Proceedings of the International Workshop on the New Applications Of Nuclear Fission: Bucharest, Romania, 7-12 September 2003

M uc 11 er

NEW

APPLICATIONS

OF

MLJCl—S^FP F=ISSIOiNI

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Proceedings of the International Workshop on the

NEW

APPLICATIONS

Bucharest, Romania

OF

7 - 1 2 September 2003

editors

A. C. Mueller Institut de Physique Nucleaire, France

M. Mirea National Institute for Physics and Nuclear Engineering, Romania

L. Tassan-Got Institut de Physique Nucleaire, France

\[p World Scientific NEW JERSEY • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONGKONG • TAIPEI • CHENNAI

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NEW APPLICATIONS OF NUCLEAR FISSION Copyright © 2004 by World Scientific Publishing Co. Pte. Ltd. All rights reserved. This book, or parts thereof, 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.

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Organized by

IDRANAP (Inter-Disciplinary Research and Applications Based on Nuclear and Atomic Physics) European Center of Excellence from the "Horia Hulubei" National R&D Institute for Physics and Nuclear Engineering

Sponsored by

European Commission under contract ICA1-CT-2000-70023 and Romanian Ministry of Education and Research

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PREFACE This volume contains the lectures and contributions presented at the International Workshop "New Applications of Nuclear Fission" (NANUF03), held at Bucharest, in Romania, from 7 September to 12 September 2003. NANUF03 is the 4 th international meeting in a series organized by the European Commission Center of Excellence IDRANAP (InterDisciplinary Research and Applications Based on Nuclear and Atomic Physics) from the "Horia Hulubei" National Institute for Physics and Nuclear Engineering (IFIN-HH). The European Commission, under contract ICA1-CT-2000-70023, generously sponsored this meeting. The workshop topics covered new experimental and theoretical studies focused on the modern developments of nuclear fission aiming at various applications in a wide range of fields. It was an occasion to bring together scientists working in different fields related to nuclear fission in order to disseminate experience and knowledge in the benefit of the community. The main topics of the workshop were: radioactive beam facilities based on nuclear fission; nuclear waste transmutations and the future accelerator driven systems; fission and spallation nuclear data and modeling; experimental and theoretical advances in the study of nuclear fission; fusion reactions and decay modes of superheavy nuclei; stability against fission and many body systems and superasymmetric and multicluster fission. A few contributions presented by very young researchers emerging from connected domains were also accepted. The atmosphere during the workshop was stimulating due to the scientific level of the excellent lectures and the interesting contributions, offering an excellent frame for discussions and raising new suggestions and ideas. The opening address was given by Dr. E. Dragulescu, General Director of the National Institute for Physics and Nuclear Engineering, and the IDRANAP European Center of Excellence was presented by Dr. F. Buzatu, the Scientific Director. The meeting took benefits from the presence of Dr. L. Biro, Minister Secretary of State with Nuclear Safety, who presented a documented image of the nuclear energy in Romania and emphasized the importance of a durable development based on nuclear power plants. Prof. A.C. Mueller illustrated the importance of international

VII

VIM

collaborations in the context offered by the 6 European Framework Program and contributed to enhance the synergies within Romanian researchers. Special thanks are addressed to Prof. Yu.P. Gangrsky who presented the concluding remarks in an outstanding manner. We also thank to the International Advisory Committee consisting of Y. Abe (Kyoto), F. Buzatu (Bucharest), R. Casten (Yale), M. Ciocanescu (Pitesti), E. Dragulescu (Bucharest), C. Gheorghiu (Pitesti), W. Greiner (Frankfurt am Main), J.H. Hamilton (Nashville), S. Hofmann (Darmstadt), M.G. Itkis (Dubna), G. Muenzenberg (Darmstadt), Y. Nagame (Tokai), W. von Oertzen (Berlin), Yu.Ts. Oganessian (Dubna), D.N. Poenaru (Bucharest), A.V. Ramayya (Nashville), W. Scheid (Giessen), K.-H. Schmidt (Darmstadt) and P. Schuck (Orsay). The scientific secretary, Dr. Amalia Pop, and the technical secretary, Mrs. Alia Orascu, have done an extremely valuable and complex activity for the preparation of the meeting and managed difficult matters during the workshop efficiently, contributing essentially to the success. We want to thank Mr. E. Pauna, Mr. A. Sokolov and Mr. G. Chisner for their technical assistance. A special acknowledgement is dedicated to Mr. M. Duma and Mrs. Cristina Aiftimiei for their activity concerning the web design. A.C. Mueller M. Mirea

CONTENTS

Preface

vii

Fission Approach to Heavy Particle Radioactivities D.N. Poenaru. R.A. Gherghescu and W. Greiner

1

MYRRHA, a Multipurpose European ADS for R&D H.A. Abderrahim

9

Fusion-fission Dynamics and Synthesis of the Superheavy Elements Y.Abe

14

Quasifission of the Dinuclear System G.G. Adamian, N.V. Antonenko and W. Scheid

25

Microscopic Optical Potential for Nuclear Transmutation, Fusion Reactors and ADS Projects M. Avrigeanu, V. Avrigeanu, M. Duma, W. von Oertzen and A. Plompen

31

Identification of Excited 10Be Clusters Born in Ternary Fission of 262Cf A. V. Daniel. G.M. Ter-Akopian, G.S. Popeko, A.S. Fomichev, A.M. Rodin, Yu. Ts. Oganessian, J.H. Hamilton, A.V. Ramayya, J. Kormicki, J.K. Hwang, D. Fong, P. Gore, J.D. Cole, M. Jandel, L Krupa, J. Kliman, J.O. Rasmussen, A.O. Macchiavelli, I.Y. Lee, S.-C. Wu, M.A. Stoyerand R. Donangelo

41

Production of Photofission Fragments and Study of their Nuclear Structure Yu. P. Gangrsky and Yu. E. Penionzhkevich

48

Variation of Charge Density in Fusion Reactions R.A. Gherghescu, D.N. Poenaru and W. Greiner

54

IX

X

Parent Di-Nuclear Quasimolecular States as Exotic Resonant States N. Grama, C. Grama and I. Zamfirescu

60

Fission Investigations and Evaluation Activities at IRMM F.-J. Hambsch. S. Oberstedt, G. Vladuca and A. Tudora

67

Investigation of GeV Proton-Induced Spallation Reactions D. Hilscher. C.-M. Herbach, U. Jahnke, V.G. Tishchenko, J. Galin, B. Lott, A. Letourneau, A. Peghaire, D. Filges, F. Goldenbaum, K. Nunighoff, H. Schaal, G. Sterzenbach, M. Wohlmuther, L Pienkowski, W.U. Schroder and J. Joke

75

Evidence for Transient Effects in Fission B. Jurado. K.-H. Schmidt, C. Schmitt, A. Kelic, J. Benlliure andA.R. Junghans

82

Traps for Fission Product Ions at IGISOL S. Kopecky. T. Eronen, U. Hager, J. Hakala, J. Huikari, A. Jokinen, V.S. Kolhinen, A. Nieminen, H. Penttila, S. Rinta-Antila, J. Szerypo and J. Aysto

89

Triple-Humped Fission Barrier and Clusterization in the Actinide Region A. Krasznahorkay. M. Csatlos, J. Gulyas, M. Hunyadi, A. Krasznahorkay Jr., Z. Mate, P.G. Thirolf, D. Habs, Y. Eisermann, G. Graw, R. Hertenberger, H.J. Maier, O. Schaile, H.F. Wirth, T. Faestermann, M.N. Harakeh, M. Heil, F. Kaeppeler and R. Reifarth

95

Microscopic Analysis of the a-Decay in Heavy and Superheavy Nuclei D.S. Delion, A. Sandulescu and W. Greiner

101

Searching for Critical Point Nuclei in Fission Products N. V. Zamfir. E.A. McCutchan and R.F Casten

110

Fission Barriers in the Quasi-Molecular Shape Path G. Rover. C. Bonilla, K. Zbiri and R.A. Gherghescu

118

XI

Probing the 11Li Halo Structure by Two-Neutron Interferometry Experiments M. Petrascu. A. Constantinescu, I. Cruceru, M. Giurgiu, A. Isbasescu, H. Petrascu, I. Tanihata, T. Kobayashi, K. Morimoto, K. Katori, A. Ozawa, K. Yoshida, T. Suda and S. Nishimura

124

Dissipation in a Wide Range of Mass-Asymmetries M. Mirea

132

Physics with SPIRAL and SPIRAL 2 M. Lewitowicz

138

Two-Proton Radioactivity of 45Fe C. Borcea

146

Optimization of ISOL UCX Targets for Fission Induced by Fast Neutrons or Electrons O. Bajeat. S. Essabaa, F. Ibrahim, C. Lau, Y. Huguet, P. Jardin, N. Lecesne, R. Leroy, F. Pellemoine, M.G. Saint-Laurent, A.C.C. Villari, F. Nizery, A. Piukis, D. Ridikas, J.M. Gautier and M. Mirea

155

The ALTO Project: A 50 MeV Electron Beam at IPN Orsay O. Bajeat. J. Arianer, P. Ausset, J.M. Buhour, J.N. Cayla, M. Chabot, F. Clapier, J.L. Coacolo, M. Ducourtieux, S. Essabaa, H. Lefort, F. Ibrahim, M. Kaminski, J.C. Lescornet, J. Lesrel, A. Said, S. M'Garrech, J. P. Prestel, B. Waastand G. Bienvenu

160

Sensibility of Isomeric Ratios and Excitation Functions to Statistical Model Parameters for the (4'68He,n,3n)-Reactions T.V. Chuvilskaya. A.A. Shirokova andM. Herman

162

Fragment Mass Distribution of the 239Pu(d,pf) Reaction via the Superdeformed (3-vibrational Resonance K. Nishio. H. Ikezoe, Y. Nagame, S. Mitsuoka, I. Nishinaka, L Duan, K. Satou, M. Asai, H. Haba, K. Tsukada, N. Shinohara and S. Ichikawa

164

XII

Fingerprints of Finite Size Effects in Nuclear Multifregimentation Ad. R. Raduta andAI. H. Raduta

166

Systematics of the Alpha-Decay to Vibrational 2+ States S. Peltonen. J. Suhonen and D.S. Delion

170

Analysis of a Neutron-Rich Nuclei Source Based on Photofission M. Mirea. L. Groza, O. Bajeat, F Clapier, S. Essabaa, F. Ibrahim, A.C. Mueller, J. Proust, N. Pauwels and S. Kandry-Rody

172

Numerical Code for Symmetric Two-Center Shell Model P. Stoica

174

Deformed Open Quantum Systems A. Isar

176

Decommissioning the Research Nuclear Reactor VVR-S Magurele-Bucharest: Analyze, Justification and Selection of Decommissioning Strategy M. Dragusin, V. Popa, A. Boicu, C. Tuca. I. lorga and C. Mustata

178

K-Shell Vacancy Production and Sharing in (0.2-1.75) MeV/u Fe, Co + Cr Collisions C. Ciortea, I. Piticu, D. Fluerasu. D.E. Dumitriu, A. Enulescu, MM. GugiuandA.T. Radu

181

Some Fission Yields for 235U(n,f), 239Pu(n,f), 238U(n,f) Reactions in ZE Neutron Spectrum C. Garlea and I. Garlea

183

Recalibration of Some Sealed Fission Chambers—France in MARK III, Mol, Belgium Facility H.A. Abderahim, I. Garlea. C. Kelerman and C. Garlea

185

XIII

Muon Decay, a Possibility for Precise Measurements of Muon Charge Ratio in the Low Energy Range (< 1 GeV/c) B. Mitrica. A. Bercuci, I.M. Brancus, J. Wentz, M. Petcu, H. Rebel, C. Aiftimiei, M. Duma and G. Toma

190

Research and Development Activities as Support for Decommissioning of the Research Reactor VVR-S Magurele M. Dragusin

193

Light Heavy-Ion Dissipative Collisions at Low Energy A. Pop. A. Andronic, I. Berceanu, M. Duma, D. Moisa, M. Petrovici, V. Simion, G. Imme, G. Lanzano, A- Pagano, G. Raciti, R. Coniglione, A. Del Zoppo, P. Piatelli, P. Sapienza, N. Colonna, G. d'Erasmo and A. Pantaleo

195

Estimates of the a Rates for Deformed Superheavy Nuclei /. Silisteanu, W. Scheid, M. Rizea andA.O. Silisteanu

197

List of Participants

201

FISSION A P P R O A C H TO HEAVY PARTICLE RADIOACTIVITIES

D. N. POENARU AND R. A. GHERGHESCU Horia Hulubei National Institute of Physics and Nuclear Engineering, RO-077125, Bucharest-Magurele, Romania, E-mail: [email protected] W. GREINER Frankfurt Institute for Advanced Studies, J. W. Goethe Universitat, Pf 111932, D-60054 Frankfurt am Main, Germany Heavy particle radioactivity predicted in 1980 was experimentally confirmed since 1984. The obtained until now data on half-lives and branching ratios relative to a-decay of 14 C, 1 8 ' 2 0 O, 2 3 F, 22,24-26Nei 28,30Mg a n d 32,34g; rad i 0 activities are in good agreement with predicted values within the analytical superasymmetric fission (ASAF) model. The strong shell effect may be further exploited to search for new cluster emitters.

1. Introduction In order to predict heavy particle radioactivities in 1980 and to arrive at a unified approach of cluster decay modes, alpha disintegration, and cold fission, before the first experimental confirmation3 in 1984, we developed and used a series of fission theories in a wide range of mass asymmetry, namely: fragmentation theory, numerical (NuSAF) and analytical (ASAF) superasymmetric fission models, and a semiempirical formula for a-decay (see the multiauthored book * and the references therein). As normally expected, being intermediate phenomena between fission and a-decay, cluster radioactivities have been treated 2 ' 1 either as extremely asymmetric cold fission phenomena or in a similar way to a-decay, but with heavier emitted particles 4 ' 5 . The main difference from model to model consists in the method used to calculate the preformation probability or the half-life. There are also different relationships for the nuclear radii, interaction potentials, as well as for the frequency of assaults on the potential barrier. Particularly useful has been the ASAF model, improved successively

1

2

since 1980, allowing us to predict the half-lives and branching ratios relative to a-decay for more than 150 different kinds of cluster radioactivities, including all cases experimentally determined so far. Several other models have been introduced since 1985 (see the cited papers in Refs. 1 and 6). The performed measurements 7 _ 1 4 of cluster decay modes, showing a good agreement with calculated half-lives within analytical superasymmetric fission model, are included in a comprehensive half-life systematics 15 from which other possible candidates for future experiments may be obtained. The experimental data on half-lives and branching ratios relative to a-decay of 1 4 C, 1 8 ' 2 0 O, 2 3 F , 22,24-26^ 28,30Mg a n d 32,34Si r a d i o a c . tivities are in good agreement with predicted values within the analytical superasymmetric fission (ASAF) model. The fine structure 16 was predicted 17 before the discovery of 1989 in Orsay. The measurements 18 with superconducting magnetic spectrometer SOLENO were repetead with the best accuracy ever obtained 19 in 1995.

2. Cold fission In the usual mechanism of fission, a significant part (about 25-35 MeV) of the released energy Q is used to deform and excite the fragments (which subsequently cool down by neutron and 7-ray emissions); hence the total kinetic energy of the fragments, TKE, is always smaller than Q. Since 1980 a new mechanism has been experimentally observed - cold fission10 characterized by a very high TKE, practically exhausting the Q-value, and a compact scission configuration. Experimental data have been collected in two regions of nuclei: (a) thermal neutron induced fission on some targets like 233,235Uj 238 Np) 239,241 p U ) 245 C n i ) ^ t h e spontaneous fission of 252

Cf; (b) the bimodal 2 1 spontaneous mass-symmetrical fission of 2 5 8 Fm,

259,260 M d ; 258,262 NO;

& n d

260104

T h e y i e M

rf

t h e c o l d

fisgion

m e c hanism

is comparable to that of the usual fission events in the latter region, but it is much lower (about five-six orders of magnitude) in the former. We have systematically studied the cold fission process viewed as cluster radioactivity within our ASAF model. 22 ' 23 The cold fission properties of transuranium nuclei are dominated by the interplay between the magic number of neutrons, N = 82, and protons, Z = 50, in one or both fragments. The best conditions for symmetric cold fission are fulfilled by 2 6 4 Fm, leading to identical doubly magic fragments 132 Sn. A spectrum of the 234 U halflives versus the mass and atomic numbers of the fragments illustrates the idea of a unified treatment of different decay modes over a wide range of

3

mass asymmetry. Three distinct groups, a-decay, cluster radioactivities, and cold fission, can be seen, in good agreement with experimental results. 3. Region of cluster emitters From the energetical point of view (released energy Q > 0) the area of heavy particle radioactivity is extended well beyond that of a-decay. Nevertheless, the largest branching ratio with respect to a emission experimentally determined up to now is ba = Ta/T ~ 10~ 9 . At the limit of experimental sensitivity, the smallest branching ratio measured already is of the order of 10~ 16 for 34 Si decay of 242 Cm and the longest upper limit of the halflife (for 24 - 26 Ne radioactivity of 2 3 2 Th) is T > 10 2 9 2 s. Consequently we

126 „ • Be

0

C

B

0

sNe oMg H S i

82

Figure 1. Part of the nuclear chart showing the predicted (within ASAF model) emitters and t h e most probable emitted heavy particles from nuclei heavier than the doubly magic 2 0 8 P b , the region where successful experiments have been performed. The line of beta-stability is marked with black squares. The selection condition was T < 10 3 0 s, ba > 1 ( T 1 7 .

selected from the very large number of cluster emitters those fulfilling simultaneously the conditions T < 10 30 s and ba > 1 0 - 1 7 . The nuclear chart of cluster emitters obtained in such a way for N > 126 and Z > 82 is plotted in Fig. 1. This is the region in which successful experiments have been performed. The cluster emitters 221 Fr, 2 2 1 - 2 2 4 - 2 2 6 Ra, 225 Ac, 228, 23 o Th) 23ip a j 230,232-236 U ; 236,238p U i

a n d

242 Cm ^

e

j t h e r p^gfofe

o r n o t far

from

stabil

.

ity nuclei. Few examples from the total of about 300 stable nuclides found in nature are shown in Fig. 1. Following Green, the line of beta stability can be approximated by A={Z-

100)/0.6 + y/(Z - 100) 2 /0.36 + 200Z/0.3

(1)

Another island of very proton-rich cluster emitters above the doubly magic 100 Sn is not shown on the above mentioned figure.

4

4. Shell effects The surface of calculated half-lives (within ASAF model) of heavy nuclei against 14 C radioactivity and the measured points are plotted in Fig. 2. A strong shell effect can be seen: as a rule the shortest value of the halflife (maximum of 1/T) is obtained when the daughter nucleus has a magic number of neutrons (Nj = 126) and/or protons {Z& = 82). For 14 C decay

Figure 2. The surface of calculated half-lives (within ASAF model) of heavy nuclei against 1 4 C radioactivity and the measured points. Daughter nuclei are P b isotopes. The peak of maximum probability (shortest half-life) corresponds to 2 2 2 R a for which the daughter is the doubly magic 2 0 8 P b .

modes the peak of maximum probability (shortest half-life) corresponds to 222 Ra for which the daughter is the doubly magic 2 0 8 Pb. As can be seen in table 1, from 26 identified emitters and 9 determined upper limits (u) one has: • 9 +2u — doubly magic daughter g^8Pb126 • 9 — magic proton number Za = 82 • 6 + 4u — magic neutron number N^ = 126. There are only 2+3u exceptions: Zd ^ 82 Nd ^ 126: 'Ac - • i 4 C 8 + I^Biiag; i n - • 1 0 JNei4 + 8 0 U g l 2 8 , 233 U -* 2 |Mg 1 6 + 2 ° 5 Hg 125 ; 23*U -+ 2 «Mg 16 + 80 M g,127) a n d 2 3 6 U -+ 28.Mg16 + 2 ° 8 Hg 128 .

225

5

We continue to present the shell effects in the next section. Table 1. Performed experiments. Prom 26 identifications and 9 upper limits 24 + 6 belong to this table. Magic nucleon numbers of the daughter. Par is an abreviation for parent. Zd == 82

Par. 222

Ra

Fragments 14

C8

8

Ra

14

8

223

Ra

14

224

Ra

i Pbl26

lo

228

20O 8 U 23F

15 8 Pbl26

Pa

14 14

c8 c8

C8

i9Pb

230'pj1

24

Ne

231

Pa

24

Ne

207

Tli26

Th

26

Ne

206

Hg126

|2°Pb 2

|2 Pb §°9Pb

Ne

i Pbl26

234n

24

Ne

§2°Pb

|§ 8 Pb!26

236

TJ

24

Ne

|2XPb

Ne

I^PblSe

235

TJ

25

Ne

l2°Pb

Mg

i8Pbl26

238pu

28

Mg

i2°Pb

232-[j

24

Ne

233 "[J

25

Ne

234

U

26

236pu

28

238pu

30 34

Ra

C8

i Pb

14

24

22

Cm

i Pbl26

226

C8

Ne

M g

Si20

I^PblSe 8

8

§§ Pbl26

Fragments

221^.

7

233 TJ

230 TJ

242

8

Nd = 126 Par.

Fragments

221

i Pb!26

231

Par.

8

226Th

Th

Zd = 82

Nd = 126

232

207 206

T1 1 2 6

Hgl26

234 TJ

28

M g

206

Hgl26

236 TJ

30

M g

206

Hgl26

Np

30

M g

238pu

32

237

T1126

Si

206

Hgi26

206

Hgl26

240pu

34

Si20

241

34

Si20

Am

207

207

T1126

i8Pbl26

5. N e w candidates By comparing the systematics of calculated values and of experimental data one can list 15 other possible candidates for future experiments: 220,222,223Fr; 223,224Ac> a n d 225 T h M u c e m i t t e r s ; 2 2 9 Th for 2 0 O radioactivity; 2 2 9 Pa for 22 Ne decay mode; 2 3 0 ' 2 3 2 Pa, 231 U, and 2 3 3 Np for 24 Ne radioactivity; 2 3 4 Pu for 26 Mg decay mode; 234 - 235 Np and 235,237pu ^ 2 8 M g emitters, as well as 238>239Am and 2 3 9 _ 2 4 1 Cm for 32 Si radioactivity. Also 33 Si decay of 2 4 1 Cm could be observed. In the table 2 one may see • 3 cases with doubly magic daughter g28Pbi26 • 6 with magic proton number Zd = 82 • 8 with magic neutron number Nd = 126. There are nine exceptions with Zd ^ 82 Nd ^ 126: 220m. _v 14/"1 i 206npi . * r ->• 6 ^ 8 + 81 1 1 1 2 5 ,

222r\. _v 14/~< _i_ 208x1 *T -t 6 2 4 Ne 1 4 + I? 6 T1 125 ; 234 Np -> 2 lMg 1 6 + I° 6 T1 1 2 5 ,

230

6 Table 2. Candidates for new experiments; 14 cases with magic nucleon numbers of the daughter out of the total number 23. Zd = 82 Par. 234pu 240 241

Cm Cm

and

Zd = 82

Nd = 126 Par.

Fragments 26Mg 32 33

238

Si Si

208pbl26 8

§0 Pb 1 2 6 i8Pbl26

14

Fragments

229Th

20

24

231U 235pu

28

237pu

28

Par.

O

209Pb

Ne

7

223Ac

§§ Pb

C8

209B;126

229pa

207Th26

24

209

Mg

|07pb

233Np

Mg

9

§° Pb

239Cm

32 Si

|07pb

239

241 C m

32

|09pb

Si

Fragments 14

22Ne

235Np

A m - • ? 2 Mg 1 8 +

6. Emission of

Nd = 126

Am

Ne

Bii26

28Mg

207Tll26

32 Si

207Tll26

2 6

° T1125.

C in competition with

12

C

14

In 1984 there was a discussion: why C and not the three alphas 12 C is emitted from 223 Ra? Based on alpha-like theory one would expect a three-a structure to be preformed and emitted with maximum probability. On the other hand let us have a closer look at the following equation expressing the halflife in terms of three model-dependent quantities (frequency of assaults, preformation probability, and the penetrability of the external part of the barrier): T=l

~T

=

~^P

l

°ST = iosF-^gS-\ogP

(2)

where F = In 2/v with v denoting the frequency of assaults on the barrier in the process of quantum penetrability. As may be seen in Fig. 3, despite a slightly smaller preformation probability, the Q-value is higher and the potential barrier for emission of 14 C is smaller so that a higher penetrability makes a shorter half-life. The shell effects of the emitted particle 64Cg with magic neutron number are also playing a role. 7. Half life estimation with the universal curve The preformation probability can be calculated within a fission model as a penetrabilty of the internal part of the barrier, which corresponds to still overlapping fragments. With good approximation, by assuming v = constant and S — S(Ae), one can obtain the universal curve for any kind of cluster decay mode, including a decay: logT = - logP - 22.169 + 0.598(Ae - 1)

(3)

7

12

13 223

'

45

14

I

•

Ra - -

40 35 7 30

15

I

—

'

Q(MeV) log T(s) -logs log P -logF(s)

- "••••^

16

I

'

j S'

~

^^

^f

25 2U

-

15

_

• ^ ^ ^

^

^

—

^ ^ " " N ^ ^

_

— — —

It)

""" "~

•

— 1

45 :

222

|

1

|

1

|

1

Ra

:

40 /

3b y

'

^ ~ ^

s

v ^"

—N(n,T) is the probability for finding the DNS in the state n at a local temperature T(Z, N) and is normalized to unity. Summing over the DNS states n, we finally obtain the master equations used in the calculations 7 :

jtPzAt) = *z~+t* pz+iMt) + *£% Pz-iMt) + A g - ^ Pz,N+i(t) + A g ' + ^

Pz,N-i(t)

- (A { -' 0 ) + A ( + ' 0 ) + A ( 0 '- } + A j ° # + A"Z{N + Afz%) Pz,N(t)

(3)

27

with ( m ( T ) = nm(T), A A

( ± - 0 )

m

_

1

S T

Z , N ( T ) - ^ - ^

A(°>±)m-

A

^(

T

:

Z

n2(T) = nn2(T) ) \2r,o(T^(l

\ n

\gni,n2\

V ^ l n

r,

|2„ m n

) = E Ag J V (n)*z, A r (n,T) >

-en2)/2H]

( T W ^ ^ ^

n?(T)(l-n,(r))

.

)2/4

„ ^ u s i n 2 [ A ^ ( e n i -e„ 3 )/2fi]

A ^ ( T )= ^ A ^ W $ ^ ( n , T ) .

n

n

Here, p n i ,„2 are transition matrix elements and eni, e„2 are single-particle energies of the DNS nuclei. This system of equations has to be solved with the initial condition Pz,jv(0) = 5z,Zi • SfftN.. The rates for the transfer of a proton or neutron from the heavy nucleus to the light one {&ZH , &Z'N ) a n d m opposite direction ( A ^ \ Az'x ) depend on the temperature-dependent Fermi occupation numbers nm(T) and nn2(T) of the single-particle states. The decay rate AqJN(T) of the DNS for quasifission depends on the height Bqf of the quasifission potential barrier at -R& = Rm + 1.5 fm where Rm is the internuclear distance of the DNS nuclei in the potential minimum. The decay rate is treated with the Kramers formula 7 . 3. Charge and Mass Yields The charge and mass yields for quasifission can be calculated as to

q

YzMh) = A J,N j Pz,N{t)dt,

(4)

o 20

where t0 w (3 — 4) • 10~ s is the reaction time which is at least ten times larger than the time of deep-inelastic collisions. This time is determined by considering the balance equation for the probabilities: to A

Y,( Z,N Z,N

+ ^zZt-z,Ntot-N)

[PzMt)dt J Q

= 1 - 5>z,Jv(*o).

(5)

Z,N

The sum on the right hand side of (5) contains the fusion probability PCN = Y^zn)

1

1

1 1

i

Trabandf89 -default (g=A/13; P=0) "~g=A/13;p-Dllg73 —I I I 1 1

20

1

Ep=80MeV]

40 En [MeV]

60

80

Figure 3. Comparison of experimental and MSD cross sections for the (p,xn) reactions on Zr.

37

20

40

60

80

100

120

140

Figure 4. Comparison of experimental and MSD cross sections for the (p,xn) reactions on 100Mo.

In the case of deuteron elastic scattering on 6Li at energies of 14.7 and 19.6 MeV (Fig. 1) search for the imaginary and spin-orbit OMP parameters led to a good description of the forward angles, while at larger angles the disagreement has been obvious. It seems that not merely accidental since it is in line with the experimental angular distributions obtained by Bingham et al. [27] and Abramovich et al. [28]. The results are improved by taking into account also the coupled reaction channel (CRC) model predictions of the code FRESCO [29]. Thus the maximum of the angular distribution at extremely backward angles is reproduced fairly well by the CRC. The coupling routes taken into account in the present analysis involve both a-particle and the sequential deuteron exchange in the 6Li nucleus, by using Timofeyuk and Thompson [30] spectroscopic factor for the a-particle in 6Li and Rudchik et al. [23] spectroscopic factor of the deuteron in the a-particle. It appears [25] that the exchange-effects probability has to decrease strongly with increasing energy of the incident particle, e.g. for the deuteron increased energy the characteristic momentum with which it captures the aparticle to form the ground state of 6Li must increase as well. At the same time the binding energy of the cluster 6H=a+d is only 1.47 MeV, the relative

38

effective momentum between its constituents not being large. Thus, the experimental elastic angular distribution [23] of 50 MeV deuterons on 6Li has been described only by pure elastic scattering calculations, as long as the experimental data are measured only up to 155 degrees 5.

Quantum-statistical MSD processes at low and intermediate energies on 90Zr and 100Mo

The quantum mechanical formalism developed by Feshbach, Kerman and Koonin [31] (FKK) for the multistep processes has been extensively used to describe a large amount of experimental data covering a broad energy range. The assumptions and simplifying approximations considered in the application of the FKK theory have been analyzed and important refinements of calculations have been made (e.g. [32] and references therein). One of the important assumptions concerns the effective NN interaction, which is taken as a single Yukawa term with 1 frn range, its strength V0 being considered as the only free parameter of the FKK theory. However, it should be noted that, even when a consistent standard parameter set has been used as well as several other effects have been taken into account, the systematics of the phenomenological V0 values still show discrepancies. Such uncertainties of the phenomenological effective NN-interaction strengths may reflect the eventual scaling of Vo compensating for some effects which have been neglected and should be added to the theory. Thus, the use a more realistic effective NN interaction, which should be consistent with the corresponding OP real part of the OM, has been stated as one of the open problems in the theoretical description of the MSD nuclear reactions. Through the trial to provide a reliable strength to be used within the FKK theory instead of the free parameter V0, we expect to overcome the uncertainties in fitting an effective interaction directly to MSD processes data. Thus an 1Yequivalent NN interaction strength V0eq obtained from the DDM3Y-Paris effective interaction has been used within MSD calculations which describes without any free parameter the experimental double-differential cross sections, the nucleon emission spectra from the (p,n) and (p,p') reactions on 90Zr (Fig. 3) and I00Mo (Fig. 4) isotopes at the incident energies of 80 MeV, 100 MeV, and 120 MeV, and makes possible predictions of MSD double-differential cross sections and nucleon emission spectra corresponding to (n,n') and (n,p) reactions on 90Zr and 100 Mo isotopes at the incident energies of 80 MeV, 100 MeV, and 120 MeV, where no experimental data exist.

39

Acknowledgments This is where one acknowledge funding bodies etc. Note that section numbers are not required for Acknowledgments, Appendix or References. This work was supported at IFIN-HH by the Contract of Association between EURATOM and MEC-Bucharest No. ERB-5005-CT-990101, and by the EC/JRC/IRMM project PA No. 59 during a three-month visit at IRMM-Geel, and the EC/FP5/INC02 project IDRANAP/WP12 of IFIN-HH during three-month visits at HMI-Berlin. M.A. gratefully acknowledges the warm hospitality at IRMM-Geel and HMIBerlin. References 1. Dao T. Khoa, W. von Oertzen and H.G. Bohlen, Phys. Rev. C49, 1652 (1994); Dao T. Khoa, W. von Oertzen and A.A. Ogloblin, Nucl. Phys. A602, 98 (1996); Dao T. Khoa and G.R.Satchler, Nucl. Phys. A668, 3 (2000). 2. M. Avrigeanu, A.N. Antonov, H. Lenske and I. Stetcu, Nucl. Phys. A693, 616 (2001). 3. M .Avrigeanu, W. von Oertzen, A.J.M. Plompen and V. Avrigeanu, Nucl. Phys. A723, 104 (2003). 4. M. Avrigeanu, G.S. Anagnostatos, A.N. Antonov and J. Giapitzakis, Phys. Rev. C62, 017001 (2000); M. Avrigeanu, G.S. Anagnostatos, A.N. Antonov and J. Gapitzakis, Phys. Rev. C62, 017001 (2000); M. Avrigeanu, G.S. Anagnostatos, A.N. Antonov and V. Avrigeanu, J.Nucl. Sci. Technol. S2, 595 (2002); Int. J. Modern Phys. E l l , 249 (2002). 5. A.Yu. Konobeyev, Yu.A. Korovin, P.E. Pereslavtsev, U. Fisher, and U. von Mollendorff, Nucl. Sci. Eng. 139, 1 (2001). 6. G.R. Satchler and W.G. Love, Phys. Rep. 55, 183 (1979). 7. I. Tanihata et al., Phys. Lett. B289, 261 (1992). 8. M.V. Zhukov et al., Phys. Rep. 231, 151 (1993). 9. Dao T. Khoa, Phys. Rev. C63, 034007 (2001). 10. L.W. Put and A.M.J. Paans, Nucl. Phys. A291, 93 (1977); L.McFadden and G.R. Satchler, Nucl. Phys. A84, 177 (1966); M. Nolte, H. Machner and J. Bojowald, Phys. Rev. C 36, 1312 (1987); V. Avrigeanu, P.E. Hodgson and M. Avrigeanu, Phys. Rev. C 49, 2136 (1994). 11. G.R. Satchler, Phys. Lett. B36, 169 (1971). 12. M. Lacombe et al, Phys. Lett. B101, 139 (1981). 13. R. Machleidt, Adv. Nucl. Phys. 19, 189 (1989). 14. D. Abbot et al, Eur. Phys. J. A7, 421 (2000).

40

15. G.C. Li, I. Sick, R.R. Whitney and M.R. Yearian, Nucl. Phys. A162, 583 (1971); T. Sinha, Subinit Roy, and C. Samanta, Phys. Rev. C48, 785 (1993). 16. K.H. Bray, et al, Nucl. Phys. A189 (1972) 35. 17. A.A. Korsheninnikov et al, Nucl. Phys. A617, 45 (1997); M. El-Azab Farid and M.A. Hassanain, Nucl. Phys. A697, 183 (2002). 18. M.E. Brandan and G.R. Satchler, Phys. Rep. 285, 143 (1997); Dao T. Khoa, Phys. Rev. C63, 034007 (2001). 19. G. Bertsch, J. Borysowicz, H. McManus and W.G. Love, Nucl. Phys. A284, 399 (1977). 20. N. Anantaraman, H. Toki and G. Bertsch, Nucl. Phys. A398, 279 (1983). 21. M. Avrigeanu, A. Harangozo, V. Avrigeanu, A.N.Antonov, Phys.Rev.C 54,2538(1996); 56,1633(1997). 22. S.N. Abramovich et al, Yad. Phys. 40, 842 (1976), and EXFOR-A0117 data-file entry; D.L. Powell et al, Nucl. Phys. A147, 65 (1970), and EXFOR-A1432 data-file entry; H.G. Bingham et al, Nucl. Phys. A173, 265 (1971), and EXFOR-A1431 data-file entry; H. Ludecke et al, Nucl.Phys. A109, 676 (1968), and EXFOR-F0002 data-file entry; S. Matsuki et al, Jap. Phys. J. 26, 1344 (1969), and EXFOR-A1435 data-file entry; V.I. Chuev et al, J. de Phys. 32 (1971) C6. 23. A.T. Rudchik, A. Budzanoki et al. Nucl. Phys. A602, 211 (1996). 24. O. Bersillon, Centre d'Etudes de Bruyeres-le-Chatel Note CEA-N-2227, 1992. 25. V.Z. Goldberg, K.A. Gridnev, E.F. Hefter, and B.G. Novatskii, Phys. Lett. B58, 405 (1975). 26. T. Yoshimura et al.,Nucl. Phys. A641, 3 (1998). 27. H.G. Bingham et al, Nucl. Phys. A173, 265 (1971), and EXFOR A1431 data-file entry. 28. S.N. Abramovich et al, Yad. Phys. 40, 842 (1976), and EXFOR A0117 data-file entry. 29. I.J. Thompson, Comput. Phys. Reports 7, 167 (1988). 30. N.K. Timofeyuk and I.J. Thompson, Phys. Rev. C61, 044608 (2000). 31. H. Feshbach, A. Kerman and S. Koonin, Ann. Phys. (NY) 125, 429 (1980). 32. M.B. Chadwick et al., Acta Phys. Slovaca 49, 365 (1999).

IDENTIFICATION OF EXCITED 10BE CLUSTERS BORN IN TERNARY FISSION OF 252CF A. V. DANIEL, G. M. TER-AKOPIAN, G. S. POPEKO, A. S. FOMICHEV, A. M. RODIN AND YU. TS. OGANESSIAN Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, Dubna 141980, Russia J. H. HAMILTON, A. V. RAMAYYA, J. KORMICKI, J. K. HWANG, D. FONG AND P. GORE Department of Physics, Vanderbilt University, Nashville, TN 37235, USA J. D. COLE Idaho National Engineering and Environmental Laboratory, Idaho Falls, ID 83415, USA M. JANDEL, L. KRUPA AND J. KLMAN Institute of Physics, Slovak Academy of Sciences, Dubravska cesta 6, Bratislava, Slovak Republic and FLNR, JINR, Dubna, Russia J. O. RASMUSSEN, A. O. MACCHIAVELLI, I. Y. LEE AND S. -C. WU Lawrence Berkeley National Laboratory, Berkeley, CA 94720, USA M. A. STOYER Lawrence Livermore National Laboratory, Livermore, CA 94550, USA R. DONANGELO Instituto de Fisica Universidade, Federal do Rio de Janeiro, Rio de Janeiro, 21945-970, Brazil Ternary fission of 252Cf was studied at Gammasphere with using eight AExE particle telescopes. The 3368 keV gamma transition from the first excited state in 10Be was undoubtedly found. The ratio of the population probabilities for these two levels was estimated as 0.160±0.025. The nuclear temperature of the neck region near the scission point was estimated as 1.0±0.2 MeV. No evidence was found for 3368 keV y rays emitted from a triple molecular state.

41

42

1.

Introduction

The interest to nuclear fission accompanied by light charged particle (LCP) emission is connected with the possibility to obtain additional data about the fission mechanism. In spite of intensive investigations of these phenomena (see reviews1'2 and papers cited there a good quantitative explanation of the observed kinematical characteristics and yield of LCPs has not been achieved. Mainly, theoretical models concentrated only on the explanation of a-particle emission in the fission for which the main experimental data have been obtained. More recently, information about the kinematical characteristics of heavy LCPs and their yields were improved3'4 for the 252Cf spontaneous fission. The problem still remained is a relatively high energy limit above which heavy LCPs were measured. A more direct way allowing the exploring of the fission nucleus characteristics may be based on the assumption5 that the LCPs could be emitted in their excited states. If thermal equilibrium is maintained near the scission point then population of the LCPs in excited state can be connected with the nuclear temperature. Reports of the observation of the 3368 keV y ray corresponding to the 10Be 2+—>0+ transition in a ternary fission experiment with 252 Cf have been made6'7. There was some evidence that the y peak of 10Be was seen without Doppler broadening. Taking into consideration the lifetime 125 fs of 2+ level in 10Be it means 6 ' 7 that the 10Be stays at rest for an unusual long time or y rays are emitted predominantly in the orthogonal direction to the 10Be momentum. It was not the undoubted result because of the poor energy resolution of Nal detectors used in the experiment. This idea has been tested by using data of y-y-y coincidences obtained at the experiment made on the Gammashpere8 with high energy resolution. The data gave support for that result, but with limited statistics and no direct LCPs identification. The possibility that the 10Be nucleus may stay between two fission fragments for a long time ~10"13s to create a so-called triple nuclear molecule opens up exciting possibility discussed in9. 2.

Experiment

The experiment has been carried out at the Lawrence Berkeley National Laboratory by using Gammasphere and eight light charged particle detectors. Gammasphere was set to record y rays with energy less then ~5.4 MeV. The efficiency varied from a maximum value ~17% to ~4.6% at the y energy 3368 keV. A sample of 252Cf giving ~4xl 06 spontaneous fissions per second was installed in the center of the reaction chamber, which was placed in a hollow

43

sphere inside Gammasphere. The source was prepared from a Cf specimen that was deposited in a 5 mm spot on a 1.8 micron titanium foil and was tightly covered on both sides by gold foils to exclude the coming out of fission fragments from source. Eight similar AExE Si detector telescopes were used to measure LCPs emitted in the ternary fission. They were arranged in the reaction chamber with four telescopes centered at the polar angle 0=30° (azimuth angles cp = 45°, 135°, 225° and 315°, and four at 0 =150° (azimuth angles were the same). Each AE detector had an area 10x10 mm2 and thickness slightly varying between 9 u and 10.5 u. Each E detector was 400 (i thick and was 20x20 mm2 in area. The distance from the source to AE detector was 27 mm and from )E detector to E detector was 13 mm in all telescopes. 3.

Results and Discussion

The resolution of the AZsxE telescopes allowed us to well identify helium, beryllium, boron and carbon nuclei, when energy deposition in the E detector was greater then 5 MeV. From this value 5 MeV, we calculated the lower primary energy of the LCPs registered in the experiment, as 9, 20, 24, 32 MeV for He, Be, B, and C LCPs, respectively. The lithium region was shadowed by the random coincidence of the ternary helium LCPs with the 252Cf a-decay particles. The detection of prompt y rays coinciding with the Be LCPs permits to search y rays corresponding to the transition from the first excited state in 10Be. The energy resolution of the AE detectors does not allow the separation of beryllium isotopes in the AExE plot, but experimental results presented in10 show that the yield of beryllium LCPs emitting in the 252Cf spontaneous fission consist of 10Be on -80%. In Fig. 1 the dotted line shows the spectrum of y rays in coincidence with the beryllium accompanied 252Cf spontaneous fission. The solid line on this figure demonstrates the same spectrum after applying a Doppler correction. The distinct peak in the last spectrum at the energy 3368 keV corresponds to the 2+->0+ transition in 10Be. The width FWHM=65.7±4.5 keV was calculated for the peak by using a Gaussian fitting. This width is compatible with the value FWHM=62.1 keV obtained by the Monte Carlo simulation of the procedure introducing a Doppler correction for the y rays emitting from the moving 10Be nucleus. The simulation has been done taking into consideration the experimental kinetic energy distribution of 10Be, the Gammasphere energy resolution and the real 3d-position of all gamma and particle detectors. For comparison, the dotted line in the Fig. 1 shows the spectrum of yrays

44

coinciding with the emission of helium nuclei. It reflects, to some extent, the background from the y rays emitted from fission fragments. One infers from Fig. 1 that the 3368 keV peak restored after Doppler correction (see the solid line histogram) is smeared in the raw spectrum (dashed line histogram) over an energy range extending from about 3000 keV to 3700 keV. Comparison made in Fig. 2 between the spectrum of y rays coinciding with Be LCPs and the spectrum obtained by Monte Carlo simulation gives evidence that the 3368 keV y rays are mainly emitted by moving 10Be

5000

Figure 1: The solid and dashed lines show the spectra of y rays coinciding with Be LCPs after and before the Doppler shift correction, respectively. The dotted line shows the spectrum of y rays coinciding with He LCPs. The last spectrum was normalized to the total number of counts obtained in the whole spectrum associated with the Be LCPs E _ 9 0 _ 5900 ke V.

nuclei. In the raw spectrum of y rays recorded in coincidence with Be LCPs we do not see any distinct peak near 3368 keV, which could be associated with y emission from stationary 10Be nuclei (see Figs. 1 and 2). Obviously, yrays emitted from the moving 10Be in directions almost orthogonal to the 10Be momentum result in a broad bump centered on the maximum of the 3368 keV peak. To get rid of this bump we picked out only such events where the angles between the trajectories of y rays and 10Be nuclei were less than 45° or greater than 135°. The resulting spectrum obtained after the background subtraction is shown in Fig. 3. The energy region around 3368 keV now has a clear zero. In

45 1 20

37

15

-_4 :!

Counts

1

10

-

:f;

-\

!*r

; j

5

0

| %-H": -i t 1; - ;.; 2 Z\ . . 3000

Iffr

(!."«- +H4i

+

'"J-

'M.rir ~* A riT' .

, i . 3100

.

!

4

i

:

'?•

. . ir

\ , :

m~u >'••i: h .n. iU^-U-jJl'dt J;;j !

I i i -,iA':'' '' 1 ! j i

:

'

! x

•

^ •

"

,

... bP

!

r

M":

fi

U Hirr^-rf-i": rn 4

'4 1 1 1 1 1 1 I 3200 3300

. 1 1 1 1 3400 E, k.V

i

L_i

I_I

.

1• l

• i

u , ; , r.^Ti'

• • 1—i

i

t

,,.. i

q- ; ' i

1 i

J 1 1 1 1 1 1 11 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1

Figure 2: Histogram drawn with a dotted line shows the spectrum of y rays coinciding with Be LCPs. It is obtained from the dashed line histogram of Fig. 1 after the subtraction of the background shown by the dotted line in Fig. 1. The solid and dashed line histograms demonstrate me spectra simulated using experimental angular distribution of 3368 keV y and under the assumption of isotropic y emission from 10Be, correspondingly. Both spectra were normalized to the number of counts obtained in the first one in the energy range 3000-3800 keV.

[!

•1

![A/ Hi 3000

3100

3200

3300

AJ 3400 E.keV

3500

3600

i 3700

3800

Figure 3: Histogram shows the spectrum of y rays detected at angles 135° to the Be momentum.

other words, there is a lack of any y line which could be attributed to the emission from 10Be standing in a triple nuclear molecule. Using results on Fig. 1 we estimated the population ratio of the excited 2+ to the ground-state 0+ levels in 10Be as 0.160+0.025. Having spin and energy of these two states and assuming thermal equilibrium near the scission point, this value allows one to estimate the temperature parameter as 1.0+0.2 MeV using

46

Boltzmann distribution. Most likely it is the estimation of the nuclear temperature of the neck region at the scission point. The upper limit for the probability that 10Be emits its y rays being in rest makes only 2% of this ratio. This result is valid for 10Be LCPs having at infinity the kinetic energy more than 20 MeV. One can not exclude that the decay channel of the hypothetical triple molecule is characterized by the low kinetic energy of the 10Be LCPs which was unreachable in our experiment. The Gammasphere experiment13 relied solely on the observation of y-y-y coincidence events, a possibility still remains open that a narrow ypeak characteristic to the motionless 10Be can be found if the low energy part of the energy distribution of 10Be LCPs is detected. The present result excludes any possibility that an effect of triple quasi molecular state, involving beryllium LCPs, could be observed in 6,7 where the energy cut off was 26 MeV for these clusters. Acknowledgments Work at Joint Institute for Nuclear Research was supported in part by the US Department of Energy contract \#DE-AC011- 00NN4125, BBW1 Agreement No.~3498 (CRDF grant RPO-10301-INEEL) and by the joint RFBR-DFG grant (RFBR No. 02-02-04004, DFG No. 436RUS 113/673/0-1(R)). Work at Vanderbilt University, LBNL, LLNL and INEEL are supported by U.S. Department of Energy under Grant No. DE-FG05-88ER40407 and Contract Nos. W-7405-ENG48, DE- AC03-76SF00098 and DE-AC07-76ID01570. References 1. I. Halpern, Ann. Rev. Nucl Sci. 21, 245 (1971). 2. C. Wagemans, The Nuclear Fission Process, (CRS Press, Boca Raton, FL, USA, 1989), chap. 12. 3. M. Mutterer et al, Proc. Int. 3rd Conf. DANF'96, Casta Papernicka, Slovakia, edited by J. Kliman and B. Pustylnik, (JINR, Dubna, 1996), pp. 250-261. 4. Yu. N. Kopach et al, 5He, 7He and 8Li, E = 2.26 MeV, Intermediate Ternary Particles in the Spontaneous Fission of252Cf., (Preprint GSI 200210, 2002). 5. G. Valskii, Sov. J. Nucl. Phys. 24, 140 (1976). 6. P. Singer et al, Proc. Int. 3rd Conf. DANF' 96, Casta Papernicka, Slovakia, edited by J. Kliman and B. Pustylnik, (JINR, Dubna, 1996), pp. 262-269.

47

7. M. Mutterer et al, Proc. Int. Conf. Fission and Properties of Neutron-Rich Nuclei, edited by J.H. Hamilton and A.V. Ramayya (World Scientific, Singapore, 1998), p. 119. 8. A. V. Ramayya et al., Phys. Rev. Lett. 81, 81 (1998). 9. W. Greiner, Acta Physica Slovaca 49, 9 (1999). 10. V. A. Rubchenya and S. G. Yavshits, Z Phys. A329, 217 (1988).

PRODUCTION OF PHOTOFISSION FRAGMENTS AND STUDY OF THEIR NUCLEAR STRUCTURE YU.P.GANGRSKY+ AND YU.E.PENIONZHKEVICH Joint Institute for Nuclear Research, Dubna, Russia

Fission fragments of heavy nuclei (Z > 90) are neutron-rich isotopes of the elements from Zn (Z = 30) to Nd (Z = 60) with a neutron number of 45 - 90. The large neutron excess in the fission fragments under study (in some cases there are 10 - 15 more neutrons, than in the nuclei situated in the (3-stability valley) could lead to an essential change in their structure and radioactive decay characteristics. The abnormal ratio of protons and neutrons in such nuclei reflects on spin-orbit interactions and can lead to another order of nucleon shell filling. This change will manifest itself in the appearance of new magic numbers of protons or neutrons, new regions of deformation, of new islands of isomerism. A striking example of such phenomena is found in light neutronrich nuclei of 31Na and 32Mg at the magic number N = 20. Contrary to our knowledge about nuclear structure, these nuclei are strongly deformed [1,2]. The same situation could occur in the case of very neutron-rich isotopes of Cu and Zn near N = 50 as well as Ag and Cd near N = 82. The high energy of p-decay can result in the appearance of new, much rare, modes of radioactive decay. They are emission of a neutron pair or an aparticle after P-decay (|32n or pa). These decay modes are an important source of new information about nuclear structure. Thus the spectroscopic properties of fission fragments are very various. They are relatively poorly known, and researching them (measurement of the nuclear moments, the level spectra, the decay schemes e. c.) allows one to establish the way in which nuclear structure changes with the increasing neutron excess. A wide set of experimental devices should be used to obtain this information. Study of the nuclear structure of fission fragments is one of the main directions of the DRIBs project, being developed in the Flerov Laboratory of Nuclear Reactions JINR. The aim of this project is the production of intense beams of accelerated radioactive nuclei in a wide range of Z and A - from He to rare-earth elements. Light neutron-rich nuclei (up to Na) will be obtained in the

[email protected] 48

49

fragmentation of bombarding ions on the 4-meter isochronous cyclotron U400M, and nuclei of a medium mass number - in the fission of uranium on the electron accelerator microtron MT-25. Nuclei chosen for study will be massseparated and transported to be accelerated in another 4-meter isochronous, cyclotron U-400. Study of reactions induced by neutron-rich or neutron-deficient nuclei essentially enlarges information about their structure. It is impossible to judge some details of this structure from radioactive decay characteristics. A striking example is observation of an unusual wide space distribution of neutrons in some neutron-rich nuclei (neutron halo), first in n Li and then in others [3]. These data were obtained from measurement of cross-sections for different reactions (fusion, stripping, nucleon exchange) with neutron-rich nuclei. Such multidirection investigation of the properties of nuclei far from the P-stability valley definitely widens our knowledge about the changes in nuclear structure with the growing neutron excess and about the appearing of new phenomena. Reactions with neutron-rich nuclei can be also used for obtaining more neutron-rich nuclei. Really, the compound-nuclei formed in these reactions contain the neutron excess, and the evaporation of charged particles increases this excess. By this technique it is possible to get the most neutron-rich nuclei and to draw near the boundary of nucleon stability. The success of study of fission fragments structure, especially the most neutron-rich fragments, depends to a great degree on their yields. These are determined by their distribution on mass and atomic numbers (A and Z). But there is poor information about these parameters in photofission as compared with neutron fission. Worthy of mention are only investigations performed in Gent (Belgium) [4,5]. The main contribution to the photofission fragment yield is induced by the energy range of 10 - 15 MeV (it is the position of the giant dipole resonance in heavy nuclei). This energy range also determines the excitation energy of fissioning nuclei. At such excitation energy, the mass spectra of the photofission fragments are asymmetric with the mean mass numbers 99 and 139 for the light and heavy groups of fragments. To get more detailed information about the isotopic yields we measured the isotopic distributions of Kr and Xe fragments independent yields in the photofission of 238U and other heavy nuclei by bremsstrahlung with the boundary energy of 25 MeV [6]. The method of transporting fission fragments by a gas flow and stopping in a cryostat with liquid nitrogen was used. The independent yields of Kr (A = 89 - 93) and Xe (A = 137 - 143) fragments at the photofission of 232Th, 238U, 237Np and 244Pu were measured by

50

the method (Table 1). The dependences of these yields on the mass number of fission fragments are approximated by Gauss curves. Table 1. Independent yields of Kr and Xe fission fragments. Fragment 89

Kr 91 Kr 92 Kr 93 Kr

232

Xe Xe Xe 140 Xe 141 Xe 142 Xe 143 Xe 139

244

U(Y,f)

Fft 0,10(2) 0,62(5) 0,59(5) 0,15(2)

Yal 0,29(1) 1,00 0,80(2) 0,25(2)

Yfr 0,18(2) 0,60(5) 0,46(4) 0,15(2)

0,85(1) 1,00 0,85(7) 0,19(1) 0,09(1)

0,53(4) 0,63(5) 0,53(5) 0,12(1) 0,06(1)

0,27(3) 0,65(3) 1,00 0,94(7) 0,53(3) 0,26(2) 0,08(2)

0,16(2)[51 0,38(4) 0,59(5) 0,56(5) 0,31(3) 0,16(2) 0,05(1)

,37

138

238

Th(y,f)

YIA 0,15(2) 1,00 0,95(1) 0,25(1)

Pu(Y,f)

iid

1ft

0,84(4) 1,00 1,03(8) 0,73(4) 0,46(4) 0,24(4)

0,47(4) 0,56(5) 0,57(5) 0,41(4) 0,26(3) 0,14(2)

The parameters of these distributions for 232Th, 238U and 242Pu photofission nuclear reactions are tabulated in Table 2 (the magnitude of the A for 238U is in good agreement with that obtained in work [4,5]). For comparison the similar parameters are presented for the fission of 235U, 233U and 238 Uby the neutrons. A comparison of those parameters permits a number of conclusions to be drawn: 1.

2.

3.

The average mass number for Kr and Xe fragments shows a slight increase as the Z and A of the fissioning nucleus increases. It is close to the magnitude of the A for the fission of 238U induced by 14.7 MeV neutrons, but substantially larger than that for the fission of 235U and 233U induced by thermal neutrons. This points to the fact that an increase in the neutron excess of the fissioning nucleus results in an increase in the A (this excess can be characterized by the ratio (N-Z)/N, which is tabulate in Table 2). At the same time the distribution dispersion shows a noticeable increase as the atomic number of the fissioning nucleus increases (for example, it increases by a factor of 1.5 from 232Th to 244Pu). This means that the yields of the most neutron-rich fragments differ significantly. For example, the yield of 143Xe for the photofission of 244Pu is one order of magnitude larger than for the photofission of 232Th, this difference increasing rapidly as the number of neutrons in the fragment increases. The deviation of the measured yields from the Gaussian distribution as well as their even-odd distinctions is not great and lies within the limits of experimental error.

51 The Kr and Xe fragments produced in the fission of 232Th are complementary, i.e. they are produced in the_same fission event.^A. comparison of the sum of their average mass numbers ( A (Xe) = 138.9 and A (Kr) = 91.3) with the mass number of the fissioning nucleus (A = 232) allows the number of neutrons emitted from those fragments to be determined. This number proves to be equal to v = 1.8(2). With the fractional yields of 91Kr and 139Xe equal to 0.8 and 0.85 respectively, it is in good agreement with reported numbers of fission neutrons from fragments of a specified mass number and their excitation energy dependence. From those data it follows that in this region of fragment mass numbers the ratio of the numbers of neutrons from the light and heavy fragments is 1.3 and has only a weak dependence on excitation energy. This corresponds to v = 1.0 for Kr isotopes and v = 0.8 for Xe isotopes.

Table 2. Isotopic distribution parameters of Kr and Xe fission fragments. Reaction

(N-Z)/N

U(Y,f)

0,366 0,370

Pu(Y,f) 235 Ufy,f) 233 U(n,f) 235 U(n,f) 238 U(n,f)

0,373 0,357 0,352 0,364 0,379

232

Th(y,f)

238

244

A

a

A

91,3(2) 91,1(2)

1-1(1) 1,3(1)

138,9(2) 139,4(2) 138,9(3) 139,7(2) 137,4(4) 137,8(1) 138,4(1) 139,5(1)

89,4(3) 89,3(1) 90,1(1) 91,5(1)

References

Xe

Kr

1,3(1) 1,5(1) 1,5(1) 1,6(1)

CT

1,2(1) 1,5(1)

* * [51

1,8(2) 1,4(1) 1,5(1) 1,6(1) 1,8(2)

* [5] [11 [11 [11

"This work

The magnitudes of v obtained allow one to determine the fragment charge shift relative to the unchanged charge distribution Z0/A0, which corresponds to the ratio of the atomic to mass number of the fissioning nucleus. For a fragment of atomic number Z, the charge shift is expressed as:

AZ = ^ ( A + v ) - Z .

(1)

4> The thus obtained magnitudes of the AZ for the average mass numbers of Kr and Xe fragments produced in the photofission of 232Th, 238U and 244Pu are tabulated in Table 3. They prove to be close to the corresponding magnitudes of the AZ for the neutron-induced fission of heavy nuclei.

52

Using these measured yields, we can estimate more correctly the yields for another fission fragments. Examples of some interesting nuclei and their yields are presented in Table 4. One of these nuclei was studied. The rare mode decay, emission of delayed neutron pair (f52n) was observed at the photofission of 238U at the boundary energy of bremsstrahlung 10 MeV. It is, probably, 136Sb, the intensity of p2nbranch is about 1CT3.

Table 3. Charge shifts of Kr and Xe fission fragments relative unchanged charge distribution. 238

232

Zo/Ao

^PuM

U(Yi) 0,387

Th(Y,f) 0,388

Z

36

54

36

54

A

91,3(2)

138,9(2)

91,1(2)

139,4(2)

V

1,0

0,8

1,0

0,8

AZ

-0,19(8)

+0,20(8)

-0,36(9)

+0,25(8)

0,385 54 139,7(2) 0,8 +0,13(6)

Table 4. Exotic fission fragments. Fission fragment and its peculiarities 80 Zn - closed neutron shell W=50 81 Ge - closed neutron shell N=50 131 In - closed neutron shell N=S2 132 Sn - double magic nuclei Z=50, N=S2 134 Sn - 2 neutrons over closed shell 100 Zr - beginning of deformation region 104 Zr - strongly deformed nuclei 160 Sm - strongly deformed nuclei 136 Sb - delayed two-neutron emitter 140 J - delayed a-emitter

7,1/f

Y, 1/s (DRIBs)

IO"6

103

3-10

-5

io-3

3-10 6

108 3

3-10" 8-10"4 IO"2 5-10"4

3-10 8

IO"

10' IO5 106

IO' 6 IO-5

10' 10' 5-10 7

Thus photofission reactions of heavy nuclei are a very handy and promising way for the production of intense beams of the most neutron-rich nuclides. The small stopping power of the y-rays allows one to use thick targets. But the low excitation energy of the fissioning nuclei and of the fission fragments results in the small values of the evaporated neutrons. This compensates for the photofission cross sections being smaller as compared with the cross sections for fission induced by charged particles and neutrons. Moreover electron accelerators are simpler and much cheaper than charged particle accelerators and atomic reactors.

53

These examples show the wide field of activity in the study of the neutronrich nuclei structure, and the DRIBs project is the first step on this way. References 1. 2. 3. 4. 5. 6.

G. Huber, F. Touchard, S. Biittgenbach et. al., Phys. Rev. C18, 2342 (1978). D. Guillemaud-Mtieller, C. Detraz, M. Langevin et. al., Nucl. Phys. A426, 37 (1984). I. Tanihata, H. Hamagaki, O. Mashimoto et. al., Phys. Rev. Lett. 55, 2676 (1985). H. Jacobs, H. Tierens, D. De Frenne et. al., Phys. Rev. C21, 237 (1980). D. De Frenne, H. Tierens, B. Proot et. al., Phys. Rev. C26, 1356 (1982). Yu.P. Gangrsky, S.N. Dmitriev, V.I. Zhemenik et. al., Particles and Nuclei Letters 6, 5 (2000).

VARIATION OF C H A R G E D E N S I T Y I N F U S I O N REACTIONS

R. A. GHERGHESCU AND D. N. POENARU Horia Hulubei National Institute for Physics and Nuclear Engineering, RO-76900, Bucharest-Magurele, Romania, E-mail: [email protected] W. GREINER Institut fur Theoretische Physik der J. W. Goethe Universitdt, Robert Mayer Str. 8-10, Frankfurt am Main, Germany

Target and projectile charge densities are treated as free parameters in the calculation of the deformation energy. Different charge density paths are proposed as a result of geometrically related law of variation of the number of protons in the non-overlapped volumes of the two partners. As a result of minimization along the distance between the two centers fusion barriers differences reach up to 4 MeV for light nuclei and 8 MeV for superheavy synthesis.

1. Introduction Changes of the charge density in the superposed target and projectile configuration are equivalent with the atomic number changes in isobaric reactions. Such systems have been studied already for intermediate nuclei l. At low energy it is shown that the dependence on charge asymmetry could decide between fusion and deep-inelastic processes. Another result of the charge influence is the increase of the cross section with the charge product of the projectile and target for the same synthesized nucleus in subbarrier fusion reactions 2 . This work reveals the changes which occur within the overlapping configuration with the variation of the projectile and target charge density. It will be shown that the fusion barrier is more sensitive to charge density variations in the last part of the reaction, close to the total overlapping configuration. There is a relation between the magnitude of the volume and the shape of the non-overlapped part of the projectile on one hand and the charge density variation on the other hand. Consequently the macroscopic and microscopic energies are affected.

54

55

2. Geometry related charge density path We consider the spheroidal shape (ai, &i, zs) with a\, 61 semiaxes and zs separation plane as having the same charge density as it were a whole nucleus {Alx,Zlx), i. e. the charge density of the shape is determined by its geometric correspondence to (A l x , Zix); thus Zyx is the atomic number if the heavy fragment is a complete spheroid with (ai, 61) semiaxes. Variation of atomic to mass numbers Z\xjA\x must also comply to: , Z\x Mx

Z0

Z\x

Z\

AQ

A\X

AI

where ZQ,A0 and Z\, A\ are the final and initial values of the target nucleus. A variation law fulfilling these conditions could be: Z\x Alx

1 A0 - A1

(A^-A^^

+ A0

iAo-A^)^

(2)

A\

For A\x — A0 we have Z\x = Z0 and for Aix = Ai results Z\x — Z\. We emphasize that Aix, Z±x, A^x and Zix are not the real mass and atomic numbers, but the ones which correspond to whole non-intersected nuclei having the same semiaxes as the real intersected ones. For the same fusion reaction, an spheroidal projectile can change its shape parameters (02,62) in different ways along the overlapping region: it can preserve its initial 620 semiaxis or 62 can become larger up to the limit where 62 = bo, the semiaxis of the compound nucleus. Between these two limits, 62 can take any values, provided that the volume V2 does not become larger then its initial value. Consequently, the corresponding intermediary atomic number Z2j changes according to the above considerations. In Fig. 1, upper part, the variation of Zix with the normalized distance between centers Rn — (R — Rf)/(Rt — Rf) is presented, where Rf and Rt are the final and the tangent configuration distance between centers. Different curves correspond to different laws of variation for the small semiaxis of real intermediary nucleus (A 2 j, Z 2 j). The plots refer to a superheavy nucleus synthesis: 5 4 Cr+ 2 3 8 U -¥ 292 116. The middle plot refers to the real intermediary atomic number variation Z^i with Rn. Variations in the last part of the fusion process ( Rn < 0.4) are due to volume differences. The smallest value for the V-z volume is for 62 = &2o(292H6) at the same Rn, the situation where the projectile preserves its initial semiaxis. The lower plot represents the proton density variation. The larger the volume, the lower the charge density, as can be seen. The highest proton density corresponds

56 120

^=Ro(2Kiif) 132=0.9 . R 0 Q 1 6 ) 1)2=0.8 ;R,(Z9Z116) •••• b2=b2„rcr)

100 & 80

N

60 40

iV

.T T — 20 0.0 0.2 0.4 0.6 0.8 1.0 60 50

^.Rol^HJ) bj-ao-RgPHle) — b2=o.s -Kfoie) • • • • b2=b2„( Cr)

•

40

N '30 20 \i 10

¥
i=AlA^ ' , where Ri=r0Ai' , one obtains the shape dependence of the frequencies: m 0 < = (at/bi)2/3 • m^li = ( a ^ ) 2 / 3 • 54.5/i?? m0w2zi = (bi/atf/3 • mowgi = ( 6 , / a i ) 4 / 3 • 54.5/i??

{

°>

The influence of the charge density on the potential manifests through the above equations. In such a way the variation of the charge density is expressed by the variation of the four frequencies via the spheroid semiaxes. The single particle energy levels are used to calculate the shell corrections by the Strutinsky method. The macroscopic energy Emacro is computed as the sum of the Coulomb Ec 3 and the nuclear Yukawa-plus-exponential term Ey 4- For two intersected nuclei system shape, the Coulomb energy can be written as 5 : 2TT

E

C = Y (fiiFci

+ p\2Fci + 2pelpe2Fcl2)

(6)

where Fa are shape dependent expressions. The Y + E energy Ey is 5 : EY = T-1[csiFEY1

+ cs2FEY2 + 2{cslcs2fl2FEY12]

(7)

A-KTQ

For the intermediate surface coefficients csu and c s2 i, with the general expression: csji = o s ( l - Kl2i) we use An, Zu from Eq. 2, with Ijt = (Nji — Zjj)/Aji

(8) where j=l, 2.

58

The total macroscopic deformation energy is given by: Emacro = (EC ~ E{°]) + (EY - E{°})

(9)

4. Results and discussion Results are presented for the light nuclei fusion reaction 36 Ar+ 6 6 Fe —^102Ru. All the curves are drawn after minimization against the %-parameter. The figures show only the variation as a function of &2- 36 Ar is a spherical nucleus, with the initial radius i? 20 ( 36 Ar)=3.3 fm, 66 Fe has an spheroidal deformation of j3fFe) =0.027 and 102 Ru is deformed with (3^°2Ru)=0.189. The projectile 36 Ar maintains its spherical shape for the four possible paths. During the overlapping process, the 36 Ar radius becomes R? if the projectile preserves its spherical shape. The i? 2 = &o(102R-u) curves correspond to the situation when the projectile ends the fusion process with its radius equal with the small semiaxis of 102 Ru. Differences are more significant in the last part of the fusion process. Microscopic influence and total deformation energy is depicted in Fig. 2 for 102 Ru synthesis and four charge density variation paths. Rn takes values far beyond the touching distance {Rn > 1), in order to comprise the whole cold fusion barrier. The variation of Esheii (upper plot) nears 2 MeV and is more pronounced in the last part of the fusion process, as (R — Rf)/(Rt — Rf) approaches zero. There is a mixed behaviour of the four curves. The lowest values are successively reached by i?2=&o(102R.u) at the beginning of the process, then by i? 2 =0.8& 0 ( 102 Ru) followed by 0.9&0(102Ru) curve in the last part. The total sum Eb = Emacro + Esheu is shown in the lower plot of Fig. 2. Differences of about 4 MeV are visible when Rn approaches zero, and the situation when the projectile enlarge its dimensions as to seize synthesized nucleus size and shape are favoured (R2 = 6 0 ( 102 Ru)). 5. Conclusion Charge density influence on cold fusion barriers manifests itself through geometrical parameters characterizing the target and projectile nuclei within the overlapping region. Changes of semiaxis ratios and magnitude triggers a modification in proton density over the non-overlapped volume of the projectile. As a free coordinate, charge density can lower the cold fusion deformation energy, as a result of minimization against 62 and \i • This

59

•••

R 2 -b„( 10z Ru) R2=0.9.b0( Ru) R2-O.S .bnl'^Ru) Rz-R^'Ar)

(R-Rf)/(Rt-Rf) Figure 2. Shell correction Es/ieu and fusion barrier Et, for the four charge density paths as in Fig. 1 for the synthesis of 102Ru. kind of influence is especially active in the last part of the fusion process, when the projectile is already half embedded in the target (Rn

Experimental Yield(M|l,M1 )

-J

••* __l i iA ki . _J 20 M„

500

1000

E* (MeV)

Figure 3. Method to determine the excitation energy from the measured multiplicities MLCP of light charge particles LCP and neutrons M„. The color code of the top middle panel is given in MeV.

The wider range of target nuclei covered with the present data, however, gives an astonishing result, that the ratio oCp-pre/oiNc-p of cross sections of PE composite-particles (cp) to INC protons depends only weakly on the target mass Ay [7]. The coalescence model discussed in ref. [6] would, instead, predict a stronger decrease of acp.pre/orNc-p with decreasing AT. For deuterons, for instance, the probability that an INC proton coalesce with an INC neutron should depend on the number of INC neutrons which can be shown [7] to be proportional to RT*Nj/AT, where RT and NT are the nuclear radius and the number of neutrons in the target nucleus, respectively. The present systematic data indicates that oCp-pre/o"iNc-p~NTMT- and not acp-pre/oiNc-p~KT*AV^T-

79 4.

Excitation energy distributions

From the measured multiplicities of evaporated light charged particles MLCP and neutrons Mn it is possible to deduce the excitation energy for each event [8]. This is shown schematically in Fig. 3. From a simulation calculation the matrix of the excitation energy E*(MB, M L C P) (middle top panel) is obtained. This correlation is folded with the experimental efficiencies and is then employed to look up the excitation energy E* for the measured M„ and MhCP. In Fig. 4 the thus deduced excitation energy distributions for the reactions 0.8, 1.2, and 2.5 GeV are compared with calculations with the ENCL [9] and LAFJET [10] codes. This figure shows that the INCL code reproduces quite well Distribution of Excitation-Energy E at p(GeV)+Au

0.8 GeV

1.2 GeV

2.5 GeV

I

E (MeV)

p(GeV) + Fe

p(GeV) + Au

Ep (GeV) Figure 4. Excitation energy distributions in the reactions 0.8, 1.2, 2.5 GeV p+Au, the lower panels displays the heating efficiencies of spallation reactions of Fe and Au nuclei as a function of proton energy.

80

the deduced experimental excitation energy distributions while the LAHET code predicts at higher bombarding energies considerable larger E* than experimentally observed. An interesting question one might ask is: how efficient is a spallation reaction in heating nuclei? This question is answered in the right panel of Fig. 4 where the ratio <E*>IEV of the mean value of E* and the incident bombarding energy is shown as a function of the proton energy Ep. The experimental data <E*>/EV for p+Au decrease rapidly from 21% at 0.8 GeV to only about 12% at 2.5 GeV, while <E*> would still increase slowly from 170 to 290 MeV. The INCL-prediction follows this decrease very closely, as does the calculation with the model of Golubeva et al. [11]. The LAHET-simulation, however, provides good agreement with the experiment only at low incident energy, while at high Ev Fig. 4 now reveals the full extend, i.e. a factor of 2, of the discrepancy between the INC models. 5.

Summary

It was demonstrated in this talk that detailed, exclusive, and systematic data is needed for the validation of and for identifying specific deficiencies in the modeling of the three stages of a spallation reaction: INC, pre-equilibrium, and evaporation. This was particularly demonstrated by the comparison of experimentally deduced and calculated excitation energy distributions. Similarly the deficiency of the LAHET code in describing the production cross sections of hydrogen and helium could be traced back [12,13] to the temperature dependent Coulomb barriers employed in this code. No satisfactory description of the pre-equilibrium cluster emission over a wide range of target nuclei is presently available. Though not directly mentioned in this short written contribution the systematic neutron production and in particular neutron multiplicities measured in thick targets of W, Hg, and W [3, 4] can be reasonably well described [5] by most of the models, including those which have deficiencies in describing the charged particle data. This latter finding is mainly due to an compensation effect [13, 14]. If in the first interaction less (more) excitation energy is transferred during the intra nuclear cascade to a nucleus more (less) energetic nucleons are emitted. In the secondary and tertiary reactions of the inter nuclear cascade these nucleons will then produce also more (less) neutrons. The obtained data was also exploited to investigate the lifetime of the window. For the same amount of neutron production in a typical target of a spallation neutron source the proton beam induced radiation damage in an Fe window could be shown to decrease almost linearly with the proton energy [15]. For heavier materials such as Ta a similar decrease of the radiation damage is found only for energies above about 3 GeV. Finally

81

preliminary results of measured fission probabilities in 2.5 GeV proton induced fission of U showed a very similar dependence on E*, MLCp, and Mn as in antiproton induced fission as investigated by the PS208 collaboration [16,17], References 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17.

U. Jahnke et al, Nucl. Instr. andMeth. A508, 295 (2003). C.-M. Herbach et al, Nucl. Instr. andMeth. A508, 315 (2003). A. Letourneau et al, Nucl. Instr. Meth. B170, 299 (2000). D. Hilscher et al, Nucl. Instr. Meth. A414, 100 (1998). D. Filges et al., Eur. Phys. J. A l l , 467 (2001). A. Letourneau et al, Nucl. Phys. A712, 133 (2002). C.-M. Herbach et al., to be published. F. Goldenbaum etal, Phys. Rev. Lett. 77, 1230 (1996). J. Cugnon et al, Nucl. Phys. A620, 475 (1997). R.E. Prael, H. Lichtenstein, Rep. LA-UR-S9-30U, (1989). Ye.S. Golubeva et al, Nucl. Phys. A483, 539 (1988). M. Enke et al, Nucl. Phys. A657, 317 (1999). C.-M. Herbach et al., J. of Nucl. Science and Tech., Suppl. 2, 252 (2002). L. Pienkowski etal, Phys. Rev. C56, 1909 (1997). D. Hilscher et al. J. Nucl. Mater. 296, 83 (2001). U. Jahnke et al, Phys. Rev. Lett. 83, 4959 (1999). B. Lott et al, Phys. Rev. C63, 034616 (2001)

EVIDENCE FOR TRANSIENT EFFECTS IN FISSION B. JURADO*, K.-H. SCHMIDT, C. SCHMTTT, A. KELIC GSI, Planckstrafie

1, D-64291 Darmstadt,

Germany

J. BENLLIURE Facultad de Fisica, Univ. de Santiago de Compostela, Spain

E-15706 S. de

Compostela,

A. R. JUNGHANS Forschungszentrum

Rossendorf, Postfach 510119, 01314 Dresden,

Germany

The aim of this work is to experimentally investigate transient effects in fission. In order to simplify the theoretical description, we have chosen peripheral heavy-ion collisions at relativistic energies to reduce the side effects and to produce highly excited fissioning systems with well-defined initial properties. Thanks to an experimental setup specially conceived for fission studies in inverse kinematics, we could determine two new observables very sensitive to transient effects in fission. Quantitative values for transient effects are deduced from the comparison of these observables with a nuclear-reaction code where dissipation effects in fission are modeled in a highly realistic way.

1.

Introduction

The deexcitation process of a highly excited heavy nucleus requires a dynamical description that takes into account the time the system needs to populate the available deformation space and reach equilibrium. A dynamical description of the deexcitation process in terms of a purely microscopic theory is not possible to the present day due to the large number of degrees of freedom involved. For this reason, most of the current theoretical models are transport theories that try to portray the process using a small number of variables. In these theories one distinguishes between collective and intrinsic degrees of freedom, and the latter are not considered in detail but in some average sense as a heat bath. The collective degrees of freedom of the nucleus correspond to the coordinate motion of part or all the nucleons, e.g. vibrations and rotations. The intrinsic degrees of freedom are the individual states of the nucleons. The collective degrees of freedom and the heat bath are coupled, that is, excitation energy can be transferred between them. The process of transfer of energy between the collective degrees of freedom and the heat bath is denominated * Present address: GANIL, Blvd. H. Becquerel, B.P. 5027, 14076 Caen, France 82

83

dissipation. Dissipation is quantified by the reduced dissipation strength (5, which measures the relative rate with which the excitation energy is transferred between the collective and intrinsic degrees of freedom. In the frame of a transport theory, fission is the result of the evolution of the fission collective coordinates under the interaction with the heat bath and an external driving force given by the available phase space. This evolution can be obtained by solving the Langevin equation or its integral form, the Fokker-Planck equation (FPE). An important parameter in these two equations of motion is the dissipation strength /3. In spite of intensive theoretical and experimental studies, the strength of /? and its variation with deformation and temperature are still subject of intense debate [1]. In 1940 Kramers [2] developed the first transport theory to describe nuclear fission and found the stationary solution of the FPE. The idea of Kramers was recovered forty years later by Grange et al. [3], who theoretically investigated the influence of dissipation on the fission time scale by solving numerically the FPE. Their results showed that it takes a transient time z,rans until the current over the saddle point reaches its stationary value. The transient time originates from the time needed by the probability distribution of the particle to spread out in deformation space. Grange et al. [3] defined r,rans as the time that the fission width r/J) needs to reach 90% of its asymptotic value. A full dynamical calculation of the fission process should consider as well the emission particles. This can be done allowing for evaporation during the dynamical evolution of the system when solving the multidimensional FPE or Langevin equation. Another procedure widely used to study fission dynamics consists on introducing a time-dependent fission decay-width .T/0 in an evaporation code. Such a treatment is equivalent to solving the above mentioned equations of motion, under the condition that the time-dependent fission decay width /}(?) is obtained by solving the Fokker-Planck or Langevin equation at each evaporation step. Unfortunately, these three procedures require a very high computational effort. However, in an evaporation code one can get around this problem by using a suitable analytically calculable expression for r/jt). This allows incorporating realistic features of fission dynamics in complex model calculations for technical applications, e.g. the nuclide production in secondary-beam facilities, in spallation-neutron sources and in shielding calculations. 2.

Experiment

The experimental manifestation of transient effects is subject of controversy nowadays [4]. However, we will show that the experimental observation of

84

transient effects in fission is possible provided the appropriate reaction mechanism is used and adequate observables are considered. To observe transient effects a reaction mechanism is required that leads to excited nuclei with small deformation, so that the we can observe the equilibration of the probability distribution in deformation space. In addition, the reaction mechanism should lead to high enough excitation energies for the particle decay time to be smaller than the transient time. In this case, transient effects show up in a drastic way, since the system is forced to emit particles because fission is suppressed. These initial characteristics of the fissioning nucleus can be obtained by applying a projectile-fragmentation reaction, i.e. a very peripheral nuclear collision with relativistic heavy ions. Besides, this reaction mechanism induces a very small angular momentum 1 < 20h [5], which avoids additional influence on the fission process. Relativistic heavy-ion collisions can be investigated at GSI where a highly intense 238U beam is available. Concerning the observables, the analysis of particle multiplicities does not allow to explore the deformation range from the ground state to the saddle point independently. Total fission or evaporation-residue cross sections are the most used observables to investigate dissipation at low deformation. However, they are not sufficient to determine transient effects in an unambiguous way. To clearly define the characteristics of transient effects we need observables that allow selecting the fission events according to the excitation energy. This new type of observables could be measured thanks to an experimental set-up specially conceived for fission studies in inverse kinematics that was developed at GSI. This set-up is schematically illustrated in figure 1. When the projectile fragment fissions, the two fission fragments are focused in forward direction and detected simultaneously in a double ionization chamber that delivers a very accurate measurement of their nuclear charges. The velocity dependence of the energy-loss signals is corrected by means of the time of flight. The efficiency for fission of the set-up is of the order of 97%. The charge identification of both fission fragments enabled us to determine two new observables: the partial fission cross sections, that is, the cross section as a function of the fissioning element, and the charge distributions of the fission fragments that result from a given fissioning nucleus. In the next lines we will qualitatively explain why these observables are adequate to investigate transient effects on the way to the saddle point. The sum charge of the fission fragments is a very significative quantity, because it is directly related to the charge of the fissioning nucleus. Besides, the charge of the fissioning element goes linearly with the charge of the prefragment and hence, it gives an indication of the centrality of the collision. Low values of Zy+Z2 imply small impact parameters and large excitation energies induced by

85

the fragmentation process. Therefore, for the lightest fissioning nuclei (lowest values of Z/+Z2) transient effects will lead to a considerable reduction of the fission probability. According to empirical systematics, the width of the mass distribution of the fission fragments is a measure of the saddle-point temperature. This experimental result has been corroborated by twodimensional Langevin calculations [6]. Due to the strong correlation between the mass distribution of the fission fragments and the charge distribution, the same relation holds for the width of the charge distribution and the temperature at saddle. Thus, for the lower values of Z!+Z2 where the initial excitation energy is large and fission is suppressed with respect to particle evaporation, the nucleus will evaporate particles while it deforms, and the temperature at saddle will be smaller than the initial temperature. Consequently, transient effects will cause a narrowing of the corresponding charge distributions. - T0F,i2 s">7m Scinttttstor I Ionization chambers

/

AE,12

\

Beam

Figure 1. Experimental set-up for fission studies in inverse kinematics.

3.

Results

To deduce quantitative results on transient effects, the experimental observables introduced in the previous section need to be compared with a nuclear-reaction code. The code we use is an extended version of the abrasion-ablation MonteCarlo code ABRABLA [7]; it consists of three stages. In the first stage the characteristics of the projectile residue after the fragmentation are described according to the geometrical abrasion model. The second stage accounts for the simultaneous emission of nucleons and clusters (simultaneous break-up) that takes place due to thermal instabilities when the temperature of the projectile spectator exceeds 5 MeV [8]. After the break-up, the ablation stage models the sequential deexcitation of the system through an evaporation cascade. A reliable study of transient effects requires a realistic description of the timedependent fission decay-width. For this reason we have implemented in the third stage of ABRABLA a description of r/j) that is based on an approximate

86

solution of the FPE [9]. In table 1 the experimental total nuclear fission cross section of the reaction of 238U at 1 A GeV on lead obtained with the previous set-up is compared with the values obtained from several ABRABLA calculations performed with different shapes of the time-dependent fission width and different values of /3. Apart from a calculation performed with the new analytical approximation of [9], table 1 includes the two most widely used approximations for the time-dependence of the fission width. Compared to our analytical approximation these two approximations are rather crude. The calculation represented in the third row of table 1 uses a step function that sets in at a time equal to the transient time. This approximation underestimates the fission width during the initial time. The approximation used in the fourth row is an exponential-like in-growth function. This approximation overestimates the initial values of the fission width and starts with a very steep slope. The important difference between the initial behaviour of both descriptions leads to very different pictures of the relaxation process. As expected, the calculation without dynamical effects of the second row of table 1 overestimates the cross section. However, the other three approximations can reproduce the total fission cross sections although with different values of the dissipation strength. These results demonstrate that total fission cross sections allow to identify an overall reduction of the fission probability but are not sensitive to the shape of f/J). Table 1. Total nuclear fission cross section of comparison with different model calculations. Experiment [1]

U (1 A GeV) on Pb in

r/f) =step function, P = 2 x l 0 2 1 s"1 r / f ) ~ l-exp(-2.3t/r,„„), 0 = 4 x l 0 2 1 s"l

af""" = 2.16 ± 0.14 b a f nucl =3.33b afnud = 2.00 b a,nucl = 2.04 b

7 X 0 = FPE [9], P = 2 x l 0 2 1 s"1

Ofnucl = 2.09 b

No dissipation

Figure 2 represents the partial fission cross sections (figure 2a) and the widths of the charge distribution (figure 2b) for different fissioning nuclei measured in the reaction of 238U (1 A GeV) on (CH2)„. The experimental data (black dots) are compared with the same approximations for r/t) as in table 1. In the case of figure 2a) the three calculations agree quite well with each other and with the experimental data for the highest values of Zj+Z2, and start to differ for the lowest values of Z1+Z2. However, the deviations are not enough to decide which function r/t) gives the best description of the measured data. On the other side, figure 2b) shows a significant disagreement between the calculation done with the exponential-like description and the measured data. This disagreement suggests that the initial overestimation of the fission width

87

implied by the exponential-like approximation yields too large excitation energies at saddle. In figure 3 the same two observables of figure 2 are compared with a calculation that includes no dissipation (dashed line), with a calculation considering a constant fission decay-width equal to Kramers result (thick dashed

;

1

1

1

70

n

80

85

i„

90

Figure 2. Partial fission cross sections a) and partial widths of the charge distributions b) for the reaction of 238 U (1 A GeV) on (CH 2 ) n in comparison with several calculations. The dashed line is the result of using the exponential-like function and fi = 4-10 21 s"1, the dotted line is done with the step function and ft = 2-10 21 s"1, and the full line with t h e / # ) of [9] and )3= 2 1 0 2 1 s"1.

line), and with several calculations that include transient effects according to the fission width of [9] with different values of /?. As expected, both observables are visibly overrated by the transition-state model, confirming their sensitivity to dissipation. The calculation performed with the constant decay width of Kramers overestimates the observables as well, in contradiction with ref. [4]. For the two observables, the best description is given by the full line that corresponds to/3 = 2-1021s"' (full line). Such value of (3 corresponds to the critical damping and thus to the shortest transient time T,rtms~ (1.7±0.4)-10~21 s,.

n

es m Z, • Z,

9Q

Figure 3. The same observables as in figure 2 in comparison with several calculations. The dotted line and the dashed-dotted lines are calculations done using the function of [9] with/3= 0.5-10 21 s"1 and/3 = 5 1 0 2 1 s"1, respectively. For the rest of the curves see text.

88

4.

Conclusion

We have considered a reaction mechanism and have introduced new observables that allow the observation of transient effects in fission. We have developed an analytical approximation for the fission width that allows including realistic transient effects in an evaporation code without increasing the computing time. The comparison of the experimental observables with model calculations has lead to a value for rlrans ~ (1.7±0.4)10 21 s indicating that, for the range of temperatures considered, the motion up to the saddle point is critically damped.

References 1. 2. 3. 4. 5. 6. 7. 8. 9.

B. Jurado, PhD Thesis, Univ. Santiago de Compostela, Spain (2002). H. A. Kramers, Physika VII4, 284 (1940). P. Grange, et al., Phys. Rev. C27, 2063 (1983). H. Hofmann, et al., Phys. Rev. Lett. 90, 132701 (2003). M. de Jong, et al., Nucl. Phys. A613, 435 (1997). D. V. Vanin, et al., Phys. Rev. C59, 2114 (1999). J.-J. Gaimard, et al., Nucl. Phys. A531, 709 (1991). K.-H. Schmidt, et al., Nucl. Phys. A710, 157 (2002). B. Jurado, et al., Phys. Lett. B553, 186 (2003).

T R A P S FOR FISSION P R O D U C T IONS AT IGISOL

S. KOPECKY, T. ERONEN, U. HAGER, J. HAKALA, J. HUIKARI, A. JOKINEN, V. S. KOLHINEN, A. NIEMINEN, H. PENTTILA, S. RINTA-ANTILA, J. SZERYPO AND J. AYSTO Department of Physics, P.O. Box 35 (YFL), FIN-40014 University of Jyvaskyla, Finland

One of the main focus of the work at the K-130 cyclotron in Jyvaskyla has been the investigation of properties of neutron-rich nuclei, which are produced in fission reactions. As the production yields of nuclei far off the /3-stability become increasingly smaller new, more efficient techniques for producing and selecting these nuclei have to be employed. Therefore a triple-trap setup has been installed at the IGISOL facility in Jyvaskyla. This new facility not only improves the experimental condition for decay-spectroscopy and collinear laser spectroscopy it also enables mass-measurements as an additional tool for studying neutron-rich nuclei.

1. Introduction A variety of experimental methods are employed for studying the nuclear structure of neutron-rich nuclei. These investigations are an important first step for understanding the structure effects - and possibly new phenomena - for nuclei along the neutron drip-line. For producing these nuclei here in Jyvaskyla proton induced fission of 238 U and IGISOL - ion guide separator on-line - are employed. In the IGISOL method the ions are stopped and thermalized in a gas-cell1, and a fraction of these ions will survive as singly charged ions. By a differential pumping scheme and electrostatic fields the ions are extracted out of the stopping cell and are accelerated to typically 40 keV. Due to the chemical insensitivity of this technique and the short evacuation time of the gas cell, very short lived nuclei as well as all refractory elements are available for experiments. It has been determined that the yield for 112 Rh is approximately 1 0 - 3 - at a proton beam with 30 MeV and a beam intensity of 10 fiA this corresponds to approximately 10 5 ions/s. Two properties of IGISOL make further ion manipulation very difficult. IGISOL provides a quasi-continuous ion beam and the energy spread of the ion beam is rather large, it can be as high as 100 eV. To overcome these

89

90 problems a cooler trap has been designed and build 2 . The ion-cooler buncher at IGISOL is working on the principle of a segmented linear Paul trap, i.e. the confinement both in radial and axial direction is accomplished by electric fields. The device itself is placed on a high-voltage platform. This platform is adjusted that the ions enter the cooler with an energy of approximately 100 eV. The RFQ is filled with He buffer gas with a pressure up to 0.1 mbar. While passing through the cooler the ions loose their radial and axial energy by collisions with the buffer gas until they are finally stopped along the center of the trap inside the potential well. Finally they can be extracted by applying a suitable extraction potential. The extracted ion bunches can have a duration of 2-3 /us and an energy spread of less than 1 eV. The transmission through this device is typically in the order of 60 -70 %. This improved beam condition do not only allow the coupling of a Penning trap to the IGISOL facility it also provide strongly improved condition for collinear-laser spectroscopy3, enabling investigations of ions with yields less than 100 ions/s.

2. Penning-trap The beam extracted from the RFQ is injected into a Penning-trap system, which is situated at the same high-voltage platform as the cooler. In a Penning trap the confinement of the ions is accomplished by a combination of electric and magnetic fields. JYFLTRAP uses the concept of an open-end Penning trap, where the electric quadrupole field, necessary for confining the ions in axial direction, is produced by cylindrical electrodes 4 . The magnetic field at JYFLTRAP is provided by a 7 T super-conducting magnet. Two homogeneous regions are located 10 cm up- and downstream of the center of the magnet. The first region with a homogeneity better than 1 0 - 6 is used for the purification trap, whereas the second with a homogeneity of 1 0 - 7 is used for the precision trap. Between these two traps is a diaphragm with a length of approximately 5 cm and an opening of 2 mm, allowing for maintaining a pressure difference between the two traps and for extracting of the ions that are located close to the center axis of the first trap. More details about the construction of the Penning trap can be found elsewhere 5,6 . The transmission through the trap is 30%, and the capturing efficiency in the first trap is 60%, therefore the total efficiency of this device is approximately 20%. It also could be demonstrated that isobarically purified beam

91 can be extracted and implanted into a tape, therefore enabling /3-decay spectroscopy for nuclei with a weak production channel. For creating isobarically pure beam the mass selective buffer gas cooling technique 7 is employed in the purification trap. In this technique ions are manipulated by buffer gas pressure and azimuthally dipole and quadrupole fields. By choosing suitable combinations of buffer gas pressure, excitation duration and excitation amplitude it can be achieved that ions with a selected charge-over-mass ratio will be accumulated along the center axes of the trap. All the other ions will be located at a distance from the center. By extracting the ions through a diaphragm, an isobaric pure beam can be created. It is possible to find trapping schemes varying in total cycle time and in mass resolving power R = -^-. At JYFLTRAP aim was to find trapping schemes with mass resolving power better than 11=15000, a value that should allow for isobaric separation for a wide variety of nuclei. It could be established that this goal could be accomplished with total cycle times as short as 90 ms. In the reaction 58 Ni(p,n) 58 Cu within a total cycle time of 450 ms a value of R=150000 could be established. It could be concluded that such conditions allow for direct mass measurements with accuracies better than 50 keV. For the precision trap the time-of-flight method is employed. This method exploits the effect that ions with different radial energy inside the magnetic field will have a different time-of-flight to a detector position outside the magnetic field, this effect is caused by the conversion of radial energy into axial energy when the ions leave the magnetic field. By selectively increasing the cyclotron motion of ions inside the trap it will be possible to determine their cyclotron frequency and therefore their masses precisely. The way to achieve this selection is as follows. At first are the already isobarically purified ions carefully moved from the purification trap into the precision trap. The trap bottom of the second trap is 3 V lower than the purification trap. To avoid further, unnecessary increase of the axial energy - too high axial energies jeopardize the possibility of observing the time-of-flight effect - the capture time of the ions in the second trap has to be chosen very carefully. This can be done by observing the time-of-flight of trapped ions in the second trap and by adjusting the closing time. After capturing of the ions a azimuthally dipole-field is applied for 15 ms, for introducing some magnetron motion - a motion which has only a very small energy content. This is followed by an azimuthally quadrupole excitation. Such an applied RF field will couple the magnetron and cyclotron motion of the ions to each other. A periodic transfer from an initial magnetron

92 118-,

40Ar 116114112g» 1 1 0 -

«*-

O

0) 108-

E i-

106104102 2688790

2688800

2688810

2688820

~1 2688830

Frequency [Hz] Figure 1. Frequency scan for precision trap

to cyclotron and back to magnetron motion will occur. As the cyclotron frequency is approximately 104 times larger, the difference in their radial energy is large. By choosing the excitation duration and excitation amplitude accordingly, a full conversion of magnetron-motion into cyclotron motion can be achieved for the ion species which cyclotron frequency matches the applied RF-frequency. By measuring the time-of-flight as a function of the applied RF-frequency the precise cyclotron frequency of the ion species inside the trap can be determined. The width of this frequency distribution will be inverse proportional to the duration of the excitation. In Fig. 1 a frequency scan for Ar-40 is shown. This measurement was done with a excitation amplitude of 50 mV and excitation duration of 200 ms, the line shape of the experimental data can be well reproduced by calculations. With such a resolution it is expected that mass measurements with accuracies of a few keV can be achieved. At the final stage it is expected that measurements with accuracies of 1 keV - or even better - will be achievable.

93 1 — i — | — i — | — i — | — i

1—i—|—i—|-

600-

i I

Zirconium 400-

5? 03

;*, 200-

i i

UJ

< 2

0-

§

§

;

?

-200-

-400 ">

96

1

"""

97

i—•—r

98

99

T—•—i—•—i—•—r

100

101

102

103

-i

1

r-

104

Figure 2. Preliminary results for experimental determined Zr-masses compared to literature values 8

3. Mass measurements The aim with JYFLTRAP is to do mass measurements in the near future. As two traps are available, the trap suitable for the required accuracy can be chosen. Studies of e.g. the Q-values of super-allowed /?-decay need accuracies better than 1 keV, an accuracy that hopefully can be achieved in the precision trap in the future. On the other hand studies on global and local shell-effects and deformation on the mass surface only require accuracies between 10-100 keV, accuracies that can be achieved by using the purification trap alone. Neutron-rich Zirconium presents a case for possible studies in the purification trap. The occurrence of a shape transition between neutron numbers 56 and 60 is well established, but so far no reliable direct mass measurements have been performed for these nuclei. Zirconium is well available at IGISOL, with intensities ranging from 200 to 4000 ions/s. By using

94

the ion manipulation of the RFQ and the Penning trap, it was possible to measure the masses ranging from Zr-96 to Zr-104. The dominant source of uncertainty of these measurements are the statistical uncertainty and the uncertainty introduced by variation of the beam intensity, the combined uncertainty is typically 50 keV. It was estimated that systematic uncertainties - as caused by imperfection of the electric quadrupole field - are of minor concern at the present level of accuracy. In Fig. 2 a comparison of these preliminary experimental results with the mass values from the recent mass evaluation 8 is shown. It becomes clear, that for the isotopes with well established masses the present results agree nicely with the data from the literature. In case of all the neutron rich isotopes, all of which have only been determined by /3-endpoint measurements so far, a clear difference between the new values and the literature data becomes visible, emphasizing the importance of direct mass measurements. 4. S u m m a r y At the IGISOL facility of the University of Jyvaskyla a triple-trap setup has been designed and constructed for ion beam manipulation. This new facility opens the possibility of investigation the properties of neutron-rich nuclei with weak production channels by means of decay spectroscopy, collinear laser spectroscopy and direct mass measurements. Acknowledgments This work was supported by the Academy of Finland under the Centre of Excellence Program 2000-2005 (project no. 44875) and by the European Union within the NIPNET RTD project under the contract no. HPRI-CT2001-50034. References J. Aysto, Nucl. Phys. A693, 477 (2001). A. Nieminen, et al., Nucl. Instrum. Methods A469, 244 (2001). A. Nieminen, et al., Phys. Rev. Lett. 88, 094801 (2002). H. Raimbault-Hartmann, et al., Nucl. Instrum. Methods B126, 378 (1997). V.S. Kolhinen, et al., Nucl. Instrum. Methods B204, 502 (2003). Veli Kolhinen, Ph.D Thesis, University of Jyvaskyla, 2003. G. Savard, et al., Phys. Lett. A158, 242 (1991). G. Audi, et al., Nucl. Phys. A624, 1 (1997).

TRIPLE-HUMPED FISSION BARRIER AND CLUSTERIZATION IN THE ACTINIDE REGION

A. KRASZNAHORKAY, M. CSATLOS, J. GULYAs, M. HUNYADI, A. KRASZNAHORKAY JR. AND Z. MATE Inst, of Nucl. Res. of the Hung. Acad, of Sci., H-4001 Debrecen, P.O. Box 51, Hungary, E-mail: [email protected] P.G. THIROLF, D. HABS, Y. EISERMANN, G. GRAW, R. HERTENBERGER, H.J. MAIER, O. SCHAILE AND H.F. WIRTH Sektion Physik, Universitdt Miinchen, D-85748 Garching,

Germany

T. FAESTERMANN Technische Universitdt Miinchen, D-85748 Garching,

Germany

M.N. HARAKEH Kernfysisch

Versneller Instituut, 9747 A A Groningen, The Netherlands M. HEIL, F. KAEPPELER AND R. REIFARTH

Forschungszentrum

Karlsruhe, Inst f. Kernphysik, 760021,Karlsruhe,

Germany

The fission probability of 236 U has been measured as a function of the excitation energy with high energy resolution. Rotational band structures have been observed, with moments of inertia corresponding to hyperdeformed nuclear shapes. From the level density of the rotational bands the excitation energy of the ground state in the third minimum was determined. The excitation energy of the lowest hyperdeformed transmission gave an upper limit for the height of the inner fission barrier. The predicted effects of the clusterization in hyperdeformed states have been studied by measuring the mass and total kinetic energy distribution of the fission fragments in case of 232 Th.

1. Introduction The study of nuclei with exotic shapes is one of the most vital fields in modern nuclear structure physics. Superdeformed (SD) nuclei in the second minimum have shapes with an axis ratio {c/a) of about 2:1, whilst

95

96 hyperdeformed (HD) nuclei in the third minimum correspond to even more elongated shapes with axis ratio (c/a) of about 3:1 1. In a program aiming at studying the super- and hyperdeformed states in the actinides we have already studied the HD states in 234 U 2 and in 236 U 3 and the SD ones in 2 4 0 Pu 4 ' 5 using the resonance tunneling method. Here we present our latest results obtained for 236 U. The 236 U is exceptional, because it is the only isotope where hyperdeformed transmission resonances have been observed 3 and at the same time a superdeformed fission isomer is well-established 6 . The first aim of the present experiment was to increase the energy resolution we used before for studying the fission resonances in 236 U and resolve the structure of the vibrational resonances in the third minimum as well as to study the mass distribution from the HD resonances. Moreover, it is predicted 13 that the density distribution of 2 3 2 Th at the third minimum resembles a di-nucleus consisting of a nearly-spherical doubly-magic nucleus ( 132 Sn) and a well deformed one ( 100 Zr). Our second aim was to study the 232 Th(n,f) reaction around the En=1.6 MeV HD resonance and study the possible effects of the HD resonances on the total kinetic energy (TKE) distribution of the fragments and on their mass distribution.

2. Experimental method The experiment was carried out at the Munich Accelerator Laboratory to investigate the 235 U(d,pf) reaction with a deuteron beam of JE7d = 9.75 MeV, and using an enriched (99.89 %), 88 /jg/cm 2 thick target of 2 3 5 U 2 0 3 on a 22 /jg/cm 2 thick carbon backing. The energy of the proton ejectiles was analyzed with a Q3D magnetic spectrograph 7 . The Q3D spectrometer was placed at ©^ = 125° relative to the incident beam and the solid angle was 10 msr. The position of the analyzed particles in the focal plane was measured with a position-sensitive light-ion cathode-strip focal-plane detector 8 . Fission fragments were detected by two parallel plate avalanche counters. The active area of the detectors and their distance from the target was 16 x 16 cm 2 and 23 cm, respectively. The detectors were placed at 55° and 125° with respect to the direction of the beam. The mass - TKE correlations were studied in the 232 Th(n,f) reaction using mono-energetic fast neutrons produced in the 7 Li(p,n) reaction. The Van de Graaff accelerator at Forschungszentrum Karlsruhe produced the 50 /uA proton beam, which impinged on a 200 /jg/cm 2 metallic Li target. The average neutron flux at the Th target was ~ 1.8xlO 6 neutrons/cm 2 s.

97

The fission fragments were detected in a twin ionization chamber with parameters similar to the one published by Budtz-Jorgensen et al. 9 . We have used a large area (12.6 cm 2 ) and thin (100 /ug/cm2) 2 3 2 T h 0 2 target as a common cathode of the ionization chambers. 2.1. Hyperdeformed

states

in

236

(7

The resonances at 5.27, 5.34 and 5.43 MeV had been previously identified as hyperdeformed resonances 3 , however without resolving their rotational structure. For the first time, this was achieved in the present experiment. The measured high-resolution fission probability in terms of the excitation energy of the compound nucleus 236 U is shown in Fig. la,c). It was obtained by dividing the proton energy spectrum measured in coincidence with fission fragments by the smoothly varying proton spectrum from the (d,p) reaction. The excitation energy region containing HD resonances was analyzed in two steps, beginning with the resonance structure above 5.2 MeV. We fit our experimental results with overlapping rotational bands with the same moment of inertia and intensity ratio for the members in a band, as we did in our previous works 3,2 .

„- 0.16

-0.025

5.15 E* (MeV) Figure 1. (a, c) Fission probability (Pj) as a function of the excitation-energy. The superimposed solid line shows a fit to the data using rotational bands with K values indicated by the numbers (see text for details). The arrows indicate the positions of the band heads. The best fit has been obtained by using hyperdeformed rotational bands, (b, d) Consistent description of the angular-correlation coefficient Ai from Ref. 10 (data points) with the fit function from panel (a, c) based on the distribution of K values as indicated in (a, c).

98

In order to allow for a consistent description of the fission probability and the angular correlation coefficient A2 from Just et al. 10 , a distribution of K values rising from K = 1 to K = 4 had to be chosen. The arrows in Fig. la,c) mark the positions of the band heads with their respective K values marked as numbers. The resulting curve for the Ai angularcorrelation coefficient calculated based on the fit function derived from the fission probability in panel a) and c) is displayed in panel b) and d) of Fig. 1. We deduced a rotational parameter of R— 2.3 ± 0.4 keV and a moment of inertia of 0 = 217 ± 38 h2/MeV from the data. This agrees nicely with the rotational parameter we obtained previously for 236 U (R= 2.3 1^4 keV) 3 and also with the values calculated by Shneidman et al., 12 who assumed dinuclear systems, suggesting the possibility of an exotic heavy clustering as predicted also by Cwiok et al., 13 before. In the second step of the analysis, the proton energy spectrum below 5.2 MeV was investigated, where no conclusive high-resolution data were so far available. The result of the analysis in the excitation energy region between 5.05 MeV and 5.2 MeV is shown in Fig. lc), where the prompt fission probability is displayed together with the results of a fit by rotational bands similar to the procedure described above for the upper resonance region. Assuming overlapping rotational bands in the second well with a spin sequence of J* = 2 + - 4 + - 6 + - 8 + and a typical rotational parameter for superdeformed bands h2/20 fa 3.3 keV, the experimental data could not be reproduced. The best fit to the data was obtained in the case of h2/29 » 2.2 keV, which suggest a hyperdeformed nuclear shape also with this assumption. The rotational parameter derived from the best fit (Fig. lc) could be determined as h2/26 = 2.4 ± 0.7 keV, corresponding to a hyperdeformed configuration. This result is in contrast to the old assumption that the decaying vibrational excitations originate from the superdeformed second minimum. The occurrence of a transmission resonance in the third well at 5.1 MeV requires a rather complete damping and an inner-barrier height EA lower than 5.2 MeV. The depth of the third well has also been determined by comparing the experimentally obtained average level distances with the calculated ones using the back-shifted Fermi-gas description with parameters determined by Rauscher et al. in a similar way as we did in our previous work on 234 U 2 . We obtained a value of 3.1 ± 0.4 MeV for the energy of the ground

99 state in the third well in perfect agreement with our previous data obtained for 234 U, and also in a fair agreement with the theoretical results 13 ' 12 . 2.2. Fission characteristic 232 Th(n,f) reaction

of the 1.6 MeV resonance

in the

In order to study the possible effects of such a dinuclear system on the decay of the HD states, the mass distribution was determined using the double energy method 9 . The width (a) of the mass distribution is shown in Fig. 2(a) as a function of the neutron energy with conditions on the total kinetic energy. This condition was used to distinguish between hot and cold fission. In the case of a wide condition, the sigma is large and we can not see any effect of the HD state. When we require colder and colder fission the a gets smaller and the effect of the HD state becomes visible. In a small fraction of the fission processes, when the excitation of the fragments is small, we can observe the predicted sharpening of the mass distribution when we cross the HD resonances.

3.5 - T

2

1.5

HD resonances

1.55

1.6

1.65

1.7 1.75 E n (MeV)

1.5

1.55

1.6

1.65

1.7 1.75 E n (MeV)

Figure 2. (a) The width a of the mass distribution as a function of the bombarding neutron energy with different conditions applied to the TKE. (b) T K E of the fission fragments as a function of the neutron energy calculated for different mass-number cuts around A = 132.

We can investigate the effect also in a different way. Let us focus on the mass split of 100 + 132, gate on it and investigate the TKE distribution as a function of the neutron energy as shown in Fig. 2(b). When the gate is wide (A = 125-155), we cannot see any effect of the HD states, but when

100 it gets sharper (A = 132 ± 2), the effect gets larger. The 100 + 132 mass split is produced in a much less excited way (larger TKE) when we are at the HD resonance. 3. Summary We have measured the prompt fission probability of 236 U as a function of the excitation energy using the (d,pf) reaction with high resolution in order to study high-lying excited states in the third well. From the analysis of the rotational band structure the rotational parameter could be extracted as h2/26=2.3± 0.4 keV. The corresponding moment of inertia ( 0 = 217 ±38 7i2/MeV) agrees with the calculated value of Shneidman et al.. The hyperdeformed rotational-band structure observed in the rather low excitation energy region around 5.1 MeV independently supports our experimental finding of a rather deep third minimum, which is in agreement with theoretical predictions. We furthermore used the lowest transmission resonance in the third well to give an upper limit for the height of the inner barrier, which is also in agreement with theoretical predictions. Acknowledgement The work has been supported by DFG under HA 1101/6-3 and 436 UNG 113/129/0, the Hungarian Academy of Sciences under HA 1101/61, the Hungarian OTKA Foundation No.T038404, and the Nederlandse Organisatie voor Wetenschappelijk Onderzoek (NWO). References 1. 2. 3. 4. 5. 6. 7.

P.G. Thirolf and D. Habs, Prog. Part. Nucl. Phys. 49, 245 (2002). A. Krasznahorkay et ai., Phys. Lett. B461, 15 (1999). A. Krasznahorkay et ai., Phys. Rev. Lett. 80, 2073 (1998). D. Gassmann et ai., Phys. Lett. B497, 181 (2001). M. Hunyadi et ai., Phys. Lett. B505, 27 (2001). S.B. Bj0rnholm and J.E. Lynn, Rev. Mod. Phys. 52 (1980) 725. H.A. Enge and S.B. Kowalsky, in Proceedings of the 3rd International Conference on Magnet Technology, Hamburg (1970). 8. H.F. Wirth, PhD thesis, TU Munich (2001), unpublished. 9. C. Budtz-Jorgensen et ai., Nucl. Instr. Meth A285 (1987) 209. 10. M. Just et ai, Proc. Symp. Physics and Chemistry of Fission, IAEA, Jiilich, 71 (1979). 11. J. Blons et ai., Phys. Rev. Lett. 35, 1749 (1975). 12. T.M. Shneidman et ai., Nucl. Phys. A671, 119 (2000). 13. S. Cwiok et ai., Phys. Lett. B322, 304 (1994).

MICROSCOPIC ANALYSIS OF T H E Q - D E C A Y IN HEAVY A N D S U P E R H E A V Y NUCLEI

D. S. DELION National Institute of Physics and Nuclear Engineering, FOB MG-6, Bucharest-Magurele, Romania A. SANDULESCU Center for Advanced Studies in Physics, Galea Victoriei 125, Bucharest, Romania W. GREINER Institut fur Theoretische Physik, J.W.v.-Goethe Universitat, Robert-Mayer-Str. 8-10, 60325 Frankfurt am Main, Germany We analyze the a-decay along N — Z chains in heavy and superheavy nuclei. The a-particle preformation amplitude is estimated within the pairing model, while the penetration part by the deformed WKB approach. We show that for JV > 126 the plateau condition is not fulfilled along any a-chain, namely the logarithmic derivative of the Coulomb function changes much faster in comparison with that of the preformation factor. We correct this deficiency by considering an a-cluster factor in the preformation amplitude, depending upon the Coulomb parameter. For superheavy region an additional dependence upon the number of interacting a-particles indicates a clustering feature connected with a larger radial component.

1. Introduction and model The aim of this analysis is to show that the shell model estimate of the aparticle preformation factor is not consistent with the decreasing behaviour of Q-values along any neutron chain l'2. In Ref. 3 we analyzed this feature by treating the a-decaying state as a resonance built in a standard way, namely by using the matching between logarithmic derivatives of the preformation amplitude and Coulomb function. In this lecture we extend our analysis of the decay widths, by connecting the heavy with superheavy regions along a-like chains. Our purpose is not only to give a correct description of absolute decay widths. We will show that in order to fulfill the resonance condition it is necessary to use an additional a-cluster compo-

101

102 nent, depending upon the Q-value. Let us consider a transition connecting two axially deformed nuclei. The decay width can be estimated by using the following ansatz T = hv

gtt](R)

D(R) = T0(R)D(R)

G0{kR)

.

(1.1)

It is given by the product between the standard spherical width, given by the Thomas formula r 0 (-R) 4 , and the deformation factor D(R) 5 . It contains a ratio between the internal and external Coulomb solutions. The decay width does not depend upon the matching radius R within the local potential approach, because the internal and external wave functions satisfy the same equation and therefore are proportional. This is the socalled plateau condition. When the value of the internal wave function 82, 82 < N < 126. Therefore the pairing description of a-decays in this region seems to be successful concerning both the ratio to the experimental width and the continuity of derivatives. The situation completely changes in the region above the magic neutron number N > 126. In Fig. 1 we investigated 12 even-even a-chains. The experimental decay widths are reproduced worse than in the previous interval, namely the quantity 70 Ri /o *min

j -*^ J

==

^

m

•*• 0\Pmi

^maxi

-*mini -^J

= F 0 (/3 — /3 m ,0,O;i?)F o (/3 R), (2.7)

105

Eeven—even i j 1 1 1 |i i 1 1

(a)

y^-

**TTTV > * - - - f 0 =0.80

=, I , , , i I i 130 135

i i i I i i i i I i i i i I i

140

145

150

M

I

M

155

M

I

M

160

1 I N

165

I I I I I M

170

I I I

175

0.4 0.3 (b)

0.2 0.1 0

1- . ^ d ? ^

-0.1 -0.2 -0.3 -0.4

~i

i

i

130

i

i

i

i

i

135

i

i

i

i

i

140

i

i

i

i

i

145

i

i

i

i

i

150

1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 [

155

160

165

170

175

Figure 1. (a) The parameter 70 versus the neutron number for different even-even enchains in Table 2. The preformation parameters are /o = 0.8, Pmin = 0.025. (b) The same as in (a), but for the slope parameter 71.

i.e. the usual preformation amplitude is multiplied by a cluster preformation amplitude with nmax = 0. Our calculations showed that indeed, this is the best choice for the slope correction of the preformation amplitude. If one uses a variable ho parameter for the second factor in the above relation one always obtains a linear decreasing trend of the slope parameter 71 along any a-chain. This is a strong argument in favour of the a-clustering nature of this correction.

106 We stress on the fact that the correction procedure has a relative character, depending upon the values /3m,Xm- We also remind that a similar technique, i.e. the use of a variable cluster ho parameter, was used in Ref. 8. The energy of the emitted particle can be splitted into two components, a pure shell model plus a cluster part, i.e. E = E0m+

E0_!3m .

(2.8)

Therefore the Q-value contains a smooth part and a fluctuation, given by four-body correlations not included in the pairing model. This representation is somehow similar to the standard Strutinsky procedure to split the binding energy into a smooth liquid drop term plus a shell-model fluctuation 9 , but of course the two terms in our case have different meanings. Let us point out that by using a constant ho parameter /3TO = 0.83 for all analyzed even-even emitters one obtains for the maximal value of the slope parameter ^(max) = 0. At this point the a-clustering is described only by the pairing correlations. It roughly corresponds to the maximal value of the Coulomb parameter Xm = 55. In this way the a-clustering process increases by decreasing the Coulomb parameter, because the ho parameter /3 in (2.6) is smaller and therefore the tail of the preformation factor increases. This is consistent with the physical meaning of the aclustering process, because a smaller Coulomb parameter correspond to a larger Q-value and consequently to a larger emission probability. Therefore in our calculations we used the parameters /3 m = 0.83, \m = 55. For the proportionality coefficient in Eq. (2.6) the regression analysis gives the value / i = 8.0 10~ 4 . From the analysis of Fig. 1 one remarks that in the superheavy region we still underestimated the slope parameter 71. The situation here can be improved by assuming a quadratic dependence of the coefficient /1 upon the number of clusters Na = (N — N0)/2 with iVo = 126, namely

h "»• h + hK •

(2-9)

We remind here that a quadratic in Na dependence of the Q-value was empirically found in Ref. 10 . We stress on the fact that this kind of dependence affects only the superheavy region, with large values of Na. In Figs. 2(a,b) we plotted the dependence of the parameters 70,71 upon the neutron number along the even-even a-chains. The improvement, especially for the slope 71, is obvious. Now the ratio to the experimental width is described within a factor of three for most of decays. We considered a correcting

107

term with / 2 = 1.28 10 6 . The mean value of the slope parameter and its standard deviation for even-even chains is 71 = —0.001 ± 0.034.

4 3 (a)

even—even

2 1 0

- / ^

-1 -2

f m = 0 . 8 3 , f, = 8.0 10" 4 f 2 =1 .28 1CT6

-3

II. I....

-4 130

135

I. I . .

140

I . . . _L

145

150

155

160

165

_L 170

J_ 175

Figure 2. (a) The parameter 70 versus the neutron number for different even-even achains in Table 2. The preformation parameters are fm = 0.83, f\ = 8.0 1 0 - 4 , j% — 1.28 10~ 6 , Pmin = 0.025. (b) The same as in (a), but for the slope parameter 71.

The quadratic dependence in Eq. (2.9) can be also interpreted in terms of the total number of interacting clustering pairs, namely N% m 2Na (Na —1)/2. Thus, our analysis based on the logarithmic derivative continuity, shows very clearly that the effect of the a-clusterisation becomes

108 much stronger for superheavy nuclei. Their half-lives are practically not influenced, but their radial tails should be significantly larger than those predicted by standard shell-model calculations.

3. Conclusions We analyzed in this lecture the a=clustering, using the decay widths for even-even a-emitters with Z > 82. We estimated the a-particle preformation amplitude within the pairing approach. We used the universal parametrization of the mean field and the empirical rule for the gap parameter A = Vl/s/A. Due to a coherent superposition of many spherical configuration the preformation factor is not sensitive to the the local fluctuation of these parameters. The penetration part was estimated within the deformed WKB approach. We showed that the decay width increases by a factor between three and five for /32 = 0.3, depending on the mass number. It turns out that the decay width is very sensitive to the sp ho parameter and the number of considered spherical configurations. They simultaneously determine the order of magnitude and the slope of the decay width with respect to the matching radius, giving the plateau condition. It is possible to describe all a-decay widths within a factor of two for Z > 82, 82 < N < 126, by using a constant, but smaller ho parameter fl = 0.8/?/v and a minimal pairing density P TO , n = 0.025. This shows that the relative amount of the a-clustering in this region can be entirely described within the pairing approach. It turns out that the slope of the decay width versus the matching radius has a strong variation for N > 126, in an obvious correlation with the Coulomb parameter. Thus, the relative amount of the a-clustering here cannot be described within the pairing approach and an additional mechanism is necessary. In order to restore the plateau condition and to improve the description of the decay widths we proposed a simple procedure. We supposed a cluster factor, multiplying the preformation amplitude. It contains exponentially an ho parameter, proportional to the Coulomb parameter. This ansatz is suggested by a similar exponential dependence of the Coulomb function upon this parameter. Therefore the energy of the emitted particle contains two terms, namely a smooth part and a cluster correction. The procedure improves simultaneously the ratio to the experimental width and the slope with respect to the matching radius, except for the

109

superheavy region. The relative increase of the a-clustering is related to the decrease of the Coulomb parameter. It is stronger for two regions, namely above N = 126 and in superheavy nuclei. It has a minimum around N = 152. An additional dependence upon the number of interacting a-particles improves the plateau condition for superheavy nuclei. This additional clustering, which seems to be very strong, may affect the stability of nuclei in this region. References 1. 2. 3. 4. 5. 6. 7. 8.

J.O. Rasmussen, Phys. Rev. 113, 1593 (1959). Y.A. Akovali, Nucl. Data Sheets 84, 1 (1998). D.S. Delion and A. Sandulescu, J. Phys. G: Nucl. Part. Phys. 28, 617 (2002). R. G. Thomas, Prog. Theor. Phys. 12, 253 (1954). P. O. Proman, Mat. Fys. Skr. Dan. Vid. Selsk. 1, no. 3 (1957). J. Dudek, Z. Szymanski, and T. Werner, Phys. Rev. C 23, 920 (1981). A.Bohr and Mottelson, Nuclear structure, vol. 1 (Benjamin, New York, 1975). P. Schuck, A. Tohsaki, H. Horiuchi, and G. Ropke, The Nuclear Many Body Problem 2001 Eds. W. Nazarewicz and D. Vretenar (Kluwer Academic Publishers, 2002) p. 271. 9. V.M. Strutinsky, Nucl. Phys. A 95, 420 (1967); Nucl. Phys. A 122, 1 (1968). 10. G. Dussel, E. Caurier, and A.P. Zuker, At. Data Nucl. Data Tables, 39, 205 (1988).

S E A R C H I N G FOR CRITICAL P O I N T N U C L E I I N FISSION PRODUCTS

N . V . Z A M F I R , E.A. M C C U T C H A N A N D R . F . C A S T E N WNSL,

Yale University, New Haven, Connecticut 06520-8124, E-mail: [email protected]

USA

The recently introduced critical point symmetries in the nuclear phase transition between spherical and deformed shapes have produced a large interest in t h e search for their empirical realizations. A review of this search in different regions of nuclear chart, including the neutron rich nuclei obtained in nuclear fission, is presented.

1. Introduction Low-lying collective nuclear structure is often understood and described in terms of shape paradigms of the harmonic vibrator, deformed symmetric rotor, and 7 - unstable models which constitute a set of idealized limits with analytical solutions. The range of structures between these benchmarks is large and complex and, until recently, the only way to describe transitional nuclei was by numerical diagonalizations of a multi-parameter Hamiltonian. A major breakthrough was made a few years ago with the discovery of new parameter free (except for scale) analytic solutions in the region of rapid change between spherical and deformed shapes. These new critical point symmetries describing nuclei close to a phase transitional point 1 - 2 ' 3 ' 4 ) defined in terms of the intrinsic state formalism of the Interacting Boson Model are called E(5) for 7-unstable nuclei 5 and X(5) for axially symmetric nuclei 6 . They were immediately supported by the discovery of empirical realizations 7 ' 8 . The idea of critical point symmetries has resulted in an intense search for new empirical examples 9 ' 10 ' 1:L > 12 ' 13 ' 14 ' 15 ' 16 . An interesting, but not yet fully explored, region of nuclei predicted to contain good candidates for the new type of symmetries is the medium mass neutron rich nuclei obtainable in nuclear fission. In fact, recently, the structure of the neutron rich Mo nuclei was discussed and compared with the X(5) symmetry 14.i5.!6 An overview of the present theoretical and experimental status of these new critical point symmetries will be presented. The predictions of new

110

111 possible critical point regions, based on a microscopic perspective related to the number of active particles, will be also discussed. 2. X(5) critical point symmetry Evidence for pronounced (3 softness in the phase/shape transition region led to the development of new symmetries, E(5) [ref. 5] for a spherical vibrator to a deformed 7-soft second order phase transition and X(5) [ref. 6] for a spherical vibrator to axially symmetric rotor first order phase transition. These symmetries consist of analytic solutions of the Bohr Hamiltonian with square well potentials in the quadrupole deformation. 1069-

Figure 1. Low-lying levels predicted by X(5) 6 . The excitation energies and the B(E2) values, indicated on the transition arrows, are given in relative units

Except for scale, the predictions for energies and electromagnetic transitions are parameter free. The low-lying spectrum and some characteristic B(E2) values are shown in Fig. 1 in units of E{2^) — E(0f) and B{E2;2f -» 0^)=100. Note that the ratio RA/2 = E(Af)/E(2f)=2.90, is indeed appropriate for a nucleus at the critical point of a vibrator to rotor phase transition 3 . Also, the yrast B(E2; J + 2 —* J ) values increase with J at a rate intermediate between that of a vibrator and a rotor. Particularly characteristic of the X(5) symmetry is that the energy of the Oj" state is fixed: Ro2 = E(02)/E(2^)=5.65. Finally, we note that the symmetry predicts inter-sequence B(E2) values. Since nuclei contain integer numbers of nucleons, their properties change discretely with N and Z and therefore, in any given transition region, there is no assurance that any specific nucleus will occur at the critical point. Nev-

112

ertheless, empirical manifestations of this symmetry were found in N=90 nuclei 152 Sm (ref. 8), 150 Nd (ref. 10), 154 Gd (ref. 12). 156 Dy (ref. 13). The Nd-Dy isotopic chains undergo a rapid transition from spherical to axially symmetric deformed structure. The two structural characteristic ratios R4/2 and Ro2 shown in Fig. 2 indicate that all four isotopic chains reach the same stage in their structural evolution, consistent with the X(5) type of structure, at precisely N=90. The energy spacings of the yrast band levels are also nearly identical to the X(5) predictions, as can be seen in fig. 3. The intraband B(E2) strengths also closely match the X(5) trend, except the B{E2; 6+ -> 4+) and B(E2; 10+ -» 8+) in 156 Dy. 3.5

3.0

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•

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I

1

1

1

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— o, i3"

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84

86

88

90

92

94

96

N Figure 2. Evolution of the 4]*" and 0^ energies, normalized to the 2+ energy across the N ~ 9 0 transition region, for the Nd, Sm, Gd, and Dy isotopic chains, compared with the X(5) predictions.

The experimental inter-sequence E2 transition strengths between the levels based on the 0 + level and the quasi-ground state band levels are in various degrees of agreement with the X(5) values. In general, the B(E2) branching ratios are close to the X(5) predictions, although the absolute values of individual B(E2) differ by an average factor of 3-4 8 ' 10 > 13 . As mentioned above, in the search for possible candidates for the X(5) symmetry, the simplest structural observable to consider is the R4/2 ratio, which reflects in general the position of that nucleus along the spherical-

113

Figure 3. Yrast band level energies and B(E2) values for the N=90 isotopes 1 5 2 S m (ref. 8), 1 5 0 Nd (ref. 10), 1 5 6 D y (ref. 13). The rotor, X(5), and vibrator predictions are shown for comparison.

deformed trajectory. Another useful and simple to use quantity that reflects the onset of deformation is the P factor 17 , given by P = NpNn/(Np + Nn), where Np(n) is the number of valence protons (neutrons) relative to the nearest closed shell. The onset of quadrupole deformation takes place in general at P ~ 5 (ref. 17). The candidates for a critical point structure in the vibrator-rotor shape/phase transition, i.e., X(5) candidates, should normally have P close to this value, as can be seen in fig. 4 . Both R4/2 and the P factor serve only as a guide to possible candidates for X(5) since R4/2 ~ 2.9 and P ~ 5 can also occur in 7-soft to axially symmetric rotor transition where the X(5) symmetry does not apply. Figure 5 illustrates the locus of P ~5 for several regions of nuclei. Of course, these contours serve only as guidelines since they ignore sub-shell closures (e.g., at Z=64) and their evolution with N and Z. An evolution of nuclear structure that is different relative to what it is expected on the basis of the standard magic numbers implies changes in shell structure, residual interactions, or both. Relative to their position to the stability line, there are two categories

114 i

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Figure 4. P-factor plots of R4/2 for the a) Z=52-66, b) Z=68-80 and c) Z = 40-48 regions. fl4/2=2.9 and P = 5 values are indivcated by dashed lines.

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N Figure 5. Section of the nuclear chart showing the nuclei with P -^5 (shaded area) which give a guide to the locus of potential X(5) critical point nuclei.

of X(5) candidates: n-deficient nuclei which can be produced through (HI, xn) reactions and n-rich nuclei which can be obtained as fission products. We will discuss here only the neutron-deficient Nd-Yb nuclei in the N~90 region and the neutron-rich Kr- Mo in the N ~ 92 region. The former is precisely the region where X(5)-type nuclei were first found and the second is a region which can be extensively studied as fission products. Figure 6 shows these two regions expanded and includes empirical -R4/2 ratio for each nuclide. It can be easily seen that the P ~ 5 contour gives the locus of the X(5) candidates (i? 4 / 2 =2.90) very well. The curve in figure 6 (top) intersects all of the X(5) candidates with N=90 discussed above. The curve continues for higher Z away from N=90. At Yale we are currently studying 162 Yb and 166Hf which, from figure 6 (top) , are potential X(5)-like nuclei.

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223

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Figure 5.

Potential barrier against emission of

14

R a parent nucleus.

a highly deformed minimum is mainly due to the proximity forces that prevent the negotiating of the scission barrier. The results for the quadrupole moment, the moment of inertia and the excitation energy7 agree roughly with the data obtained recently on the superdeformed bands in 4 0 Ca, 4 4 Ti, 48 Cr, 56 Ni, 84 Zr, 132 Ce, 152 Dy and 192 Hg. Predictions are given for the 126 Ba nucleus presently under investigation (see Fig. 6). 6. Very heavy elements The heaviest elements decay via a emission and the predictions of the halflives given by the formulas derived from the GLDM agree well with the data when the selected theoretical Qa is the one proposed by a recent version

122 i

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Figure 6. Sum of the deformation and rotational energies for 1 2 6 B a as functions of the angular momentum (h unit) and the distance r between the mass centers. The vertical dashed line indicates the transition from one-body to two body shapes (r=9.2 fm).

of the Thomas-Fermi model 6 . The fission barriers are one-humped barriers since the nuclear proximity forces can no more compensate for the high repulsive Coulomb forces. Due only to shell effects the barrier height can still reach 5 MeV, the value of the next proton magic number playing a major role (see Fig. 7). 4 N

2

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Figure 7. Symmetric fission barriers for 2 8 3 112. The full line, dotted curve and dashed and dotted curve include the shell effects given by the Droplet Model assuming respectively a proton magic number of 114, 120 and 126.

The potential barriers governing the entrance channel leading possibly to superheavy elements have been investigated with this model. For moderately asymmetric reactions (cold fusion reactions : 64 Ni, 70 Zn, 76 Ge, 82 Se, 86 Kr on 2 0 8 Pb) double-hump potential barriers stand and fast fission of compact shapes in the outer well is the main exit channel. Very asymmetric reactions (warm fusion reactions : 4 8 Ca on 238 U, 2 4 4 Pu or 2 4 8 Cm ) lead to one hump barriers which can be passed only with an energy much higher

123

than the ground state energy of the superheavy element. Then, only emission of several neutrons or an a particle can stabilize the nuclear system and allows to reach a ground state. The formation of superheavy elements via almost symmetric reactions is hardly likely (see Fig. 8).

r(fm) Figure 8. Potential barriers for different reactions leading to the 2 7 0 110 nucleus, r is the distance between mass centres. The vertical bar corresponds to the contact point.

7. Conclusion The potential barriers appearing in the quasi-molecular shape path have been investigated within both a Generalized Liquid Drop Model taking into account the interaction energy between the close nucleons when a deep neck or a gap exists and the shell corrections. The main characteristics of the symmetric and asymmetric fission, the light nucleus and a emissions, the highly deformed rotating states and the superheavy formation and decay can be described in this fusion-like deformation path. References 1. 2. 3. 4. 5. 6. 7.

G. Royer and B. Remaud, J. Phys. G: Nucl. Phys 10, 1057 (1984). R. A. Gherghescu and G. Royer, Phys. Rev. C68, 014315 (2003). G. Royer and K. Zbiri, Nucl. Phys. A697, 630 (2002). G. Royer, J. Phys. G: Nucl. Part Phys 26, 1149 (2000). G. Royer and R. Moustabchir, Nucl. Phys. A683, 182 (2001). G. Royer and R. A. Gherghescu, Nucl. Phys. A699, 479 (2002). G. Royer, C. Bonilla and R. A. Gherghescu, Phys. Rev. C67, 34315 (2003).

PROBING THE "LI HALO STRUCTURE BY TWO-NEUTRON INTERFEROMETRY EXPERIMENTS M. PETRASCU, A. CONSTANTINESCU1,1. CRUCERU, M. GR7RGIU*, A. ISBASESCU AND H. PETRASCU Horia Hulubei National Institute for Physics and Nuclear Engineering, P. O.Box MG-6 Bucharest, Romania I. TANMATA, T. KOBAYASHI, K MORMOTO, K. KATORI, A. OZAWA, K. YOSHIDA, T. SUDA AND S. NISHMURA RIKEN, Hirosawa 2-1 Wako, Saitama, 351-0198, Japan

A recent experiment with a new array detector aiming the investigation of halo neutron pair pre-emission in Si( u Li, fusion) is described. A new approach for testing the true n-n coincidences against cross-talk has been worked out. An experimental evidence for residual correlation of the pre-emitted neutrons is presented. The results obtained in building the n-n correlation function by using the available denominators are discussed. A recent iterative method for calculation of the intrinsic correlation function was also applied. An experiment for precise measurement of the intrinsic correlation function is proposed.

1.

Introduction

The neutron halo nuclei were discovered by Tanihata and co-workers [1]. These nuclei are characterized by very large matter radii, small separation energies, and small internal momenta of valence neutrons. Recently was predicted [2] that, due to the very large dimension of n Li, one may expect that in a fusion process on a light target, the valence neutrons may not be absorbed together with the 9Li core, but may be emitted in the early stage of the reaction. Indeed, the experimental investigations of neutron pre-emission in the fusion of u Li halo nuclei with Si targets [3,4], have shown that a fair amount of fusions (40±12)% are preceded by one or two halo neutron pre-emission. It was also found that in the position distribution of the pre-emitted neutrons, a very narrow neutron peak, leading to transverse momentum distribution much narrower than that predicted by COSMA model [5], is present. Some indication based on preliminary n-n coincidence measurements, concerning the presence of neutron pairs within the narrow neutron peak, has been mentioned in [3,4]. In the light of this indication, the narrow neutron distribution could be caused by the final state interaction [6,7] between two pre-emitted neutrons. Therefore, Permanent address: Bucharest University, Romania Permanent address: Technical University, Bucharest, Romania 124

125 on the basis of these first results, was decided to perform a new experiment aiming to investigate the neutron pair pre-emission in conditions of much higher statistics, by means of a neutron array detector. This experiment has been performed at the RTKEN-RIPS facility. 2.

Experimental Results

2.1. The Experimental Setup The experimental setup is shown in Fig. 1[8]:

D

F2

Q-L PI P2 MUSI c

llf

1

VI

I

111 II SLIT

A

V2 JwM 1 MBA ISBN 11! WW

MM?

w SiS ARRAY D.

Figure 1. The general setup of the experiment. Detectors F2, P2(PPAC2), Vl(Vetol), SiS, V2(Veto2) were used in the trigger F 2 * PPAC 2 * Veto 1 * SiS * Veto 2 • MUSIC was used for suppression of energy degraded beam. The neutron array detector consisting of 81 modules, was placed in forward direction at 138 cm from the target.

In this setup, three main parts are present: The first part contains the detectors used for the beam control: a thin scintillator at the F2 focus of the RIPS, two parallel plate avalanche counters (PI, P2) and a Vl(Vetol) scintillator, provided with a 2x2 cm2 hole. The second part consists of a MUSIC Chamber [9], containing inside a 500 fim thick strip silicon detector-target (SiS) and a V2(Veto2) Si detector, 200 jum thick. MUSIC was used for the identification of the inclusive evaporation residues spectra produced in the detector-target, and for suppression of the energy degraded beam particles. The third part is the neutron array detector [10]. It consists of 81 detectors, made of 4x4x12 cm3 BC-400 crystals, mounted on XP2972 phototubes. This detector, placed in forward direction at 138 cm from the target, was used for the neutron energy determination by time of fight and for neutron position determination. The distance between adjacent detectors was 0.8 cm. The array

126

components were aligned to a threshold of 0.3 MeVee, by using the cosmic ray peak at 12 MeV (8 MeVee). The numbering of the detectors was performed in the following way: The central detector was labeled 1. The 8 detectors surrounding detector 1, were labeled counter clock wise 2-9. The 16 detectors of the second circle were labeled 10-25 and so on. In the present paper the coincidences between adjacent detectors are denoted as ""first order coincidences". Coincidences between two detectors separated by one detector are denoted as ""second order coincidences" and so on. With the trigger specified in Fig. 1 caption, one could investigate inclusively the 911 Li + Si fusion. The large 5x5 cm2 silicon Veto2 detector, placed behind the Si-strip target-detector, eliminated the elastic, inelastic, and breakup processes at forward angles. The measurements were performed with 13A MeV "Li and 9Li beams. 2.2. The Forward Neutron Peak The energy range corresponding to the neutron pre-emission process was established between ~8 and -15 MeV [11]. In Fig. 2, the position spectrum measured along the horizontal line connecting detectors 58-74 is shown [12]. The FWHM of this spectrum is ~ 13 cm and corresponds to a solid angle of ~9 msr. Within this narrow peak, a large number of n-n coincidences were observed for u Li [8], by comparing the data obtained with u Li and with 'Li beams.

240220 200' 180. 160

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?140

«

? 120-

806040' -20 -15 -10 -5

0

5

10 15 20

Distance from the center (cm)

Figure 2. The position spectrum measured along the horizontal line connecting detectors 58-74, is shown. The neutron energy was selected between 6-16 MeV. The FWHM of this spectrum is -13 cm and corresponds to a solid angle: ~9 msr.

127

2.3. True Neutron-Neutron Coincidences and Cross-Talk Cross-talk (at.), is a spurious effect in which the same neutron is registered by two or more detectors. A complete simulation of the array detector performances by using MENATE program [13], was recently performed [12]. We have investigated in this way the c.t. distribution as a function of t=t2-tx for different coincidence (1 st to 4th) orders. The simulation was performed by firing the central detector 1 by neutrons of given energy and by extracting the crosstalk events corresponding to detectors 2-9 (first order), to detectors 10-25, (second order) and so on. For each event, the space and time coordinates and also the light output were available. In these simulations was found a notable suppression of short neutron trajectories between detectors 1 and 2 [12]. For example in 1000 c.t. events there are no trajectories shorter than 1.8 cm. The number of 1.8 cm trajectories is less than 5 in 1000 c.t. events. Due to this concentration of events caused by c.t., appears a remarkable improvement of oti time resolution of detector 1 [12]. In Fig. 3, the experimental n-n coincidence (true and c.t.) are denoted by open up-triangles with un-capped error bars. The distribution of simulated first order c.t. as a function of t2-t\ is indicated by solid squares with capped error bars. The simulations were performed by taking three different neutron energies: 8, 11, and 15 MeV, representing respectively, the lower limit, peak and upper limit of the neutron pre-emission spectrum. A number of 1000 c.t. were calculated in each case. One may see that in all three figures (a, b, c) there is a window, denoted by TC (true coincidences), in which the yield of c.t. is very low (near 0.1 counts). The width of TC window is the same (0.6 ns) for 11 and 15 MeV and is larger (0.8 ns), for 8 MeV neutrons. TC is separated by a vertical dotted line, from the CT (cross-talk) window in which c.t. yield is much larger. The first c.t. point in CT window is by a factor -10 higher than the c.t. points in TC window. This means that a change in the c.t. mechanism is taking place by passing from the CT to the TC window. A two-parameter (time-trajectory length) analysis shows that in the majority of events the trajectory length in TC window is larger than ~6 cm. Since a neutron cannot cover this distance in such a short time, it follows that c.t. is realized in TC window predominantly by y rays. This explains also why c.t. yield is so low in the TC window. The vertical arrows in Fig. 3, are indicating that the remaining 46 true coincidences after d^n rejection [14] are well inside the TC window. In Fig. 4, the c.t. simulation for second order coincidences is shown. One may see that the number of true coincidences (71) remaining after drain rejection is also well inside the TC window. In this Fig. the entire c.t. peak

128 is shown. It is remarkable that MENATE program is able to describe fairly well the experimental c.t. distribution.

Vt, (ns) Figure 3. Monte Carlo simulation of the first order c.t. The open up-triangles with uncapped error bars represent the experimentally measured coincidences. The solid squares with capped error bars represent the simulated c.t.

2.4. Experimental Evidence for Residual Correlation of Single Detected Halo Neutrons The two-neutron correlation function [15] is given by : C(q)=kNc(q)/Nnc(q), in which Nc(q) represents the yield of coincidence events and Nnc(q), the yield of uncorrelated events. The normalization constant k is obtained from the condition that C(q)=l at large relative momenta. The relative momentum q is given by: q=l/2 I p r p 2 1, p t and p 2 being the momenta of the two coincident neutrons. A crucial problem for getting the correlation function is the construction of denominator in the upper formula. A thorough analysis of this problem is presented in [16]. Two approaches are commonly used: one is the event mixing technique, the other is the single neutron product technique. In the event mixing approach the denominator is generated by randomly mixing the neutrons from the coincidence sample. This method has the advantage that the uncorrelated distribution corresponds to the same class of collisions and kinematic conditions as in the case of the numerator, but has the disadvantage

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nuclei produced in a low energy fission of uranium in the proposed SPIRAL 2 facility 4 . A full description of the nuclear physics topics and interdisciplinary applications which might be covered with the SPIRAL 2 beams is beyond the scope of this contribution, but one can mention that both high-intensity stable and fission-fragment radioactive beams can be used to cover very broad range of nuclei very far from stability (Fig. 5). A use of these high-intensity beams at the GANIL low-energy ISOL facility or their acceleration to a few tens of MeV/nucleon opens new possibilities in nuclear structure physics, nuclear astrophysics, reaction dynamics studies as well as in atomic physics, condensed matter studies, radio-biology and radiochemistry (see Ref. 4). A layout of SPIRAL 2 is presented in figure 4. A new superconducting linear driver (LINAG) will deliver a high intensity, 40 MeV deuteron beam as well as a variety of heavy-ion beams with mass over charge ratio equals to 3 and energy up to 14.5 AMeV. Using a carbon converter and the 5 mA deuteron beam, a neutroninduced fission rate is expected be 1.3 x 10 13 fissions/s with a low density UCa; target, and up 5.3 x 10 13 fissions/s for high-density UC X . The expected intensities of RNBs after acceleration should reach, for example, 109 pps for 132 Sn and 10 10 pps for 92 Kr. Besides the method which uses a carbon converter, a direct irradiation of the UCX with beams of d, 3,4 He, e ' 7 Li, or

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Q value Q 2p (MeV) Figure 5. Barrier-penetration half-life as a function of the two-proton Q value, Qiv, for 45 Fe. The barrier penetration was calculated by assuming a spectroscopic factor of unity. Different model predictions 2,3,4,12,13,14,15,16,17 w e r e u s e d for Q2p- The experimentally observed Q value of Qp = 1.14 MeV of 4 5 Fe implies a di-proton barrier-penetration half-life of 0.024 ms.

Ormand 3 of 1.28(18) MeV, and from Cole 4 of 1.22(5) MeV. These models use the isobaric-multiplet mass equation and shell-model calculations as well as Coulomb-energy shifts to determine masses of proton-rich nuclei from their neutron-rich mirror partners. Q-value predictions from models aiming at predicting masses for the entire chart of nuclei are in less good agreement with our present result. All the 2p Q-value predictions are summarized in Figure 5, where they are used in barrier-penetration calculations using the simple di-proton model for two-proton emission (the model used in 2 with R = 4.2 fm). For Ep = (1.14±0.05) MeV, these calculations predict a di-proton barrier penetration half-life of (0.024+Q 017) ms, if one assumes a spectroscopic factor of unity. Brown 2 ' n calculated a spectroscopic factor of 0.195 for a direct 2p decay of 45 Fe which increases the barrier tunnel time to a predicted half-life of (0.12lo'o9) rns. This di-proton model yields, for a given Q value, a lower limit for the partial half-life for the two-proton emission 5 . An upper limit can be obtained by calculating the decay width as the product of the penetrability for the two individual protons with half the decay energy each. Using the same spectroscopic factor, this gives a half-life of

153 about 200 s. A sequential decay seems to be excluded for 45 Fe, as the intermediate state, the ground state of 44 Mn, is, depending on the prediction used, either not in the allowed region or at the very limit of the allowed region. The model predictions 2 ' 3 ' 4 range from Qip = -24 keV to +10 keV. As the intermediate state is most probably rather narrow (barrier-penetration calculations yield a value of about T = 50 meV), the first proton would have a very long half-life (hours or even days), which makes this decay mode very unlikely. 5. Summary and outlook The results of a GANIL experiment concerning the decay of 45 Fe have been presented. The measured decay energy yielded a peak at 1.14 MeV, the determined half-life was of 3.8 ms, and, in particular, no coincident f3 or 7 radiation was observed for the events in the decay-energy peak. In addition, strong indications were found for the decay of the 2p daughter, 43 Cr, after implantation of 45 Fe. Additional support comes from the width of the 45 Fe peak, which does not show any broadening due to /3-particle pile-up. The energy of the observed peak is in nice agreement with theoretical predictions for the 2p decay energy. A consistent picture arises, if one assumes that a two-proton ground-state emission occurs. 45 Fe is thus the first case of a nucleus which decays by two-proton ground-state radioactivity with a half-life longer than typical reaction times ( « 10 _ 2 1 s). Whereas the 2p ground-state decay of 45 Fe is established with the present data, future high-statistics data should definitively allow to conclude on the nature of the two-proton decay, 2 He emission or three-body decay. This question can be addressed by measuring the individual proton energies and the relative-angle distribution for the two protons emitted which should be either isotropic (three-body decay), forward-peaked (2He emission), or a mixture of both. For this purpose a time projection chamber with a spatial resolution of about 200 microns on all three dimensions has been built and is actually being tested together with its associated integrated electronics. Acknowledgments The experiment was the fruit of collaboraive efforts of research teams from CENBG-Bordeaux, GANIL-Caen, GSI-Darmstadt, Warsaw University and IFIN-HH-Bucharest. Their agreement to present the above results

154 is warmly acknowledged. References 1. V.I. Goldansky, Nucl. Phys. 19, 482 (1960). 2. B.A. Brown, Phys. Rev. C 4 3 , R1513 (1991). 3. W.E. Ormand, Phys. Rev. C 5 3 , 214 (1996). 4. B.J. Cole, Phys. Rev. C54, 1240 (1996). 5. L. Grigorenko et al, Phys. Rev. Lett. 85, 22 (2000). 6. B. Blank et al., Phys. Rev. Lett. 77, 2893 (1996). 7. B. Blank et al., Phys. Rev. Lett. 84, 1116 (2000). 8. J. Giovinazzo et al., Eur. Phys. J. A10, 73 (2001). 9. M. Pfiitzner et al., Eur. Phys. J. A14, 279 (2002). 10. J. Giovinazzo et al, Phys. Rev. Lett. 89, 102501 (2002). 11. B.A. Brown, Phys. Rev. C44, 924 (1991). 12. P. Haustein, At. Data Nucl. Data Tab. 39, 185 (1988). 13. P. Moller, J. R. Nix, W. D. Myers, and W. J. Swiatecki, At. Data Nucl. Data Tab. 59, 185 (1995). 14. J. Duflo and A. Zuker, Phys. Rev. C52, R23 (1995). 15. Y. Aboussir, J. Pearson, A. Dutta, and F. Tondeur, At. Data Nucl. Data Tab. 61, 127 (1995). 16. G. Audi and A. H. Wapstra, Nucl. Phys. A625, 1 (1997). 17. H. Koura, M. Uno, T. Tachibana, and M. Yamada, Nucl. Phys. A674, 47 (2000).

OPTIMIZATION OF ISOL UCX TARGETS FOR FISSION INDUCED BY FAST NEUTRONS OR ELECTRONS O. BAJEAT*, S. ESSABAA, F. IBRAHIM, C. LAU, Institut de Physique Nucleaire, 91406 Orsay,

France

Y. HUGUET, P. JARDIN, N. LECESNE, R. LEROY, F. PELLEMOINE, M.G. SAINT-LAURENT, A.C.C. VILLARI GANIL, Bd H. Becquerel 14076 Caen cedex 5, France F. NTZERY, A. PLUKIS, D. RIDIKAS DAPN1A, CEA Saclay, 91191 Gifsur

Yvette,

France

J.M. GAUTIER LPC, 6, Bd du Marechal Juin, 14050 Caen cedex,

France

M.MIREA NIPNE, P.O. Box, MG-6, Bucharest,

Romania

Two ways of production of radioactive beams using uranium carbide targets are taken into consideration: fission induced by fast neutrons and by bremsstrahlung radiation. For the SPIRAL 2 project, the fission of the uranium carbide target will be induced by a neutron flow created by bombarding a carbon converter with a 40 MeV high intensity primary deuteron beam. Calculations and design of the target in order to reach 1013 fission events per second with good release have been done. The second way is the photofission using an electron beam. In 2004 the ALTO project (Accelerateur Lineaire Aupres du Tandem d'Orsay) will give a 50 MeV/lOuA electron beam. This facility will allow more than 1011 fissions/s. In this case, the electron beam hits the target without converter. Calculations are realized in order to estimate the production and to choose the best target shape.

1. UCx targets For both projects: Spiral 2 with fast neutrons and Alto with electrons, the same kind of targets will be used. Targets are conceived in agreement with the ISOLDE method [1,2]. A such type of thick target is constructed by an assembly of disks (thickness of about 1 mm) composed from a mixing of Uranium carbide and graphite. The graphite allows to limit the carbide grain size for diffusion paths minimization. These pellets are obtained by * Corresponding author: [email protected] 155

156

compressing a mix of Uranium oxide and graphite powders. The carbonation is made by heating the pellets up to 2000 °C under vacuum. During irradiation, the targets are heated up to 2200 °C. 2.

Comparison between the two ways of production

Some experimental results are available for rare gas productions using fast neutrons and bremsstrahlung radiation [3]. In the case of neutrons, a deuteron beam hits a graphite converter. In the case of bremsstrahlung, an electron beam is focused on a tungsten converter or directly on the uranium carbide target itself. The experiments carried out in the frame of the PARRNE program described in the reference [3] showed that, with the same target of 14 mm diameter and 60 mm length, the production in atoms per microcoulomb is about two times higher with 50 MeV electrons without converter than with 80 MeV deuterons. For a high intensity primary beam, the main limitation of the photofission method is the energy deposited in the target which can produce failures. 3.

SPIRAL 2 target

For the SPIRAL 2 project the specification is to reach 1013 fission events per second using an UCx target, a 40 MeV / 5 mA deuteron beam and a rotating carbon converter. The production of a target irradiated by fast neutrons is estimated using the FICNER code [4]. This code offers the possibility to estimate the effects of geometrical parameters onto the production. The Fig. I Effect of the distance converter-target on the production target 80 mm diam, / 80 mm length CO

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157 emphasizes the importance to place the target as close as possible to the converter. The results obtained within the mentioned numeric code showed that a conical target would not be better for the production than a cylindrical one having the same volume. For the SPIRAL 2 project, it is planned to make a target of 80 mm diameter and of 80-mm length placed at about 40 mm from the entrance of the converter (Fig. 2). graphite container I

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The target has to work at a temperature higher than 2000 °C in order to allow an efficient release of the produced radioactive elements. The power deposited inside the target by the fission reactions is about 500 Watt for 1.6 1013f/s. Then, an extra heating must be added in order to reach convenient temperatures. Moreover the transfer tube between the target and the ion source has to be heated at 2000°C too, for the ionization of non volatile nuclei. 4.

ALTO target

For this project the goal is to reach 1011 fission events per second using a 50 MeV/10 uA electron beam [5]. The production of the target is estimated using the FICEL code [6]. Due to the absorption of photons, the production does not increase proportionally with the target density. The case of a conical shape was also studied. The table 1 shows that a conical target 3 times larger would produce only 30 % more fission events than the cylindrical one.

158 Table 1. Comparison of a cylindrical and a conical target for photofission (target density = 3.6 g/cm3) 1st diameter mm 14 14

2nd diameter mm 14 34

Volume cm3 15 47

Length mm 100 100

No fission/s forlOuA 1.0 10" 1.3 10"

4.1. Example for a converter The production in the target by using a tungsten converter has been studied. In this case, a part of the fission events is due to the photons emitted from the converter. Another part is due to the bremsstrahlung radiations produced in the target by the electrons which hit the target if the converter thickness is lower than the electron range in the tungsten. target production with converter UCx target 14 mm diam, 100 mm length; tungsten converter irradiated by 50 MeV electron beam

without conv

1 mm

2 mm

4 mm

5 mm

8 mm

converter thickness

Figure 3. Fission yields produced in the target with different converter thicknesses. In black: fission induced by photons produced in the target. In gray: fission induced by photons produced in the converter. The converter is in direct contact with the target.

These results show that the production is better without converter. Nevertheless, a converter could be useful to reduce the energy deposited in the target. In fact if the converter thickness is equal to the range of electrons, no electrons will hit the target and only the energy due to photon absorption will be deposited in the target. The results given in the table 2 show that the converter would reduce the production by a factor 5 while the energy deposited would be reduced by a factor 10.

159 Table 2. Production and energy deposited in the target without converter and with a 10 mm tungsten converter.

Without converter Converter W 10 mm

No of fission per UC 1.3 1010 0.26 1010

Energy deposition inMeV 35 3.4

For the ALTO project, an assembly of about 90 pellets of 14 mm diameter, 1 mm thickness and within a small spacing between each pellets will be used. For such a combination, about 350 Watt of the 500 Watt incident beam will be absorbed in the target, 150 Watt being re-emitted out of the target as photon radiation. 5.

Release times (SPIRAL 2 and ALTO)

Some effusion calculations using the Monte-Carlo method are under way to find the best spacing between the pellets. A large spacing will decrease the mean number of collisions of radioactive atoms in their way to reach the entrance of the ion source but, in the same time, the production will be lower due to the lower effective density of the target. References 1. H.L. Ravn et al., Nucl. Instr. Meth. B 26, 183 (1987). 2. C. Lau et al., Nucl. Instr. Meth. B204, 246(2003). 3. F. Ibrahim et al., Europ. Phys. J A15, 357 (2002). 4. M. Mirea et al., Europ. Phys. J. A l l , 59 (2001). 5. O. Bajeat and al., Proceedings of the NANUF03 workshop, Bucharest, Sept. 2003, to be published at World Scientific. 6. M. Mirea et al., Nucl. Instr. Meth. B201, 433 (2003).

THE ALTO PROJECT: A 50 MEV ELECTRON BEAM AT IPN ORSAY O. BAJEAT*, J. ARIANER, P. AUSSET, J.M. BUHOUR, J.N. CAYLA, M. CHABOT, F. CLAPJER, J.L. COACOLO, M. DUCOURTEUX, S. ESSABAA, H. LEFORT, F. IBRAHIM, M. KAMINSKI, J.C. LESCORNET, J. LESREL, A. SAID, S. M'GARRECH, J.P. PRESTEL, B. WAAST Institut de Physique Nucleaire, F-91406 Orsay cedex, France G. BIENVENU Laboratoire de I' accelerateur lineaire, F-91406 Orsay cedex, France

The PARRNE 2 device allows the production of neutron-rich isotopes beams using the ISOL method on a thick 238U target. With fast neutrons produced by 26 MeV / 1 uA deuteron beam, 109 fission/s are induced in the UCx target. In order to improve this production, it has been decided to use the photofission method. A 50 MeV electron accelerator connected with the PARRNE 2 separator is now under construction at IPN.

1.

Specifications

Some calculation of production with electrons has been carried out [1, 2]. For the same uranium target used to produce exotic beams with the on line isotope separator PARRNE 2 through fast neutron induced reactions, it seems possible to induce up to 1011 fission events per second using a 50 MeV / 1 0 pA electron beam (against 109 with the 26 MeV / 1 pA deuteron beam obtained in the past). Using the PARRNE 2 separator, about 5 photofission experiments of 3 weeks of irradiation per year are expected to be feasible. Several ion sources will be adapted on this set up: ISOLDE FEB IAD type, surface ionization, laser... Moreover the electron beams can be used also for other applications: for example in biochemistry (irradiation of proteins, study of DNA under irradiation...) or for industrial applications (irradiation of electronic components). The exploitation is planned to start in 2005. The price of the device is rather low (about 1 M€ without manpower) due to the fact that some equipments have been supplied by other laboratories: the accelerating section was offered by CERN (the LEP injector), other RF equipments are obtained * Corresponding author: [email protected] 160

161 from the Laboratoire de l'Accelerateur LinSaire (LAL Orsay) and a substantial part of the infrastructure already exists [3]. 2.

Characteristics

The maximum energy is 50 MeV with a maximum average intensity of 10 uA. The repetition rate is 100 Hz with an impulsion current duration between 2 ns to 2 us. The maximum emitance is estimated at 6 n- mm- mrad at 50 MeV. 3.

Implantation

The Fig. 1 displays schematically the set up of the installation. The beam line is equipped by instruments for the beam diagnostic: measurement of current, beam position, energy and energy dispersion. The use of the deuteron beam will remain possible.

Figure 1: lay- out of ALTO and the PAR

/ Tandem accelerator of Orsay.

References 1.

2. 3.

M. Mirea, O. Bajeat, F. Clapier, S. Essabaa, L. Groza, F. Ibrahim, S. Kandry-Rody, A.C. Mueller, N. Pauwels and J. Proust, Nucl. Instr. Meth. B201, 433 (2003). O. Bajeat et al., Proceedings of the NANUF03 workshop, Bucharest, Sept. 2003, to be published at Word Scientific. S. Essabaa et al., IPNO report 02-01, 2002.

SENSIBILITY OF ISOMERIC RATIOS A N D EXCITATION F U N C T I O N S TO STATISTICAL MODEL P A R A M E T E R S FOR T H E ( 4 ' 6 ' 8 H E , N , 3 N ) - R E A C T I O N S

T. V. CHUVILSKAYA AND A. A. SHIROKOVA Institute of Nuclear Physics Moscow State University, Russia M. HERMAN IAEA Nuclear Data Section, Vienna, Austria The calculations of the isomeric ratios erm/