A REVIEW OF THE FISSION DECAY OF THE GIANT RESONANCES IN THE ACTINIDE REGION

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A REVIEW OF THE FISSION DECAY OF THE GIANT RESONANCES IN THE ACTINIDE REGION

M. Harakeh

To cite this version:

M. Harakeh. A REVIEW OF THE FISSION DECAY OF THE GIANT RESONANCES IN THE ACTINIDE REGION. Journal de Physique Colloques, 1984, 45 (C4), pp.C4-155-C4-184.

�10.1051/jphyscol:1984413�. �jpa-00224078�

J O U R N A L D E PHYSIQUE

Colloque C4, suppl6ment au n03, Tome 45, mars 1984 page C4-155

A REVIEW OF THE FISSION DECAY OF THE GIANT RESONANCES IN THE ACTINIDE REG I ON

M.N. Harakeh

Kernfysisch VersneZZer I n s t i t u u t , 9747 AA Groningen, The Netherlands and

NucZear Physics Lab., University of Washington, SeattZe, WA 98195, U.S.A.

Resume - La decroissance par f i s s i o n des resonances geantes dans l a region des actinides e s t passee en revue. Les r e s u l t a t s invariablement contradic- t o i r e s de diverses experiences sont discutes. Cel les-ci comprennent des reactions inclusives de f i s s i o n induite par electron ou positron, e t des exp6riences ob l e s fragments de f i s s i o n sont detectes en coincidence avec l e s electrons ou hadrons diffuses inelastiquement. Nous nous concentrons sur une exp6rience ( a , a l f ) recente oO 1 'on etudie l a d6croissance par f i s - sion de l a resonance geante monopolaire en detectant l e s fragments de f i s s i o n en coincidence avec l e s a inelastiques autour de, e t ?I 0'

.

Abstract - The fission decay of giant resonances in the actinide reqion is reviewed. Results from various experiments which are invariably conflicting are discussed. These include inclusive electzun and wsitron induced fission, as well as experiments in which fission fragments were detected in coincidence with inelastically scattered electrons or hadrons. Attention is focussed on a recent ( a , a ' f ) experiment in which the fission decay of the giant monopole resonance was investigated by measuring fission fragments in coincidence with inelastically scattered a-particles at and around 00.

I - INTRODUCTION

The study uf the fission decay of the isoscalar giant resonances in the actinide region has been marred by claims and counter-claims concerning the magnitude of the fission probability of the giant quadruple resonance (QR). This is especially true for the 2 3 8 ~ nucleus, which is the most studied by ex~~,hnentalists, where the fission probab-ility for the GQR obtained using various probes at various bombiarcling energies, ranged from 40% /1,2/ down to 4% /3/, an order. of magnitude difference1 These differences were not Limited to the now classical bouridaty line between investigations with electromagnetic probes versus those W e with ha&.orric prolx?s, but even the results obtained with electmmagnetic probes were in disagreement. The same was true for experiments with hadronic probes. At the heart of the issue, of course, is the question of whether the decay of the GQR into fission is dominated by statistical conskderations or by direct fission ifecay. The first point of view stems from the general belief that the fission process for moderate excitation energies and low angular momenta takes a very long time (perhaps orders of magnitude longer) compared to the transit time needed for a bound nucleon to cross the boundaries of the nucleus (which is of the order of a 2x10-~* sec). During this time the nucleus, which is initially excited into the collective lp-lh giant resonance mode by a

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1984413

direct reaction such as inelastic hadron or electron scattering, would have enough time to mix into the more complicated 2p2h states which in turn spread into the more complicated 3p3h states, and so on and so forth until the equilibrated compound nuclear stage is reached. At this stage the fission decay probability is completely determined by the density of states at the saddle point versus ttle density of states in the (A-1) nucleus because of competition with neutron decay (the other dominant decay channel). This point of view is supported by experimental observation of the fission decay of the isovector giant dipole resonance (GDR). For the nuclei 232T?1 and 2 3 8 ~ it is found /4,5/ to have fission probabilities similar to the Fission probabilities obtained from the (n,f) compound nuclear reaction at similar excitation energies, and also agrees with the Z /A 2 Systematics from cornpourid nuclear fission probabilities as extrapolated from heavier nuclei / 6 / .

'l't~e second pint of view stems from the idea that the small amplitude oscillation of the giant resonances, especially the isoscalar ones and in pazkicular the GQR, can couple strongly to the large amplitude oscillation of the Fission W e . Therefore once the nucleus gets a small kick which starts it oscillating in a giant resonance mx3e it is easily driven in the direction of Fission. In this case the fission Will not take a considerable time to occur. This will have the following consequences on both the fission probability of the giant resonance and on the angular correlations of the Fission fragments: i) the fission probability of the giant resonance will be considerably larger than that of the compound nucleus, and ii) the angular correlation will be characteristic of the initial K-value (here K refers to the projection of the total angular momentum on the symmetry axis of the nucleus) of the excited giant resonance.

Interestingly enough the interpretations of tne experimentally obtained fission probabilities for the W R in 2 3 8 ~ did not always conform with either of the above ideas. For instance, in one experiment /1,2/ where a lxrge fission probability was deduced for the GQR (about a factor of two larger. than that of the GDR) t?le authors tried to justify /2/ their results on the basis of a statistical morlel calculation. Unfortunately, tttis was based on the wrong assumption that the Ireigtlts of the fission barriers a e different for positive and negative parity states for all excitation energies. If this were true, it could indeed lead Co 1aZge differences in the fission probabilities of the GDR ( J ~ .- 1-) and the GQR (J= = 2 + )

since the fission probability is determined by the density of states above the barrier. However, fission probabilities could differ substantially only al:

excitation energies slightly above the barrier because of the different excitation energies of low-lying positive and negative parity transition states above the barrier. At higher excitation energies above the barrier the densities of positive and negative parity states are expected to be the same, which should lead to similar fission probabilities for them.

In another experiment /3/, where conversely a very low fission probakxility was deduced for the GQR (about a factor of five less than that of the GDR), the authors conjectured /3/ that their data supported a strong coupling between the GQR mode and the fission mode because experimentally they observed a peak at the location of the GQR which apparently had an angular distribution similar to a = 0 + component.

I therefore have the difficult job of reviewing these conflicting reports on the fission decay of the isoscalax giant resonances in the actinide region. Alt?~ougll this seems like a formidable task, I will try to cover most of what ha8 W e n

p u b l i s h e d o n the s u b j e c t up till now. However, some v e r y i n t e r e s t i n g r e s u l t s o n t h e f i s s i o n probabilities of t h e v a r i o u s isoscalar g i a n t r e s o n a n c e s i n 2 3 8 ~ llave b e e n p u b l i s h e d r e c e n t l y /3,7,8/ s i n c e m y last r e v i e w /9/ o n t h i s s u b j e c t . These r e s u l t s i n c l u d e i ) a c o i n c i d e n c e e l e c t r o f i s s i o n 2 3 8 ~ ( e , e * f ) e x p e r i m e n t /7/ which measured t h e sum o f E2 and EO s t r e n g t h from t h e first f i s s i o n barrier u p t o 1 1 . 7 MeV, i i ) a measurement /3/ o f t h e f i s s i o n p r o b a b i l i t y i n the r e g i o n of the 3 f i w h i y h e n e r g y o c t u p o l e r e s o n a n c e (HEOR) b y i n e l a s t i c a - s c a t t e r i n g at E a

-

I1 - FISSION INDUCED BY ELECTROMAGNETIC PROBES

P h o t o a b s o r p t i o n c r o s s s e c t i o n s are c o m p l e t e l y dominated b y electric d i p o l e y - a b s o r p t i o n . Thus f o r the p a s t f o u r d e c a d e s p h o t o n u c l e a r r e a c t i o n s h a v e b e e n used t o i n v e s t i g a t e t h e v a r i o u s p r o p e r t i e s of t h e GDR and i n p a r t i c u l a r its d e c a y p r o p e r t i e s . I n the a c t i n i d e r e g i o n both the ( y e n ) and t h e ( y , f ) r e a c t i o n s h a v e b e e n s t u d i e d f o r 232Th and 2 3 8 ~ b y two g r o u p s /4,5/ w i t h r e a s o n a b l e agreement between t h e e x p e r i m e n t a l r e s u l t s . F o r 2 3 8 ~ t h e d i f f e r e n t i a l c r o s s s e c t i o n s d i f f e r b y 15% where the q u o t e d s y s t e m a t i c u n c e r t a i n t y f o r the Livermore d a t a /5/ is s 7% and for t h e S a c l a y d a t a /4/ i s < 10%. The Livermore g r o u p /5/ has a l s o s t u d i e d the above p h o t o n u c l e a r r e a c t i o n s on o t h e r n u c l e i i n t h e a c t i n i d e r e g i o n . Their r e s u l t s Showed t h a t t h e f i s s i o n p r o b a b i l i t i e s f o r 232Th and 2 3 8 ~ were e s s e n t i a l l y f l a t Ccom 1 7 MeV

u p t o t h e second chance f i s s i o n t h r e s h o l d s w i t h the deduced f i s s i o n probabilities b e i n g i n agreement w i t h t h o s e o b t a i n e d from t h e compound n u c l e a r ( n , f ) r e a c t i o n s and the Z 2 /A s y s t e m a t i c s / 6 / . The f i s s i o n p r o b a b i l i t y o f t h e GDR i n t h e r e g i o n o f 7-12 MeV i n 2 3 e ~ , which w i l l s e r v e as a s t a n d a r d a g a i n s t which t t ~ e f i s s i o n p r o b a b i l i t i e s o f t h e iSoScalar g i a n t r e s o n a n c e s w i l l be compared, was found from t h e p h o t o f i s s i o n e x p e r i m e n t s /5/ t o be Pf = 0.22i0.02.

Because o f t h e dominance o f electric d i p o l e a b s o r p t i o n i n p h o t o n u c l e a r r e a c t i o n s , these r e a c t i o n s c a n n o t g e n e r a l l y be u s e f u l for s t u d y i n g m u l t i p o l a r i t i e s o t t e r t h a n E l . A more s e n s i b l e way t o i n v e s t i g a t e t h e o t h e r m u l t i p o l a r i t i e s ( i . e . M 1 , E2, e t c . . ) is by s t u d y i n g electron-induced r e a c t i o n s . T h i s i s b e c a u s e the v i r t u a l photon s p e c t r a f o r i n c l u s i v e e l e c t r o n induced r e a c t i o n s h a v e h i g h e r i n t e n s i t i e s for E2 and M 1 m u l t i p o l a r i t i e s t h a n f o r E l and are t h u s more s e n s i t i v e t o t h e e x c i t a t i o n o f these m u l t i p o l a r i t i e s t h a n i n photo-induced r e a c t i o n s i n which t h e real photon spectra h a v e e q u a l i n t e n s i t i e s f o r a l l m u l t i p o l a r i t i e s . T h i s is i l l u s t r a L e d i n F i g . 1, where t h e v i r t u a l p h o t o n spectra /lo/ c a l c u l a t e d i n DWBA b y G a r g a r o and Onley /11/ for e l e c t r o n s o f e n e r g y Eo = 9 . 5 MeV i n c i d e n t upon a Uranium ( 2 = 9 2 ) n u c l e u s are shown. I t is clear from t h i s f i g u r e t h a t a l l t h e way up t o 9.0 MeV the E2 and M 1 m u l t i p o l e i n t e n s i t i e s are favoured b y l a r g e f a c t o r s as compared w i t h that o f t h e E l .

The early r e s u l t s o n t h e d e c a y of t h e i s o s c a l a r GQR i n 2 3 8 ~ came from i n c l u s i v e e l e c t r o n - i n d u c e d ( e , x ) e x p e r i m e n t s , where x r e p r e s e n t s a n e u t r o n , a n a - p a r t i c l e o r a f i s s i o n fragment. I n t h e s e e x p e r i m e n t s t h e i n c l u s i v e e l e c t r o n - i n d u c e d cross s e c t i o n s u are measured. These are r e l a t e d to t h e p h o t o a b s o r p t i o n c r o s s s e c t i o n s by:

e.x

where ahL is t h e p h o t o a b s o r p t i o n c r o s s s e c t i o n f o r m u l t i p o l a r i t y AL ( A L = E l , U l ,

Y , X AL

E 2 , etc.. ) and N ( E , E O ) is t h e v i r t u a l photon s p e c t r u m o f m u l t i p o l a r i t y At c a l c u l a t e d i n DWBA f o r an e l e c t r o n o f e n e r g y E The c o n t r i b u t i o n o f t h e El m u l t i p o l a r i t y to t h e e l e c t r o n - i n d u c e d r e a c t i o n c r o s s s e c t i o n 0' is deduced b y f o l d i n g t h e v i r t u a l photon s p e c t r u m N ~ ,c a l c u l a t e d i n DWBA, i n t o t h e e x p e r i m e n t a l l y measured p h o t o a b s o r p t i o n cross s e c t i o n which is assumed t o be t o t a l l y d u e t o e l e c t r i c d i p o l e a b s o r p t i o n i n t o t h e GDR r e g i o n . A f t e r s u b t r a c t i n g t h e E l c o n t r i b u t i o n t h e r e m a i n i n g e l e c t r o n - i n d u c e d cross s e c t i o n is d i s e n t a n g l e d i n t o t h e v x i o u s c o n t r i b u t i o n s from the o t h e r m u l t i p o l a r i t i e s by making c e r t a i n a s s u m p t i o n s c o n c e r n i n g t h e l o c a t i o n s , w i d t h s a n d s t r e n g t h s o f t h e v a r i o u s g i a n t r e s o n a n c e s c o n n e c t e d w i t h t h e s e d i f f e r e n t m u l t i p o l a r i t i e s .

F i g . 1 - V i r t u a l photon s p e c t r a ( r e f . 1 0 ) f o r E l , M I and E2 m u l t i p o l e s c a l c u l a t e d ( r e f . 1 1 ) i n DWBA f o r e l e c t r o n s o f 9 . 5 MeV I n c i d e n t o n a Uranium (2=92) n u c l e u s .

Photon Energy (MeV)

Thus t h e above method r e q u i r e s n o t o n l y a p r e c i s e d e t e ' ~ m ' i n a t i o n o f t h e a b s o l u i e e l e c t r o n - i n d u c e d and p h o t o a b s o r p t i o n c r o s s s e c t i o n s b u t a l s o a p r e c i s e C a l c u l a t i o n of t h e v i r t u a l photon s p e c t r a f o r t h e v a r i o u s m u l t i p l e s . The o n l y r i g o r o u s e x p e r i m e n t a l test o f t h e v i r t u a l p h o t o n s p e c t r a was perfvrmed by Doifye e t a l . /12/

r e c e n t l y . I n t h i s t e s t , t h e e l e c t r o - and p h o t o e x c i t a t i o n o f a n i s o l a t e d r e s o n a n c e , t h e 16.28 MeV 1- i s o b a r i c a n a l o g state (IAS) i n "2r, and its p r o t o n d e c a y wore i n v e s t i g a t e d f o r e l e c t r o n bombarding e n e r g i e s i n t h e r a n g e 1 7 - 1 0 5 MeV. Because o f t h e a l m o s t d i s c r e t e n a t u r e o f t h e r e s o n a n c e and its w e l l d e f i n e d s p i n and p a r i t y ( ~ c 1 - ) , Eq. (1) s i m p l i f i e s /12/ to:

where t h e i n t e g r a l y i e l d s t h e p h o t o a b s o r p t i o n cross s e c t i o n i n t o t h i s l e v e l l e a d i n q t o p o p u l a t i o n o f t h e "Y ground state b y p r o t o n d e c a y :

The q u a n t i t y r r /r was deduced /12/ from the e l e c t r o n - i n d u c e d p r o t o n d e c a y c r o s s P Y

s e c t i o n u s i n g tge above e q u a t i o n s and the v i r t u a l E l photon s p e c t r u m c a l c u l a t e d i n DWBA. T h i s s p e c t r u m was c o r r e c t e d f o r n u c l e a r s i z e e f f e c t s which become i n c r e a s i n q l y i m p o r t a n t f u r h i g h e l e c t r o n bombarding e n e r g i e s . Tt~e r e s u l t was i n v e r y g o d agreement ( o n t h e 2-3% l e v e l ) w i t h t h e v a l u e o b t a i n e d from t h e p h o t o a b s o r p t i o n measurements performed b y t h e same g r o u p /12/ u n d e r s i m i l a r e x p e r i m e n t a l c o n d i t i o n s . This t e s t i n c r e a s e s o u r c o n f i d e n c e i n the c a l c u l a t e d ~l v i r t u a l photon s p e c t r a more t h a n p r e v i o u s tests /33/ which had i n t e c j r a t e d o v e r the b r o a d ~i GDR w i t h o u t a c c o u n t i n g f o r p o s s i b l e e x c i t a t i o n o f o t h e r m u l t i p o l a r i t i e s . A test f o r t h e E2 v i r t u a l photon s p e c t r a s i m i l a r t o t h e test performed b y Dodge e t a l . /12/ f o r t h e E l v i r t u a l photon s p e c t r a is h i g h l y d e s i r a b l e .

I n t h e earliest r e p o r t e d e l e c t r o n - i n d u c e d measurement o f t h e e x c i t a t i o n and d e c a y o f t h e GQR i n 2 3 8 ~ , Wolynec e t a l . /14/ r e p o r t e d t h e o b s e r v a t i o n o f y-ray a c t i v i t y from

234Tt1 f o l l o w i n g a bombardment o f 2 3 8 ~ b y e l e c t r o n s . The i n t e g r a t e d 2 3 8 ~ ( e , a ) c r o s s s e c t i o n n e c e s s a r y t o a c c o u n t f o r t h e o b s e r v e d a c t i v i t y amounted t o a b o u t 50-100% of t h e E2 e n e r g y w e i g h t e d sum r u l e (EWSR). T h i s was t o t a l l y u n e x p e c t e d s i n c e a - d e c a y of the GQR i n ^{Z 3 B ~} s h o u l d be s t r o n g l y i n h i b i t e d b e c a u s e o f the h i g h Coulomb barrier. S e v e r a l e x p e r i m e n t a l g r o u p s l a t e r s e a r c h e d u n s u c c e s s f u l l y /15-17/ for t h i s a-decay c h a n n e l either b y a search f o r y - a c t i v i t y from t h e r e s i d u a l 2 3 4 ~ h p r o d u c t s or b y d i r e c t o b s e r v a t i o n of a-particles d u r i n g t h e e l e c t r o n bombardment. These u n s u c c e s s f u l a t t e m p t s i n d i c a t e d t h a t t h e measurement b y Wolynec e t a l . /14/ h a d some e x p e r i m e n t a l problems. A s u b s e q u e n t aCtempt b y L e e s at a l . /18/ to d e t e r m i n e t h e p o s s i b l e s o u r c e o f t h e 234Th a c t i v i t y v i a a s t u d y o f t h e ( y , a ) and t h e ( n , n v a ) r e a c t i o n s on 2 3 8 ~ y i e l d e d n e g a t i v e r e s u l t s . Although it is now g e n e r a l l y accepteO t h a t no a-emission o c c u r s from t h e r e g i o n of the GQR i n 2 3 8 ~ , t h e problem b e h i n d t h e o b s e r v a t i o n o f t h e 234Th a c t i v i t y b y Wolynec e t a l . /14/ i s s t i l l u n r e s o l v e d .

Another s u r p r i s i n g r e s u l t was o b t a i n e d b y M a r t i n s e t a l . /19/ for t h e e l e c t r o n - induced e m i s s i o n o f n e u t r o n s i n t h e g i a n t r e s o n a n c e r e g i o n . T t ~ e y found /19/ t h a t the a o b t a i n e d from t h e i r 2 3 8 ~ ( e , n ) measurement c o u l d be s a t i s f a c t o r i l y e x p l z i n e d b y

e , n

E l e x c i t a t i o n o n l y , w i t h a t most 8% of t h e E2, EWSR i n t h e ( e , n ) c h a n n e l . ?I~-is i n d i c a t e d t h a t a l m o s t a l l o f t h e E2 s t r e n g t h g o e s i n t o t h e o n l y o t h e r a v a i l a b l e d e c a y c h a n n e l i.e. f i s s i o n , a l t h o u g h o n g e n e r a l grounds one would have expected a statistical d e c a y o f t h e GQR similar t o t h a t o f the GDR, t h u s f o r 2 3 8 ~ r / r f a 3.5. A later ( e , n ) measurement b y S h o t t e r e t a l . /20/ c o r r o b o r a t e d t h i s r e s u l t , b u t w i t h an u p p e r l i m i t of 1 6 % of t h e E2, EWSR. Along w i t h t h e earlier e l e c t r o f i s s i o n measurement o n 238u b y S h o t t e r e t a l . /21/ t h i s y i e l d e d a rn/rf = 0.6-0.8 f o r t h e GQR /20/ which i s t o be c o n t r a s t e d w i t h t h e v a l u e o f 3 . 5 f o r the GDR.

These e a r l y r e s u l t s f o r t h e d e c a y o f the GQR were a l r e a d y c o n t r o v e r s i a l b e c a u s e o f t h e unexpected d i f f e r e n c e I n f i s s i o n p r o b a b i l i t i e s f o r the GDR and t h e GQR. However.

it was n o t u n t i l t h e e x t e n s i v e e l e c t r o f i s s l o n measurements of Arruda-Neto e t al. /22/ o n a number o f Uranium i s o t o p e s , w i t h an acclaimed h i g h p r e c i s i o n o n t h e P e r c e n t a g e s of E2, EWSR s t r e n g t h e x h a u s t e d i n t h e e l e c t r o f i s s i o n c h a n n e l , t h a t i n t e r e s t i n t e n s i f i e d i n the e l e c t r o f i s s i o n o f t h e GQR i n t h e a c t i n i d e n u c l e i . In t h e i r i n i t i a l a n a l y s i s Arruda-Neto e t a l . /22/ l o c a t e d a b o u t 100% o f the E2, EWSR

and a significant M1 component in three isotopes of Uranium: 234,236.23EU. However in a later analysis /1,2,10,23/ of their data, the percentages of E2, EWSR were found to be about 20% lower than their original values for all three isotopes. Nevertheless, the amount of E2 strength deduced from the (e,f) measurements indicated that a large percentage of the GQR decays'by fission. The resulting fission strength functions for the 234,236,238

U isotopes /l/ are shown in Fig. 2. These are obtained from the electrofission cross sections following the procedure described above to deduce the cE2 cross section which is then related to

Y . f

the fission strength function by:

where dB/do represents the E2 strength function and T f / T , which in principle is a function of excitation energy, is the fission probability of the GQR. These E2 strength functions peak at different energies than the absorption cross sections which were incorrectly quoted as the GQR peak energies in earlier publications /10,22,23/.

PHOTON ENERGY ( M ~ v )

F i g . 2 - F i s s i o n s t r e n g t h (dB/dw) (Tg/T) f o r t h e GQR f o r t h e

2 3 9 2 3 6 9 2 3 8 ~ i s o t o p e s a s determined ( r e f . 1) from ( e , f ) c r o s s s e c t i o n s . For more d e t a i l s c o n c e r n i n g t h e e x p e r i m e n t and t h i s f i g u r e s e e r e f . 1.

The r e s u l t s for the three Uranium isotopes are summarized /1/ i n T a b l e 1. A number o f remarks can be made: i ) the peak e n e r g i e s d i f f e r a p p r e c i a b l y from t h o s e d e t e r m i n e d from i n e l a s t i c h a d r o n s c a t t e r i n g s i n g l e s measurements where a bump, which c o u l d be a combination o f a number o f m u l t i p o l a r i t i e s , was o b s e r v e d i n 2 3 8 ~ a t a r o u n d 10.5 MeV /24,25/ and at 11 MeV /26,27/ and i n 2 3 2 ~ h /28/ a t 11 MeV. i i ) l ? ~ e w i d t h s (F'WHM) a r e also a p p r e c i a b l y l a r g e r t h a n t h o s e o b t a i n e d Erom h a d r o n i c s c a t t e r i n g e x p e r i m e n t s . i i i ) The p e r c e n t a g e s o f t h e E2, EWSR s t r e n g t h e x h a u s t e d i n t h e f i s s i o n c h a n n e l a r e v e r y l a r g e f o r a l l t h r e e i s o t o p e s a n d e v e n t h e e s t i m a t e d /1/

f i s s i o n p r o b a b i l i t i e s a t the o f t h e E2 s t r e n g t h f u n a t j . o n are s t i l l l a r g e ( a f a c t o r o f 2 f o r 2 3 8 ~ ) compared t o t h o s e u £ t h e GDR. A t t h e f i s s i o n b a r r i a + , t h e f i s s i o n p r o b a b i l i t y deduced f o r t h e E2 StrenqCh f u n c t i o n is a l s o v e r y l a z q e . For 2 3 8 ~ , it is found /2/ t o be Pf = 0.8 Conlpared to a f i s s i o n p r o b a b i l i t y o f 0.4 o b t a i n e d from o t h e r s t u d i e s /29/. i v ) I t is n o t c l e a r why o n l y E l a n 8 E2 m u l t i p u l t i r i t i e s h a v e b e e n i n c l u d e d i n t h e c a l c u l a t i o n o f t h e e 1 e c f ; r o f l s s i o n c r o s s s e c t i o n s a p a r t from t h e hand-waving argument b y Arruda-Neto e t a l . / l o / . T h i s s t a t e d t h a t f o r t h e i n c i d e n t e l e c t r o n e n e r g i e s under c o n s i d e r a t i o n t h e i n t e y ~ a t e d e l e c t r o n - i n d u c e d c r o s s s e c t i o n s a r e dominated b y low nwmentum t r a r l s f c r e v e n t s t h u s

l e a d i n g t o v a n i s h i n g c o n t r i b u t i o n s from EO, E3 and t h e r e f o r e a l s o Erom i s o s c a l a + E l and h i g h e r m u l t i p o l a r i t i e s . M 1 c o n t r i b u t i o n was n e g l e c t e d b e c a u s e o f l a c k o f e x p e r i m e n t a l e v i d e n c e f o r g i a n t M 1 s t r e n g t h .

T a b l e 1

F i s s i o n d e c a y p a r a m e t e r s o f t h e GQR s t r e n g t h f u n c t i o n i n 2 3 8 ~ from ( e, f ) measurements /I/.

NuCle~lS P e a k e n e r g y FWHEf EWSR PE(E2 )

( MeV ) ( M ~ v ) ( % ) ( % )

23aU 8 . 2 f 0 . 4 4 . 8 t 1 . 0 8 7 f 1 4 70*15

236" 8 . 9 f 0 . 4 4 . 7 f 1 . 0 7 2 f 1 0 60*10 238" 8 . 3 t 0 . 4 5 . 0 t 1 . 0 5 5 f 1 0 4 0 k 1 0

The j u s t i f i c a t i o n f o r t h e h i g h f i s s i o n p r o b a b i l i t y o f t h e CQR i n cornpaxison t o the GDR as p r o p o s e d b y Arruda-Neto and Berman /2/ was b a s e d o n a wrorlg assumption as was d i s c u s s e d i n t h e i n t r o d u c t i o n . T h e r e f o r e o n e s h o u l d s e e k t h e r e a s o n f o r t h e s e h i g h

f i s s i o n p r o b a b i l i t i e s i n o t h e r q u a r t e r s . T h i s h a s b e e n d i s c u s s e d r a t h e r extctertsively by Aschenbach e t al. /30/ and StrOher. e t a l . /31,32/.

I n t h e i r c r i t i q u e o f t h e reSul.ts o f A r ~ u d a - N e t o e t al. / l , z / , Asc?lenbach e t al. /30/

and S t r O h e r e t a l . /31,32/ emphasized t h a t t h e r e s u l t s o f t h e i r a c a l y s i s depend s e n s i t i v e l y [see Eq. ( I ) ] o n t h r e e f a c t o r s . i ) F i r s t l y , t h e r e s u l t s depend on t h e r e l i a b i l i t y o f t h e c a l c u l a t e d v i r t u a l p h o t o n spectra, e s p e c i a l l y t h e E l c0mponen.t. The E l v i r t u a l pttoton s p e c t r a w e r e c o n c l u s i v e l y t e s t e d w i t h i n a few p e r c e n t i ~ y Dodge e t a l . /12/ as d i s c u s s e d earlier b u t o n l y £ o r a medium-heavy n u c l e u s ( Z = 4 0 ) . The o n l y t e s t o f t h e E2 v i r t u a l photon s p e c t r a i s t h e o n e performed by Arruda-Neto et a l . /13/ by comparing a n g u l a r d i s t r i b u t i o n s f o r E2 e x c i t a t i o n n e a r t h e f i s s i o n b a r r i e r , i.e. i n t h e r a n g e o f 6-7 MeV. T h e i r q u o t e d u n c e r t a i n t y i s 20%. i i ) S e c o n d l y , t h e a n a l y s i s d e p e n d s o n t h e a b s o l u t e p h o t o f i s s i o n c r o s s s e c t i o n s a n d t h e i r e x t r a p o l a t i o n s t o e n e r g i e s above t h e GDR where n o e x p e r i m e n t a l d a t a a r e a v a i l a b l e . S i n c e E l a b s o r p t i o n i s still t h e dominant mode i n e l e c t r o e x c i t a t l o n , u n c e r t a i n t i e s i n t h e p h o t o f i s s i o n cross s e c t i o n s are r e f l e c t e d i n t h e c a l c u l a t e d a a c c o i d i n g t o Eq. ( 1 ) . T h e s e w i l l be r e f l e c t e d e v e n more s t r o n g l y i n t h e

e, ^f

e x t r a c t e d E2 s t r e n g t h from t h e e l e c t r o f i s s i o n measurements. A v a i l a b l e e x p e r i m e n t a l p h o t o f i s s i o n cross s e c t i o n s d i f f e r b y 15%. Iicrwevsr, t h e e x t r a & w l a t i o n t o e n e r y i e s

above t t t e GDI? i s n o t v e r y critical, s i n c e e x p e r i m e n t i i l r e s u l t - ? C u r e l c c t r o n c r 4 1 . r ( ~ c f ? ~ ; above 2 0 MeV p < x r l y d e t e x n i i l ~ ~ , CQR p,ir;lrr.et.c?rs a s ~ K ~ ' i n t c ( J o u t by hcruil&-12~:to et 21. /23/. T h i s g r o u p ilri~lcatet3 /23/ t h - l t Chatter F ? t a1. /21/ w l , f o u r t d h l c , t ' r c ~ i : ~ their

;~nalyr.i:; of 20-123 I<eV e l e c t r o f i s s i v n dat.a, t o t l c i - c r m i r t e w l ~ c t ? l c r t?rc l i ~ c y c E%

s t r e n g t h t h e y found was l o c a t e d a t 9 MeV or 22 MeV. i i i ) T h i r d l y , t h e a n a l y s i s d e p e n d s o n t h e p r e c i s e a b s o l u t e v a l u e and s h a p e o f t h e e l e c t r o f i s s i o n cross s e c t i o n s where s i g n i f i c a n t and i m p o r t a n t d i f f e r e n c e s c a n be n o t e d between t h e r e c e n t r e s u l t s o f Arruda-Neto e t a l . /1,2/ and t h o s e o f o t h e r g r o u p s . 'This is i l l u s t r a t e d i n F i g . 3 ( t h i s f i g u r e and F i g . 4 are o b t a i n e d from r e f . 31; updated c r o s s s e c t i o n d a t a b y S t r e h e r e t al. w i t h r e d u c e d s y s t e m a t i c errors h a v e a p p e a r e d i n r e f . 32), where t h e d a t a o b t a i n e d by d i f f e r e n t g r o u p s are compared. The e- d a t a from measurements performed w i t h d i f f e r e n t t e c h n i q u e s /21,30,31,32,33/, i n c l u d i n g an o l d e r measurement b y Arruda-Neto e t al. /33/ a g r e e . The o n l y e x c e p t i o n are t h e more r e c e n t d a t a o f Arruda-Neto e t a l . /1,2/ from which l a r g e p e r c e n t a g e s o f E2 s t r e n g t h i n t h e f i s s i o n c h a n n e l were d e r i v e d .

The p o s i t r o n - i n d u c e d f i s s i o n d a t a i n F i g . 3 are t h o s e o f S t r o h e r e t a l . /31,32/. The h a t c h e d curves r e p r e s e n t /31,32/ p r e d i c t e d e l e c t r o f i s s i o n and p o s i t r o f i s s i o n c r o s s s e c t i o n s c a l c u l a t e d a c c o r d i n g t o Eq. ( 1 ) . The E l v i r t u a l photon spectra were

f Arruda Neto et al.

1 Arruda Neto et.at.

3 Aschenbach et.al

0 Shotter et.al

fi (th~ck target) this work

1 (thin target

$ Calculation

F i g . 3 - Comparison o f a b s o l u t e e l e c t r o f i s s i o n c r o s s s e c t i o n s . For more d e t a i l s s e e t e x t and r e f s . 31 and 32.

c a l c u l a t e d i n DWBA w i t h o u t i n c l u d i n g n u c l e a r s i z e effects. Wle a b s o l u t e p h o t o f i s s i o n c r o s s s e c t i o n s o f C a l d w e l l e t a l . /5/ w i t h t h e s t a t e d u n c e r t a i n t i e s o f 7% were u s e d . These were e x t r a p o l a t e d for y - e n e r g i e s 2 1 8 MeV. The e- and e d a t a l i e below +

t h e c a l c u l a t e d E l c u r v e s , e x c e p t f o r t h e d a t a o f Arruda-Neto e t a l . /1,2/. This l e d Aschenbach e t a l . /30/ and s t r o h e r e t a l . /31,32/ t o c o n c l u d e t h a t t h e i r d a t a a r e c o n s i s t e n t w i t h v a n i s h i n g E2 s t r e n g t h i n t h e f i s s i o n d e c a y c h a n n e l .

The m a j o r d i f f i c u l t y i n h e r e n t i n t h e method d e s c r i b e d above f o r d e d u c i n g E2 s t r e n g t h from e l e c t r o f i s s i o n c r o s s s e c t i o n s lies i n the s e n s i t i v i t y t o t h e p r e c i s e d e t e r m i n a t i o n o f a b s o l u t e e l e c t r o f i s s i o n and p h o t o f i s s i o n cross s e c t i o n s . I t was p o i n t e d o u t b y S t r o h e r e t a l . /31,32/ that a more s e n s i b l e method would be t o compare t h e c r o s s s e c t i o n r a t i o o f o-/u+ f o r e l e c t r o n - and p o s i t r o n - i n d u c e d r e a c t i o n s , s i n c e i n the c a l c u l a t e d r a t i o the a b s o l u t e scale o f t h e photoinduced cross s e c t i o n n e a r l y c a n c e l s o u t . Moreover, it is e x p e r - i m e n t a l l y easier t o o b t a i n reliable r e l a t i v e c r o s s s e c t i o n s t h a n t o measure a b s o l u t e ones. The r e s u l t s o f such a measurement /31,32/ for e l e c t r o n - and p o s i t r o n - i n d u c e d f i s s i o n o f 2 3 8 ~ are shown i n F i g . 4. V a r i o u s symbols r e p r e s e n t /31/ t h e r e s u l t s of d i f f e r e n t e x p e r i m e n t a l r u n s which are o b v i o u s l y c o n s i s t e n t w i t h each o t h e r . The dashed l i n e i s t h e r e s u l t of PWEIA c a l c u l a t i o n where the v i r t u a l p h o t o n s p e c t r a for e l e c t r o n s and p o s i t r o n s are t h e same. The f u l l c u r v e r e p r e s e n t s /31/ t h e r e s u l t o f a c a l c u l a t i o n of t h e E l v i r t u a l p h o t o n s p e c t r a i n DWBA w i t h o u t i n c l u d i n g n u c l e a r s i z e effects. The p h o t o f i s s i o n d a t a o f C a l d w e l l et a l . /5/ were u s e d i n t h i s c a l c u l a t i o n . The u-/u C

d a t a l i e w e l l below t h e f u l l E l c u r v e . S m a l l c h a n g e s i n the scale of t h e v i r t u a l p h o t o n s p e c t r a would l e a d /31/ t o good agreement between t h e d a t a and the f u l l E l c u r v e . Such a change c a n be o b t a i n e d ^/32/ b y i n c l u s i o n o f n u c l e a r s i z e e f f e c t s . The h a t c h e d area r e p r e s e n t s a c a l c u l a t i o n where, i n a d d i t i o n t o t h e E l s t r e n g t h , 65*7%

of t h e E2, EWSR is i n c l u d e d . It is o b v i o u s l y too h i g h compared w i t h t h e d a t a . The comparison m a d e i n t h i s f i g u r e s u p p o r t s the c o n t e n t i o n that i n t h e f i s s i o n c h a n n e l t h e r e i s l i t t l e E2 s t r e n g t h , a c o n c l u s i o n which i s i n disagreement w i t h the r e s u l t s of ~ r r u d a - N e t o e t a l . / 1 , 2 / .

Fig. 4 Ratio of electrofission to positro- fission cross sections 0-/o+ as a function of incident energy for 2 3 8 ~ . For more details see text and refs. 3 1 and 32.

The most i n t e r e s t i n g o f t h e e l e c t r o n - i n d u c e d f i s s i o n measurements i s a c o i n c i d e n t e l e c t r o f i s s i o n e x p e r i m e n t performed b y Dowell e t al. ^{/ 7 / . Illis} h a s t h e a d v a n t a g e o v e r t h e p r e v i o u s l y d i s c u s s e d e l e c t r o n induced e x p e r i m e n t s i n t h a t : i ) it is f r e e from t h e i n c l u s i v e e n e r g y i n t e g r a t e d measurement and t h e r e f o r e t h e e x a c t s h a p e of

t h e m u l t i p o l e s t r e n g t h c a n be d e t e r m i n e d . i i ) The momentum t r a n s f e r c a n be chosen t o enhance v a r i o u s m u l t i p o l a r i t i e s t h u s making it easier t o d i s e n t a n g l e t h e c o n t r i b u t i o n s o f these v a r i o u s m u l t i p o l a r i t i e s . i i i ) I t is r e l a t i v e l y model i n d e p e n d e n t . Moreover. it has t h e a d v a n t a g e o v e r h a d r o n s c a t t e r i n g e x p e r i m e n t s i n t h a t it is f r e e from t h e huge n u c l e a r continuum u n d e r l y i n g the g i a n t r e s o n a n c e s i n t h e a c t i n i d e n u c l e i . I n hadrwn s c a t t e r i n g e x p e r i m e n t s a s s u m p t i o n s h a v e t o be made c o n c e r n i n g the s h a p e and magnitude o f t h i s background.

I n the c o i n c i d e n t e l e c t r o f i s s i o n e x p e r i m e n t / 7 / , e f f e c t i v e momentum t r a n s t e r s v a r i e d from 0 . 3 6 t o 0.59 fm-' f o r which o n l y low m u l t i p o l e s (AGZ) are e x c i t e d . Moreover, b e c a u s e the EO a n d E 2 form f a c t o r s are i n d i s t i n g u i s h a b l e a t low q, t h e d a t a a n a l y s i s

i s l i m i t e d t o d i s e n t a n g l i n g t h e E l c o n t r i b u t i o n from t h e combined EO/E2 c o n t r i b u t i o n t o t h e c o i n c i d e n t e l e c t r o f i s s i o n c r o s s s e c t i o n . I n the a c t u a l a n a l y s i s t h e ( y , f ) d a t a of C a l d w e l l e t al. /5/ were i n c l u d e d o n a n e q u a l f o o t i n g w i t h t h e ( e , e l f ) d a t a . The r e s u l t s are shown i n F i g . 5 . The E2/EO s t r e n g t h has the u s u a l c h a r a c t e r i s t i c b e h a v i o u r n e a r t h e f i s s i o n b a r r i e r ( s e e F i g . 5 a ) . The most

w (MeV)

Fig. 5 - The E2/EO s t r e n g t h and i t s measured a n g u l a r asymmetry deduced from t h e ( e , e l f ) e x p e r i m e n t o f Dowel1 e t a l . 171.

i n t e r e s t i n g f e a t u r e o f t h e E2/EO s t r e n g t h , however, is i t s f l a t n e s s from 7 t o 11.7 MeV. N o r e s o n a n t behaviour is observed s i m i l a r t o t h e one e x t r a c t e d by Arruda Net0 e t al. /1,2/, o r similar t o t h e g i a n t resonance bump observed i n hadron s c a t t e r i n g /24-28/. The a n i s o t r o p y , r e p r e s e n t e d by t h e r a t i o o f t h e 1800 t o 900 f i s s i o n y i e l d s , i s l a r g e n e a r t h e f i s s i o n b a r r i e r i n d i c a t i n g a dominance o f E2 c o n t r i b u t i o n . Above 7 MeV, however, t h e i s o t r o p y c o u l d be due e i t h e r t o a l a r g e EO c o n t r i b u t i o n o r t o K-mixing i n t h e decay o f E2 s t r e n g t h .

I n F i g . 6 , t h e E2 p h o t o f i s s i o n c r o s s s e c t i o n deduced from t h e ( t 3 , e . f ) measurement o f Dowel1 e t al. is compared /7/ w i t h t h e E2 p h o t o f i s s i o n Cross S e c t i o n d e r i v e d by Arruda-Neto e t al. /1,2/ from their i n c l u s i v e ( e , f ) measurement. I t is clear from t h i s comparison and t h e f o r e g o i n g d i s c u s s i o n t h a t Arruda-Neto e t a l . have o v e r e s t i m a t e d t h e E2 s t r e n g t h above 7 MeV, which indeed c a s t s doubt on t h e i r d a t a .

5.0 7.5 10.0 12.5 15.0 17.5 20.0

w (MeV)

Fig. 6 - Comparison between the E2 photofission cross sections deduced from the coincident electrofission measurement 171 and the inclusive electro- fission results of Arruda-Neto et al. /1,2/.

The i n t e g r a t e d E2/EO s t r e n g t h observed b y Dowel1 e t al. between 7 and 11.7 MeV corresponds t o 10% o f t h e i s o s c a l a r E2 EWSR w i t h an u n c e r t a i n t y o f 25%. The a u t h o r s a r g u e t h a t i f E2 s t r e n g t h h a s t h e same f i s s i o n p r o b a b i l i t y as t h e GDR t h e n t h e r e would be i n t o t a l 45% o f t h e E2 EWSR i n t h i s e x c i t a t i o n energy r e g i o n . However, one should remark t h a t i n f a c t t h i s experiment can riot d i f f e r e n t i a t e between E2 and EO s t r e n g t h or between i s o s c a l a r and i s o v e c t o r s t r e n g t h . Although from t h e o r e t i c a l c o n s i d e r a t i o n s one would n o t e x p e c t much i s o v e c t o r E2 o r EO s t r e n g t h i n t h i s enerqy r e g i o n , t h e r e is evidence /8/ f o r s u b s t a n t i a l i s o s c a l a r EO s t r e n g t h as w i l l be d i s c u s s e d later. This would l e a d t o about 7% E2, EWSR s t r e n g t h between 7 and 11.7 MeV i n t h e f i s s i o n channel and t h e r e f o r e a t o t a l o f 32% E2, EWSR s t r e n g t h i n t h i s r e g i o n i f t h e f i s s i o n p r o b a b i l i t y o f t h e q R is t h e same as t h a t o f t h e GDR.

Before ending t h i s s e c t i o n , it is worth mentioning t h e r e s u l t o f Lhe muon-induced f i s s i o n e x p r i m e n t by Johansson e t a l . /34/. I n t h i s experiment, f i s s i o n induced through t h e r a d i a t i o n l e s s 9.6 MeV quadrupole 3d-1s t r a n s i t i o n , which is i n t h e