HAL Id: jpa-00216586
https://hal.archives-ouvertes.fr/jpa-00216586
Submitted on 1 Jan 1976
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.
EXPERIMENTAL SITUATION IN DEEP INELASTIC
REACTIONS WITH RESPECT TO THE RAPIDLY
RELAXED MODES.
Jöel Galin
To cite this version:
JOURNAL DE PHYSIQUE
Colloque
C5,
supplément au n°
11,
Tome 31, Novembre
1976,,
page
C5-83
EXPERIMENTAL SITUATION IN DEEP INELASTIC REACTIONS WITH RESPECT TO THE RAPIDLY RELAXED MODES.
Joel Galin
Institut de Physique Nucléaire B.P. n° 1, 91406 Orsay, France
Résumé : Après avoir rapidement passé en revue les différentes techniques les plus fré-quemment utilisées dans l'étude du processus très inélastique, la question relative au nombre de corps dans la voie de sortie est examinée. Il y a maintenant de très fortes preuves expérimentales indiquant que seuls deux principaux ensembles nucléaires nais-sent de l'interaction quelle que soit la taille des nuclëides dans la voie d'entrée. Ensuite, parmi les trois degrés de liberté collectifs les plus significatifs mis en jeu dans les réactions très inélastiques (assymétrie de masse, mouvement relatif, et rap-port du nombre de protons à celui de neutrons) nous avons considéré les deux derniers qui semblent être relaxés de façon rapide. L'évolution en temps est étudiée en considé-rant systématiquement- la distribution des produits individuels de réaction en fonction, à la fois, de leur énergie cinétique et de leur distribution angulaire. Une tentative de classement des systèmes étudiés, basée sur l'allure des distributions angulaires, est donnée en fonction d'un paramètre semblable au paramètre de Sommerfeld. L'action des forces de viscosité qui sont responsables de l'amortissement du mouvement relatif est étudiée par le biais des degrés de liberté internes des produits de réaction (éner-gie d'excitation et de déformation, spin). Enfin, il est montré que la relaxation du degré de liberté lié à l'excès de neutrons est très rapidement atteinte (même plus rapidement que ne l'est la relaxation du degré de liberté associé au mouvement relatif).
Abstract : After having briefly surveyed the different techniques the most commonly used in deep inelastic studies the problem of the body number in the exit channel is discussed. There are now strong experimental evidences that only two major nuclear pieces are left at the scission stage whatever is the size of the nucleides in the entrance channel. Then, among the most three relevant collective degrees of freedom involved in deep inelastic collisions (mass asymmetry, relative motion, neutron to proton ratio) the last two ones which appear to be rather rapidly relaxed are considered. The time evolu-tion is looked at by surveying the individual nucleus yield distribuevolu-tions as a funcevolu-tion of their kinetic energy and angular distribution. A tentative classification of the in-teracting systems based on the angular distribution pattern of the products is given as a function of a Sommerfeldlike parameter. The action of the viscous forces which are -responsible of the kinetic energy damping is investigated through the analysis of the internal degrees of freedom of the reaction products (excitation energy, deformation energy and spin). Finally the relaxation of the neutron excess degree of freedom is shown to be very rapidly achieved (even more rapidly than is the relaxation of the degree of freedom associated to the relative motion).
INTRODUCTION
During the last three or four years deep inelastic reaction studies have known an explosive growth. The availability of heavy-ion accelerators delivering heavier and heavier beams with good intensities is largely responsible for the success of the field. Nevertheless the massive projectiles such as Kr and Xe are not necessarily involved in
these studies and more and more work has been con-ducted on tandems with "light" heavy ions in order to study the macroscopic aspects of nuclear colli-sion phenomena.
Deep inelastic collisions between heavy ions were first observed 15 years ago in the
n e r work o f Kaufmann and Wolfgang
(
II
.
However, f o r a l o n g time t h e s e r e a c t i o n s d i d n o t r a i s e much i n t e r e s t . They were s e e n a s a by--product i n most of t h e s p e c t r o s c o p i c s t u d i e s b u t s c a r c e l y c o n s i d e r e d . And, a p a r t some i s o l a t e d experiments c a r r i e d o u t around 1970, mainly a t Dubna f2] and Orsay [3-41, one h a s t o w a i t u n t i l 1973-1974 t o s e e a f a n t a s t i c b u r s t i n t h e development of b o t h e x p e r i m e n t a l and t h e o r e t i c a l approaches. T h i s sudden i n t e r e s t was somewhat t r i g g e r e d by t h e f a i l u r e i n s y n t h e t i z i n g super-heavy s p e c i e s . Q u i t e soon, i t was r e a l i z e d t h a t super-heavies could n o t be produced a s com- pound n u c l e i because of t h e i m p o s s i b i l i t y of f u s i n g completely t o g e t h e r two massive n u c l e i . I n s t e a d , d i f f e r e n t r e a c t i o n channels were opened which brought a l o t o f i n t e r e s t .A s i t was a l r e a d y p o i n t e d o u t by L e f o r t [5], when two heavy i o n s i n t e r a c t t h e p o s s i b l e r e a c t i o n mechanisms cannot be simply d i v i d e d i n t o f a s t d i r e c t p r o c e s s e s and slow compound n u c l e u s p r o c e s s e s , It a p p e a r s t h a t o t h e r i n t e r a c t i o n s do o c c u r i n v o l v i n g t h e whole r e a c t i o n time r a n g e from d i r e c t i n t e r a c t i o n t o compound n u c l e u s c h a r a c t e r i s - t i c times. Furthermore f o r some d e g r e e s of freedom t h e number of nucleons which a r e involved i s l a r g e r t h a n t h e few nucleons involved i n d i r e c t r e a c t i o n s b u t does n o t r e a c h t h e t o t a l i t y of them a s i n com- pound n u c l e u s p r o c e s s e s .
There have been some semantic d i f f i c u l - t i e s t o q u a l i f y t h e s e new r e a c t i o n mechanisms. Ac- c o r d i n g t o t h e d i f f e r e n t groups t h e y a r e c a l l e d " q u a s i - f i s s i o n " o r " f i s s i o n - l i k e " ( f o r t h o s e who have i n mind t h e f i s s i o n p r o c e s s ) , " s t r o n g l y dam- ped" o r "relaxed" phenomena, "hard g r a z i n g " o r "
"deep i n e l a s t i c " c o l l i s i o n s . The l a t e r e x p r e s s i o n b e i n g s o f a r t h e most commonly used we s h a l l adopt i t a l l a l o n g t h i s t a l k .
A deep i n e l a s t i c c o l l i s i o n between two
n u c l e i could be roughly d e p i c t e d a s f o l l o w s . During such a c o l l i s i o n , a l a r g e amount of t h e k i n e t i c energy i n t h e r e l a t i v e motion i s d i s s i p a t e d i n t o t h e i n t e r n a l d e g r e e s o f freedom a s w e l l a s some amount of t h e o r b i t a l a n g u l a r momentum i s conver- t e d i n t o i n t r i n s i c a n g u l a r momentum of t h e p r o d u c t s . I n t h e c o u r s e o f such a p r o c e s s t h e r e a r e some rearrangements i n b o t h t h e r e l a t i v e s i z e (mass) of t h e p a r t n e r s (A;) and i n t h e i r n e u t r o n e x c e s s ( A ~ - z ~ ) . / Z ~ ) . However t h e i n t e r a c t i o n time i s n o t s u f f i c i e n t t o a l l o w a complete s t a t i s t i c a l e q u i l i - b r a t i o n i n a l l t h e degrees of freedom. The d i s r u p -
t i o n of t h e t r a n s i t o r y complex system o c c u r s b e f o r e a compound n u c l e u s regime i s e s t a b l i s h e d .
As s u g g e s t e d by S w i a t e c k i and Bjornholm [6] t h e deep i n e l a s t i c p r o c e s s resembiks t h e f i s s i o n p r o c e s s i n many r e s p e c t s . The f i r s t s t a g e of t h e i n t e r a c t i o n p r o c e s s , when t h e two n u c l e i come i n t o c o n t a c t , can be c o n s i d e r e d a s analogue t o t h e r e v e r - s e of t h e f i s s i o n p r o c e s s . However, one must keep i n mind t h a t t h e s e two p r o c e s s e s a r e q u i t e d i f f e r e n t a s f o r t h e deformation d e g r e e s of freedom. I n t h e e x i t channel t h e neck i s n o t d i s r u p t e d b e f y e a l a r g e s t r e t c h i n g of t h e fragments has t a k e n p l a c e , a s opposed t o what o c c u r s i n t h e e n t r a n c e c h a n n e l . These f e a t u r e s a r e e x p r e s s e d by t h e e x i s t e n c e of two m i s a l i g n e d v a l l e y s i n t h e p o t e n t i a l energy s u r - f a c e drawn v e r s u s t h e s e p a r a t i o n and necking p a r a - meters. The deep i n e l a s t i c e v e n t s a r e t h o s e f o r which t h e system i s i n j e c t e d from t h e f u s i o n v a l l e y d i r e c t l y i n t o t h e f i s s i o n v a l l e y w i t h o u t p a s s i n g t h e s a d d l e p o i n t when t h i s one e x i s t s .
The macro n u c l e a r p h y s i c s which h a s been v e r y s u c c e s s f u l i n t h e u n d e r s t a n d i n g of t h e b a s i c f e a t u r e s o f t h e f i s s i o n phenomena i s now b e i n g widely a p p l i e d t o heavy i o n r e a c t i o n s . The know- l e d g e of t h e n u c l e a r i n t e r a c t i o n p o t e n t i a l between two n u c l e i i s one of t h e c r u c i a l problems i n a l l t h e t r e a t m e n t s . Numerous a t t e m p t s have been made i n which t h e s e p a r a t i o n d i s t a n c e of t h e n u c l e i i s t h e o n l y c o n s i d e r e d degree of freedom [7-131. On t h e o t h e r hand, bunches of p o t e n t i a l energy s u r - f a c e s f o r complex systems have been computed a s a f u n c t i o n of s e p a r a t i o n d i s t a n c e , mass-asymmetry, neck s i z e , e c c e n t r i c i t y of t h e n u c l e i [14-171. The d i s s i p a t i o n of t h e c o l l e c t i v e k i n e t i c energy i n t o i n t e r n a l e x c i t a t i o n i s t r e a t e d c l a s s i - c a l l y by assuming a r e l a t i v e n a t i o n of t h e undefor- med n u c l e i a l o n g c l a s s i c a l t r a j e c t o r i e s i n t h e f i e l d of c o n s e r v a t i v e f o r c e s and d i s s i p a t i v e f r i c - t i o n a l f o r c e s [18-261. Some improvements have been made i n t h e s e c l a s s i c a l t r e a t m e n t s by i n c l u d i n g
i q o r t a n t e f f e c t s such a s mass t r a n s f e r [23,26] and deformation e f f e c t s [25,26]
.
Furthermore, some m i c r o s c o p i c d e s c r i p t i o n s of energy d i s s i p a t i o n have been c a r r i e d o u t on l i g h t systems [27-281.
Non e q u i l i b r i u m quantum s t a t i s t i c a l mecha- n i c s h a s a l s o been a p p l i e d t o t h e deep i n e l a s t i c phenomena .in o r d e r t o d e s c r i b e t h e t r a n s p o r t o r d i f f u s i o n p r o c e s s e s [29-301
.
DEEP INELASTIC REACTIONS
t h e e x p e r i m e n t a l r e s u l t s t h e ones which a r e more s p e c c f i c a l l y r e l a t e d t o t h e dynamics of t h e deep i n e l a s t i c p r o c e s s . I n t h e f o l l o w i n g r e p o r t , Moretto w i l l d i s c u s s t h e complementary a s p e c t s , d e a l i n g with t h e n u c l e o n i c exchange between t h e n u c l e i i n terms of a d i f f u s i o n p r o c e s s .
I do n o t i n t e n d t o r e s t r i c t myself t o i n t e r a c t i o n s between e i t h e r l i g h t o r heavy systems a l t h o u g h some d i f f e r e n c e s i n t h e behaviour o f heavy systems a s compared t o l i g h t e r ones may have l e d i n t h e p a s t t o c l a s s i f y t h e corresponding r e a c t i o n s i n t o two w e l l s e p a r a t e d c a t e g o r i e s . R a t h e r , one can show t h a t b o t h r e a c t i o n p r o c e s s e s a r e very s i m i l a r i n many r e s p e c t s and t h a t a slow e v o l u t i o n from one t o t h e o t h e r can be followed. I n t h i s e v o l u t i o n t h e product Z1Z2 of t h e atomic numbers i n t h e e n t r a n c e channel does n o t seem t o be t h e o n l y r e l e v a n t p a r a - meter governing t h e p r o c e s s . A s s u g g e s t e d by r e c e n t experiments, t h e bombarding energy ( o r t h e v e l o c i t y i n t h e r e l a t i v e motion) must a l s o b e c o n s i d e r e d a s a determinant f a c t o r .
T h i s paper i s d i v i d e d i n f i v e s e c t i o n s . I n t h e f i r s t one t h e p r i n c i p a l e x p e r i m e n t a l t e c h n i - ques c u r r e n t l y used i n t h e i d e n t i f i c a t i o n of deep i n e l a s t i c r e a c t i o n p r o d u c t s a r e reviewed. The second p a r t i s devoted t o a survey of t h e e x p e r i - mental knowledge w i t h r e g a r d t o t h e number of nu- c l e a r p i e c e s i n t h e e x i t channel ( t h e two body q u e s t i o n ) . I n t h e t h i r d s e c t i o n t h e energy damping phenomenon i s analyzed i n connection w i t h t h e reac- t i o n time ( g i v e n by t h e a n g u l a r d i s t r i b u t i o n ) and t h e n u c l e a r m a t t e r exchange. The f i r s t r e s u l t s dea- l i n g w i t h t h e e x c i t a t i o n energy and s p i n l e f t i n t o t h e deep i n e l a s t i c r e a c t i o n p r o d u c t s a r e d i s c u s s e d i n s e c t i o n
4 .
F i n a l l y t h e l a s t s e c t i o n c o n s i d e r s t h e r e l a x a t i o n of t h e n e u t r o n e x c e s s mode i n some d e t a i l s . I . EXPERIMENTAL PROCEDURESThe c o n s i d e r a b l e p r o g r e s s which h a s been made i n t h e l a s t y e a r s i n t h e n u c l e u s i d e n t i f i c a - t i o n t e c h n i q u e s i s l a r g e l y r e s p o n s i b l e f o r t h e b e t t e r i n s i g h t we have gained i n t h e r e a c t i o n pro- c e s s e s . T h e r e f o r e , I would l i k e t o devote t h i s f i r s t s e c t i o n t o a r a p i d survey of t h e d i f f e r e n t t e c h n i q u e s most commonly met i n deep i n e l a s t i c s t u - d i e s [3 I]
.
The fundamental parameters one would wish t o know a r e t h e f o l l o w i n g :
-
t h e n a t u r e of t h e e m i t t e d p r o d u c t s (atomic number or/and mass number)-
t h e a n g u l a r d i s t r i b u t i o n-
t h e k i n e t i c e n e r g i e s-
t h e e x c i t a t i o n e n e r g i e s-
t h e s p i n s . I n most of t h e experiments t h e f i r s t t h r e e c h a r a c t e r i s t i c s , which a r e by f a r t h e e a s i e s t t o r e a c h , have been measured and w i l l be c o n s i d e r e d t h e r e a f t e r . The l a s t two,which r e q u i r e a c o i n c i d e n c e measurement between t h e p r o d u c t s and t h e i r evapora-t e d p a r t i c l e s o r y,rays,are more d i f f i c u l t t o o b t a i n ( e s s e n t i a l l y due t o t h e low c o u n t i n g r a t e ) , and s o f a r v e r y few a t t e m p t s have been made i n such a way.
Furthermore c o i n c i d e n c e experiments b e t - ween t h e massive r e a c t i o n p r o d u c t s a r e n e c e s s a r y t o know whether o r n o t t h e r e a c t i o n ends up by o n l y two major b o d i e s i n t h e e x i t c h a n n e l .
F i r s t , l e t ' s examin i n some d e t a i l s t h e atomic number and mass i d e n t i f i c a t i o n t e c h n i q u e s . Both d e t e r m i n a t i o n s r e q u i r e k i n e t i c energy measu- rements performed e i t h e r by s o l i d s t a t e o r g a s c o u n t e r s . For masses h e a v i e r t h a n mass 50 t h e energy d e t e r m i n a t i o n i n SSD becomes a worrying problem. An energy d e f e c t h a s been observed w i t h such heavy i o n s . Charge r e c o m b i n a t i o n s , n u c l e a r c o l l i s i o n s and o t h e r l e s s known e f f e c t s can be g r o s s l y accounted f o r by e m p i r i c a l methods. Never- t h e l e s s improvements should be done i n t h e f u t u r e i n o r d e r f o r t h e energy r e s o l u t i o n not t o be t h e l i m i t i n g parameter i n time o f f l i g h t measurements. One might hope t h a t g a s c o u n t e r s c o u l d improve energy r e s o l u t i o n . A- Atomic number i d e n t i f i c a t i o n
.
1 O ) Te-lescopes AE-E. Due t o t h e d i f f i c u l t i e s encountered t o b u i l d t h i n and homogeneous t r a n s m i s s i o n s o l i d s t a t e d e t e c t o r s (SSD),in heavy i o n s t u d i e s t h e t e l e s c o p e % a r e o f t e n composed of a gas AE c o u n t e r a s s o c i a t e d w i t h a g a s o r a SSD E-counter. Two t y p e s of g a s c o u n t e r s a r e f r e q u e n t l y used : p r o p o r t i o n a l coun- t e r s and i o n i z a t i o n chambers. The t y p i c a l energy r e s o l u t i o n i n p r o p o r t i o n a l c o u n t e r s i s about 5% [32] and t h i s does n o t a l l o w t o r e s o l v e t h e e l e - ments above Z = 2 0 . I o n i z a t i o n chambers e x h i b i t a much b e t t e r r e s o l u t i o n [33-341. The e f f e c t i v e reso- l u t i o n depends v e r y much on t h e amount of energy dropped i n t h e c o u n t e r . Under f a v o r a b l e energy con- d i t i o n s elements up t o Z = 50 c a n s t i l l b e r e s o l v e dments and h a s been e x t e n s i v e l y used d u r i n g t h e two p a s t y e a r s . A t y p i c a l example of Z i d e n t i f i c a t i o n o b t a i n e d a t Orsay i s given i n Figure 1 .
F i g . 1
-
Example of Z i d e n t i f i c a t i , o n performed by means o f an i o n i z a t i o n ctiamber[75].
2') X-rays.
Reaction p r o d u c t s can be c o l l e c t e d i n c a t c h e r s and X-rays a c t i v i t i e s a r e measured o f f - l i n e . D i f f i c u l t i e s a r e encountered t o determine t h e a b s o l u t e y i e l d s because a g i v e n Z c o n s i s t s of seve-
r a l
i s o t o p e s each decaying w i t h d i f f e r e n t h a l f l i v e and w i t h d i f f e r e n t branching r a t i o s f o r K c a p t u r e v e r s u s 6+ emission, gamma decay v e r s u s i n t a r n a l conversion and X-ray f l u o r e s c e n c e v e r s u s Auger decay. N e v e r t h e l e s s t h i s t e c h n i q u e h a s proved i t s u s e f u l n e s s i n a n g u l a r d i s t r i b u t i o n s , I t allows t o s t u d y e i t h e r low energy o r heavy e l e m n t s which cannot be i d e n t i f i e d by t h e c l a s s i c a l t e l e s c o p eL36-377
.
B- Mass i d e n t i f i c a t i o n .
1 ') C o r r e l a t e d fragment energy measurements. The k i n e t i c e n e r g i e s o f two c o r r e l a t e d fragments a r e measured by two s o l i d s t a t e d e t e c t o r s s e t a t j u d i c i o u s a n g l e s . T h i s technique h a s been e x t e n s i v e l y a p p l i e d i n f i s s i o n s t u d i e s . When a b i - nary s p l i t i s assumed i t i s made use of t h e conser- v a t i o n of both t o t a l mass and l i n e a r momentum t o c a r r y o u t t h e i n d i v i d u a l masses from energy measu- rements. The method has been u t i l i z e d i n deep i n e - l a s t i c s t u d i e s on heavy systems C38-39)
.
F u r t h e r - more t h e c o i n c i d e n c e requirement allows t o t e s t t h e f u l l momentum t r a n s f e r and t o e v a l u a t e t h e r a t e ofb i n a r y s p l i t s . However t h e l i m i t e d accuracy of t h e energy measurement l e a d s t o l a r g e and, i n some c a s e s , s y s t e m a t i c e r r o r s i n t h e mass d e t e r m i n a t i o n . For v e r y asymmetric s p l i t s t h e method i s very poor. Moreover i t cannot be used a t very forward and back- ward a n g l e s ,
2") Time-of-flight s p e c t r o m e t e r s .
P r e s e n t l y , t h e T.O.F. t e c h n i q u e seems t o be t h e most c o m n mass i d e n t i f i c a t i o n method [40,
411
.
From T.O.F. ( i . e . v e l o c i t y ) and energy naoasu- rements t h e mass can be e x t r a c t e d unambiguously. The mass r e s o l u t i o n i s depending on both v e l o c i t y and energy r e s o l u t i o n s .For a given time r e s o l u t i o n t h e v e l o c i t y r e s o l u t i o n can be optimized by i n c r e a s i n g t h e f l i g h t p a t h a t t h e expense of t h e g e o m e t r i c a l e f f i c i e n c y . However, i n deep i n e l a s t i c s t u d i e s i n d i v i d u a l c r o s s s e c t i o n s a r e o f t e n low and t h e f l i g h t p a t h s c a r c e l y exceeds 100-150 cm. T h e r e f o r e , d i f f e r e n t ways a r e e x p l o r e d i n o r d e r t o r e a c h t h e b e s t time r e s o l u t i o n . Timing s i g n a l s a r e o b t a i n e d from t h e f o l l o w i n g devi- c e s : a s o l i d s t a t e d e t e c t o r s .
-
b
t h i n p l a s t i c s c i n t i l l a t o r s a s s o c i a t e d w i t h-
p h o t o m u l t i p l i e r s.
4b 0 ;4;
i 3 d4 MASSEc t h i n carbon f o i l s a s s o c i a t e d w i t h e l e c t r o n mul-
-
t i p l i e r s (channel p l a t e s ) o r s o l i d s t a t e d e t e c - t o r s.
d t h i n g a s c o u n t e r s working i n t h e avalanche-
mode.
I n p r i n c i p l e a l l t h e s e t i m i n g systems can be a s s o c i a t e d t v oby
two t o p r o v i d e s t a r t and s t o p s i g n a l s ' However, t h e most common combinations have been ( a+
a ) , ( b+
a ) (example i 6 given i n f i g . 2 ) , ( c+
a ) , ( c + c ) and(d
+
d ) .
The dB@ of a SSD f o r d e l i v e r i n g t h e s t o p s i g n a l i s advantageous s i n c e b o t h t i m i n g and energy i n f o r m a t i o n s a r e pro- v i d e d by t h e saw! c o u n t e r . On a v e r a g e , when opera- t i n g undet t e a l i s t i c beam c o n d i t i o n s t h e time reso- l u t i o n f o r most of t h e s e systems v a r i e s from 150 ps t o 300 p s . I t i s d i f f i c u l t t o compare t h e q u a l i t i e s of t h e d i f f e r e n t systems s i n c e some of them a r e s t i l l i n t h e e a r l y s t a g e s of t h e i r o p e r a t i o n ,3') Magnetic s p e c t r o m e t e r s
Magnetic a n a l y s i s w i t h simultaneous measurements of p a r t i c l e energy and p o s i t i o n i n t h e
o u t p u t f o c a l p l a n e has been c u r r e n t l y used i n deep i n e l a s t i c s t u d i e s [42-431
T h i s method p r o v i d e s
a
h i g h mass reso- l u t i o n and p e r m i t s t o remove t h e e l a s t i c a l l y s c a t - t e r e d i o n s l o a d i n g t h e d e t e c t o r by u s i n g t h e d i f - f e r e n c e of p a r t i c l e magnetic r i g i d i t i e s . But t h i s method does n o t e n s u r e unique i d e n t i f i c a t i o n of p a r t i c l e s s i n c e p a r t i c l e s having t h e same o r v e r y c l o s e q 2 / ~ cannot be s e p a r a t e d . These a m b i g u i t i e s a r e removed by adding a 2 i d e n t i f i c a t i o n by means of a AE-E t e l e s c o p e . A d d i t i o n a l time of f l i g h t mea- surement may be u s e f u l t o b e t t e r r e s o l v e two neigh- bour elements w i t h v e r y d i f f e r e n t masses and c l o s eq 2 / ~ .
C- Mass
+
Z i d e n t i f i c a t i o n .l o ) Combination of AE-E and TOF t e c h n i q u e s . An example of such a method can be found i n r e f . [44] where a TOF i s measured between a p l a s t i c f o i l s c i n t i l l a t o r and a SSD. A AE-ionisa- t i o n chamber s e t i n f r o n t of t h e SSD a l l o w s t o de- termine t h e 2 . C o r r e c t i o n s a r e made t o account f o r t h e slowing down i n t h e g a s .
2 ') Combination of magnetic a n a l y s i s and A E - E
.
I n mass d e t e r m i n a t i o n s i t h a s been shown why t h e combination of t h e s e two methods was q u i t e n e c e s s a r y t o t i d e over t h e d i f f i c u l t i e s duet o t h e d i f f e r e n t charge s t a t e s . This t e c h n i q u e h a s proved
i t s
h i g h s e l e c t i v i t y i n t h e s e a r c h o f i s o t o - p e s removed from t h e s t a b i l i t y r e g i o n [2].
Moreover i t a l l o w s t o measure p a r t i c l e s e m i t t e d very forward by g e t t i n g r i d of t h e e l a s t i c a l l y s c a t t e r e d beam. However t h e h i g h s e l e c t i v i t y can a l s o b e c o n s i d e r e d a s a d i s a d v a n t a g e : i n a s t u d y of r e a c t i o n mecha- nisms, f o r e a c h d e t e c t i o n a n g l e , t h e magnetic f i e l d must be v a r i e d s e v e r a l times i n o r d e r t o g e t t h e whole energy s p e c t r a . (beam time consuming).
3') I n beam y r a y s p e c t r o s c o p y .
The r e a c t i o n p r o d u c t s a r e i d e n t i f i e d by t h e energy of t h e i r y t r a n s i t i o n s a s i n r e f [ 4 5 ] .
Some informatioris about t h e r e c o i l e n e r g i e s can be reached by means of t h e Doppler e f f e c t . Cross s e c - t i o n s and a n g u l a r d i s t r i b u t i o n cannot be known, T h i s technique could be a p p l i e d i n c o i n c i d e n c e i n o r d e r t o i d e n t i f y c o r r e l a t e d l i g h t and heavy f r a g - ments.
4') Off-beam y and a s p e c t r o s c o p y
Thick t a r g e t s i n which r e c o i l p r o d u c t s a r e stopped c&t be chemically processed &6-44. y- s p e c t r o s c o p y i s then a p p l i e d t o t h e d i f f e r e n t che- mical f r a c t i o n s . A wide survey of r e a c t i o n p r o d u c t s i s t h u s o b t a i n e d b u t few i n f o r m a t i o n s can be c a r - r i e d o u t a s f o r t h e r e a c t i o n mechanisms.
When u t i l i z i n g t h i n t a r g e t s t h e r e c o i l p r o d u c t s a r e c o l l e c t e d i n s t a c k e d c a t c h e r s s o t h a t b o t h k i n e t i c e n e r g i e s and a n g u l a r d i s t r i b u t i o n s can be determined a f t e r y-ray o r a-ray a n a l y s i s . T h i s method i s of p a r t i c u l a r i n t e r e s t f o r s t u d y i n g heavy p r o d u c t s , t h e energy of which i s too low f o r conven- t i o n a l AE-E o r TOF i d e n t i f i c a t i o n s t o be c a r r i e d o u t L50-5
.
11. THE DEEP INELASTIC REACTIONS : A TWO-BODY PROCESS.
J. GALIN
The b i n a r y c h a r a c t e r of completely damped c o l l i s i o n s was s u s p e c t e d w i t h o u t any c o i n c i - dence measurements j u s t by c o n s i d e r i n g t h e a b s o l u t e k i n e t i c energy o f t h e p r o d u c t s . Indeed, t h i s energy corresponds roughly t o t h e Coulomb r e p u l s i o n energy due t o t h e complementary fragment (assuming two s p h e r i c a l n u c l e i i n c o n t a c t ) . However t h i s c l u e can- not be c o n s i d e r e d a s a completely convincing argu- ment f o r t h e two f o l l o w i n g r e a s o n s . F i r s t , f o r some mass asymmetric c o n f i g u r a t i o n s t h e Coulomb energy
r e s u l t i n g from t h e r e p u l s i o n of two d i s t i n c t f r a g - ments on a t h i r d one i s not expected t o be much d i f - f e r e n t from t h e one a r i s i n g i n a b i n a r y s p l i t . More- over, due t o t h e fragment deformation, t h e o r b i t a l a n g u l a r momentum and t h e e f f e c t s of subsequent eva- p o r a t i o n i n t h e f r a g m e n t s , one cannot know a c c u r a t e - l y what k i n e t i c energy i s t o b e expected from a b i -
t i o n . A t l e a s t 90% of t h e e v e n t s i n Kr+Bi and Cu+Au experiments were r e p o r t e d a s b i n a r y o n e s .
I n o t h e r c o i n c i d e n c e experiments,in a d d i t i o n t o t h e k i n e t i c energy m e a s ~ r e m e n t s ~ o t h e r p a r a m e t e r s were measured. These supplementary p a r a - m e t e r s a r e n o t n e c e s s a r y f o r proving t h e b i n a r y cha- r a c t e r of t h e s p l i t b u t t h e y may a l l o w t o g e t some i n s i g h t i n t o t h e l i g h t p a r t i c l e ( n , p ,a) emission p r i o r o r / a n d a f t e r t h e s p l i t a s we s h a l l s e e i n sec- t i o n 4 . The way i n which such experiments a r e analy- zed depends s t r o n g l y on t h e n a t u r e of t h e a d d i t i o n a l measured p a r a m e t e r s . So f a r we can d i s t i n g u i s h t h r e e c a t e g o r i e s :
i)
%he l i g h t fragment atomic numberi s
measured a s i n t h e 2 2 ~ e ( 2 5 2 MeV)+ 1 0 7 - 1 0 9 ~ g experiment c a r r i e d o u t a t Berkeleyp21
-
.
nary s p l i t even though a complete damping of t h e i i ) Mass i d e n t i f i c a t i o n i s achieved f o r one fragment r e l a t i v e motion i s assumed. and atomic number f o r t h e c o r r e l a t e d one a s i n t h e
50 some h i n t s of the binary cha- H e i d e l b e r g experiment f o r t h e 3 2 ~ ( ~ 4 ~ MeV)+ T i sys- r a c t e r of t h e deep i n e l a s t i c r e a c t i o n s were a l s o tem C7 I]
.
found i n u n c o r r e l a t e d experiments where b o t h l i g h t i i i ) Mass
+
atomic n ~ m b e r ~ i d e n t i f i c a t i o n f o r t h e and assumed heavy c o r r e l a t e d p r o d u c t s were measured. l i g h t fragment and mass i d e n t i f i c a t i o n f o r t h e cor-6 4
I n t h e s t u d y of t h e ( 4 0 ~ a + Ni) system [54] i t was r e l a t e d one a s i n t h e Orsay experiment : 4 0 ~ r ( 2 8 8 found t h a t , q u a l i t a t i v e l y , b o t h energy and a n g u l a r M ~ v ) + ~ * N ~
.
d i s t r i b u t i o n s f o r two assumed c o r r e l a t e d p r o d u c t s
The common r e s u l t o f a l l t h e s e works e x h i b i t e d complementary p a t t e r n s i n t h e c e n t e r of
i s , t h a t , f o r a t l e a s t 90% of t h e e v e n t s ( t h e expe- mass frame. Moreover,when c o n s i d e r i n g two e x p e c t e d
r i m e n t a l l i m i t ) , t h e p r o c e s s i s b i n a r y . Furthermore; c o r r e l a t e d fragments a t 90' c.m. t h e i r mean k i n e t i c
s o f a r , t o my knowledge t h e r e i s no r e p o r t e d c a s e of e n e r g i e s were found i n t o t a l agreement w i t h what i s
c o i n c i d e n c e experiments i n which a m i s s i n g mass r e q u i r e d from t h e momentum c o n s e r v a t i o n . I n a d d i t i o n ,
amount could n o t be e x p l a i n e d by l i g h t p a r t i c l e and w i t h i n t h e e x p e r i m e n t a l s t a t i s t i c a l u n c e r t a i n -
emission. (The f i s s i o n i n g heavy r e c o i l p r o d u c t b e i n g t i e s ( ? l o % ) , t h e c r o s s s e c t i o n s were a l s o found t o c o n s i d e r e d a s a s p e c i a l c a s e ) . We s h a l l come back i n be i n agreement. More d i r e c t e v i d e n c e s of t h e b i n a r y s p l i t t i n g i n deep i n e l a s t i c r e a c t i o n s were c l e a r l y s t r e s s e d i n c o i n c i d e n c e experiments. According t o t h e n a t u r e of t h e measured p a r a m e t e r s we can d i s t i n - g u i s h d i f f e r e n t k i n d s of c o i n c i d e n c e experiments. I n f i s s i o n t y p e experiments [85-391 it was assumed t h a t t h e p r o c e s s was b i n a r y and o n l y t h e ' fragment k i n e t i c e n e r g i e s were measured. Assu- ming f u r t h e r m o r e t h e f u l l momentum t r a n s f e r and t h e mass c o n s e r v a t i o n , t h e i n d i v i d u a l masses were ex- t r a c t e d i n a p p l y i n g t h e momentum c o n s e r v a t i o n law. It was shown t h a t t h e fragments r e l a t i v e emi'ssion a n g l e i n t h e c e n t e r o f mass system was on average
180° and t h a t t h e width of t h e d i s t r i b u t i o n was com- p a t i b l e w i t h d i s t o r t i o n s e f f e c t s due t o subsequent d e e x c i t a t i o n of t h e fragments by p a r t i c l e evapora-
s e c t i o n 4 t o t h e problem of t h e p a r t i c l e s e v a p o r a t e d by t h e f r a g m e n t s .
111. THE KINETIC ENERGY DAMPING.
The most s t r i k i n g f e a t u r e s r e v e a l e d i n deep i n e l a s t i c c o l l i s i o n s a r e connected w i t h a l a r g e energy damping i n t h e r e l a t i v e motion. As i t w i l l be shown i n M o r e t t o ' s paper [52] deep i n e l a s t i c c o l l i - s i o n s do n o t n e c e s s a r i l y r e s u l t i n i m p o r t a n t n u c l e a r m a t t e r exchanges and t h e r e f o r e , one cannot r e l y on
DEEP INELASTIC REACTIONS
F i g . 3
-
Contour p l o t of t h e c e n t e r of mass c r o s s s e c t i o n i n t h e E , 0 p l a n e f o r d i f f e r e n t elements i n t h e r e a c t i o n 4 0 ~ r ( 2 8 0 M ~ v ) + ~ ~ N ~ [53]. The c r o s s s e c t i o n s a r e given i n ub/MeV.rad.r e a c t i o n s have been s e l e c t e d i n o r d e r t o g i v e some h i n t s of what can be observed i n v a r y i n g t h e e n t r a n - c e channel p a r a m e t e r s . F i r s t , two medium mass s i m i -
5
8
l a r systems ( 4 0 ~ r + Ni)
154
and ( 4 0 ~ a + 6 4 ~ i ) [54] a r e c o n s i d e r e d w i t h d i f f e r e n t bombarding energy con- d i t i o n s ( r e s p e c t i v e l y 2.5B and 1.5B, where B i s t h e i n t e r a c t i o n b a r r i e r ) . Then a much massive system86 , 197Au
( Kr+ ; E = 1.4B) [35,55] w i l l be surveyed.
l o ) 4 0 ~ r + 5 8 ~ i (288 MeV)
[54.
g l e s . It seems r e a s o n a b l e t o assume t h a t s m a l l e r and s m a l l e r p a r t i a l R waves a s compared t o R g r a z i n g a r e i n v o l v e d , l e a d i n g t o a l a r g e r and l a r g e r o v e r l a p of n u c l e a r m a t t e r and, hence, t o an i n c r e a s i n g energy dAmping and more and m r e forward d i s t o r d e d t r a j e c - t o r i e s a s compared t o p u r e l y Coulomb o n e s . The cor- responding c o l l i s i o n s might be of t h e h i t and r u n type d e f i n e d by S w i a t e c k i k6]. The c o n t i n u a t i o n of t h i s r i d g e could p r o b a b l y l e a d t o n e g a t i v e d e f l e c - t i o n a n g l e s . As p o i n t e d o u t e a r l i e r .by Wilczynski I n f i g u r e 3 , q u i t e d i f f e r e n t p a t -
[57],
d u e t o symmetry of t h e phenomenon around O",t e r n s i n t h e c o n t o u r p l o t s can be d i s t i n g u i s h e d ac-
t h e e x t e n s i o n of t h e p r e v i o u s r i d g e could be t h e c o r d i n g t o t h e p r o d u c t i d e n t i t y . Two r i d g e s can be
r i d g e observed a t p o s i t i v e a n g l e s w i t h c o n t i n u o u s l y observed i n t h e y i e l d d i s t r i b u t i o n f o r t h o s e n u c l e i
d e c r e a s i n g energy. I n s u c h a p i c t u r e and assuming c l o s e t o t h e p r o j e c t i l e . The h i g h energy r i d g e ex-
t h e c l a s s i c a l d e f l e c t i o n f u n c t i o n a s meaningful t e n d s from Q.E.peak ( e l a s t i c s c a t t e r i n g e n e r g y , gra-
C5-90 3. GALIN
s i d e r e d ) one would g e t a p a t t e r n a s d e s c r i b e d i n f i - gure 4 . A s i n g l e rainbow a n g l e a r i s e s s l i g h t l y f o r - ward of t h e g r a z i n g a n g l e w i t h a c o r r e s p o n d i n g con- c e n t r a t i o n of c r o s s s e c t i o n a s s u g g e s t e d i n t h e K
contour p l o t , r a p i d l y d e c r e a s i n g backward and slowly d e c r e a s i n g forward.
Another a l t e r n a t i v e e x p l a n a t i o n s k e t - ched i n f i g u r e 4 h a s been s u g g e s t e d by Deubler and D i e t r i c h [25]. According t o t h e dynamical c a l c u l a -
eavy system
+
I
1
Deubler1
\
/DletrichRight- P o s s i b l e d e f l e c t i o n f u n c t i o n which could e x p l a i n t h e 8-focusing e f f e c t observed i n t h e s t u d y of heavy systems.
-
t i o n s c a r r i e d o u t by t h e s e a u t h o r s on t h e Ar+Th sys- tem a second rainbow a n g l e a r i s e s n e a r 0'. One can assume t h e same p a t t e r n f o r a system l i k e Ar+Ni w i t h some accumulation of c r o s s s e c t i o n i n t h e v e r y f o r - ward d i r e c t i o n . However t h e r e i s no way, i n t h e p r e - s e n t e x p e r i m e n t a l d a t a , t o d e c i d e which one of t h e Wilczynski o r Deubler-Dietrich e x p l a n a t i o n i s t h e r i g h t one. I n t h a t r e s p e c t a d d i t i o n a l measurements c l o s e t o
6'
might b e v e r y v a l u a b l e . 1 t l w l I C z y n S k l I I Anyway, t h e r e i s d e f i n i t e l y a c o n t i - nuous e v o l u t i o n between q u a s i e l a s t i c phenomena and completely damped ones. The c o l l i s i o n s l a b e l l e d by S w i a t e c k i a s g r a z i n g c o l l i s i o n s , h i t and r u n c o l l i - s i o n s and completely damped c o l l i s i o n s a r e b o t h involved i n t h e formation of n u c l e i such a s C 1 , A r and K.F i g . 4
-
L e f t - Schematic d e f l e c t i o n f u n c t i o n s a s suggested by Wilczynski on t h e one hand and by Deubler-Dietrich on t h e o t h e r hand.The p r e v i o u s p i c t u r e can be p r e c i s e d i n s t u d y i n g t h e c o n t o u r p l o t p a t t e r n s f o r t h e d i f - f e r e n t i s o t o p e s of a given element n e a r t h e p r o j e c - t i l e ' ( f i g . 5 ) . For example, t h e most abundant K i s o t o p e i s 4 1 ~ . I t corresponds t o t h e s i m p l e s t exchange : a s i n g l e p r o t o n pick-up by t h e p r o j e c - t i l e . A s we! l o o k a t i s o t o p e s f o r which more and more complex nucleon exchanges a r e i-nvolved we do
Fig. 5
-
Contour p l o t of the c e n t e r of mass c r o s s s e c t i o n i n t h e E , 8 p l a n e f o r K i s o - t o p e s i n t h e r e a c t i o n4 0 ~ r
(280 MeV) + 5 8 ~ iDEEP INELASTIC REACTIONS C5-91
s e e a d e c r e a s e i n the peak i n t e n s i t y a s w e l l a s t h e l o c a t i o n of t h i s peak i s s h i f t e d towards s m a l l e r an- g l e and energy v a l u e s . The slow t r a n s i t i o n from gra- z i n g c o l l i s i o n s t o i n n e r 6nes i s w e l l p e r c e i v e d , however,as i t i s a continuous process,one cannot s e t any boundary between g r a z i n g , h i t and run and deep i n e l a s t i c c o l l i s i o n s .
The same s t r - i k i n g e v o l u t i o n can be f o l - lowed c o n s i d e r i n g elements f a r t h e r and f a r t h e r remo- ved from t h e p r o j e c t i l e < f i g . 3 ) . P r o g r e s s i v e l y , g r a z i n g c o l l i s i o n s c o n t r i b u t e l e s s and l e s s i n t h e formation of e i t h e r l i g h t e r o r h e a v i e r elements a s compared t o t h e p r o j e c t i l e . Then, t h e same t r e n d i s t r u e c o n s i d e r i n g t h e i n t e r m e d i a t e h i t and run c o l - l i s i o n s . 'The average i h t e r a c t i o n time becomes l a r g e r and l a r g e r a s i n n e r and i n n e r R waves a r e involved. As
a
r e s u l t t h e y i e l d s a r e more s p r e a d a l l ' over t h e space.For t h e s t r o n g l y damped phenomena t h e i n t e r a c t i o n time i s l a r g e enough f o r t h e t r a n s i t o r y e x i s t e n c e of a "composite" system [58] o r "Pnterme- d i a t e complex" [?9] o r "double n u c l e a r system" [59]
t o be considered. E i t h e r , t h i s composite system does s u r v i v e long enough f o r t h e two n u c l e i t o f u s e f i r s t
(complete l o s t of t h e i r i d e n t i t y ) and f i n a l l y r e a c h t h e complete e q u i l i b r a t e d compound n u c l e u s s t a g e . O r , t h e , d i s r u p t i o n occurs a f t e r t h e system has r o t a - t e d d u r i n g a f r a c t i o n o f p e r i o d o r even s e v e r a l pe- r i o d s . When t h e s p l i t o c c u r s i n t h e completely equi- l i b r a t e d compound nucleus,then, a t r u e f i s s i o n pro- c e s s i s observed. There i s a c o n t i n u i t y i n t h e whole p r o c e s s d e s c r i b e d above and i t i s q u i t e d i f f i c u l t i n many c a s e s t o d i s t i n g u i s h a t r u e f i s s i o n phenomenon
(C.N. f i s s i o n w i t h h i g h e x c i t a t i o n energy and angu- l a r momentum) from a f i s s i o n b e f o r e complete e q u i l i - brium has been reached. A good example i s given by
t h e Z = 6 contour p l o t p a t t e r n , i n which t h e angu- l a r d i s t r i b u t i o n i s only s l i g h t l y more forward pea- ked t h a n t h e one expected i n a t r u e f i s s i o n p r o c e s s .
2") 4 0 ~ a + 6 4 ~ i (182 MeV) 1543 ( F i g . 6)
When comparing t h i s system w i t h t h e p r e v i o u s one ( v e r y s i m i l a r a s f a r a s t h e s i z e of i n t e r a c t i n g n u c l e i i s concerned) i t i s q u i t e i n s - t r u c t i v e t o s e e t h e e f f e c t s of bombarding energy on t h e contour p l o t p a t t e r n s ( f i g . 6 ) . Due t o t h e smal- l e r energy d i f f e r e n c e between t h e e n t r a n c e and t h e f u l l y damped e x i t channel (0.5B i n s t e a d of 1.5B), t h e appearance of t h e two r i d g e s i s n e a r l y comple- t e l y masked. I n s t e a d , a s shown f o r Z = 21 a broad
d i s t r i b u t i o n i s observed. N e v e r t h e l e s s t h e r e a r e some c l u e s i n d i c a t i n g t h a t t h e behavior observed a t h i g h bombarding energy remains v a l i d a t low energy. The c r o s s s e c t i o n i s d e c r e a s i n g forward a s w e l l a s a f l a t r i d g e i s e x t e n d i n g f u r t h e r backward. However n e a r (and forward o f ) t h e g r a z i n g a n g l e i t seems u n r e a l i s t i c t o t r y t o e v a l u a t e t h e two c o n t r i b u - t i o n s a s i t could be done a t h i g h bombarding energy.
As we c o n s i d e r l i g h t r e a c t i o n p r o d u c t s (from Z = 18 t o Z = 12) a n i c e smooth t r a n s i t i o n can be observed from a s i d e peaking t o a forward peaking. At t h e same time t h e k i n e t i c energy of t h e maximum p r o g r e s s i v e l y i s g e t t i n g c l o s e r t h e one measured a t l a r g e a n g l e s . A t f i r s t g l a n c e a l l t h e s e c h a r a c t e r i s t i c s resemble v e r y much what has been seen i n t h e s t u d y of more massive systems.
3") 8 6 ~ r + 1 9 7 ~ u (620 MeV) C35,55] ( f i g . 7)
The bombarding energy i s approximately
1.4B
a n d , i n t h i s r e s p e c t , t h e e n t r a n c e channel con- d i t i o n s a r e approximately t h e same a s f o r t h e (Ca +Ni)system. Q u a l i t a t i v e l y t h e same e v o l u t i o n from s i d e peaking t o forward peaking i s observed a s one c o n s i d e r s n u c l e i more and more removed from t h e pro- j e c t i l e . There i s a l s o some evidence f o r t h e d i f f e - r e n t product c r o s s s e c t i o n s n o t t o be completely n e g l i g e a b l e n e a r 0 " . However; " t h e r e l a t i v e c r o s s s e c t i o n i n t h e forward d i r e c t i o n a s compared t o the one measured a t t h e maximum of t h e d i s t r i b u t i o n i s much s m a l l e r f o r t h e heavy,system than f o r t h e l i g h t one i n d i c a t i n g a s t r o n g e r f o c u s i n g i n t h e y i e l d d i s t r i b u t i o n .This main d i f f e r e n c e i n t h e behavior of l i g h t and heavy systems i s r a t h e r unexpected. Indeed, i t i s known t h a t f o r l i g h t systems an impor- t a n t p a r t o f t h e r e a c t i o n c r o s s s e c t i o n i s found i n t h e compound n u c l e u s formation. T h i s is o p p o s i t e t o what has been seen i n heavy n u c l e i i n t e r a c t i o n . Therefore t h e II wave range l e a d i n g t o o t h e r chan- n e l s t h a n C.N. i s much wider f o r heavy s y s t e m t h a n f o r l i g h t ones and hence,the y i e l d s a r e expected t o be more s c a t t e r e d i n t h e s p a c e .
The s t u d y of t h e product d i s t r i b u t i o n
FWHM
can h e l p t o understand t h i s b e h a v i o r . I f we assume t h e l i f e time o f t h e system a s a d e c r e a s i n g f u n c t i o n of t h e impact parameter and t h e p r o d u c t d i s t r i b u t i o nFWHM
a s an i n c r e a s i n g f u n c t i o n of t h eDEEP INELASTIC REACTIONS C5-93
F i g . 7
-
Contour p l o t of t h e c e n t e r of mass c r o s s s e c t i o n i n t h e E, 8 p l a n e f o r some elements w i t h atomic numbers below t h ep r o j e c t i l e i n t h e 8 6 ~ r (620 M ~ V ) + ~ ~ ~ A U s t u d i e d a t Berkeley [357. The contour l i n e s a r e e q u a l l y spaced w i t h t h e f o l l o w i n g s t e p s
-
Z = 20a 2 a / a e a ~
= 5 pb/rad.MeV - 2 ~ 2 5 I t = 20 11 - Z = 2 8 ,? = 30 I1-
z
= 31 I 1 = 50"
- Z = 3 2 11 = 100 11 - z = 3 3 1, = l o o"
- z = 3 5 f 1 = 250 d i a t e a n g l e s t h e FWHM was t h e s m a l l e s t ( l a r g eII
) ,f o r backward a n g l e s t h e FWHM was t h e Largest ( s m a l l
R)
and f o r forward a n g l e s t h eFWHM
was i n t e r m e d i a t e ( i n t e r m e d i a t e R). T h i s g i v e s r i s e t o t h e two r a i n - bow a n g l e s d e f l e c t i o n f u n c t i o n a s shownin f i g u r e5
w i t h t h e c r o s s s e c t i o n focused i n a narrow a n g u l a rrange
.
Now, i f one c o n s i d e r s i n t e r m e d i a t e sys- tems between t h e ones surveyed s o f a r i n t h i s s e c - t i o n ( l i k e (Ar+Au) [60-6
11
,
(Cu+Au) [62],
(Cu+Sm)[51]) t h e i r b e h a v i o r s seem t o depend s t r o n g l y on t h e bombarding energy ( f i g . 8)
.
A t low bomb&dingF i g . 8
-
Angular d i s t r i b u t i o n s f o r quasi-Cu r e a c t i o n p r o d u c t s i n t h e system 6 3 ~ u + 1 9 7 ~ u a t 365 MeV a n d , 4 4 3 MeV bombarding energy.energy t h e a n g u l a r d i s t r i b u t i o n s appear t o be r a - t h e r of t h e (Kr+Au) type whereas a t h i g h energy they resemble more t h e ones observed i n t h e (Ar+Ni) s t u d y . An i n t e r m e d i a t e p a t t e r n h a s a l s o been p o i n t e d o u t by Wolf e t a 1 [ 6 a .for t h e Kr+Ho system a t 714 MeV, by Webb e t a 1 [64] f o r t h e Kr+La system a t 710 MeV and by Berlanger e t a 1 [65] f o r t h e Cu+Nb sys-
tem a t 280 MeV. So, i t i s c l e a r l y seen t h a t t h e s i z e of t h e n u c l e i d e s and t h e i r mass asymmetry i n t h e
To classify the studied systems, a pa-
rameter similar to the Sommerfeld parameter
n'
=
zpzTe2/hv', where v' is the relative velocity
when the two nucleides come in contact (correspon-
ding to E-B), might be more relevant than the usual
discrimination based on the interacting nucleus
sizes. It can be noticed that the Sommerfeld like
parameter
rl'is proportional to the ratio of a Cou-
lomb force ~ ~ ~ ~ e ~ / ( r ~ + r ~ ) ~
to a friction force if
the later is expressed as F =-Kvf/rlr2
(this expres-
sion is similar to the one proposed by Tsang
[lo]with the nuclear densities
pproportional to -I/r
which is a reasonable assumption in the nuclear
tails).
Thus, the reaction mechanism seems to
be strongly influenced by the delicate balance bet-
ween the Coulomb force and the friction force. For
a strong Coulomb force and comparatively small fric-
tion force (this is the example of heavy nucleides
interacting near the Coulomb barrier &d
hence with
small
v
'
)
the dynamics appears to be dominated by
Coulomb (short interaction time). Conversely for
light systems at high bombarding energy the Coulomb
effects are washed out by the friction force (lar-
ger interaction time)
.
I have tried to get together in Table
I some systems for which the deep inelastic colli-
sions have been studied by measuring the light reac-
tion products. The bombarding energies are compared
to the interaction barriers calculated within the
framework of the energy density formalism using the
sudden approximation [
1
2
]
.
In heavy combinations
(ZpZt>2800) for which the barrier is no longer exis-
ting but is replaced by a plateau, the height of
this plateau has been estimated. It can be seen that
most of the experiments have been done at
1.3cE<1.7B. It seems to me that a lot could be learned
from all these systems if extensive contour plots
were available for the different reaction products.
Numerous informations are contained in such graphs,
and, furthermre, this could allow the different
models to be easily tested.
From the available data, a continuous
evolution can be quantitatively depicted as a func-
tion of the Sommerfeld-like parameter
,I'
as fol-
lows
:-
for low
rl'values Capproximately
Q'<150-2001
the angular distribution are rather very broad with
their maximum peaked well forward the grazing angle
(orbiting picture)
;-
-
for large
Q'values (approximately ,1'>250-3001
most of the cross eection is focused close to the
grazing angle with an increase in the focusing phe-
nomenon as
q'increases.
-
for intermediate
b'values there is
a transi-
tion region 'w'here orbiting and focussing processes
have somewhat comparable intensities.
If this systematic were true, (Kr+Bi)
experiments at 10
MeVper nucleon b~mbibarding
energy
would lead to a dominant orbiti~g
picktire for the
reaction products and Kr(450
&lev)+&on the contra-
ry
would show a dominant focusing effect.
1 / 1 1 1 , , , 1 1 , / , 1
175 MeV : z ~ e
+
107sl,q9~Ag
Coulomb
energy4
60
Fig. 9
-
Average c.m. kinetic energies as a
function of Z for various lab angles
without any correction for light particle
evaporation. The Couclomb
energy is given
for two spheres and two spheroids at
equilibrium deformation. The radius para-
meter is ro
=1.224 and the nuclei are
C5-9 6 J. GALIN T a b l e I : ZpZT a t o m i c n u m b e r p r o d u c t f o r t a r g e t a n d p r o j e c t i l e S Y S T E M ZPZ t M ~ / " ~ B 1 a b E c . m .
/
B rl rl l B r e f . M H / $ m a s s a s y m m e t r y i n t h e e n t r a n c e c h a n n e l B : B a r r i e r c o m p u t e d i n t h e e n e r g y d e n s i t y f o r m a l i s m [ I 2 1 When t h e p o t e n t i a l e n e r g y c u r v e v e r s u s s e p a r a t i o n d i s t a n c e d o e s n o t e x h i b i t a n y b a r r i e r ( Z p Z t > 2 8 0 d t h e v a l u e of t h e remaining p l a t e a u estimated 0 : S o m m e r f e l d p a r a m e t e r ~ p ~ t &r l l : S o m m e r f e l d l i k e p a r a m e t e r z p z t 6 5J2E
*A-G=-B)
6 3 + ~"'AU ~ " ~ r + 1 6 5 ~ ~ 1 3 6 ~ e + l o 7 - l o 9 ~ ~ 8 6 ~ r + l a l ~ a 3 6 ~ r+
l g 7 ~ u " ~ r + 2 0 9 ~ i 1 3 6 ~ e + 1 5 9 ~ b 3 6 ~ e + 1 8 1 ~ a'
3 6 ~ e + 1 9 7 ~ ~ 1 3 6 ~ e + 2 0 8 ~ b 1 3 6 x e + 2 0 g B i-
l B i s t h e a n g u l a r momentum f o r t h e two n u c l e i d e s a t a c l o s e s t d i s t a n c e o f a p p r o a c h c o r r e s p o n d i n g t o t h e b a r r i e r t o p . F o r Z p Z t > 2 8 0 0 , w h e r e t h e r e i s n o l o n g e r a b a r r i e r t h e d i s t a n c e h a s b e e n e s t i m a t e d b y e x t r a p o l a t i n g t h e c o m p u t e d d i s t a n c e s f o r l o w e r Z p Z t p r o d u c t s . T h e c a l c u l a t e d 1 v a l u e s d o n o t c o r r e s p o n d t o 1 max s i n c e t h e n u c l e a r p o t e n t i a l a t t h i s d i s t a n c e i s a b o u t 4 0 MeV. T h e y a r e s h o w n t o g i v e some h i n t o f t h e 1 w a v e s i n v o l v e d i n t h e d i f f e r e n t s y s t e m s . (MeV) ( M ~ v ) 2 2 9 1 3 . 1 2 4 8 3 6 5 1 . 1 1 4 9 . 8 4 6 3 . 0 9 9 [ 8 31
4 4 3 1 . 3 1 3 6 . 2 2 6 7 . 3 1 7 1 1 6 21
2 4 1 2 1 . 9 2 6 7 7 1 4 1 . 8 1 3 1 . 9 2 0 1 . 0 2 7 9 [ 6 31
2 5 3 8 1 . 3 2 7 6 1 1 2 4 1 . 8 1 3 9 . 0 2 0 8 . 2 3 0 4 1 6 31
2 6 2 8 2 . 1 2 8 8 6 2 0 1 . 5 1 5 4 . 2 2 7 5 . 0 2 3 5t
8 43
2 8 4 4 2 . 3 % 3 0 7 6 2 0 1 . 4 1 6 6 . 8 3 1 0 . 0 2 3 3 [ 3 52
5 0 5 1 . 1 5 1 9 2 . 1 5 4 3 . 3 1 4 2 1 3 81
2 9 8 8 2 . 5 Q 3 1 5 5 2 5 1 . 2 0 1 8 8 . 4 4 7 4 . 3 1 6 2 [ 8 5 1 5 9 8 1 . 3 5 1 7 8 . 5 3 5 2 . 0 2 2 0 [: 3 91
7 1 4 1 . 6 0 1 6 3 - 5 2 6 6 . 6 2 9 1 [ 6 32
3 5 1 0 1 . 2 s 3 6 6 9 7 9 1 . 4 2 4 7 . 5 3 7 2 . 0 3 0 1 [ 8 61
3 9 4 2 1 . 3 ~ 4 0 9 1 1 2 0 1 . 6 2 1 6 . 5 3 6 0 . 9 3 7 5 [ 8 71
4 2 6 6 1 . 4 Q 4 3 1 9 7 9 1 . 3 2 9 0 . 4 4 9 5 . 5 3 1 0 [ 8 61
4 4 2 8 1'.5 Q, 4 4 8 1 1 2 0 1 . 5 2 4 3 . 1 4 1 8 . 0 3 9 0 [ 8 7 1 4 4 8 2 1 . 5 % 4 5 4 1 1 3 0 1 . 5 2 4 4 . 8 4 2 1 . 5 3 9 3 1 8 81
The "relaxed" energy.
It was shown, i n t h e y i e l d contour p l o t s f o r t h e d i f f e r e n t e l e m e n t s , t h a t t h e i r mean k i n e t i c energy a f t e r d e c r e a s i n g w i t h d e c r e a s i n g 8 was r e a c h i n g a lower l i m i t . Very e a r l y Volkov [78, 801 p o i n t e d o u t t h a t t h i s energy was i n good agree- ment w i t h t h e k i n e t i c energy one would e x p e c t from a p u r e Coulomb r e p u l s i o n between two c o r r e l a t e d fragments A n i c e proof of t h e Coulomb o r i g i n of t h e k i n e t i c energy was given a t Berkeley [89]. The r e - l a x e d k i n e t i c energy of a given element i s s u e d from e i t h e r (,8Ar+47Ag) o r (36Kr+2gCu) system was found t o be t h e same i n both systems. T h i s i s expected from a Coulomb r e p u l s i o n s i n c e t h e t o t a l charge i s t h e same f o r b o t h systems. For v e r y asymmetric s p l i t s i n l i g h t - s y s t e m s t h e r e i s g e n e r a l l y a f a i r l y
However, when approaching mass symmetry i n t h e e x i t channel, t h e e x p e r i m e n t a l v a l u e i s g e n e r a l l y lower t h a n t h e computed one a s shown i n f i g u r e 9 [73]. T h i s i s even more c l e a r l y s t r e s s e d i n systems i n - v o l v i n g h e a v i e r n u c l e i d e s where t h e p r o j e c t i l e - l i k e k i n e t i c energy i s much lower t h a n t h e i n t e r a c t i o n b a r r i e r energy. Thus, t h e r a t i o between t h e i n t e r a c - t i o n b a r r i e r and t h e k i n e t i c e n e r g y i n t h e e x i t channel d r o p s from 1 .*0.05 f o r (Ar+Ne) t o 0.76% .08 f o r (Ar+Ag) o r t o 0 . 8 1 k . 1 0 f o r (Ar+Au).
An e x p l a n a t i o n of t h i s d i f f e r e n c e may be found i n t h e fragment deformation a t t h e s c i s - s i o n p o i n t . Coulomb e n e r g i e s computed i n conside- r i n g t h e fragments a s s p h e r o i d s , allowed t o a t t a i n t h e i r e q u i l i b r i u m deformation, a r e
i n
b e t t e r a g r e e - ment w i t h experiment.good agreement between t h e measured energy and t h e
However, such c a l c u l ~ t i o n s a r e n o t ex- Coulomb energy r e p u l s i o n of two s p h e r i c a l n u c l e i .
DEEP INELASTIC REACTIONS C5-97 s i n c e two e f f e c t s a r e n o t accounted f o r . A f i r s t c o r r e c t i o n should be i n t r o d u c e d i n t h e e x p e r i m e n t a l energy v a l u e s t o account f o r t h e p a r t i c l e s e m i t t e d by t h e i n - f l i g h t p r o d u c t . However,this c o r r e c t i o n i s d i f f i c u l t t o e s t i m a t e s i n c e , most of t h e t i m e , v e r y l i t t l e i s e x p e r i m e n t a l l y known about t h e e x c i t a t i o n energy l e f t i n t o t h e fragments. Moreover depending on t h e n a t u r e of t h e p r o d u c t , t h e s p i n and e x c i t a - t i o n energy, p r o t o n and a - p a r t i c l e s may be s t r o n g l y competing w i t h n e u t r o n s . This would r e q u i r e more s o p h i s t i c a t e d c o r r e c t i o n s t h a n t h e ones g e n e r a l l y i n t r o d u c e d assuming only n e u t r o n e v a p o r a t i o n .
The second c o r r e c t i o n i s r e l a t e d t o a n g u l a r momentum. I n t h e computed k i n e t i c energy i n a d d i t i o n t o t h e dominant Coulomb term, one must con- s i d e r t h e c e n t r i f u g a l term. A s i t w i l l be shown i n t h e n e x t s e c t i o n , due t o t h e t a n g e n t i a l f r i c t i o n involved i n t h e p r o c e s s , a p a r t of t h e e n t r a n c e channel o r b i t a l a n g u l a r momentum i s found a s i n t r i n - s i c a n g u l a r momentum i n t h e r e a c t i o n p r o d u c t s . The- r e f o r e , t h e amount of t h e remaining c e n t r i f u g a l e n e r g y depends on t h e s t r e n g t h of t h e t a n g e n t i a l f o r c e and s o f a r v e r y l i t t l e i s e x p e r i m e n t a l l y known i n t h i s r e s p e c t . I n t h e framework of t h e s t i c k i n g model one can g e t an e s t i m a t e about t h e importance of t h e c e n t r i f u g a l term. L e t ' s c o n s i d e r a s an exam- p l e t h e (Ne+Ag) r e a c t i o n w i t h II; = 755. When t h e two n u c l e i d e s j u s t come i n c o n t a c t t h e c e n t r i f u g a l energy i s e q u a l t o 58 MeV. Then, assuming a s t i c k i n g c o n d i t i o n w i t h o u t any mass t r a n s f e r , t h e remaining o r b i t a l a n g u l a r momentum P.5 i s given by :
T h i s g i v e s a c e n t r i f u g a l c o n t r i b u t i o n t o t h e k i n e - t i c energy Ec920 MeV. T h i s v a l u e h a s t o be compared w i t h t h e 60-70 MeV of t o t a l Coulomb energy and i s shown t o be q u i t e i m p o r t a n t . We can n o t i c e t h a t , assuming t h e two n u c l e i r o l l i n g on e a c h o t h e r , i n s - t e a d of s t i c k i n g , t h e c e n t r i f u g a l term would be even l a r g e r (Q30 MeV). This amounts f o r n e a r l y 50% of t h e Coulomb term.
To b e t t e r u n d e r s t a n d t h e importance of t h e d i f f e r e n t terms c o n t r i b u t i n g t o t h e measured k i - n e t i c energy s e v e r a l experiments were done on a g i - ven system w i t h d i f f e r e n t bombarding e n e r g i e s [ 8 3 ,
621. A s shown a l s o i n f i g u r e 7 [73] t h e bombarding energy does n o t i n f l u e n c e i n an a p p r e c i a b l e way t h e k i n e t i c e n e r g i e s i n t h e e x i t channel. However, a s i t
h a s been observed i n s e v e r a l c a s e s 1901, w i t h t h e i n c r e a s e of bombarding energy one would e x p e c t an i n c r e a s e of t h e p a r t i a l average % wave v a l u e s c o n t r i - b u t i n g t o deep i n e l a s t i c . r e a c t i o n s and t h u s an i n - c r e a s e of t h e c e n t r i f u g a l term. But, on t h e o t h e r hand, more e x c i t a t i o n energy i s l e f t i n t o t h e f r a g - ments l e a d i n g t o l a r g e r l o s s e s of nucleons and maybe a l a r g e r s t r e t c h i n g i s t a k i n g p l a c e . These t h r e e e f - f e c t s seem t o c o u n t e r a c t each o t h e r . A s i m i l a r beha- v i o r has been p o i n t e d o u t i n heavy i o n induced f i s -
s i o n
[91-94
.
As f a r a s s p e c t r a f a r from t h e g r a z i n g a n g l e a r e c o n s i d e r e d , t h e energy spectrum FWHM seems
n o t t o be Z dependant f o r most of t h e s t u d i e d s y s - tems. An i n c r e a s e i n
FWHM
can be observed w i t h i n - c r e a s i n g bombarding energy [TO]. And a s f o r t h e mean k i n e t i c energy, i t i s d i f f i c u l t t o account p r e c i s e l y f o r t h eFWHM
s i n c e shape f l u c t u a t i o n s , a n g u l a r mo- mentum d i s t r i b u t i o n s , e x c i t a t i o n energy and p a r t i c l e e v a p o r a t i o n a l l c o n t r i b u t e t o t h e observed w i d t h .I V . EXCITATION ENERGY AND SPIN I N THE REACTION PRODUCTS.
As shown p r e v i o u s l y , a l a r g e amount of t h e k i n e t i c energy i n t h e r e l a t i v e motion i s l o s t i n deep i n e l a s t i c p r o c e s s e s . I n o r d e r t o b e t t e r unders- tand t h e r e a c t i o n mechanism, t h e knowledge of b o t h e x c i t a t i o n energy ( h e a t and deformation energy) and s p i n f o r e i t h e r c o r r e l a t e d r e a c t i o n p r o d u c t would be a v a l u a b l e i n f o r m a t i o n . From t h e s p i n v a l u e s one could e s t i m a t e t h e importance o f t a n g e n t i a l f r i c t i o n i n t h e energy damping. Experimentally t h e measurements of b o t h q u a n t i t i e s ( e x c i t a t i o n energy and s p i n ) i s a d i f f i - c u l t t a s k . E x c i t a t i o n e n e r g i e s can be reached through t h e measurements of l i g h t p a r t i c l e s and y- r a y s e m i t t e d by t h e p r o d u c t s . S p i n s can be e s t i m a t e d from t h e number of y-rays e m i t t e d d u r i n g t h e r e a c - t i o n i f e v a p o r a t e d p a r t i c l e s a r e assumed t o n o t c a r - r y away much a n g u l a r momentum.
Coincidence experiments between t h e fragments and i t s evaporated p a r t i c l e s and y-rays a r e t h u s r e q u i r e d and t h i s g e n e r a l l y i m p l i e s v e r y low c o u n t i n g r a t e s . Most of t h e s e experiments a r e i n t h e i r e a r l y s t a g e and t h e c o n c l u s i o n we can draw o u t a r e r a t h e r u n c e r t a i n .
A- Emission of l i g h t p a r t i c l e s i n deep i n e l a s - t i c r e a c t i o n s .
process most of the heat might be concentrated in
the neck which has developed between the colliding
nuclei. It is likely 'that one or several particles
will be emitted from the corresponding hot spot.
Such particles are expected to have rather high
energies as in preequilibrium emission. Then, provi-
ded the life time of the system is long enough, the
remaining heat is likely to diffuse throughout the
composite system until a uniform temperature is
reached. If it were so, the excitation energies
left in the two correlated nuclei would be roughly
in the ratio of their masses [93-941.
Are there any experimental evidence to
sustain the previous assumptions
?i.e.
:-
high energy particles emitted prior to scis-
sion.
-
post scission emission.
In the experimental results we can
distinguish four types of measurements
:1')
Detection of charged particles (p,cx) in heavy
ion interactions without coincidence require-
ments with correlated fragments.
It was shown very early
[95]that the
angular distribution of charged particles emitted
in heavy ion interactions was not always symmetric
around
90'as expected from compound nucleus der
excitation. Instead,
aforeward peaking distribu-
tion, in excess as compared with the backward dis-
tribution, strongly substantiates the existence of
additional reaction mechanisms. Non-compound
a-particles are generally more abundant than non-
compound protons and deuterons in 12c,
1 4 ~ , 160I I I I I I I I '
