study was undertaken on an exhaustive list of proton-induced fission cross sections l4 and on (n,x) reactions 15. In general, no coincident neutron and light charged-particle distributions nor fission-fragment mass distributions were measured. Also only a few independent isotope yields 8,9 have been determined. However, the need for neutrons and proton induced fission reactions on actinides at the energies between 20 and 200 MeV have been clearly stressed 16. We have proposed, as a first step of a long-range program, cross section measurements for proton-induced fission of 238U and 239Pu nuclei at 26.5 and 62.9 MeV incident proton energies. As it is already established, the proton-induced fission cross-section on 238U may be considered as a standard data which can be used to check our detection system, efficiency and data-analysis methods. In coincidence with the fission fragments, the multiplicities, energy and angular distributions of the emitted neutron are measured at Louvain-la-Neuve, for both targets, using DEMON neutron array. 173,495.
10311,12,13
2. Experimental setup Figure 1 displays the detector positions inside the reaction chamber. Three different types of detectors were used. Two microchannel-Si diode detector assemblies GJ1 and GJ2 measure, in singles mode at different laboratory angles, the time-of-flight and the energy, and thus, the mass of the fission fragments (FF) emitted by the target. The resolutions of these detectors in energy and time are 40 keV (at 6 MeV alpha) and 700 psec, respectively.
247
-* hlicrochnnnel-Si diodc
\.I\\ Pc'1,Z Large active area X,Y Multi Wire l'rupurtional gas Counters Figure 1. General scheme of the experimental setup.
Simultaneously, two X and Y position sensitive Multi-Wire Proportional gas Counters (MWPC), located on both sides of the target, detect the coincident FF emitted back to back in the center-of-mass frame. Their high angular (0.4 deg) and time (0.7 ns) resolutions lead to a good determination of both FF velocities and angular distributions. Around the reaction chamber, up to 96 liquid-scintillator cells allow the determination of the neutron energy and angular distributions associated with the fission process. Both targets, 238U (106 ,ug/cm2) and 239Pu (180 pg/cm2), are "sealed" between two 12Clayers, thick enough (50 pg/cm2) to stop either the recoiling target nucleus or the evaporation residues of the induced reactions but not the FFs. In order to monitor the reaction-chamber residual activity (contamination from the target), up to two thin Si detectors, shielded from the target by thick aluminum blocks, allow the detection of the 5 MeV alpha particles emitted by any U or Pu eventual contamination on the reaction chamber wall. 3. Results
3.1. Fission fragment angular distribution The GJ1 and GJ2 assemblies (see Fig. 2) where placed colinearly with the target position as shown in Fig. 1. They thus allow a direct determination of the FF masses knowing their energies and velocities (time-of-flight). The mass distributions of these FF is extracted at several detection angles
t
10
nmeJbmi
Figure 2. Microchannel plates-silicon diode assemblies. The left side panel shows the incident FF crossing a 500 A gold layer before stopping in the Si diode. Secondary electrons escaping from the Au layer are accelerated towards the microchannel plates delivering a fast timing signal. On the right side panel an energy-time bidimensional spectrum is shown. The start time is given by the cyclotron radio-frequency.
(usually four positions of these detectors inside the reaction chamber were chosen). However, the extracted mass distributions have poor statistics due to the small solid angle covered by these detectors. An energy versus time-of-flight bidimensional spectrum is shown on the right side panel of Fig. 2. The FF are clearly seen whereas the thick uncorrelated low-energy line corresponds to the alpha radioactivity of the Pu target.
y:
'mesignal
Figure 3. Multi-wire X,Y position sensitive proportional gas counters. The wires pitch is of 1.28 mm and they are assembled 2 by 2. The spots on the right side panel locate the crossing points of fission products in the X,Y plane after passing through holes in a geometrically calibrated A1 frame.
249 160
I
20 _.
30 ~~
AD
50 ~~
60 70 Theta1 (deg)
_ r
0
10
20
30
40
50
60
Excnanon energy (MeV)
Figure 4. On the left side panel: fission fragment angular correlation (0, versus 0,) observed in the 239Pu(p,f) reaction at 60 MeV proton energy. On the right side panel: remnant excitation energies as calculated hy CASCADE after the nuclear cascade mechanism but before the light particle evaporation process.
A good coverage of the FF angular distribution is provided by the two MWPCs. The angular correlation between FFs emitted from 239Pu (p,f) reaction at 60 MeV proton energy is shown in Fig. 4. The dotted line shows the expected correlation in case of zero linear-momentum transfer (LMT), whereas the solid lines display the expected correlation for a full linear momentum transfer with various fission mass partitions. One clearly sees that the LMT is neither null nor full. The fraction of LMT to the fissioning nucleus reduces the 180" back-to-back emission angle in the center-of-mass frame to a less open emission angle in the laboratory frame. This is comfirmed by a simulation performed using the CASCADE code of J. Cugnon l7 predicting the properties of the emitted neutrons and protons in the reaction of 60 MeV protons on a 239Pu target (see Fig. 5). High-energy nucleons up to 60 MeV are emitted mostly at forward angles, whereas an isotropic low-energy distributions due to the evaporation process does not exceed 20 MeV. It follows from these simulations that around 18% of the reactions proceeds through a complete fusion reaction (proton energy totally absorbed by the target) and consequently gives a full momentum transfer. The contribution of such events decreases when the projectile energy increases (71% at 20 MeV and 18% in contrast to 60 MeV projectile energy). The remaining 82% of the reaction events which populate the high-energy tails of Figs. 5, realize only a partial energy linear-momentum
250 p(60 MeV)+239Pu
i 'i 1 !;., '.
'
0
,
.'..,
L '>
.'!.'T!Q
20
,lo
,.
, 40
,
, 60 0
En (MeV)
165
!'.:, ;>.
".,"
:!t!!,,
20
,
1
40
60
EP W W
Figure 5 . Neutron and proton simulated energy spectra for various emission angles (degree) in the laboratory frame when a 239Putarget is bombarded with 60 MeV proton beam as predicted by the code CASCADE (see text).
transfer. As a result, the residual excitation energy of the fissioning nucleus ranges between 0 and 60 MeV (see right side panel of Fig. 4). It will cool down by evaporating successive nucleons (low energy parts of Fig. 5). After scission, and before leaving the target, the FF evaporate nucleons in
251
directions correlated with each fragment's momentum vector. The FF will then slow down as they cross the target material before finally reaching the detectors. To evaluate the F F masses one needs to trace back all these processes.
3.2. Fission fragment mass distributions Since the MWPC detectors cannot determine kinetic energies, an iterative procedure is applied to extract the FF mass partition taking into account the energy losses of the FF in the target. As previously explained, to achieve this goal and correctly identify the primary FF mass we need also to evaluate the mean post-scission neutron multiplicity emitted from each fragment before leaving the target. This can be obtained, on average, from the neutron angular and multiplicity distributions included within the DEMON data set. After some iterative loops, this procedure should converge in a correct FF mass determination, which can be checked by comparison with the mass distribution extracted from the GJ1 and GJ2 detectors. The full procedure has not yet been applied to our raw data shown in Fig. 6.
26.5 MeV
Figure 6. Preliminary FF mass distribution, using MWPC's, for proton-induced fission on 238Uand 239Pu at two proton beam energies i.e. 26.5 MeV (left panels) and 62.9 MeV (right panels).
252
Since 238Udata are used to certify the quality of the applied procedure, we also show in Fig. 7 a comparison of our "crude" first results with the published ones from the Uppsala l8 facility. An improvement is expected when the full data analysis procedure is applied.
B) p (62.9MeV)
A) p (26.5MeV)
I
4
O
0
7
16004
0 Mass ( m a )
Mass ( m a )
Figure 7. Our preliminary FF mass distributions (solid thick black lines) obtained from proton induced fission on 238U at 26.5 and 62.9 MeV bombarding energies. These data are compared to Uppsala published results taken at 20 MeV (thin solid line) 35 MeV (dotted line on the left side panel) and 60 MeV (dotted line on the right side panel).
4. Prospectives
Apart from the mass distribution of FF, the associated neutron multiplicities are also important. This is inherently part of the analysis and matches well with the possibilities of the DEMON detectors in the Louvain-la-Neuve setup. Table 1 shows the scarceness of this kind of data in the actinide region. As it was announced in the beginning of this program, we would like to extend these measurements to new actinide nuclei such as 237Np,232Th and 241Amusing the same experimental setup and the same proton beam energies (26.5 and 62.9 MeV). Again the target thickness will range between 120 and 150 pg/cm2 with a 50 pg/cm2 carbon backing on each of their sides. In such a case our complete results will constitute an important data base for any future transmutation project for long-lived radioactive wastes.
253
Table 1. Presently available data on proton-induced reactions on actinide targets between 10 and 80 MeV.E, stands for the proton energy; #tot for the total number of experiments; u(p,f), Mff,(p,xn), v for the number of fission cross section, mass distribution, xn reaction, neutron multiplicity results respectively. Targets
Ref.
HINDAS Ohtsuki
1 1 Rubchenya
E,
10-80 233-238u 10-80 Z37Np 12-80 239Pu 20-80 238u 65 232Th 9-22 8-25 237Np 10-32 239Pu 10-18 2 4 1 - - 2 4 3 ~ ~ 9-16 2381 20-60
#tot 11 12 2 1 1 1 1 1 1 1 1
u(p,f) 8 11 2
Mff 5 3
2 1 1 1 1 1 1
1 1 1 1 1 1
Dates 1980-1996 1980-1991 1980-1991 1991 in progress 1991 1991 1991 1991 1991 2001
References 1. L. StuttgB, Seminar on Fission Pont d'Oye IV World Scientific 215, 215 (1999). 2. M.C. Duijvestijn et al., Phys. Rev. C64,014607 (2001). 3. P. Froment et al., Nuclear Instrument and Method A493 165 (2002)and references therein. 4. A. Billebaud et al., The MUSE4 experiment: prompt reactivity and neutron spectrum measurements, PHYSOR 2002, Seoul, Korea, October 7-10,2002 5. Short report derived from the TRADE FINAL FEASIBILITY REPORT http://t~ga.ga.com/triga_italy/Lavori%2OCongresso/session~/ (March 2002). 6. V.P.Eismont et al., An Experimental Database on Proton-Induced Fission Cross Sections of Tantalum, Tungsten, Lead, Bismuth, Thorium and U r a nium, Proc. of 2nd C o d . On ADTT, Kalmar, Sweden, June 3-7, 1996, ed. H. Cond0, p.592. 7. V.P. Eismont et al., Fission Cross Sections of Heavy Nuclei at Intermediate Energies for Hybrid Nuclear Technologies. Proc. of Int. Conf. on Future Nuclear Systems - GLOBAL 97, October 5-10 1997, Yokohama, Japan, p. 1365-1370. 8. M.C. Duijvestijn et al., Phys. Rev. C59,776 (1999). 9. T. Ohtsuki et al., Phys. Rev. C44,1405 (1991). 10. V.P. Eismont, Measurements of neutron induced fission cross sections in energy region 15 <En 5160 MeV for basic and applied researches; Final Project Technical Report of ISTC 540-97. 11. V.P. Eismont et al., Neutron-induced fission cross section of natPb and lg7Au in the 35-180 MeV energy region - Proc. 3rd International Conference on Accelerator Driven Transmutation Technologies and Applications, Praha (Pruhonice), Czech Republic, June 7-11, 1999. 12. V.P. Eismont et al., Neutron-induced fission cross sections of lalTa, natW,
254
lg7Au,natHg, 'O'Pb, natPb and 209Binuclei in the energy range 35-175 MeV. TSL Progess Report 1998-1999, Ed. A. Ingemarsson, Uppsala University 38 (2000). 13. 14. 15. 16.
I. Ryzhov et
al., Private communication, 2003 A.V.Prokofiev, Nuclear Instrument and Method A463, 557-575 (2001). Yu. A. Korovin et al., Nuclear Instrument and Method A463, 544-556 (2001). OECD NEA Data Bank, High-Priority Nuclear Data Request List for Intermediate Energies. http://unuw. nea.j?/html/trw/nucdat/iend/docs/highpri. html. 17. J. Cugnon et al., Nucl. Phys. A620, 475 (1997) , Dresner code, F. Aitchison, Jul. Conf-34,1980. 18. V.A. Rubchenya et al., Nucl. Instr. And Method A463, 653 (2001).
HIGH RESOLUTION MEASUREMENTS OF THE 234U(n,f) CROSS SECTION
J. HEYSE EC-JRC-IRMM, Retieseweg, B-2440 Geel, Belgium E-mail: jan. heyseocec. eu.ant C. WAGEMANS, K. W. CHOU AND L. DE SMET University of Gent, Proeftuinstraat 86, B-9000 Gent, Belgium
J. WAGEMANS
SCK*CEN, Boeretang 200, B-2400 Mol, Belgium 0. SEROT CEA-Cadarache, DEN/DER/SPRC/LEPh, Bat. 230, F-13108 Saint Paul lez Durance, France
Accurate 234U(n,f) cross section data are needed for various applications like the study of the Th-cycle and the incineration of actinides. Data in the resonance region are scarce and huge discrepancies exist between the values for the thermal cross section reported in the commonly used data files. The 234U(n,f) reaction has been studied with thermal neutrons at the ILL in Grenoble (France) and is presently under investigation at the linear accelerator of the IRMM (Belgium) for neutron energies between 10 meV and 1 MeV. This paper reports on the results of a measurement campaign on a 30 m flight path, focusing on the resonance region between 100 and 1000 eV.
1. Introduction 234U is a very important nucleus in the U-Th fuel cycle, since it can initiate unwanted 232U production through (n,3n) reactions. Moreover, it will contribute significantly to the long-lived radioactive waste from used fuel elements. As mentioned in a recent evaluation by Maslov et al.' , an accurate fission data description remains almost the only constraint for a complete evaluation of 234Udata. Due t o a lack of accurate experimental data, the commonly used data files for 234U show huge discrepancies. In order to
255
256
improve this situation, an experimental campaign was set up to study the neutron induced fission cross section, both for thermal and resonance neutrons. For both measurements highly enriched material and high quality neutron beams were used. The measurements with thermal neutrons were performed at the reactor of the ILL in Grenoble (France) resulting in a thermal cross section value of (67 f 14) mb as reported before2. This value has been adopted in the recent evaluation by Maslov et al.' . A measurement campaign with resonance neutrons has been started at the GELINA neutron facility of the Institute for Reference Materials and Measurements (IRMM) in Gee1 (Belgium), since also in the resonance region experimental 234Ucross section data are scarce. James and Rae3 performed measurements with a fairly poor neutron energy resolution at the Harwell linear accelerator (United Kingdom). These data were improved in a series of experiments at the Oak Ridge linear accelerator by James et aL4. More recently, low-energy measurements with a very poor energy resolution at the pulsed reactor in Dubna (Russia) were reported by Borzakov et aL5. The campaign at GELINA aims at measuring the neutron induced fission cross section for neutron energies between 10 meV and 1 MeV. 2. Experimental conditions
2.1. Umnium target
For the measurements a highly enriched uranium sample with a layer thickness of (137 f 1) pg/cm2 and an active diameter of 5 cm was used. The isotopic composition of the sample is given in Table 1. Table 1.
Isotopic composition of the uranium sample.
Isotope
23.3~
Abundance (at.%)
0.001
2 3 4 ~
99.868
235u
2 3 6 ~ 2 3 8 ~
0.076
0.048
0.007
2 . 2 . Energy resolution
At the GELINA facility electrons are accelerated in a 150 MeV pulsed linear accelerator. These electrons generate Bremstrahlung in a mercury cooled rotating uranium target, where neutrons are mainly produced through (7,n) and (y,f) reactions. The moderation of the neutrons in waterfilled Becontainers results in a broad neutron spectrum with energies ranging from
257
a few meV up to a few MeV. The energy of the neutrons is determined through the time-of-flight (TOF) method. By measuring the time t between the production of the neutron and the detection of the studied reaction, the neutron energy En is easily obtained through the classical relation
L being the length of the neutron flight path and m, the neutron mass. Differentiation of this equation leads to an expression for the energy resolution:
Several phenomena affect the uncertainty on the time-of-flight (&t)and on the flight path length (6L). The time dependent component is mainly determined by the finite duration of the electron burst, the time jitter related t o the detector response and the finite time bin width of the electronics and data acquisition system. The uncertainty on the flight path length results from the effective path the neutron follows from its production site until it reaches the detector or the sample. As can be clearly seen from Eq. 2, the GELINA time-of-flight facility owes its extremely good energy resolution to the combination of a very short pulse duration of less than 1 ns and its very long flight paths of up to 400 m. 2.3. Detector setup
Fission fragments were detected using a Frisch gridded ionisation chamber filled with very pure CHI gas and operating a t a pressure slightly higher than 1 atm. A double ionisation chamber was used (see Fig. l), allowing the simultaneous determination of the neutron flux during the experiment. The 234Usample was covered with a thin polyimide foil, which allows fission fragments t o pass but which stops the recoil nuclei from a-decay, preventing a contamination of the chamber. Performing experiments a t a longer flight path results in a better energy resolution but has the disadvantage that the neutron flux decreases with increasing flight path length following L-’. Furthermore the neutron flux depends on the accelerator repetition frequency, which is variable between
258
c--7 neutron beam
Anode
Cathode
Anode
Figure 1. Schematic overview of the double ionisation chamber.
1 and 800 Hz. As can be easily seen from Eq. 1,the repetition frequency and the flight path length determine the neutron energy interval which can be studied. Taking into account these considerations and the limited number of atoms in the sample, the detector was positioned at the end of a 30 m flight path for the present experiment. The accelerator was operated at a repetition frequency of 800 Hz. 3. Measurements and analysis
3.1. Cmss section determination The standard procedure to determine the fission cross section is to measure both the neutron induced fission and the neutron flux. The latter is done with a loB target, making use of the well known cross section u~ for the 'oB(n,a)7Li reaction. The cross section uu as a function of the neutron energy En is given by
with
Nu NB
the total number of 234Uatoms in the beam,
Cu
the background corrected count rate for 234U(n,f),
CB
the background corrected count rate for "B(n,a),
(TB
cross section taken from ENDF/B-VI. the "B(n,~x)~Li
the total number of loB atoms in the beam,
259
3.2. Background reduction
A test measurement showed a non-negligible background contribution to the pulse-height spectrum on the loB side of the chamber. This was caused by &decaying daughter nuclei of 234U,producing electrons with energies comparable to those of the a-particles from the "B(n,a)'Li reaction. Therefore the loB target was removed and replaced by a 235Utarget. A separate flux measurement was performed with the loB and 235Utarget, with the 235U acting as a reference link between the flux measurement and the 234Umeasurement. 100
80
20 0 0
1000
2000
3000
CHANNEL Figure 2. Typical pulse-height spectrum for 234U(n,f). The dashed line indicates the window which is set during the analysis. The dotted spectrum shows the contribution of a-pile-up to the spectum.
The anode signals of both sides of the chamber were sent in parallel to a Timing Single Channel Analyser (TSCA) and an Analog to Digital Convertor (ADC). The TSCA provided a gate sent t o the ADC as well as a fast timing signal sent to a time coder for the determination of the timeof-flight. Special attention was given to the lower limit of the TSCA, since for 234Usimultaneous detection of multiple a-particles from a-decay causes considerable pileup peaks on the low energy side of the pulse-height spectrum. During the analysis a window was set on the two fission fragment
260
peaks in the pulse-height spectrum, eliminating any remaining contribution by a-pile-up events to the time-of-flight spectrum. Fig. 2 shows a typical pulse-height spectrum for the 234U(n,f)measurement together with the result of a separate measurement of the a-pile-up contribution. With a similar procedure a-particles are selected for the 1°B(n,cr) neutron flux measurement. Remaining background contributions to the spectra are determined by performing a background measurement with so-called “black” resonance filters. 4. Results and outlook
Figure 3 shows the 234U(n,f)cross section in the neutron energy region between 100 and 1000 eV, nicely illustrating the intermediate structure in the fission cross section due t o the double humped fission barrier. I
I
I
1
I
1000
100
qeVI Figure 3.
The first cluster of intermediate resonances in the 234U(n,f)cross section.
In Fig. 4 a detail of the first cluster of intermediate resonances is shown, comparing the present measurement with previous results by James et aL4. A clear improvement of the resolution can be seen. In the near future the measurement campaign will be continued on a shorter flight path with the GELINA accelerator running at a 40 Hz repetition frequency. Under these conditions, sufficient statistics can be gathered
26 1
E" [evl Figure 4. Detail of the first cluster of intermediate resonances in the 234U(n,f) cross section. The dotted line corresponds to the results of James et aL4.
to allow an accurate determination of the 234Uneutron induced fission cross section in the neutron energy region from 10 meV up to 100 eV. This will also permit a cross-check of the normalisation with the thermal fission cross section. References 1. V. M. Maslov, Yu. V. Porodzinskij, N. A. Tetereva, A. B. Kagalenko, N. V. Kornilov, M. Baba and A. Hasegawa, Neutron Data Evaluation of 234U, INDC(BLR)-017, 7 (2003). 2. C. Wagemans, J. Wagemans and 0. Serot, Nucl. Sci. Eng. 141,171 (2002). 3. G. James and E. Rae, Nucl. Phys. A118,313 (1968). 4. G. D. James, J. W. T. Dabbs, J. A. Harvey, N. W. Hill, Phys. Rev. C15,2083 (1977). 5. S. B. Borzakov, M. Florek, V. Yu. Konovalov, I. Ruskov, Yu. S. Zamyatin, ShS. Zeinalov, AIP Conference Proceedings 447,Woodbury, New York, 269 (1998).
THE 233PaFISSION CROSS SECTION MEASUREMENT AND EVALUATION A. OBERSTEDT, F. TOVESSON
Department of Natural Sciences, Orebro University, SE- 70182 Orebro, Sweden F.-J. HAMBSCH, S. OBERSTEDT, V. FFUTSCH EC-JRC Institute for Reference Materials and Measurements, B-2440 Geel, Belgium B. FOGELBERG, E. RAMSTROM Department of Radiation Science, Uppsala Universiw, SE-61182 Nykoping, Sweden G. VLADUCA, A. TUDORA Faculty ojphysics, Bucharest University, RO- 76900 Bucharest, Romania
The cross section for the neutron-induced fission of 233Pahas been measured from the threshold at about En= 1.0 MeV to E, = 8.5 MeV, which is just above the threshold for second chance fission. The experimental results are then evaluated in terms of extended statistical model calculations. The obtained data are important for the design of future reactor concepts involving advanced fuel cycles.
1.
Introduction
All over the world major research efforts are currently being carried out in order to develop a new concept of nuclear power generation, so-called accelerator driven systems (ADS) for energy production and transmutation of radioactive nuclear waste. One suggested approach is the energy amplifier [1,2], which is a sub-critical reactor, based on the thorium-uranium fuel cycle and a spallation neutron source, supposed to provide clean and almost inexhaustible nuclear energy. Apart from necessary new technical developments, the realization of these concepts depends strongly on the availability of accurate nuclear reaction data. In particular, precise knowledge about cross sections for fission, neutron capture and scattering is required for the nuclides involved in the Th-U fuel cycle (see Fig. 1). As first priority isotopes 232Th,2313233Pa and 232, 2332 234, 236U were named by the IAEA [3]. Of specific interest for ADS is 233Pa,since it plays an important role as an intermediate nucleus in the formation of the fissile 233U from the fertile 232Th.With its half-life of 27.0 days for P-decay, 233Pais not a "long-lived" nucleus, but it still requires careful attention in the design and operation of thorium-fueled reactors. The build-up and the decay of 233Paaffect 262
263
Th2a0 7.5-10‘ y
Pa230
n,,
17 d
Figure 1 Transformation scheme for the most important isotopes involved in the thorium-uranium fuel cycle
both the breeding of the main fuel 233Uand the reactivity behavior. Each neutron capture in 233Panot only causes a neutron to be lost, but it also causes a 233U nucleus to be lost as well. The reactions involving 233Paare thus responsible for the balance of nuclei as well as the average number of prompt fission neutrons in a contemplated reactor scenario [4]. Moreover, when a thorium-fueled reactor is stopped, the present amount of 233Pawill continue to decay into 233U,leading to an increase in reactivity, which may even cause criticality. This mechanism is known as “protactinium effect” [ 11 and is proportional to the power level of the reactor [5]. The determination of the amount of protactinium in the fuel is thus strongly related to the knowledge of cross sections for reactions competing with the P-decay of 233Pa.For fast neutrons used in ADS neutron induced fission is totally dominating over neutron capture, which is why especially the fast fission cross section of 233Pais required to be known with reasonable precision, i.e. an accuracy of at least 20% [3]. However, not at least due to the fact that the rather short half-life of 233Pamakes experiments very difficult, the knowledge about this nucleus is quite poor. The only known experimental data for the fast neutron induced fission cross section was published in 1967 [6], but the value of 775+190 mb obtained back then is quite uncertain due to a complicated and not very well known incident neutron spectrum coming from a reactor. Neither the existing evaluated data files for 233Pa(ENDFm-VI [7] and JENDL-3.3 [S]),
264
which represent the results of two different model calculations, provide the demanded accuracy, since they exhibit different threshold energies as well as differing cross section magnitudes by approximately a factor of 2. In this paper we present the latest results from the first direct measurements of the 233Pa(n,f)cross section with monoenergetic neutrons between En = 1.0 and 8.5 MeV. The experimental results are then discussed in terms of evaluations in the framework of an extended statistical model and compared to a recent indirect derivation from the reaction 232Th(3He,pf)234Pa [9].
2.
Experiment
The experiments were performed at the Institute for Reference Materials and Measurements in Geel, Belgium, by irradiating a 233Pa sample with quasimonoenergetic neutrons. The sample material was produced by exposing thorium nitrate, Th(N03)4,to a thermal neutron flux in the R2 reactor facility at the Studsvik Neutron Research Laboratory in Nykoping, Sweden. The 233Pawas then separated in a sequence of chemical procedures, eventually leading to very high purity corresponding to a ratio of compared to other metallic elements such as 232Thand 233U.A detailed description of the chemistry, finally leading to an organic 233Pasolution, can be found in Ref. [lo]. In total, three samples were produced for the same number of experimental campaigns. Two different methods were applied to deposit the protactinium on a polished tantalum backing. For the first sample the solution was dropped onto the Ta foil and evaporated to dryness, while for the following two samples the previously developed technique of electrodeposition [ 111 was used. The amount of 233Pain the samples was determined twice: by y-spectroscopy directly after sample preparation and by a-spectroscopy of the decay product 233U several months later, when most of the 233Pahad decayed. The masses that were found are 0.564k0.025 pg, 0.425k0.026 pg and 1.09k0.05 pg, respectively. Due to the short half-life of 27.0 days and the corresponding high pactivity, a significant background of p’s and y’s is present, which requires a fast and efficient experimental set-up for the counting of fission events. This is provided by a twin Frisch-gridded ionization chamber, whose construction and operation is described in Ref. [12]. Since the chamber can be operated in backto-back geometry, the protactinium sample was mounted on one side together with a known 237Npsample as reference on the other side. Because both sides of the chamber are identical with respect to geometry and efficiency, the 233Pa(n,f) cross section can in principal easily be determined by counting fission events on both sides and using the well-known fission cross section of 237Np.How the fission fragments were separated from the background and details about the
265
experimental set-up including associated electronics is described in Ref. [ 131. However, since 233Pais continuously decaying into 233U,whose fission cross section is about five times higher, a considerable amount of the fission events on the protactinium side actually originates from 233U.This effect increases with time, which limits the use of a sample longer than two months due to the requirements for a maximum statistical uncertainty. This effect can be corrected for, if the fission cross section for 233Uis known. Therefore, every measurement with a 233Pasample is followed up with one with a known 233Usample under exactly the same conditions. The measurements were carried out by irradiating the samples with neutrons produced in the reactions T(p,t~)~He and D(d,r~)~He in the energy range En = 1.0 - 3.8 MeV and En = 5.0 - 8.5 MeV, respectively. The proton and deuteron ions were accelerated with a 7 MV Van de Graaff accelerator. Three different neutron production targets were used: a solid tritium target (TiT), a solid deuterium target (TiD) and a D2-gas target. For both reactions, the widths of the resulting neutron energy distributions are less than a few percent (FWHM), with a negligible low-energy contribution, which only for neutron energies above 7 MeV amounts in the order of 2-3% [14]. The results are presented and discussed in the following chapter.
3.
Results and discussion
As mentioned above, the determination of the 233Pa(n,f) cross section was performed relative to the known fission cross section for 237Np,and carried out in iwo stages for each neutron energy: measurements with a protactinium and subsequently with a 233Utarget. Since the present number of 233Uatoms in a given 233Pasample is known at all times by the radioactive decay law for 233Pa, the precise knowledge of the fission cross section provides the number of fission events originating from 233U,which then can be subtracted. However, precise experimental data in the desired energy region were not available and theoretical data from different evaluated libraries do not agree with one another with an uncertainty better than 10%. This, of course, would affect the accuracy with which the 233Pa(n,f)cross section can be determined. Therefore, the decision was made to measure the 233U(n,f)cross section, too. The results are shown in Fig.2 as full circles and compared to the latest evaluations from ENDFB-VI, JENDL-3.3 and JEFF-3.0. It is obvious that the experimental data deviate considerably from the evaluations for neutron energies below 2 MeV and above 6 MeV.
266
e
h
D-
' ~ ,, ,
,
,
,
,
'
,
~1~
W ( n 0 correclion
- ENDFr%VI
- - -- - JENDL-33
095
..,
.JEFF.30
0 0
2
4
6
8
10
E (MeV) Figure 2 Measured 233U(n,f)cross section as a function of neutron energy, compared to the latest evaluations The full circles represent experimental data obtained with shielding and a solid production target, the open circles correspond to data taken without shielding (6< 4 MeV) or a gas target (En> 4 MeV), respectively
The discrepancies below 2 MeV could be attributed to the presence of a low-energy component in the incident neutron spectrum. Simulating the experimental set-up for the 233Pa measurements including the extensive shielding with the Monte Carlo code MCNP [ 151, this effect could be quantified [lo]. Due to unusually high neutron fluxes used in order to achieve reasonably high fission rates for the low-mass 233Pasamples, it was necessary to shield the ionization chamber with layers of boron carbide and paraffin, otherwise the laboratory's annual dose limit would have been exceeded soon. However, this gave rise to the observed low energy neutrons and thus the virtually increased fission cross section for 233U.In order to prove that experimentally, the shielding was removed and the measurements were repeated. The results are also depicted in Fig. 2 as open circles in the mentioned energy region. As shown in Ref. [lo] this effect decreases with increasing neutron energy and does not influence the determination of the 233Pa(n,f)cross section. The deviations above 6 MeV could be explained by contributions of parasitic neutrons produced in the reaction '60(d,n)'7F*,where mainly the first excited state in "F is populated due to spin and parity conservation laws. The oxygen is present as titanium oxide in the solid deuterium target that was used for the neutron production in some of the experiments. The difference of the Qvalues for both intended and parasitic reaction (AQ = 5.389 MeV) explains why this effect does not occur for neutron energies beiow 6 MeV (see Fig. 3). Since
267
2
3
4
5
6
7
8
9
10
E" (MeV) Figure 3. Neutron energy spectra obtained with the time-of-flight technique using a TiD neutron production target. Apart from the given intended neutron energies, the peaks from the parasitic reactions are visible.
the cross sections for both reactions are well known [8,16], this effect could be accounted for. Moreover, using a deuterium gas target instead, the measured cross section is in excellent agreement with the evaluations (cf. open circles above 3 MeV in Fig. 2). A detailed description will be given in Ref. [17]. The fission cross section of 233Pafor a given neutron energy E may be determined from the measured number of fission events C for the involved nuclides, and by knowing the cross sections for 233U(n,f),237Np(n,f),D(d,r~)~He and '60(d,n)17Fas well as the number N of atoms in the sample, accordi g to
The ratio of the fluxes for intended and parasitic neutrons in Eq. (l), $(E) and $(E-AQ), respectively, is determined by the known production cross sections and by adjustment to the difference of the 233U(n,f)cross section with and without shielding. As mentioned above, parasitic neutrons did only occur for measurements with the TiD production target, thus in all other cases the parasitic flux is $(E-AQ) = 0. The results are presented in Fig. 4, together with other recently obtained data derived indirectly from the reaction 232Th(3He,pf)234Pa[9]. The experimental values are compared to results of previous evaluations (ENDFB-
268
E (MeV) Figure 4 Compilation of 233Pa(n,f)cross section data as function of incident neutron energy
VI [7] and JENDL-3.3 [S]) and a new one, based on calculations in the framework of the extended statistical model code STATIS. The latter was already used successfully for evaluations of 23sU and 237Np neutron cross sections [18,19] and now applied to the system n+233Pa (cf. Ref. [20] for details). From Fig. 4 it is obvious that the values for the 233Pa(n,f)cross section obtained in this work are lower than the predicted ones from the previous evaluations, while the results from the STATIS calculations are in very good agreement. Even the location of the thresholds for fission and second chance fission are well reproduced by the recent calculations. The data derived from the substitution reaction [9] are in good agreement concerning the thresholds, but in general they are slightly higher in magnitude. The reason for that may be found in the model dependence in the fission cross section determination. From the reaction 232Th(3He,pf)234Pa the fission probability for 234Pawas obtained, which then was multiplied by the cross section for compound nucleus formation in order to deduce the neutron-induced fission cross section. The compound nucleus creation cross section however had to be calculated in the framework of models, which always implies uncertainties and, thus, a drawback of this method. A direct measurement, in contrast, allows the determination of model parameters, which in turn improves the models.
4.
Summary and conclusions
In this paper we have presented the first directly measured cross sections for neutron-induced fission of 233Pa.The experiments were performed with quasimonoenergetic neutrons in the energy range En = 1.0 - 8.5 MeV, which covers the thresholds for fission and second chance fission. The results are described
269
well by the calculations with the statistical model code STATIS and provide valuable input data for the modeling of ADS. The accuracy, with which the cross section was determined, meets the requirements posed by the IAEA. We conclude that the experimental technique presented here is superior for cross section measurements since there is no model dependence.
References 1. C. Rubbia et al., CERN report No. CERN/AT/95-44(ET) (1995). 2. F. Carminati et al., CERN report No. CERN/AT/93-7 (ET) (1993). 3. V. G. Pronyaev, IAEA report No. INDC(NDS)-408 (1999). 4. B. D. Kuzminov and V. N. Manokhin, Nuclear Constants, Issue No. 3-4, 41 (1997). 5. S. Ganesan and H. Wienke, in “Proceedings of the Tenth International Conference on Emerging Nuclear Energy Systems ICENES 2OOO”, Petten, The Netherlands, ISBN 90-805906-2-2,(2000). 6. H.-R. von Gunten et al., Nucl. Sci.Eng. 27, 85 (1967). 7. Cross Section Evaluation Working Group, ”ENDFB-VI Summary Documentation”, ed. by P. F. Rose, National Nuclear Data Center, Brookhaven National Laboratory Report No. BNL-NCS-17541 (ENDF201) (1991). 8. T. Nakagawa et al., J. Nucl. Sci. Technol. 32, 1259 (1995). 9. G. Barreau et al., Seminar on Fission, Pont d’Oye V (2003), these proceedings. 10. F. Tovesson et al., Phys. Rev. Lett. 88,062502-1 (2002). 11. M. FlenCus and C. Gustafsson, Thesis Orebro University, OU-Na-ExFysOlD (2001). 12. C. Budtz-Jerrgensen et al., Nucl. Instr. and Meth. A 258,209 (1987). 13. F. Tovesson et al., J. Nucl. Sci.Technol. Supplement 2,210 (August 2002). 14. L. Cranberg, A. H. Armstrong, and R. L. Henkel, Phys. Rev. 104, 1639 (1956). 15. “MCNPTM- A General Monte Carlo N-Particle Transport Code”, edited by J. F. Briesmeister, Los Alamos National Laboratory Report No. LA-13709M, 2000. 16. W. Gruhle, W. Schmidt, and W. Burgmer, Nucl. Phys. A 186, 257 (1972). Data retrieved from the CSISRS database, file EXFOR 10236.002-2 dated mars 9, 1992. 17. F. Tovesson et al., to be published in Nucl. Phys. A. 18. G. Vladuca et al., Nucl. Phys. A 707, 32 (2002). 19. G. Vladuca et al., Nucl. Phys. A 720,274 (2002). 20. G. Vladuca et al., to be published in Phys. Rev. C.
DETERMINATION OF THE 233Pa(n,f)REACTION CROSS SECTION FROM 0.5 TO 10 MEV USING THE TRANSFER REACTION 232Th(3He,p)234Pa
M.PETIT, M.AICHE, G.BARREAU, S.BOYER, S.CZAJKOWSK1, D.DASS1, C.GROSJEAN, A.GUIRAL, B.HAAS, D.KARAMANIS, C.RIZEA, F.SAINTAMON CEN Gradignan, F33175 Gradagnan Cedex E.BOUCHEZ, F.GUNSING, A.HURSTEL,C. THEISEN CEN Saclay, O n e des Merisiers F91191 Gif-sur- Yvette Cedex A. BILLEBAUD, L.PERROT LPSC 53 Avenue des Martyrs F38036 Grenoble Cedex S.FORTIER IPN Orsay 15, rue G.Clmenceau F91466 Orsay Cedex The 233Pa(n,f) cross section has been obtained using the 232Th(3He,p)234Pato measure the fission probability of 234Paand then multiplying this fission probability by calculated compound nucleus neutron reaction cross section. The validity of the method has been tested with existing neutron induced fission of 230Th and 231Pa as well as recent direct neutron measurements of the reaction 233Pa(n,f).
1. Introduction The Thorium cycle is the object of a renewal of interest. One think that reactors using this fuel could provide safer and cleaner nuclear energy as highly radiotoxic actinide waste ( Pu, Am and Cm isotopes) will be produced in lower quantities than the currently used Uranium fueled reactors. The primary reaction of importance using the Thorium cycle is the one producing the fissile nucleus 233U from neutron capture on 232Th. The net production of 233U is controlled by the 27 days half-life of 233Pa:a fertile nucleus (232Th) is transformed into a fissile nucleus (233U) after neutron capture and 2 successive beta decays. Thus the 233U inventory will depend
270
27 1
strongly on the neutronic properties of 233Pa: every neutron captured by 233Pa will affect neutron economy( a neutron is lost) and will cause a 233U to be lost as well. There is no such effect in the well sudied 238U-23gPufuel cycle as the equivalent intermediate isotope 239Nphas a relatively shorter half-life (2.35 days). When we started these studies, only an average fast fission cross section has been determined (in 1967!)by H.R. Gunten' using reactor neutrons: the published value(775f190 mb) was rather uncertain owing to the not well known neutron energy spectrum. On the other hand, the recommended values for the capture and fission cross sections extracted from several data banks are based on theoretical estimates and they still exhibit large discrepencies: The evaluated 233Pa(n,f) cross sections from ENDF/B-VI and JENDL-3 show a difference of a factor 2 as well as different fission threshold energies. The lack of reliable experimental data could be explained by the short half life of 233Pa, its high specific P-activity ( 7 . 7 ~lo8 Bq/pg) and build up of 233Uwhich have been a true challenge for the experimentalists. In order to overcome these problems, we have used the transfer reaction techniques to measure the fission probability of 234Paformed in the reaction 232Th(3He,p)234Pa.The neutron induced fission cross section of the corresponding target 233Pa has been deduced from the multiplication of this experimentally determined fission probability with an optical model calculation of the compound nucleus 234Paas a result of the capture of a neutron by the target 233Pa. This method has been first used by J.D. Cramer and H.C. Britt2 in order to estimate the (n,f) reaction cross sections of short lived systems at the back of beyond any direct neutron measurements.
2. Experimental procedures and data reduction 2.1. E x p e r i m e n t a l conditions The IPN Orsay tandem Van de Graaff was used to provide beam of 3He beams at an energy of 30 MeV. Targets were prepared by electromagnetic separation, they consisted of 100 pg/cm2 232Th deposited on 40pg/cm2 carbon backing. The target was placed in the middle of a spherical vaccum chamber at 45 degrees relative to the direction of the projectile. The outgoing light particles (p, d, t and 4He) were detected by two AE-E telescopes placed respectively at 90° and 130' with respect to the beam axis. The AE detectors were 300 and 150 pm fully depleted Si detectors. The E detectors were 5 mm thick lithium drift silicon detectors. The telescopes were protected from fission fragments with 30pm aluminium foils placed in front
272
of the AE detectors, they were placed respectively at 5 cm (90') and 7 cm (130') from the target. The fission fragment detector system was designed to achieve a large efficiency and a good granularity for fission fragment angular distribution measurements.The system consists of 15 photovoltaic cells (20x40 cm2) distributed among 5 units, each unit is made of 3 cells. all the units are placed normal to the reaction plane define by the two telescopes. The last unit , the furthest back, was placed at 180' with respect to the foremost unit, it adds one point more to backward angular distribution measurements. The relative total solid angle subtended by the fission fragment detector was measured with a calibrated 252Cfspontaneous fission source, it corresponds to 48.4% in good agreement with a simulation code using the geometric dimensions of the set up. The data divide into 2 groups, namely (a) the particle identification (AExE and their energy spectra [ Nsingle(E*)](b) the particle energy spectra in coincidences with the fission fragments [NCOinc (E*)]and the particlefission time spectra: a time window of 390 ns is used to measure the relative delay of the detected fission fragments against the light charged particle arrival. E* being the excitation energy of the associated fissioning system.It has been calculated using Q values extracted from the recent mass evaluation3. Four reaction channels have been clearly identified and analyzed. These are ( 3He,p), (3He,d), ( 3He,t) and (3He,4He). The singles spectra have been corrected for the contribution from the carbon backing by subtracting the spectra from a separate carbon irradiation run . The coincidence spectra have been corrected for random coincidence events using particle spectra generated in a time window far from the coincidence peak of the particle-fission time spectra. The fission probability is defined as follows:
e f f ( E * )represents the fission fragment detection efficiency which includes the geometrical efficiency as well as angular correlation of the fragments with respect to the recoil angle of the fissioning system . The fission probabilities of 232Pa,233Pa,234Paare displayed in figure 1. Error bars in these plots include statistical errors as well as uncertainties related to the background substraction. The neutron separation energies (labeled Sn) related to each channel are indicated on the plots. For all the nuclei investigated in this work, the fission probabilities have been measured beyond the second chance fission. A significant feature of these measurements is the low fission probability of 234Pa(15% ) as compared to the
273 0.7
5
6
7
8
9
10
11
,*
13
1I
15
Excitation Energy (MeV) nuclei Figure 1. The measured fission probabilities of the 232,233,234Pa
lightest 0ne('~~Pa)(30%).233Pais the heaviest Z=91 isotope the fission probability of which has been measured. The 2327233Pafission probabilities have been already measured by the same method using a 24 MeV 3He beam. First measurements have been reported by B.B. Back4 up to an excitation energy of 8 MeV. A few years later, these have been extended by A. Gavron' up to 11 MeV, just before the second chance fission opening. A good overall agreement of the present experiment with these earlier works has been observed.
3. Determination of the neutron induced fission cross section of 233Pa
3.1. P r e s e n t a t i o n of the method
As stated before, the fission cross-sections have been obtained from the measured fission probabilities multiplied by the total compound nuclear neutron cross-section at the corresponding incident neutron energy En.
274
where (Sn + Y E n ) represents the excitation energy of the compound nucleus A , Sn being the neutron separation energy. This approximate relation can be justified in the following way. It is generally assumed that fission of actinide nuclei excited in transfer reactions proceeds in two independent and complimentary steps: in the first step compound nuclear states are excited by the transfer process, in the second step, these compound states decay by fission, neutrons and y rays. At a given excitation energy E*, the theoretical expression for the fission probability averaged over many compound states can be written as:
cut(E*,J , T ) represents the average probability of populating compound states (JT) at excitation energy E* while p f ( E * ,J,a)denotes the fission probability of these states where I?,, I?-, and ,?I are their partial widths for fission, y and neutron emission respectively. In the same way, the fission cross section calculated at an incident neutron energy En takes the form: m ( E n ) = wc(En).ZJ,aan(En,J , T).Pf(E*,J , T ) Where an(En,J , a) represents the average probability of populating compound states (Ja) after capture of an incident neutron of energy En. In both reaction, the fission probability p f ( E * ,J , a) is independant of the nuclear formation process. As well as in transfer reaction we can define an summed fission probability at a neutron energy En :
P1'(E*)= E.J,,an(E*, J,a).pg(E*,J,a) The differences between the two quantities Pj(E*)and Pfn(E*)originate from the relative number of states (JT)which are populated by each reaction. Following J. D. Cramer and H. C. Britt2 we have assumed that
275
these differences become negligible when the nucleus acquires enough excitation energy so that many fission channels contribute to observed fission. This should hold if the excitation energy is greater than the pairing energy at the top of the fission barrier. This critical energy has been estimated t o correspond to 1.5 to 2 MeV neutron energy. It should be emphasized that this asumption could be justified with the ratio rn/I'f which is closely related to the fission probabilities. A large body of experimental values for this ratio has been obtained by A.Gavron5 from the fission probability of a series of Pa, U,Np, Pu, Am and Cm using the (3He,df) and (3He,tf) transfer reactions at excitation energies which correspond roughly to 2 MeV and 5 MeV neutron energy respectively. These data are in good agreement with the general systematic trends observed by R. Vandenbosch and J. Huizenga' which are based on (n,f), (y,f) and (cY,xnf) spallation measurements: the ratios I'@f are weakly dependent on excitation energy but depend strongly on mass and atomic number of the fissioning system. One has t o conclude that fission probabilities depend very slightly on excitation energy and reaction mechanism involving neutrons, gammas and light charged particles. Nevertheless, the reliability of the calculated compound formation cross section could be also of potential concern. J. D. Cramer and H. C. Brit@ have shown that the resulting computed fission cross sections are strongly dependent of the optical model parameters used in the calculations . At a neutron energy of 1 MeV differences up t o 20 % have been observed with different set of parameters, thus these differences reflect the limit of accuracy with which the compound nucleus formation could be calculated using the old phenomenological optical models7. Within the last 30 years, much effort has been paid t o the development of nucleon-nucleus optical potentials on microscopic grounds . The fully microscopic approach or the semimicroscopic ones have successfully explained the scattering of nucleons ( neutrons and protons) on spherical or deformed target nuclei .
3.2. Validation of the method and Fission cross section
determination
Our compound nucleus formation cross section has been calculated with a microscopic optical model code developped J. P. Delaroche and coworkers a t Bruyres le chatels. The underlying model is based on the coupled channel formalism extended to include dispersion relations corrected for non locality. The coupled calculations include the first six states of the rotational ground state band of 233Pa. In order to validate our approach, we
276
have first considered the two reactions 230Th(n,f)and 231Pa(n,f),the crosssections of which have been directly measured by neutron capture. The corresponding compound system (231Th and 232Pa)have been observed in this ( ~He 231 T h and 232 T h ( He,t)232Pa work through the c h a n n e l ~ : ~ ~ T ,4He) h respectively. Our determination for these cross-sections are displayed on the figures 2 and 3.
0.7
0.6
0.5
0.2
0.1
0
Neutron energy (MeV)
Figure 2. The determined neutron fission cross section of 231Th(n,f) compared to direct neutron measurements lo and to the ENDF/B-VI and JENDL-3 evaluations
In both cases, the comparison is done with the ENDF-B/VI and JEFF3 librariesg as well as the latest measurements performed by J. Meadows1' (230Th(n,f)) and S. Plattard" (231Pa(n,f)). In the neutron energy range from 0.5 to 7 MeV our determination of the 230Th(n,f) cross-section is in good agreement with the direct measurements of Meadows and the ENDFB/VI evaluation, the overall fission cross-section is well reproduced as well as the onset of second chance fission threshold as observed by J. Meadows. One can note that the JENDL-3 recommended fission cross section is on the average 30% lower than the one proposed by the ENDF-B/VI library. Concerning the 231Pa(n,f), a similar but inverse trend is observed while
277 2.5
1
.
.
i.
.......... ~.++cm~; .
2.25
.
/
;
. ............. .......... .
...
j
,..
...
231'
...
:
.
i... . .... ..: ........... Pa(.n.,f).. . . .
.
.
5
7
8
2
1.75
E -
1.5
01.25 c 0
1
0.75
0.5
0.25
0
0
1
2
3
4
5
9
Neutron energy (MeV)
Figure 3. The determined neutron fission cross section of 231Pa(n,f)compared to direct neutron measurementsll and t o the ENDF/B-VI and JENDL-3 evaluations
comparing the ENDF-B/VI and JENDL-3 files. Our determination agrees fairly well with the latter as well as the measurements of S. Plattard below 2 MeV. At higher energy up t o the second chance fission threshold, our values are on the average 10% t o 15% lower than the ones reported by S. Plattard. One should emphasize that in both cases, the onset of first chance fission is correctly reproduced when compared t o the most experimental findings. As long as the average fission cross section is considered, it appears that, down t o 0.5 MeV neutron energy, our determined values do not reveal large differences between the neutron and charged particle mean momenta transfer. Our determination of the 233Pa(n,f) cross section is shown on figure 4, it is compared t o the recent direct measurements of F. Tovesson12. They consist of four points distributed between 1 and 3 MeV, one can see that these data are in good agreement with us except at 2MeV where the directly measured cross section is 50 % lower than our determination. One can note that the onset of first chance fission is well reproduced using either transfer induced fission or neutron induced fission. According t o our results, the classical fission threshold occurs around 1.5 MeV. The two
278
P
Figure 4. The determined neutron fission cross section of 233Pa(n,f)compared to recent direct neutron measurementd2 and to the ENDF/B-VI and JENDL-3 evaluations
independant measurements can now be compared to the fission cross section data contained in the ENDF-B/VI and JENDL-3 libraries. The two sets of recommended values have been determined using different methods. In the neutron energy range from 0.5 to 12 MeV, the ENDF-B/VI file has been constructed empirically from the 238U(n,f) cross section using different systematics on the well known 234U(n,f),236U(n,f) and 237Np(n,f) cross sections. The JENDL-3 has been generated from the 231Paneutron induced fission and statistical model calculations to determine the 233Pa(n,f) cross section.As is evident in fig x, the ENDF-B/VI are largely at variance with the experimental findings, except for the near first chance fission threshold which is correctly predicted. Therefore, the above threshold cross section up to 6 MeV neutron energy is fairly well reproduced by the JENDL-3 library. Nevertheless, significant differences can be noted on the onsets of the first and second chance fission which occur earlier( about 0.5 MeV below our measurements) in the JENDL-3 file as well as the second chance peak value which is found to be 25 % higher than the one determined in this work.
279
4. Conclusion In the present work, the fission probability of 234Pahas been measured using the transfer reaction 233Pa(3He,p)234Pa. From these measurements, we have determined the equivalent fast neutron induced fission cross section of 233Pa up to an equivalent neutron energy of 10 MeV. The equivalent 233Pa(n,f) has been obtained from the multiplication of the 234Pafission probability with the cross section for the formation of the compound nucleus 234Paafter absorption of a neutron by the target n u c l e u ~ ~ ~ The ~Pa. latter cross section has been computed with a microscopic optical mode calculations. The validity of the method has been tested with existing neutron induced fission of 230Th and 231Paas well as recent direct neutron measurements of the reaction 233Pa(n,f). Our results are in good agreement with these data up to 6 MeV (first chance fission). On the average , the overall 10 % discrepancy has to be compared with the estimated uncertainties on absolute fission probabilities ( 5 to 10 %) and calculated compound nucleus cross sections ( 5 to 10 %). The reliability of the data contain in the nuclear data libraries ENDF-B/VI and JENDL-3 has been checked.We have shown that large discrepancies exist in the evaluated 233Pa(n,f)cross section extracted from the ENDF-B/VI library.
Acknowledgments We have appreciated the effort and enthusiasm shown by the Orsay tandem staff for the success of the measurements. Thanks also to the Mass Separator crew of the CSNSM Orsay for the preparation of the targets used in this work. J .P. Delaroche, E . Baug and P.Romain are gratefully acknowledged to make available to us the results of their Optical Model Calculations. This work has been supported by the CNRS programme PACE (Programme Aval du Cycle Electronuclaire) and the Conseil Rgional d’llquitaine.
References 1. H. R. von Gunten, R. F. Buchanan, A. Wyttenbach and K. Behringer, Nucl. Sci. and Eng. Vol. 27 (1967) 85, 2. J. D. Cramer and H. C. Britt, Nucl. Sci. and Eng. 41 (1970) 177. 3. G. Audi and A.H. Wapstra, Nucl. Phys. A432 (1985) 1. 4. B. B. Back, H. C. Britt, 0. Hensen et B. Leroux, Phys. Rev. C10 (1974)
1948. 5. A. Gavron, H. C. Britt, J. Weber et B. Wilhelmy, Phys. Rev. C13 (1976) 2374.
280 6. R. Vandenbosch and J. R. Huizenga, Nuclear fission ACADEMIC PRESS New-York and London (1973) 216. 7. E. H. Auerbach and S. 0. Moore, Phys. Rev. 135 (1964) 895 8. E. Bauge, J. P. Delaroche and M. Girod, Phys. Rev. C63 (2001) 024607. 9. NNDC Online Data Service, telnet.nndc. bnl.gov 10. J. W. Meadows, ANL/NDM-83 (1983) 11. S. Plattard, G. F. Auchampaugh, N. W. Hill, G. de Saussure, J. A. Harvey and R. B. Perez, Phys. Rev. Lett. 46 (1981) 633. 12. F. Tovensson, F-J. Hambsch, A Oberstedt, B. Fogelberg, E. Ramstrom and S. Oberstedt, Phys. Rev. Lett. 46 (1981) 633. 13. F. B. Simpson and J. W. Codding Nucl. Sci. and Eng. [23 (1967) 133. 14. R. B. Firestone, Table of Isotope Vol I1 (1996) 2568 et 2595.
This page intentionally left blank
LIST OF PARTICIPANTS
ARMBRUSTER Peter GSI Postfach 110552 D-64220 Darmstadt Germany
CASOLI Pierre Commissariat a 1’Energie Atomique Dept. de Physique Theorique et AppliquC, SPN B.P. 12 F-91680 Bruyeres-le-Chfitel France pierre.casoli@,cea.fr
BARREAU GCrard CEN Bordeaux-Gradignan Le Haut Vigneau F-33 175 Gradignan Cedex France barreau@,cenba.in2~3.fr
DE FRENNE Denis Universiteit Gent Dept. of Subatomic and Radiation Physics Proeftuinstraat 86 B-9000 Gent Belgium denis.defrenne@,UGent.be
BERNAS Monique Institut de Physique NuclCaire d’Orsay B.P. 1 F-91406 Orsay Cedex France bernas@i~no.in2~3 .fr
DEMETRIOU Paraskevi UniversitC Libre de Bruxelles Institut d’Astronomie et d’Astrophysique CP 226, Bd du Triomphe B-1050 Bruxelles Belgium [email protected]
CARJAN Nicolae CEN Bordeaux-Gradignan Le Haut Vigneau F-33 175 Gradignan Cedex France carian@,in2~3 .fr
D’HONDT Pierre SCKoCEN Boeretang 200 B-2400 Mol Belgium pdhondt@,sckcen.be 283
284
elmasri@,,fvnu.ucl.ac.be
GOENNENWEIN Friedrich Universitat Tubingen Auf der Morgenstelle 14 D-72076 Tubingen Germany friedrich. aoennenwein@,unituebinaen.de
FAUST Herbert Institut Laue-Langevin BP 156 F-38042 Grenoble France [email protected]
GOUTTE Dominique GANIL B.P. 5027 F-14076 Caen Cedex 5 France goutte@aanil .fr
FIONI Gabriele Commissariat a 1’Energie Atomique Strategy and Evaluation Division 3 1 rue de la Federation F-75752 Paris Cedex 15 France [email protected]
GOUTTE HBloise Commissariat a 1’Energie Atomique Dept. de Physique Theorique et Applique Service de Physique Nucleaire B.P. 12 F-91680 Bruykres-le-Chitel France heloise.aoutte@,cea.fr
GIARDINA Giorgio University of Messina Dipartimento di Fisica Salita Sperone 3 1 1-98166 Messina Italy giardina@,nucleo.unime.it
HAMBSCH Franz-Jozef EC-JRC Institute for Reference Materials and Measurements Retieseweg B-2440 Gee1 Belgium hambsch@,irmm.irc.be
EL MASRI Youssef Universitk Catholique de Louvain Institut de Physique Nucleaire Chemin du Cyclotron 2 B- 1348 Louvain-La-Neuve Belgium
285
HANAPPE Francis Universite Libre de Bruxelles CP 229, av. F.D. Roosevelt 50 B- 1050 Bruxelles Belgium [email protected]
KALININ Valeri V.G. Khlopin Radium Institute 2nd-MurinskyAv. 28 R-194021 St. Petersburg Russia kalinin@,atom.nw.ru
HEYSE Jan EC-JRC Institute for Reference Materials and Measurements Retieseweg B-2440 Gee1 Belgium jan.hevse@,irmm.-irc.be
KOESTER Ulli CERN ISOLDE CH- 121 1 Geneva Switzerland ulli.koster@,cern.ch
HUYSE Marc Katholieke Universiteit Leuven Instituut voor Kern- en Stralingsfysica Celestijnenlaan 200D B-3001 Leuven Belgium Marc.Huyse@,,fys.kuleuven.ac.be -
MATERNA Thomas Universite Libre de Bruxelles CP 229, av. F.D. Roosevelt B-1050 Bruxelles Belgium tmaterna@,!ulb.ac.be
JACOBS Etienne Universiteit Gent Dept. of Subatomic and Radiation Physics Proeftuinstraat 86 B-9000 Gent Belgium etienne.iacobs@,UGent.be
MUTTERER Manfred Technische Hochschule Schlossgartenstrasse 9 D-64289 Darmstadt Germany mutterer@,ikr,.tu-darmstadt.de -
286
OBERSTEDT Andreas Orebro University Dept. of Natural Science SE-70 182 drebro Sweden andreas.oberstedt@,nat.oru.se
PRIEELS Rent5 UniversitC Catholique de Louvain Institut de Physique (FYNU) Chemin du Cyclotron 2 B-1348 Louvain-La-Neuve Belgium [email protected]
PANOV Igor Institute for Theoretical and Experimental Physics B. Cheremushkinskaya 25 117259 Moscow Russia iPor.uanov@,iteu.ru
SAMYN Mathieu UniversitC Libre de Bruxelles Institut d’Astronomie et d’Astrophysique CP 226, Bd du Triomphe B-1050 Bruxelles Belgium [email protected]
PFEIFFER Bernd Universitat Mainz Institut fur Kernchemie Fritz-Strassmann-Weg 2 D-55128 Mainz Germany
SCHILLING Klaus FZ Rossendorf Institute of Nuclear and Hadron Physics P.O. Box 510119 D-0 1314 Dresden Germany
Bernd.Pfeiffer@,uni-mainz.de
k.schillina@,fz-rossendorf.de
POKROVSKY Igor Joint Institute for Nuclear Research Flerov Laboratory of Nuclear Reaction Zholiot-Curie Str. 6 141980 Dubna Russia [email protected]
SEROT Olivier Commissariat a I’Energie Atomique DENDEWSPRCLEPh Biit. 230 F- 13108 Saint Paul Lez Durance France [email protected]
287
STUTTGE Louise IReS 23 rue du Loess, B.P. 28 F-67037 Strasbourg Cedex 2 France [email protected]
TSEKHANOVICH Igor Institut Laue-Langevin BP 156 F-38042 Grenoble France tsekhanoai 11. fr
THOMAS Jean-Charles Katholieke Universiteit Leuven Instituut voor Kern- en Stralingsfysica Celestijnenlaan 200D B-3001 Leuven Belgium
WAGEMANS Cyriel Universiteit Gent Dept. of Subatomic and Radiation Physics Proeftuinstraat 86 B-9000 Gent Belgium cvrillus.wanemans(UGent. be
JeanCharles.thomas0lfvs.kuleuven.ac. be
TRZASKA Henryk University of Jyvaskyla Dept. of Physics PO Box 35 FIN-40014 Jyvaskyla Finland trzaska&hvs.ivu.fi
WAGEMANS Jan SCK-CEN Boeretang 200 2400 Mol Belgium [email protected]
This page intentionally left blank
Author Index Aiche,M. 270 Ait Abderrahim, H. 209 Alexandrov, A.A. 102 Alexandrova, I.A. 102 Amar,N. 191 Aoust, T. 209 Arien, B. 209 Aritomo, Y. 191 Armbruster, P. 223
DeBruyn,D. 209 De Smet, L. 255 Demetriou, P. 21 Devlin, M. 65 Dorvaux, 0. 191 Drake,D. 65 Dufauquez, C. 245 Dufauquez, C.H. 232 Dushin, V.N. 73
Barreau,G. 270 Becker, J.A. 65 Belge, D. 245 Benlliure, J. 223 Benoit, P. 209 Berger, J.F. 39 Bernas,M. 223 Billebaud, A. 270 Bogatchev, A. 191 Bouchat, V. 191 Bouchez, E. 270 Boudard, A. 223 Boyer, S . 270
El Masri, Y. 232,245 Enqvist, T. 223 Ethvignot, T. 65 Fan, S. 201 Faust, H.R. 92 Fazio, G. 181 Florko, B.V. 102 Fogelberg, B. 262 Fortier$. 270 Fotiades, N. 65 Fritsch, V. 262 Garret, P.E. 65 Geltenbort, P. 142, 151 Giardina, G. 181,191 Gonnenwein, F. I 13 Goriely, S . 13,21 Goutte,H. 39 Granier, T. 65 GrBvy, S. 191 Grosjean, C. 270 Grosse, E. 201 Guiral, A. 270
Cabrera, J. 232 Casajeros, E. 223 Casoli, P. 39,65 Charity, R. 245 Charity, R.J. 232 Chou, K.W. 255 Czajkowski, S. 223,270 D’hondt, P. 209 Dassi, D. 270 289
290
Gunsing, F. 270 Haas,B. 270 Haeck, W. 209 Hage1,K. 232 Hambsch, F.-J. 47, 73,262 Hanappe, F. 181, 191 Hartmann, A. 201 Heyse, J. 142, 151,255 Hurstel, A. 270 Itkis, I. 191 Itkis, M. 191 Jakolev, V.A. 73 Jandel, M. 191 Janssens, P. 142 Jongen, Y. 209 Junghans, A.R. 20 1 Kalinin, V.A. 73 Kamanin, D.V. 102 Kanokov, Z. 181 Karamanis, D. 270 Keutgen, T. 232,245 Khlebnikov, S.V 102 Khugaev, A.V. 181 Kliman, J. 191 Knyajeva, G . 191 Kolbe, E. 3 Kondratiev, N. 191 Kosev, K.M. 201 Kozulin, E. 191 Kratz, K.-L. 3,29 Krupa,L. 191 Kupschus, P. 209 Kuznetsova, E.A. 102
Lamberto, A. 181 Laptev, A.B. 73 Legrain, R. 223 Leray, S. 223 Maes, D. 209 Malambu, E. 209 Materna, T. 181, 191 Mitrofanov, S.V. 102 Muminov, A.I. 181 Mutterer, M. 135 Napolitani, P. 223 Nasirov, A.K. 181 Natowitz, J.B. 232 Nelson, R.O. 65 Ninane, A. 245
Oberstedt, A. 262 Oberstedt, S. 47,262 Orlandi, R. 55 Palamara, R. 181 Panov,I.V. 3 Pavliy, K.V. 181 Penionzhkevich, Yu E. 102 Pereira, J. 223 Perrot,L. 270 Peter, J. 191 Petit, M. 270 Petrov, B.F. 73 Pfeiffer, B. 3,29 Pokrovski, I. 191 Pokrovsky, I.V. 167 Prieels, R. 245
29 1
Prokhorova, E. 191 Pyatkov, Yu V. 102 Ramstrom, E. 262 Rauscher, T. 3 Rejmund, F. 223 Ricciardi, M.-V. 223 Rizea, C. 270 Roberfioid, V. 232 Rochman,D. 55 Ryabov, Yu V. 102
Tsekhanovich, I. 55 Tudora, A. 47,262 Van Mol, J. 232,245 Van Tichelen, K. 209 Vandeplassche, D. 209 Vermeersch, F. 209 Vladuca, G. 47,262 Volant, C. 223 Vorobyev, A.S. 73 Voskresenski, V. 191
Saintamon, F. 270 Samyn, M. 13,21 Scherillo, A. 55 Schilling, K.D. 20 1 Schmidt, K.-H. 223 Schmitt, C. 191 Serot, 0. 142, 151,255 Sharma, H. 201 Shcherbakov, O.A. 73 Simpson, G. 55 Sobiella, M. 201 Sobolev, V. 209 Sokol, E.A. 102 Sokolov, V. 55 Soldner, T. 142 Stephan, C. 223 Stuttge, L. 181, 191
Wada,R. 232 Wagemans, C. 142,255 Wagemans, J. 151,255 Wagemans$. 151 Wagner, A. 201
Taieb, J. 223 Tassan-Got, L. 223 Theisen, C. 270 Thielemann, F.-K. 3 Tilquin, I. 232 Tishchenko, V.G. 102 Tjukavkin, A.N. 102 Tovesson, F. 262 Trzaska, W.H. 102
Yamaletdinov, S.R. 102 Younes, W. 65
