SPIN DETERMINATION OF HIGHLY EXCITED NUCLEI FROM LIGHT PARTICLE EMISSION STUDIES

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SPIN DETERMINATION OF HIGHLY EXCITED NUCLEI FROM LIGHT PARTICLE EMISSION

STUDIES

D. Guerreau, R. Babinet

To cite this version:

D. Guerreau, R. Babinet. SPIN DETERMINATION OF HIGHLY EXCITED NUCLEI FROM

LIGHT PARTICLE EMISSION STUDIES. Journal de Physique Colloques, 1980, 41 (C10), pp.C10-

217-C10-228. �10.1051/jphyscol:19801022�. �jpa-00220641�

JOURNAL DE PHYSIQUE CoZZoque C10, suppZ&rnent au n012, Tome 41, de'cembre 1980, page C10-217

SPIN DETERMINATION OF HIGHLY EXCITED NUCLEI FROM LIGHT PARTICLE EMISSION STUDIES

D. Guerreau and R. ~ a b i n e t *

J n s t i t u t de Physique Nucldaire, B.P. N o l , 91406 Orsay, France.

CEN Saclay, Ddpartement de Physique Nucldaire, B.P. N02, 91190 Gf-Sur-Yvette, France.

Among the d i f f e r e n t mechanisms involved i n heavy i o n r e a c t i o n s , deeply i n e l a s t i c c o l l i s i o n s have been s t u d i e d e x t e n s i v e l y t h e s e l a s t t e n y e a r s . I t i s n o t t h e aim of t h i s t a l k t o d e s c r i b e i n d e t a i l s t h e va- r i o u s f e a t u r e s of t h e s e d i s s i p a t i v e c o l l i s i o n s . Se- v e r a l reviews of a l l t h e new a s p e c t s t h a t appeared r e c e n t l y may be found i n t h e Let us r e c a l l however some of t h e o u t s t a n d i n g c h a r a c t e r i s - t i c s of t h i s p r o c e s s . One of the most s t r i k i n g f e a - t u r e s i s the r a p i d damping of the t r a n s l a t i o n a l k i - n e t i c energy a s s o c i a t e d w i t h the r e l a t i v e motion

i n t o i n t e r n a l e x c i t a t i o n energy, an i n d i c a t i o n of a l a r g e v i s c o s i t y c o n s t a n t f o r n u c l e a r m a t t e r . I t h a s been d e s c r i b e d i n term of a f r i c t i o n f o r c e a c t i n g between t h e two n u c l e i . T h i s f r i c t i o n f o r c e might a r i s e , f o r example, from t h e one body d i s s i p a t i o n mechanism i n t r o d u c e d by Blocki e t a l S 7 . I t l e a d s n a t u r a l l y t o a damping of t h e r e l a t i v e motion b u t , due t o i t s t a n g e n t i a l component, i t should a l s o show up i n a n g u l a r momentum d i s s i p a t i o n . It i s thus c l e a r t h a t one should not s t u d y s e p a r a t e l y t h e r e l a x a t i o n of t h e two b a s i c degrees of freedom a s s o c i a t e d r e s - p e c t i v e l y w i t h energy and angular momentum. They have t o be understood simultaneously and indeed we s h a l l s e e l a t e r t h a t one h a s t o know how t h e e x c i - t a t i o n energy i s shared between t h e b o fragments b e f o r e deducing any i n f o r m a t i o n on the a n g u l a r mo- mentum t r a n s f e r . More g e n e r a l l y , one can s t u d y how t h e angular momentum d i s s i p a t i o n i s r e l a t e d t o o t h e r dynamical parameter such a s t h e nucleon exchange. I t appears then t h a t deeply i n e l a s t i c c o l l i s i o n s give us the unique chance t o follow, d u r i n g t h e c o l l i s i o n time, t h e t r a n s f e r of o r b i t a l a n g u l a r momentum i n t o i n t r i n s i c s p i n s of t h e fragments.

Many experiments have been devoted t o t h i s pro- blem. Average fragment s p i n s and/or s p i n alignment have been deduced from s e q u e n t i a l f i s s i o n s t u - dies9-13, gamma r a y m u l t i p l i c i t y 14-'0 and c i r c u l a r

21-23 p o l a r i s a t i o n measurements

.

Angular momentum e s t i m a t e s from y m u l t i p l i c i t y masurements a r e however s u b j e c t t o some ambigui- t i e s . The f i r s t d i f f i c u l t y a r i s e s from t h e assump-

t i o n which has t o be made on t h e average m u l t i p o l a r i - t y of t h e observed y t r a n s i t i o n s ^{( E 2 ,} s t r e t c h e d , un- s t r e t c h e d , M1

..

^.)

.

Also, one h a s t o n e g l e c t ( o r t o c a l c u l a t e ) the a n g u l a r momentum removed by l i g h t par- t i c l e s . Nambodiri e t a ~have shown very c l e a r l y . ~ ~ t h e b a s i c l i m i t a t i o n s of t h i s method. This i s i n d i c a - t e d i n F i g . ] which i s a contour diagram of average y- m u l t i p l i c i t i e s a s a f u n c t i o n of average a n g u l a r mo- mentum and masses ( t h e s e r e s u l t s come from r e c e n t measurements i n a number of f u s i o n r e a c t i o n s ) . I t ap-

I d

OO 10 20 30 40 50

AVERAGE ANGULAR MOMENTUM, h

Fig.1. Systematics of the measured mean gamma multi- p l i c i t y b+ as a function o f the average angu- Zar momenturn of one comporozd nucleus, for ua- r i o m mass numbers f r e f . 2 0 ) .

p e a r s c l e a r l y t h a t f o r l i g h t masses (M<70), My i s no more s e n s i t i v e t o t h e a n g u l a r momentum of t h e emit- t i n g system. For such l i g h t system, most of t h e an- g u l a r momentum i s indeed removed by l i g h t p a r t i c l e emission (mainly a - p a r t i c l e s ) . The &ty technique i s t h u s most a p p r o p r i a t e f o r lnedium mass systems where t h e c o m p e t i t i o n i s r e s t r i c t e d t o n e u t r o n and y-rays

.

For t h e h e a v i e s t systems, t h e b e s t method i s c l e a r l y ' t o look a t s e q u e n t i a l f i s s i o n . It has l e d t o very i n t e r e s t i n g i n f o r m a t i o n b u t t h i s i s e v i d e n t l y l i m i - t e d t o p r o d u c t s f o r which the f i s s i o n b a r r i e r i s s u f - f i c i e n t l y low. A t t h i s p o i n t , i t should be s t r e s s e d

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19801022

t h a t n e i t h e r of these two methods allows a simple de- t e r m i n a t i o n of t h e a n g u l a r momentum s h a r i n g between the two fragments.

F i n a l l y , a t h i r d method,that turned o u t t o be t h e most a c c u r a t e , a t l e a s t f o r l i g h t systems (com- p o s i t e systems w i t h masses lower than 100) i s r e l a - t e d

t o

l i g h t p a r t i c l e e m i ~ s i o n ~ ~ - ~ ~ and we s h a l l de- velop i t s s p e c i f i c advantages i n t h e n e x t s e c t i o n . This t a l k w i l l be c e n t e r e d around a complete study of the System ' ' ~ r + ' ' ~ i a t 280 MeV. We s h a l l t r y t o show, through t h a t s p e c i f i c example, t h e i n t e r e s t t h e r e i s i n s t u d y i n g l i g h t p a r t i c l e emission i n D I C and more g e n e r a l l y i n any d i s s i p a t i v e r e a c t i o n .

The paper w i l l be d i v i d e d i n t o f o u r s e c t i o n s . The g e n e r a l motivation f o r p a r t i c l e emission s t u d i e s w i l l be given f i r s t a s w e l l a s t h e k i n d of informa-

t i o n they can presumably b r i n g t o our knowledge of heavy i o n d i s s i p a t i v e r e a c t i o n s . Then, t h e o r i g i n of

the a - p a r t i c l e s observed i n t h e A r + N i r e a c t i o n w i l l be d i s c u s s e d . I n a t h i r d p a r t , we p r e s e n t r e s u l t s on

t h e angular momentum t r a n s f e r a s deduced from o u t of p l a n e a n g u l a r d i s t r i b u t i o n s and charged p a r t i c l e mul- t i p l i c i t i e s . F i n a l l y , a s t o t h e g e n e r a l use of par- t i c l e emission p r o p e r t i e s i n o t h e r s i t u a t i o n s than DIC s t u d i e s , we conclude by g i v i n g few examples where i t may a l r e a d y be f o r s e e n t h a t such methods would be most advantageous.

1 . D i s s i p a t i v e p r o c e s s e s and l i g h t p a r t i c l e emission:

an approach t o a n g u l a r momentum.

L i g h t p a r t i c l e s e m i t t e d i n a heavy i o n c o l l i s i o n may be considered a s t e s t p a r t i c l e s to probe t h e evo- l u t i o n of the r e a c t i o n . T h e i r c h a r a c t e r i s t i c s , ener- gy and a n g u l a r d i s t r i b u t i o n , should indeed r e f l e c t t h e degree of e q u i l i b r i u m of t h e c o l l i d i n g system.

I n p r i n c i p l e , they can be e m i t t e d a t any s t a g e of, t h e r e a c t i o n . F a s t , knock-out p a r t i c l e s may a r i s e a t t h e very beginning of the c o l l i s i o n . One would t h e n e x p e c t t y p i c a l p r o p e r t i e s of a one-step d i r e c t , reac- t i o n . They can a l s o be e m i t t e d some time a f t e r w a r d s when a composite system i s c l e a r l y formed between

the two i n t e r a c t i n g n u c l e i , d u r i n g t h e approach of the thermodynamical e q u i l i b r i u m i n t h e system. This f a s t p a r t i c l e emission h a s been observed i n s e v e r a l 24'26,29-30 systems a t r a t h e r h i g h r e l a t i v e e n e r g i e s

It h a s been stiggested t h a t some h o t s p o t h a s been formed d u r i n g t h e c o l l i s i o n , which i m p l i e s t h a t h i g h temperatures a r e l o c a l i s e d i n some r e s t r i c t e d p a r t of t h e composite system. The a s s o c i a t e d p a r t i c l e emission time w i l l then be s o s h o r t t h a t emission could a c t u a l l y occur b e f o r e t h e s c i s s i o n of t h e com-

p o s i t e system. That k i n d of emission can thus r e v e a l t h e n a t u r e of t h e e a r l y s t a g e of the energy and angu- l a r momentum d i s s i p a t i o n .

Looking now a t l a r g e r i n t e r a c t i o n time, many de- grees of freedom of t h e composite system should have time t o reach e q u i l i b r i u m (N/Z r a t i o , r e l a t i v e motion, r o t a t i o n a l degrees) and f i n a l l y , t h e system d i s r u p t s i n t o two very e x c i t e d fragments which a r e going t o emit l i g h t p a r t i c l e s ( n , p , a ) and y-rays o r even t o f i s s i o n f o r very heavy p r o d u c t s . These secondary par- t i c l e s have w e l l d e f i n e d c h a r a c t e r i s t i c s r e l a t e d n o t only t o t h e e x c i t a t i o n energy b u t a l s o t o t h e a n g u l a r momentum of t h e e m i t t i n g n u c l e u s . As we a r e i n t e r e s -

t e d i n t h i s conference t o the behaviour of n u c l e i a t h i g h angular momentum, i t may seem worthwhile t o re- c a l l b r i e f l y t h e e f f e c t s of high a n g u l a r momentum on t h e d e e x c i t a t i o n s t a g e of t h e n u c l e u s .

F i r s t , i t i s w e l l known t h a t high s p i n s t a t e s w i l l f a v o r a - p a r t i c l e emission. This i s simply. be- cause they can c a r r y away a l a r g e amount of o r b i t a l angular momentum a s compared t o o t h e r l i g h t p a r t i c l e s .

Fig.2. Avemge mZues of orbital anguZar momenta re- moved by clparticles as a finct-im of the i n - t r i n s i c spin J for d o u s emitting fragments excited to 60 MeV.

F i g . 2. shows f o r example t h e o r b i t a l a n g u l a r momentum removed by a - p a r t i c l e s a s a f u n c t i o n of i n t r i n s i c s p i n of the e m i t t i n g n u c l e u s f o r t h r e e d i f f e r e n t com- pound n u c l e i a t 60 MeV e x c i t a t i o n energy ( t h e calcu- l a t i o n h a s been done u s i n g t h e a n a l y t i c a l e x p r e s s i o n s e x t r a c t e d from t h e s t a t i s t i c a l model by Catchen e t a ~ . ~ ' ) . As t h e emission w i d t h of a given channel i s p r o p o r t i o n a l t o t h e r a t i o of l e v e l d e n s i t i e s i n t h e daughter and t h e p a r e n t n u c l e u s , i t i s c l e a r t h a t f o r high s p i n s t a t e s i n t h e p a r e n t , l a r g e R v a l u e removed by a - p a r t i c l e s w i l l s t r o n g l y f a v o r t h i s channel r e l a -

t i v e l y t o the emission of o t h e r p a r t i c l e s . Thomas 3 2 and Grover and ~ i l a t ~ ~ have d i s c u s s e d e x t e n s i v e l y t h e s p i n dependence of n , p and a: emission probabi- l i t i e s . Let us j u s t show a s an example t h e r e s u l t of a GROG12 c a l c u l a t i o n f o r t h e emission p r o b a b i l i t y of n, p, a a s a f u n c t i o n of the a n g u l a r momentum of the

6 2nucleus e x c i t e d a t 5 4 MeV ( f i g . 3 ) . ~ ~ It i s c l e a r

2 9

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GROG1 Z - flrsf Step

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E*)= 54 MeV

I I I I

poses e x p e r i m e n t a l l y a d e t e c t i o n p l a n e , one d e f i n e s a l s o t h e d i r e c t i o n of a n g u l a r momentum i n t h e en- t r a n c e channel and of the s p i n s of t h e fragments i s s u e d from the c o l l i s i o n ( t h i s i s of course t h e i d e a l case of complete alignment of the fragments). F i n a l l y , t h e a n g u l a r d i s t r i b u t i o n of l i g h t p a r t i c l e s e m i t t e d by the a l i g n e d n u c l e i should be i s o t r o p i c i n the r e a c t i o n plane b u t should show an out-of-plane a n i s o t r o p y which i s d i r e c t l y r e l a t e d t o the a n g u l a r momentum of t h e e m i t t i n g fragments. This problem was f i r s t considered by E r i c s o n and ~ t r u t i n s k i ~ ~ twenty y e a r s ago. More re- c e n t l y , i t has been d i s c u s s e d by ~ ~ s sand Catchen i n ~ ~ ~ e t a ~ . ~ ' . I t may a l s o be n o t i c e d t h a t these p r o p e r t i e s have a l r e a d y been used i n compound s t u d i e s t o determi- ne t h e c r i t i c a l a n g u l a r momentum f o r f ~ s i o n ~ ~ - ~ ' .

The l a s t p o i n t which i s worth t o be s t r e s s e d con- c e r n s the k i n e t i c energy of t h e e m i t t e d p a r t i c l e s . C l a s s i c a l l y , when a r i g i d body i s r o t a t i n g , t h e par- t i c l e e m i t t e d from t h e s u r f a c e g e t s an e x t r a i n i t i a l v e l o c i t y Vs e q u a l t o t h e s u r f a c e v e l o c i t y of t h e nu-

where R, J and

3

a r e r e s p e c t i v e l y t h e nucleus r a d i u s , t h e a n g u l a r momentum and the moment of i n e r t i a of t h e Fig. 3 . Re Zat-ive emission probabi Zities of neutrons,

nucleus and $ i s t h e angle between t h e d i r e c t i o n of J

protons, and a - p a r t i c k s and muZtipZicity ra-

and t h e d i r e c t i o n of emission. This spin-off e f f e c t t i o %/Ma from 6 2 & frngments a t < 9 > = 5 4 MeV.

w i l l t h e n be maximum i n t h e d e t e c t i o n p l a n e perpendi- from t h i s p l o t t h a t measurement of p o r a m u l t i p l i -

c i t i e s o r even b e t t e r Mp/M, may l e a d t o a r a t h e r a c c u r a t e s p i n d e t e r m i n a t i o n . This r e q u i r e s of cour- s e e x t e n s i v e e v a p o r a t i o n c a l c u l a t i o n a s w e l l a s , i f p o s s i b l e , c a l i b r a t i o n measurements.

' ~ e g i d e s t h i s ' e f f e c t on , t o t a l ,emission p r o b a b i l i - t y , h i g h s p i n s i n t h e e m i t t e r w i l l a l s o show up i n the s p a t i a l d i s t r i b u t i o n of t h e e v a p o r a t e d p a r t i - c l e s . To e x p l a i n these e f f e c t s , l e t us c o n s i d e r t h e p a r t i c u l a r s i t u a t i o n of deeply i n e l a s t i c c o l l i s i o n s . Assum t h a t t h e composite system i s formed f o r a s i n g l e incoming p a r t i a l wave. I n t h e l i m i t of long i n t e r a c t i o n time, because of the t a n g e n t i a l f r i c t i o n , t h e e n t i r e composite system w i l l r o t a t e r i g i d l y w i t h a s p i n J and a t t h e time of s c i s s i o n , t h e c l a s s i c a l p i c t u r e i s s i m i l a r t o t h e o n e encountered i n f i s s i o n . The two fragments w i l l be e m i t t e d p r e f e r e n t i a l l y i n a p l a n e p e r p e n d i c u l a r t o J and moreover a s the compo- s i t e system was r i g i d l y r o t a t i n g , they w i l l appear w i t h i n t r i n s i c s p i n p a r a l l e l t o J, t h a t i s perpen- d i c u l a r t o t h e d e t e c t i o n p l a n e . I n t h e same way, fragments w i l l then e v a p o r a t e p a r t i c l e s w i t h a ma- ximum l o c a t e d i n a p l a n e p e r p e n d i c u l a r t o t h e i r i n - t r i n s i c s p i n d i r e c t i o n s . A c c o r d i n g l y , when one im-

c u l a r t o J . It corresponds t o an a d d i t i o n a l energy AE e q u a l t o

where m i s t h e p a r t i c l e mass.

R e s u l t i n g a d d i t i o n a l a - p a r t i c l e e n e r g i e s as a f u n c t i o n of t h e a n g u l a r momentum of t h e e m i t t e r a r e shown i n f i g . 4 f o r t h r e e d i f f e r e n t n u c l e i (V,Cu,Br)

Fig. 4 . AdditionaZ centrifugal energies (due tb spin- o f f e f f e c t ) as

a

function o f the i n t r i n s i c spin of various emitters.

e x c i t e d a t 60 MeV. It i s c l e a r l y seen t h a t i t could be an a l t e r n a t i v e approach t o t h e angular momentum of

t h e fragments i n deeply i n e l a s t i c c o l l i s i o n s . However, whereas s p i n d e t e r m i n a t i o n s t h a t may b e o b t a i n e d from t o t a l p a r t i c l e m u l t i p l i c i t i e s ( s e e above) a r e independent on any assumption an t h e alignment of t h e D I C fragment, t h i s i s c l e a r l y n o t t h e case f o r t h e l a s t two p r o p e r t i e s ( o u t of p l a n e a n i s o t r o p y and s p a t i a l dependence of t h e average e n e r g i e s ) . In f a c t , i t i s hoped t h a t comparison be- tween t h e s e v a r i o u s methods may l e a d t o a determina- t i o n of both the average s p i n and t h e alignment of the e m i t t e r . Anyhow, f o r any of t h e s e v a r i o u s e s t i - mates t o be meaningful, i t i s c l e a r t h a t t h e l i g h t p a r t i c l e s must come from a secondary e v a p o r a t i o n p r o c e s s . This i m p l i e s t h a t one h a s f i r s t t o e x p e r i - m e n t a l l y check t h a t t h e e x c i t e d fragments a r e i n thermodynamical e q u i l i b r i u m and t h a t some p r o p e r t i e s which a r e not s p i n dependent r e f l e c t c o r r e c t l y t h i s e q u i l i b r i u m .

2. The 280 MeV ~ r + ~ ' ~ i experiment. The o r i g i n of par- t i c l e e m i s s i o n .

Many reasons p o i n t e d t o t h a t s p e c i f i c r e a c t i o n a s a good c a n d i d a t e t o look a t p a r t i c l e emission.

P a r t i c l e i n c l u s i v e e x p e r i m e n t s 4 0 7 4 1 , fragment-f rag- ment coincidence s t u d i e s 4 * and y-ray m u l t i p l i c i t y m e a ~ u r e m e n t s ~ ~ had a l r e a d y been performed on t h e same s y s tem. These p r e v i o u s experiments have i n d i c a - t e d t h e p o s s i b l e e x i s t e n c e of an i m p o r t a n t c r o s s - s e c t i o n f o r charged p a r t i c l e emission. Moreoversthe e v a p o r a t i o n r e s i d u e c r o s s - s e c t i o n uER was a l s o mea- s ~ r e d ~ ~ . It i n d i c a t e d t h e e x i s t e n c e of a r a t h e r l a r g e c r o s s - s e c t i o n f o r compound nucleus formation.

From the measurement of OER and ODIC one i s able t o d e f i n e a v e r y narrow window of i n i t i a l a n g u l a r mo- mentum t h a t l e a d s t o D I C 74hRDIG&9&. It i s of cour- s e an i d e a l case t o s t u d y the a n g u l a r momentum t r a n s - f e r , m u c h b e t t e r than i n h e a v i e r s y s t e m s w h e r e most of the p a r t i a l waves c o n t r i b u t e t o t h e deeply i n e l a s t i c channe 1.

The experimental s e t up h a s been d e s c r i b e d e l s e - wherez5. However, i t should be n o t e d t h a t i n t h e s e experiments, both i n p l a n e and o u t of p l a n e a n g u l a r d i s t r i b u t i o n s of p r o t o n s and or-particles were measu- r e d i n coincidence w i t h D I C fragments d e t e c t e d a t

'9x30' ( i n p l a n e angle)

.

^As t h i s angle was much l a r g e r t h a n t h e g r a z i n g a n g l e , only the, D I C l e a d i n g t o a t o t a l energy d i s s i p a t i o n were considered.

As

i t has been p o i n t e d o u t b e f o r e , a necessary c o n d i t i o n t o apply- t h e s t a t i k t i c a l t h e o r y t o t h e de- e x c i t a t i o n of DIC fragments i s t o i d e n t i f y p r e c i s e l y t h e d i f f e r e n t emission s o u r c e s which could be f o r i n s t a n c e t h e composite system o r t h e fragment them-

s e l v e s . It i s then v e r y u s e f u l to e x p r e s s t h e e x p e r i - mental r e s u l t s i n terms of an i n v a r i a n t cross-section p l o t as a f u n c t i o n of the p a r a l l e l and t r a n s v e r s e ve- l o c i t i e s (V,,, V,)

.

The i n v a r i a n t c r o s s - s e c t i o n may be d e f i n e d by

I

where p i s t h e l i n e a r momentum of t h e l i g h t d e t e c t e d p a r t i c l e (a o r proton)

.

The i m p o r t a n t p o i n t i s t h a t

OI i s i n v a r i a n t i n a Galilean transformation s i n c e i t corresponds t o a simple t r a n s l a t i o n i n t h e

"3

s p a c e . The iso-contour l i n e s corresponding t o a s i n g l e i s o - t r o p i c s o u r c e w i l l appear, i n t h i s r e p r e s e n t a t i o n , a s c i r c l e s c e n t e r e d around the t i p of the v e l o c i t y vec- t o r c h a r a c t e r i z i n g the s o u r c e . Fig.5 shows an example of t h i s k i n d of r e p r e s e n t a t i o n f o r or-particles i n

Fig.5. Invariant cross-section plot for a-par-hkks i n coincidence with fragments of charge Z=16.

The s i z e of the dots i s an increasing ftpzction of GI. Arrcejs give the man r e c o i l for

detected fmgment fPZ=16), and i t s asswned two-body reaction compkmntury P Z cow,.

.

^SoJid

oircZes correspond t o evaporation emission.

(man linear mmentwnl from the detected frag- ment (upper c i r c k l m d from i t s conplement

(Zarer c i r p l e )

.

&shed circles in&cate the experimental detection ~ s h o l d s

.

coincidence w i t h a l i g h t fragment Z=I6. Labels an t h e

+6

- -

P I - ^{d 3 0}

^-

-5 -6

:

. . . . . . . . .

.. 1

a in coincidence

-.

with z = 16

a x i s r e p r e s e n t a - p a r t i c l e momentum i n u n i t of 0.1 GeV/c i n p l a c e of v e l o c i t y (p=ma.V)

.

I n any d i r e c t i o n , t h e maximum of the d i s t r i b u t i o n c o i n c i d e s w i t h what i s expected when c o n s i d e r i n g eva- p o r a t i o n from two moving s o u r c e s ( t h e two D I C f r a g - ments with average r e c o i l v e l o c i t y VZ and V

z comp. 1.

These maxima a r e symbolized by the f u l l l i n e c i r c l e s i n t h e p l o t , whereas t h e dashed l i n e c i r c l e s simply i n d i c a t e the experimental d e t e c t i o n t h r e s h o l d s . One should n o t i c e a l s o t h a t a t forward a n g l e s , when the two v e l o c i t y c i r c l e s o v e r l a p , t h e r e i s a c l e a r p i l e up of tile c r o s s - s e c t i o n l e a d i n g t o a very s t r o n g asymmetry of the a - p a r t i c l e s p e c t r a with r e s p e c t t o t h e beam a x i s . Average v e l o c i t i e s seemed t o be i n r a t h e r good agreement w i t h p r e f e r e n t i a l emission from t h e l i g h t fragment (Z=16) a t + l o o and by t h e heavy one a t -10'. Another i n t e r e s t i n g p o i n t i s t h a t , by an a p p r o p r i a t e choice of the i n p l a n e angle ( f o r example ?60°) where t o make t h e out-of-plane d i s t r i - b u t i o n , one s e l e c t s almost uniquely a s i n g l e source

( t h e l i g h t fragment a t +60° and t h e heavy one a t -60"). This i s of course a g r e a t advantage of t h e l i g h t p a r t i c l e measurements o v e r t h e o t h e r methods such as t h e y m u l t i p l i c i t y t e c h n i c s .

To check more q u a n t i t a t i v e l y t h e e v a p o r a t i v e o r i - g i n of the l i g h t p a r t i c l e , a two dimensional f i t of t h e i n v a r i a n t d i s t r i b u t i o n s has been performed. For t h i s f i t , it was assumed t h a t two i s o t r o p i c sources were c o n t r i b u t i n g t o t h e a emission. The shape of

t h e l i g h t p a r t i c l e energy spectrum was assumed t o be of a s h i f t e d Maxwell type :

P(E)dE a exp -(E-B)/T

E-B

[ I

^{( 4 )}

where T i s the n u c l e a r temperature and B an e f f e c - t i v e t h r e s h o l d energy. This crude e q u a t i o n , which n e g l e c t s p e n e t r a b i l i t y e f f e c t s h a s been convoluted w i t h a Gaussian d i s t r i b u t i o n t o improve t h e f i t a t

low energy n e a r the t h r e s h o l d f o r a - p a r t i c l e emis- s i o n .

Recoil e f f e c t s have been taken i n t o account ex- p l i c i t e l y whdn t h e a - p a r t i c l e was e m i t t e d by t h e d e t e c t e d fragment

.

For each source, t h e r e were t h e n t h r e e parameters : t h e b a r r i e r B, t h e temperature T and t h e i n t e n s i t y .

The c o n c l u s i o n of t h i s f i t shows very c l e a r l y t h a t the d a t a can be n i c e l y e x p l a i n e d by an i s o t r o - p i c emission from t h e two f u l l y a c c e l e r a t e d f r a g - ments i n s t a t i s t i c a l e q u i l i b r i u m , w i t h one e x c e p t i o n a t forward a n g l e s where i t d e f i n i t e l y remains a n o t h e r component corresponding t o h i g h energy a - p a r t i - c l e s . Comparison w i t h experiment i s shown i n f i g . 6

f o r a - p a r t i c l e i n coincidence w i t h 2=16 a t t h r e e d i f - f e r e n t emission a n g l e s . A t -55' a pure a emission from t h e haavy undetected fragment i s observed. A t 55O i t corresponds mainly t o an a-emission from t h e d e t e c t e d fragment although i t remains a low energy c o n t r i b u t i o n from t h e complementary fragment. And f i n a l l y B - l o 0 , when t h e two components a r e s t r o n g l y mixed, a n addi- t i o n a l p r e e q u i l i b r i u m component appears w i t h a r a t h e r h i g h m a n k i n e t i c energy.

Temperatures deduced from the f i t a r e t h e same f o r t h e two complementary fragments, which i s expected i f thermodynamical e q u i l i b r i u m has been reached i n the composite system b e f o r e s c i s s i o n .

EN

(MeV) Figure 6a

-emiss~on from the

0 10 20 3 0 4 0 5 0 60

E, ( M e V ) Figure 6b

I I I I I I

Z = 16

- ^-

- -

-

-

p r e e q u i l ~ b r ~ u m emlsslon component

- -

- - - -

1 I

0 10 20 30 40 50 60

E m

(MeV) Figure 6c

Fig. 6 a, b,c. An ex-le o f a two dimensional f i t o f the invariant cross-section plot for Z=16.

Fitted a-spectra ( s o l i d l i n e s ) are compared t o the eqeriment (histograms) a t three d i f - ferent radial angles.

3 . The s p i n of D I C fragments deduced from out-of- p l a n e a n g u l a r d i s t r i b u t i o n s of a - p a r t i c l e s

.

A s t h e s t a t i s t i c a l o r i g i n of t h e l i g h t p a r t i c l e s has been w e l l e s t a b l i s h e d ( i f one e x c e p t s t h e v e r y

forward a n g l e s ) , we mentionned b e f o r e t h a t t h e out- of-plane d i s t r i b u t i o n s should p r e s e n t an a n i s o t r o p y t h a t c h a r a c t e r i z e s t h e angular momentum of t h e emit- t i n g fragment and i t s degree of alignment. We s h a l l j u s t r e c a l l h e r e t h e b a s i c equation34 which expres- s e s t h e p r o b a b i l i t y f o r a p a r t i c l e , with an o r b i t a l a n g u l a r momentum

R

and energy E t o be e m i t t e d by a nucleus w i t h s p i n I a t a given a n g l e 8 w i t h r e s p e c t

t o t h e d i r e c t i o n of t h i s s p i n I

J i s the z e r o t h o r d e r a s s o c i a t e d Bessel f u n c t i o n

3

and T a r e t h e moment of i n e r t i a and temperature of the r e s i d u a l n u c l e u s .

T%is e q u a t i o n may b e a p p l i e d d i r e c t l y t o out- of-plane a n i s o t r o p y i f one u s e s average v a l u e s of E and R. ~ i t e r n a t i v e l ~ i t i s p o s s i b l e t o i n t e g r a t e over a l l p o s s i b l e R-values and e n e r g i e s of t h e emit- t e d p a r t i c l e 3 6 . Using t h e s h a r p cut-off approxima- t i o n f o r t h e t r a n s m i s s i o n c o e f f i c i e n t s , t h e follow-

pR2, t h e r e l a t i v e moment of i n e r t i a of t h e p a r t i c l e a t t h e n u c l e a r s u r f a c e , e n t e r s v i a t h e e f f e c t of t h e c e n t r i f u g a l b a r r i e r on t h e t r a n s m i s s i o n c o e f f i c i e n t s . I t i s important t o keep i n mind t h a t t h i s r e l a t i o n i m p l i e s a complete alignment of t h e s p i n of t h e emit- t i n g nucleus and a f i r s t s t e p a emission.

The out-of --p lane measurements have been performed a t +60° and -60°, t h a t i s i n a region where only one fragment i s c o n t r i b u t i n g t o the emission. Some of t h e r e s u l t s a r e p l o t t e d i n f i g . 7 i n t h e r e s t frame of t h e corresponding e m i t t i n g fragment. S o l i d curves a r e l e a s t square f i t s of t h e experimental d a t a assuming W(8) a exp(-a s i n 2 8 )

.

I n comparison w i t h a - p a r t i - c l e s , p r o t o n out-of-plane d i s t r i b u t i o n s a r e q u i t e f l a t . This i s i n agreement w i t h the f a c t t h a t a proton cannot remove a s much a n g u l a r momntum a s an a - p a r t i - c l e do. Experimental a a n i s o t r o p i e s have been conver- t e d i n D I C fragment s p i n s u s i n g e q u a t i o n ( 6 ) . The nu- c l e a r temperature T h a s been o b t a i n e d from t h e energy s p e c t r a (T % 2.7 MeV). The moment of i n e r t i a

3

has been taken e q u a l t o t h e r i g i d body v a l u e w i t h ro = 1.2

fm. paR2 was e v a l u a t e d f o l l o w i n g Mac Mahan &d Alexander 45 :

R e s u l t i n g v a l u e s of 1- a r e p r e s e n t e d i n f i g . 8 and compared t o t h e p r e d i c t i o n of a c l a s s i c a l s t i c k i n g model f o r two p o s s i b l e shapes of the composite system a t s c i s s i o n . The s t i c k i n g h y p o t h e s i s seems t o be a reasonable assumption a s we a r e looking a t completely damped e v e n t s . A mean i n t e r a c t i o n time of 10-'~s can be e s t i m a t e d , much l a r g e r than the angular momentum r e l a x a t i o n time f o r t h e same system which i s about 3 46. The s t i c k i n g l i m i t leads simply t o

'31 and r e f e r t o t h e moment of i n e r t i a of each sepa- r a t e fragment. A s the a n g u l a r momentum window t h a t l e a d s t o D I C i s very narrow, i t i s a good approxima- t i o n t o choose a s i n g l e average v a l u e Ioa86-6.

i n g e x p r e s s i o n can b e o b t a i n e d :

~r (280 M ~ V ) +"NI

Out of plane ongular d~str~but~ons

I

I I 1

d

90 60 30 0

Angle in movlng frame of ernibter i d e g Fig. 7 . T c i c a l o u t - o f p M rmgukzr correlations for

a ~ a r t i c i l e s plotted i n the rest frame of their respective emitters (indicated i n the figurn). Solid o m s are Zeast s q u u ~ s f i t s of the data.

Experimental r e s u l t s a r e i n c l e a r disagreement w i t h a s t i c k i n g h y p o t h e s i s between s p h e r i c a l n u c l e i I n f a c t , t h i s i s n o t s u r p r i s i n g , a s when one t r i e s t o reproduce t h e e x p e r i m e n t a l average k i n e t i c e n e r - g i e s of t h e fragments, t a k i n g i n t o account t h e Cou- lomb p o t e n t i a l and a l s o t h e c e n t r i f u g a l term, one i s l e d t o i n c l u d e deformation e f f e c t s . By matching

t h e fragment deformation (assuming e l l i p s o i d a l sha- pes) t o t h e average energy r e s u l t s and assuming again a s t i c k i n g l i m i t , one g e t s t h e second curve ( s o l i d l i n e i n fig.8) which i s i n good agreement w i t h the

Charge of heavy fragment

.

_z~

4 0 35 30 25 23

I 1 I

I

4 0 ~ r ( 2 8 0 MeV) + 5 8 ~ 1

\

\ \ ~ntrinsic sp~ns or the f r a g m e n t

\ deduced from the exper,ment -

\ ^{( b Z L}

' .

^z~

^'

'\

Calculated wlkh the shcktnp hypothestr

---

^spheres

-

ellipsoids

-

Charge of Ilght fragment

.

_ZL

K g . 8 . ExperimentaZ i n t r i n s i c spins of t h e individuaZ fragments c o n p a r e d with t h e results of c a b u -

Zatims for the sticking Limit for r i g i d bodies.

experimental d a t a b u t , may be, f o r t h e h e a v i e s t pro- d u c t s (2>37). A p o s s i b l e e x p l a n a t i o n could b e a R f r a c t i o n n a t i o n . I f one assumes t h a t t h e l a r g e s t mass a s p t r i e s come from the lowest R waves (R%?M) t h e s t i c k i n g h y p o t h e s i s f o r deformed n u c l e i would then l e a d t o 1=2& i n s t e a d of 286 f o r ~ = 3 6 6 . However, a s we have a l r e a d y s a i d , e q u a t i o n ( 6 ) which i s used t o g e t I does n o t t a k e i n t o account a p o s s i b l e d i s - alignment of t h e fragment a n g u l a r momentum. I n a way, v a l u e s deduced from e q u a t i o n (7) a r e t o be considered a s lower limits of t h e a c t u a l a n g u l a r momenta. A con- s i s t e n t i n t e r p r e t a t i o n of both t h e average k i n e t i c e n e r g i e s and t h e out-of-plane a n i s o t r o p i e s i s never- t h e l e s s a good i n d i c a t i o n of a r a t h e r s t r o n g align-.

ment

.

A b e t t e r check of t h i s should e v i d e n t l y come from an independent s p i n e s t i m a t e from t h e t o t a l a - p a r t i - c l e and p r o t o n m u l t i p l i c i t i e s which a r e n o t s e n s i t i v e t o t h e alignment b u t t h i s i s t h e s u b j e c t of the n e x t s e c t i o n .

4. The s p i n of D I C fragments deduced from p a r t i c l e m u l t i p l i c i t i e s .

A s i t h a s been p o i n t e d o u t b e f o r e i n s e c t i o n 1 ,

t h e emission p r o b a b i l i t y of a - p a r t i c l e s i s p r e d i c t e d t o i n c r e a s e very r a p i d l y w i t h i n c r e a s i n g s p i n of the e m i t t e r . As protons follow t h e o p p o s i t e t r e n d , mul- t i p l i c i t y r a t i o b$/% i s thus s t r o n g l y c o r r e l a t e d with s p i n ( s e e f i g . 3 ) . Fig.9 shows very c l e a r l y what has been observed i n two s e r i e s of experiments con- c e r n i n g " ~ r and 'I7T.e compound n u c l e i 3 8 , 3 9 , 4 9 . This

0 20 40 6 0 8 0

..

^I I 1

9.0

-

^OBSERVED

E"

0 7 5 ~ r 49 MsV

-

0 . 8 - v 7 % r 80

A

0 ' I 7 ~ e 107

\

z

0.6

- z

I

0.4

-

0.2

-

Fig.$. Right : MuZtipZieity r a t i o M /M caZeuZated

He H

from evaporation

thaw

for indizriduaZ i n i - t i a l spin values JCN

.

eft'

^: Measured m t i o s of

' x ~ / ' H

euapomted from 7 5 ~ r j t ( m f . 3 8 ) and 1 " ~ e x ( m f . 4 9 ~ f F i g . 7 of ref.31).

p l o t , e x t r a c t e d from t h e work of Catchen e t a l . 3 1 shows the experimental m u l t i p l i c i t y r a t i o M /M as a

a P f u n c t i o n of the average s p i n value i n t h e e n t r a n c e channel ( f o r R-waves l e a d i n g t o compound n u c l e u s f o b a t i o n )

.

I n t h e r i g h t s i d e of t h e fi'gure i s shown t h e c a l c u l a t e d v a l u e of M /M deduced from 1st s t e p

a P

p a r t i c l e e m i s s i on. As the c a l c u l a t i o n corresponds t o s i n g l e s p i n s , t h e p r e d i c t e d curve a r e much s t e e p e r . This i s e x a c t l y t h e i n i t i a l condition i n D I C where very e x c i t e d fragments h a v e a r a t h e r narrow s p i n d i s - t r i b u t i o n ( a t leas't f o r l i g h t sys tems)

.

Accordingly, experimental r e s u l t s of M i l l e r e t a l S 4 ' on 7 s ~ r do n o t seem t o be d i r e c t l y u s a b l e f o r our purpose. We s h a l l need t o r e l y on a s t a t i s t i c a l model c a l c u l a - tion t o e x t r a c t a corr&spondance b e t w e e n ' s p i n s and m u l t i p l i c i t y i a t i o t h a t a p p l i e s t o our experimental s i t u a t i o n .

F o r t u n a t e l y , t h e previous 7 5 ~ r compound n u c l e u s experiment h a s l e d t o e x t e n s i v e and s u c c e s s f u l s t a - ti? t i c a l model c a l c u l a t i o n s by G i l a t and Grover 50

.

This allows us' t o know h a t h e r p r e c i s e l y t h e parame- t e r s t o be used i n t h e Br region, which corresponds

t o t h e h e a v i e s t D I C fragments i n t h e A r + N i r e a c t i o n . Consequently, s t a t i s t i c a l model parameters (mainly l e v e l d e n s i t i e s , moment of i n e r t i a and s h e l l e f f e c t s due t o the v i c i n i t y of t h e 28 p closed s h e l l ) have n o t been taken a s f r e e parameters i n the c a l c u l a t i o n b u t f i x e d a t t h e v a l u e s determined by G i l a t . The only r e a l f r e e parameter was t h e i n i t i a l s p i n of the emit- t e r .

The i n i t i a l d i s t r i b u t i o n i n e x c i t a t i o n ' energy of t h e primary fragments has been deduced from s i n g l e and coincidence wasurements of t h e D I C fragments. It has been assumed t h a t , f o r a given product, t h e r a t i o of the two f i r s t moments were the same f o r both the k i n e t i c energy and the e x c i t a t i o n energy d i s t r i b u t i o n s

( i . e . i n t h i s case <E%/FWHM = 3.75). The i n i t i a l con- d i t i o n s of e x c i t a t i o n energy and a n g u l a r momentum a r e shown i n f i g . 1 0 f o r t h e 7 5 ~ r product i n t h e (E*,J) p l a n e . On t h e same p l o t , appear t h e i s o p r o b a b i l i t y contours f o r a-emission. I t i s c l e a r l y seen t h a t a s m a l l e r r o r i n t h e width of the E R d i s t r i b u t i o n does n o t a f f e c t t h e a emission. Another remark concerns

t h e p l a c e of t h e a emission along t h e e v a p o r a t i o n c h a i n . This i s an important p o i n t as i n the out-of- p l a n e a n a l y s i s , i t was i m p l i c i t e l y assumed t h a t a emission t a k e s p l a c e a t t h e f i r s t s t e p . C a l c u l a t i o n s i n t h e 2=30-36 r e g i o n show t h a t f i r s t chance a emis- s i o n c o n t r i b u t e s f o r more t h a n 40% of t h e t o t a l a c r o s s - s e c t i o n . Adding t h e n a and 2na channels (which b a r e l y change t h e a n g u l a r momentum of t h e e m i t t e r b e f o r e

a

e m i s s i o n ) , t h i s f i g u r e i n c r e a s e s t o about 65% (and t o 80% w i t h p a ) . This j u s t i f i e s sowwhat our p r e v i o u s assumption i n s e c t i o n 3.

Pig. 10. ~ n i t i a 2 'conditions o f e z d t a t i o n e n e m (PWHM) and a n g u h momentum for

7 5 ~ r

frag- ments i n t h (#,J) pZ-. OY1 the s- plot appear the isoprobabi Zity contours for a- emission.

Complete c a l c u l a t i o n s , i n c l u d i n g a l l the p o s s i - b l e d e e x c i t a t i o n channels, have been performed f o r t h r e e n u c l e i only (2123, 29 and 35). For a l l o t h e r charges, and t o save computer time, only p a r t i a l c a l - c u l a t i o n s have been made ( i n c l u d i n g a, xna, p a and pna channe 1 s )

.

The r e s u l t i n g c r o s s - s e c t i o n s were t h e n e m p i r i c a l l y c o r r e c t e d f o r t h e m i s s i n g y i e l d on t h e b a s e of t h e t h r e e complete c a l c u l a t i o n s . I n f i g . l 1 emission p r o b a b i l i t i e s f o r each p a r t i c l e and e m i s s i o n

fig.21. Re lative emission probabi l i t i e s of neutrons, protons and a - p a r t i c k s from 7 5fragments ~ ~

( f i r s t s t e p calculation). Dots corraspond t o calmluted ratios %/Ma deduced from conpkte calculation as the dashed mu?* i s related t o the same caZcuZation for the f i r s t step.

width r a t i o M /M a r e p l o t t e d as a f u n c t i o n of J f o r P a

7 5 ~ r ( 1 s t s t e p c a l c u l a t i o n )

.

Dots correspond t o c a l - c u l a t e d r a t i o M /M deduced from complete c a l c u l a -

P a

t i o n s . I t i s c l e a r l y seen t h a t t h e f i r s t s t e p g i v e s a l r e a d y a v e r y good p i c t u r e of the d e e x c i t a t i o n

..

^A

l a s t remark should b e made on t h e primary mass d i s - t r i b u t i o n f o r e a c h charge. Although t h e c a l c u l a t i o n corresponds t o the most probable mass r a t i o , t h a t i s t h e one which minimizes t h e p o t e n t i a l energy of t h e system f o r a given charge asynrmetry (N/Z e q u i l i b r a - t i o n ) , i t does take i n t o account the d i f f e r e n t p a r t i - c l e emission width of t h e two neighbouring i s o t o p e s .

A good t e s t of t h i s type of c a l c u l a t i o n i s t h a t i t should n o t only reproduce p and a m u l t i p l i c i t i e s b u t a l s o t h e e x p e r i m e n t a l energy s p e c t r a . Fig.12

shows t h e r e s u l t i n g c a l c u l a t e d a-spectrum , f o r Z=29 (complete c a l c u l a t i o n ) . .The agreement with t h e expe- r i m e n t a l one (histogram) i s f a i r l y good. Unfortunate- l y , t h e shape of t h e energy spectrum i s n o t s e n s i t i v e enough t o t h e average a n g u l a r momentum t o determine it t h i s way. T h i s i s seen i n f i g . 1 3 where t h e e x p e r i -

E&

(MeV) Fig.12. a-particles emitted by Cu f r a p n t s . A good

agreement i s obtained between the experimen- t a l spect& (histogram) and the calculated one ( s o l i d curve).

0 10 2 0 30

E

(MeV)

Fig.13. a p a x t i c k s emitted by B r fragments. A c m a - rison i s made beetween

the

eseperimentaZ spec- trum (histogram) and resulting .caZcuZated spectra d t h various angular momenta of the emitt2ng nucleus.

mental a-spectrum f o r Z=35 i s compared t o complete c a l c u l a t i o n s w i t h t h r e e d i f f e r e n t s p i n s of t h e e m i t t e r (J=15,21,24fi)

.

These t h r e e v a l u e s give a l l a reasona- b l y good agreement w i t h t h e experiment. However a much b e t t e r s t a t i s t i c s might have allowed a p o s s i b l e

s p i n d e t e r m i n a t i o n from t h e shape of t h e energy spec- t r a .

Much more p r e c i s e i n f o r m a t i o n should be o b t a i n e d from the p a r t i c l e m u l t i p l i c i t i e s . For example, i t i s seen from f i g . 1 1 t h a t i n the r e g i o n of i n t e r e s t ( J =

1 6 - 3 6 ) , a m u l t i p l i c i t y i n c r e a s e s by about 13% e v e r y

2fi

and t h a t a t t h e same time M /M d e c r e a s e s by 20%.

P a

Using t h e s p i n d e t e r m i n a t i o n o b t a i n e d from t h e out- of-plane a n i s o t r o p y , we have computed both t h e pro- ton and t h e a - p a r t i c l e m u l t i p l i c i t i e s f o r a l l heavy e m i t t e r s . The r e s u l t s a r e d i s p l a y e d i n f i g . 1 4 and compared t o t h e experiment.

a -

particles

0 2 0 2 5 3 0 35

erni t ter

Fig.14. CaZcuZated ( s o l i d c w s e s ) and experimentaZ p cuzd a-pa&cZe rnuZtipZicities as

a

f m c C i m of the cha;rge o f , *he emitting n u c k u s

.

The agreement i s reasonable i n t h e region 2 ~ 2 8 - 36 b u t i s n o t s o good f o r lower Z . T h i s l a s t case i s

A p o s s i b l e e x p l a n a t i o n could be an o v e r e s t i m a t e of t h e moment of i n e r t i a of t h e r e s i d u a l nucleus i n e q u a t i o n (7), a s some a - p a r t i c l e s may come from a n a o r p a channel. However, c o n s i d e r i n g the model uncer- t a i n t i e s , i t i s probably b e t t e r n o t t o t a k e t h e above d i f f e r e n c e t o o s e r i o u s l y . I n f a c t b o t h methods g i v e very s i m i l a r r e s u l t s and t h i s i s a c l e a r s i g n a t u r e of a s t r o n g alignment of t h e a n g u l a r momentum t r a n s f e r r e d i n t h i s r e a c t i o n . I d e n t i c a l conclusions have been rea- ched i n h e a v i e r systems u s i n g s e q u e n t i a l f i s s i o n me- thod12. This i s a l s o the r e s u l t t h a t t h e o r e t i c a l in- v e s t i g a t i o n of angular momentum d i s s i p a t i o n on t h e b a s i s of Fokker Planck e q u a t i o n l e a d s t o 46,5 1

F i n a l l y , t h i s experiment may be compared t o a y- m u l t i p l i c i t y measurement on t h e same system by Bock e t a1.43. This i s done i n f i g . 1 5 and i t shows t h a t p a r t i c l e r e s u l t s a r e l y i n g w e l l above t h e y - m u l t i p l i - c i t y d a t a . The d i f f e r e n c e corresponds t o a n g u l a r mo- mentum removed by t h e l i g h t p a r t i c l e s , which has n o t been taken , i n t o account i n t h e y - m u l t i p l i c i t y measu- rements. I t i s w e l l accounted f o r by the s t a t i s t i c a l model u s i n g t h e e x p e r i m e n t a l p a r t i c l e m u l t i p l i c i t i e s .

Sum of the tragment splns deduced

from out. of. plane anlsotropies 1

i

\\ St~cklng hypothesis :

---

^spheres

-

ellipsoids

\

\

\

^{\ \} _\

\

\

\ \ -

---__

(and 100 96 stretched E2 transitions)

most probably r e l a t e d t o our choice of the s t a t i s t i - c a l model parameters. We have indeed a good c o n f i -

4 0 ~ r ( 2 8 0 M ~ V ) + 5 8 ~ ~ dence i n t h e p a r a m t e r s f o r t h e high Z region b u t

t h e r e i s no s p e c i a l reason why t h e y should a l s o work _{" o 2 0}

i n t h e r e g i o n 2=20-25 where the i n f l u e n c e of t h e 20 Charge of light fragment , 2'

p ,shqll h a s t o b e taken i n t o account p r o p e r l y . I f we Ng.15. Sum of the spins of the t u o conpZementary then r e s t r i c t the comparison t o t h e r e g i o n Z=28-36, fragments as deduced porn the a c t - o f - p h we can * n e v e r t h e l e s s n o t i c e t h a t , on average, the pre- data conpamd with those deduced from y- d i c t e d a - p a r t i c l e m u l t i p l i c i t i e s a r e a b i t t o o h i g h m l t i p Z i & t y m a s m e m n t s of m f . 43.

whereas t h e o p p o s i t e t r e n d is found f o r the p r o t o n s . T h i s c o u l d e a s i l y be c o r r e c t e d f o r by, d e c r e a s i n g slowly t h e i n i t i a l s p i n of the fragments. P a r t i c l e m u l t i p i i c i t y e s t i m a t e w i l l then tend t o be '2 o r 36

units lower than the anisotropy one.

5 . Conclusion.

Charged p a r t i c l e s t u d i e s i n coincidence w i t h deeply i n e l a s t i c fragments appear t o be a very power- f u l t o o l f o r s t u d y i n g energy d i s s i p a t i o n a s w e l l a s a n g u l a r momentum t r a n s f e r . Combining t h e d i f f e r e n t emission p r o p e r t i e s ( a n g u l a r d i s t r i b u t i o n s , energy s p e c t r a , p a r t i c l e m u l t i p l i c i t i e s ) , i t h a s been pos- s i b l e t o measure r a t h e r p r e c i s e l y t h e a n g u l a r momen- tum t r a n s f e r . A good a g r e e w n t w i t h t h e s t i c k i n g l i m i t h a s been o b t a i n e d . Pbreover, the degree of a l i g n m n t of t h e D I C fragments was found t o be very s t r o n g .

A t l e a s t , f o r l i g h t systems, l i g h t charged p a r

-

t i c l e masurement should be p r e f e r r e d t o t h e y- technique a s they a r e more d i r e c t l y connected w i t h t h e fragment i n i t i a l s p i n of t h e e m i t t e r . Moreover, t h i s method i s t h e only one t h a t g i v e s a p r e c i s e measurement of the i n d i v i d u a l s p i n of b o t h comple- mentary fragments.

S y s t e m a t i c s t u d i e s a r e s t i l l needed t o i n c r e a s e o u r knowledge of DIC. For example, t h e r e a r e s t i l l very few experiments on t h e time e v o l u t i o n of angu- l a r momentum d i s s i p a t i o n a s might be o b t a i n e d by s t u d y i n g a l s o t h e f l u c t u a t i o n s a n d / o r t h e energy d i s s i p a t i o n .

More g e n e r a l l y , we t r i e d i n t h i s paper t o show through a s p e c i f i c experiment how powerful1 t h e use of charged p a r t i c l e emission can be t o s t u d y any d i s s i p a t i o n mechanism. Indeed, a l l what has been des- c r i b e d i n t h i s paper on s p i n d e t e r m i n a t i o n may be a p p l i e d t o any nucleus i n s t a t i s t i c a l e q u i l i b r i u m . From t h i s p o i n t of view, i t i s s u r p r i s i n g t h a t only very few such experiments have been perfonoed i n

compound nucleus s t u d i e s where p r o t o n s and a - p a r t i - c l e s t o g e t h e r w i t h

y- coincidence^^^

could b e of a g r e a t h e l p t o know v e r y p r e c i s e l y t h e e n t r y s t a t e s .

I n t h e same s p i r i t , p a r t i c l e p a r t i c l e angular c o r r e l a t i o n s can a l s o be very s e n s i t i v e t o t h e angu- l a r momentum of t h e emitter53, and i t seems p o s s i b l e t o s e l e c t t h i s way, continuum s t a t e s with h i g h angu- l a r momenta. As a l a s t example, l e t us c o n s i d e r t h e problem of t h e p o s s i b l e e x i s t e n c e of a R-window i n f u s i o n r e a c t i o n s . TDHF c a l ~ u l a t i o n s ~ ~ p r e d i c t an i n - c r e a s e of t h e R minimum and a narrowing of t h e -.9 window i t s e l f w i t h i n c r e a s i n g energy. This i s a ty-

~ i c a l case where an e x c i t a t i o n f u n c t i o n of p a r t i c l e m u l t i p l i c i t i e s might very simply g i v e t h e answer a s

t o t h e e x i s t e n c e of such 11 l i m i t a t i o n .

F i n a l l y , coming back t o D I C r e a c t i o n s , i t i s worth t o s t r e s s again t h a t , f o r l i g h t systems, a ra-

t h e r narrow window of a n g u l a r momenta c o n t r i b u t e s t o

t h i s process a s opposed t o f u s i o n r e a c t i o n s where t h e compound nucleus i s formed w i t h a v e r y wide a n g u l a r momentum d i s t r i b u t i o n . T h i s should be k e p t i n mind i n high s p i n s t a t e s t u d i e s a s i t should be p o s s i b l e t o

t a k e advantage of t h i s s i t u a t i o n where t h e e n t r a n c e channel i s w e l l d e f i n e d w i t h r e s p e c t t o the a n g u l a r momen tum

.

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