DISSIPATIVE EFFECTS IN PROJECTILE FRAGMENTATION AND PARTICLES EVAPORATION

HAL Id: jpa-00226491

https://hal.archives-ouvertes.fr/jpa-00226491

Submitted on 1 Jan 1987

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

DISSIPATIVE EFFECTS IN PROJECTILE FRAGMENTATION AND PARTICLES

EVAPORATION

A. Bonasera, M. Di Toro, C. Gregoire

To cite this version:

A. Bonasera, M. Di Toro, C. Gregoire. DISSIPATIVE EFFECTS IN PROJECTILE FRAGMENTA- TION AND PARTICLES EVAPORATION. Journal de Physique Colloques, 1987, 48 (C2), pp.C2- 175-C2-178. �10.1051/jphyscol:1987225�. �jpa-00226491�

48, juin 1987

DISSIPATIVE EFFECTS IN PROJECTILE FRAGMENTATION AND PARTICLES EVAPORATION( )

A. BONASERA* " * , M . D1 TORO' * and C . GREGOIRE* ' *

* ~ y c l o t r o n L a b o r a t o r y , Michigan S t a t e U n i v e r s i t y , E a s t L a n s i n g , MI 4 8 8 2 4 , U.S.A.

* *

I s t i t u t e N a z i o n a l e d i F i s i c a N u c l e a r e , S e z i o n e d i C a t a n i a , Corso I t a l i a 5 7 , I-95129 C a t a n i a , I t a l y

* * * G A N I L , BP 5027, F-14021 Caen Cedex, France

A b s t r a c t : A modified p a r t i c i p a n t - s p e c t a t o r model is d i s c u s s e d , s u i t a b l e t o s t u d y medium e n e r g y h e a v y - i o n c o l l i s i o n s . P h a s e - s p a c e c o n s t r a i n t s a n d one-body d i s s i p a t i o n terms imply n o t i c e a b l e m o d i f i c a t i o n s i n t h e h i g h energy f i r e b a l l m o d e l . T h e s t a t i s t i c a l compound d e c a y t h e o r y is u s e d t o c a l c u l a t e p i o n a n d gamma e v a p o r a t i o n from t h e h o t s o u r c e .

P i o n a n d h a r d p h o t o n p r o d u c t i o n i n heavy i o n c o l l i s i o n s a r e among t h e most s t r i k i n g f e a t u r e s o f medium energy r e a c t i o n s . Many experiments, mostly o f i n c l u s i v e t y p e , have been performed u s i n g d i f f e r e n t combinations o f t a r g e t s and p r o j e c t i l e s a t d i f f e r e n t beam e n e r g i e s [1,2]. Pions have been observed a t e n e r g i e s f a r b e l o w t h e t h r e s h o l d f o r pion production i n f r e e Nucleon-Nucleon c o l l i s i o n s .

Some e x p e r i m e n t a l f e a t u r e s a r e s u g g e s t i n g t h e r e l a t i v e i m p o r t a n c e o f s t a t i s t i c a l mechanism:

i ) Pion and gamma s p e c t r a have e x p o n e n t i a l l y d e c r e a s i n g t a i l s .

i i ) I t is p o s s i b l e t o f i n d a r e f e r e n c e frame where t h e a n g u l a r d i s t r i b u t i o n o f t h e e m i t t e d p a r t i c l e s is i s o t r o p i c .

Such f r a m e is t h e C.M. frame system i n t h e c a s e o f e q u a l p r o j e c t i l e and t a r g e t masses. For asymmetric n u c l e i t h e s o u r c e frame seems t o be n e i t h e r t h e N-N c e n t e r of mass nor t h e nucleus-nucleus c e n t e r o f mass. T h e r e f o r e we a r e f o r c e d t o r u l e o u t a p u r e compound n u c l e u s mechanism [ 3 ] and t o i n t r o d u c e a s m a l l e r h o t s o u r c e w i t h s o m e f o r m a t i o n p r o b a b i l i t y , number o f n u c l e o n s a n d e x c i t a t i o n e n e r g y . T h e s e parameters can e i t h e r be chosen t o reproduce experimental t r e n d s [ 4 ] o r deduced from a more g e n e r a l d e s c r i p t i o n o f medium energy heavy-ion c o l l i s i o n s . I n t h i s r e s p e c t i n r e f . [51 t h e h i g h energy p a r t i c i p a n t - s p e c t a t o r model h a s been p r o p o s e d i n o r d e r t o e v a l u a t e a l l t h e s e q u a n t i t i e s j u s t on t h e b a s i s o f t h e geometry o f t h e r e a c t i o n ( i . e . impact parameter).

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1987225

C2-176 JOURNAL DE PHYSIQUE

However, i t is well known t h a t t h e p u r e p a r t i c i p a n t - s p e c t a t o r model is n o t a b l e t o r e p r o d u c e s e v e r a l f e a t u r e s o f medium e n e r g y heavy-ion c o l l i s i o n s . A r e v i s e d p a r t i c i p a n t - s p e c t a t o r r e a c t i o n mechanism c a n be i n t r o d u c e d where a l l t h e medium e n e r g y f e a t u r e s a r e u n d e r s t o o d j u s t u s i n g q u i t e simple phase-space arguments 1 6 1 . To a o n s i d e r t h e i n t e r p l a y between d i s s i p a t i v e p r o c e s s e s a n d t h e h i g h e n e r g y c o l l i s i o n a l dynamics a two-stage mechanism is analyzed. I n t h e f i r s t s t a g e we have a one-body d i s s i p a t i o n p r o c e s s , w i t h neck formation and i n c o h e r e n t nucleon exchange, q u i t e w e l l d e s c r i b e d w i t h i n t h e window formula p i c t u r e . Some r a d i a l k i n e t i c energy is converted i n t o i n t r i n s i c energy and some o r b i t a l r o t a t i o n a l energy i n t o i n t r i n s i c s p i n s . D u r i n g t h e f i r s t s t e p t h e d i n u c l e a r s y s t e m s u f f e r s some d e f l e c t i o n w i t h r e s p e c t t o t h e beam a x i s . The medium e n e r g y c a s e d i f f e r s f r o m t h e u s u a l d e e p - i n e l a s t i c p i c t u r e s i n c e n u c l e o n s f r o m o n e n u c l e u s i n t o continuum s t a t e s o f t h e p a r t n e r n u c l e u s a r e n o t c o n t r i b u t i n g t o exchanges through t h e n e c k , a n d t h e window formula must be s u i t a b l y renormalized.

T h e second s t a g e is t h e a b r a s i o n mechanism, modified n o t o n l y by t h e p r e v i o u s r a d i a l a n d o r b i t a l d i s s i p a t i o n , b u t a l s o because t h e p a r t i c i p a n t n u c l e o n s have o n l y p a r t o f t h e p r o j e c t i l e ( t a r g e t ) momentum d i s t r i b u t i o n a v a i l a b l e s i n c e t h e two F e r m i s p h e r e s a r e p a r t i a l l y overlapping a t t h e s e e n e r g i e s [ b ] . I n p a r t i c u l a r , t h e number o f abraded nucleons is modified by

where AGeom is t h e g e o m e t r i c a l a b r a s i o n v a l u e and R(Prel ) is t h e r a t i o b e t w e e n t h e o v e r l a p p i n g volume o f t h e momentum d i s t r i b u t i o n and t h e volume o f a Fermi s p h e r e . The e x c i t a t i o n e n e r g y o f t h e f i r e b a l l i s a l s o s u b s t a n t i a l l y m o d i f i e d by P a u l i b l o c k i n g e f f e c t s . A s d i s c u s s e d i n r e f . [ b ] , a t medium e n e r g i e s we have a n i n t r i n s i c mean momentum p e r p a r t i c l e <pZ>a and <pZ>b d i f f e r e n t from z e r o f o r t h e p a r t i c i p a n t n u c l e o n s . I n d e e d , i n t h e C.M. system, a low momentum p a r t o f t h e n u c l e o n s i n t h e o v e r l a p p i n g r e g i o n is blocked. Consequently, t h e e x c i t a t i o n energy o f t h e f i r e b a l l w i l l be

where

is t h e t r a n s l a t i o n a l k i n e t i c e n e r g y o f t h e f i r e b a l l a n d SAa,SBb t h e s e p a r a t i o n e n e r g i e s . < P , > ~ , ~ a r e t h e mean momenta p e r p a r t i c l e o f t h e p a r t i c i p a n t n u c l e o n s , c a l c u l a t e d j u s t from t h e momentum space geometry. Thus, t h e use o f a p u r e f i r e b a l l model a t medium e n e r g i e s can be q u i t e i n c o r r e c t . Of c o u r s e a t h i g h e r e n e r g i e s ( 2 150 MeV/u), when P r e l . t 2PF, t h e p a r t i c i p a n t - s p e c t a t o r p i c t u r e is f u l l y recovered, w h i l e a t low enough beam e n e r g i e s f i r e b a l l formation is n o t p o s s i b l e .

U s i n g t h e r u l e s d e s c r i b e d a b o v e , we a r e a b l e t o c a l c u l a t e f o r a g i v e n system t h e PLF and TLF-like fragments, t h e s i z e and e x c i t a t i o n e n e r g y o f a h o t s o u r c e a t

p a r t i c l e s i n o r d e r t o c o o l down. A s t u d y o f t h e h o t zone formation and o f its decay i s c l o s e i n s p i r i t t o t h e two s t e p model o f r e f . [ 5 1 , i n s p i t e o f s u b s t a n t i a l d i f f e r e n c e s c o n c e r n i n g t h e e m i t t i n g z o n e , which s h o u l d b e c o n s i d e r e d i n t h e i n t e r m e d i a t e energy domain. These d i f f e r e n c e s a r e e s s e n t i a l l y two:

i ) t h e mass number o f t h e f i r e b a l l d i f f e r s a t low and i n t e r m e d i a t e e n e r g i e s f r o m t h e crude g e o m e t r i c a l model used i n r e f . 151. While our approach g i v e s a d e c r e a s i n g number of nucleons with d e c r e a s i n g bombarding energy, a crude g e o m e t r i c a l a p p r o a c h g i v e s a c o n s t a n t h o t s o u r c e mass number.

i i ) The e x c i t a t i o n energy o f t h e p a r t i c i p a n t region is l a r g e r i n o u r model t h a n i n t h e p u r e g e o m e t r i c a l o n e , s i n c e P a u l i b l o c k i n g h i n d e r s some c o n t r i b u t i o n o f low momenta nucleons t o t h e h o t zone.

I f o n e a s s u m e s t h a t t h e f i r e b a l l h a s r e a c h e d t h e r m a l e q u i l i b r i u m , i t i s p o s s i b l e t o u s e t h e s t a n d a r d Weiskopft theory [ 3 , 6 , 7 ] t o c a l c u l a t e t h e p r o b a b i l i t y o f p a r t i c l e s e v a p o r a t i o n from t h e h o t s o u r c e . I n t h i s work we w i l l p r e s e n t only c a l c u l a t i o n s f o r Y and n-production.

I n f i g u r e 1 , we p l o t 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 f o r t h e s y s t e m s ' 2 C + 2 " U , 5 a N i , ' ' C a t E/u= 8 4 MeV. The a g r e e m e n t w i t h e x p e r i m e n t a l d a t a [ l ] i s r e a s o n a b l e , n o t e h o w e v e r , t h a t t h e c r o s s - s e c t i o n i s o v e r e s t i m a t e d o f a f a c t o r 2-4 f o r low n - k i n e t i c e n e r g i e s . For h i g h energy p i o n s , t h e c r o s s s e c t i o n is u n d e r e s t i m a t e d . However, t h e

0 5 0 100 150 discrepancy between t h e o r e t i c a l

TT and e x p e r i m e n t a l s l o p e s is much

l e s s t h a n i n t h e p u r e f i r e b a l l Figure 1

model of r e f . [ 5 ] .

The u n d e r e s t i m a t i o n o f t h e h i g h e n e r g y p a r t o f t h e p i o n s p e c t r a c o u l d b e a t t r i b u t e d t o e i t h e r t h e f i r e b a l l r e a c h e s a n h i g h e r temperature t h a n we c a l c u l a t e o r a n o n - s t a t i s t i c a l mechanism is more i m p o r t a n t . F i n a l l y , we would l i k e t o s t r e s s t h a t o u r s t a t i s t i c a l model is n o t a b l e t o r e p r o d u c e t h e y i e l d s observed i n low energy experiments (E/uS 35 MeV). In f a c t i n t h e s e c a s e s t h e f i r e b a l l e x c i t a t i o n energy is l e s s than t h e pion mass.

In t h e c a s e of Y-production, we o b t a i n a r e a s o n a b l e agreement with e x p e r i m e n t a l s l o p e s , b u t t h e t o t a l c r o s s - s e c t i o n is overestimated i n some c a s e s . In f i g u r e 2 we show a comparison with t h e experimental spectrum f o r t h e 1 4 N + 1 2 C r e a c t i o n a t E/u=30- 40 MeV [ 2 ] .

In c o n c l u s i o n , we have shown how a s t a t i s t i c a l approach t o t h e d e c a y o f a h o t s o u r c e ( f i r e b a l l ) can account f o r a l a r g e p a r t o f t h e observed pion and hard photon

C2-178 JOURNAL DE PHYSIQUE

, . . . . I . . . . l . . . . I p r o d u c t i o n r a t e i n m e d i u m e n e r g y h e a v y - i o n c o l l i s i o n s . T h e a s s u m p t i o n o f a r a p i d f o r m a t i o n o f a n e q u i l i b r a t e d c o m p o s i t e s u b s y s t e m w h i c h d e c a y s a c c o r d i n g t o s t a t i s t i c a l laws p r o b a b l y is t o o s t r o n g and a c t u a l l y l e a d s t o o v e r e s t i m a t e t h e s t a t i s t i c a l mechanism. The p o i n t we would l i k e t o s t r e s s

10-8

1 , ,

1

40 60 80 100 f o r m e d i t s c h a r a c t e r i s t i c s

E, (MeV) ( c r o s s - s e c t i o n , n u m b e r o f nucleons, e x c i t a t i o n e n e r g i e s , F i g u r e 2

v e l o c i t y ) a r e completely d i f f e r e n t from t h e e v a l u a t i o n s o f a pure p a r t i c i p a n t - s p e c t a t o r m o d e l , a s u s e d i n h i g h energy p r o c e s s e s . Indeed i n t h e energy region E/u 5 150 MeV P a u l i b l o c k i n g and d i s s i p a t i v e e f f e c t s a r e s u b s t a n t i a l l y changing t h e pure a b r a s i o n p i c t u r e .

REFERENCES

[ l ] E. Grosse, p r o c . " W i n t e r C o l l e g e o n F u n d a m e n t a l N u c l e a r P h y s i c s " , e d s . K . D i e t r i c h e t a l . , p . 1459 and r e f e r e n c e s t h e r e i n .

[ 2 ] J. Stevenson e t a l . , Phys. Rev. L e t t . x ( 1 9 8 6 ) 5 5 5 . [ 3 ] J. Aichelin and G. B e r t s c h , Phys. L e t t . -(1984)350.

[ 4 ] J. A i c h e l i n , Phys. Rev. L e t t . 52(1984)2340.

[ 5 ] M. Prakash e t a l . , Phys. Rev.

m(

[ 6 ] A. Bonasera, M . D i Toro, C . Gregoire, Nucl. Phys. =(1987)653, and s u b m i t t e d f o r p u b l i c a t i o n .

[ 7 ] V. Weisskopft, Phys. Rev. z ( 1 9 3 7 ) 2 9 5 .