HEAVY-ION ELASTIC AND QUASI-ELASTIC SCATTERING ABOVE E/A = 30 MeV

HAL Id: jpa-00225783

https://hal.archives-ouvertes.fr/jpa-00225783

Submitted on 1 Jan 1986

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.

HEAVY-ION ELASTIC AND QUASI-ELASTIC SCATTERING ABOVE E/A = 30 MeV

J. Barrette

To cite this version:

J. Barrette. HEAVY-ION ELASTIC AND QUASI-ELASTIC SCATTERING ABOVE E/A = 30 MeV. Journal de Physique Colloques, 1986, 47 (C4), pp.C4-141-C4-154. �10.1051/jphyscol:1986417�.

�jpa-00225783�

JOURNAL DE PHYSIQUE

Colloque C4, supplgment au n o 8, Tome 47, aoQt 1986

HEAVY-ION ELASTIC AND QUASI-ELASTIC SCATTERING ABOVE E/A = 30 MeV

J. BARRETTE

Service de Physique NuclBaire. Basse Energie, CEN-Saclay.

F-91191 Gif-sur-Yvette Cedex, France

Resum6 - A haute 6nergie l a d i f f u s i o n Elastique d'ions lourds devient sensi-

ble p o t e n t i e l noyau-noyau dans un 1 arge . domai ne nettement 'a ¹ ' ⁱ n t 6 r i eur du rayon d'absorption f o r t e . Ceci permet une d6termination plus pr6cise de l a p a r t i e r 6 e l l e de c e t t e i n t e r a c t i o n e t une image consistante de l a v a r i a t i o n de c e t t e i n t e r a c t i o n avec l ' z n e r g i e commence Z b e r g e r . Les d i s t r i b u t i o n s angul a i res i n6l astiques sembl e n t conteni r moi ns d ' e f f e t s r 6 f r a c t i f s e t donc de c o n t r i b u t i o n s de 1 1 i n t 6 r i e u r du noyau. Les e f f e t s de voies couplees des 6 t a t s i n e l a s t i q u e s sont encore t r 6 s importants jusqu'B 2 0 MeV/n e t peuvent changer l ' i n t e r a c t i o n nucl6aire e f f e c t i v e . Les r6actions de t r a n s f e r t i n d u i - tes par l e s ions lourds ont une section e f f i c a c e f a i b l e mais prgsentent une f o r t e s 6 l e c t i v i t 6 pour l e s h a t s de hauts spins e t sont donc prometteuses pour l e s Etudes spectoscopi ques.

Abstract - At high energy, heavy-ion e l a s t i c s c a t t e r i n g probes the ion-ion p o t e n t i a l i n a l a r g e domain much i n s i d e the strong absorption radius. This r e s u l t s i n a more precise determination o f the r e a l p a r t o f the nuclear po- t e n t i a l and a consistent p i c t u r e o f i t s e v o l u t i o n w i t h energy begins t o emer- ge. It i s r e l a t i v e l y s i m i l a r t o t h a t observed i n l i g h t i o n scattering. Even i f the i n e l a s t i c angular d i s t r i b u t i o n s seem t o contain l e s s r e f r a c t i v e or i n t e r i o r contribution, coup1 ed channel e f f e c t s from these states are s t i l l important a t l e a s t up t o 2 0 MeV/n. Heavy-ion induced t r a n s f e r reactions t o d i s c r e t e states have small cross sections b u t present a very strong s e l e c t i - v i t y f o r states w i t h the highest a v a i l a b l e spin and could thus provide new and i n t e r e s t i n g spectoscopic information.

I. INTRODUCTION

The energy domain covered by t h i s conference i s characterized by a change i n a l l the dominant nuclear r e a c t i o n mechanisms since mean f i e 1 d e f f e c t s which dominate the nuclear i n t e r a c t i o n a t low energy give way t o two-body d i s s i p a t i o n as the energy i s increased. This t r a n s i t i o n should a l s o appear i n the energy dependence o f the ion- i o n p o t e n t i a l . This i s shown by the few microscopic c a l c u l a t i o n s o f such p o t e n t i a l s /1-4/ and w i l l be discussed i n more d e t a i l s by A. Faessler a t t h i s conference /5/.

The study o f complex r e a c t i o n mechanisms such as fragmentation o r incomplete fusion may eventually t e l l us something about the e v o l u t i o n o f mean f i e l d e f f e c t s a t high temperature o r as a f u n c t i o n of density. However, a t present, the r e l a t i o n between t h e o r e t i c a l concepts and experimental observabl es i s hindered by the d i f f i c u l ;i es i n t r e a t i n g r e a l i s t i c a l l y a l l aspects o f the nuclear dynamics. The study o f the b e t t e r understood" e l a s t i c scattering, and i n general o f quasi-el a s t i c reactions, may thus be a useful f i r s t t e s t o f our understanding o f t h i s question i n the l i m i t o f low temperature and normal density .

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986417

JOURNAL DE PHYSIQUE

11. ELASTIC SCATTERING 11.1 Dynamical aspects

I t i s i n t e r e s t i n g t o discuss f i r s t some dynamical aspects o f heavy-ion e l a s t i c scat- t e r i n g a t t h e p r e s e n t energy. Because o f t h e s t r o n g absorption, heavy-ion e l a s t i c s c a t t e r i n g a t l o w energy i s o n l y s e n s i t i v e t o t h e n u c l e a r i n t e r a c t i o n f a r i n t h e t a i l o f t h e n u c l e i , i.e. c l o s e t o t h e s t r o n g a b s o r p t i o n r a d i u s /16,17/. As t h e ener- gy i s increased t h e s i t u a t i o n changes and we become s e n s i t i v e t o t h e i n t e r a c t i o n i n a more i n t e r i o r region. T h i s i s shown i n f i g . 1 f o r t h e 160 + 12C system a t EL : ⁹⁴

MeV/n /8/. T h i s f i g u r e presents t h e range o f Woods-Saxon type o p t i c a l p o t e n t i a l s which f i t t h e data. They a r e a l l very s i m i l a r i n a domain r a n g i n g from = 3.5 t o 7 fm. T h i s conclusion does n o t depend on t h e f u n c t i o n a l form used f o r t h e p o t e n t i a l /8/. The e x t e n t o f t h i s s e n s i t i v e r e g i o n i s confirmed by t h e r e s u l t o f a notch t e s t shown as an i n s e r t i n f i g . l b . A t t h i s energy, t h e s e n s i t i v e r e g i o n extends consi- derably i n s i d e t h e s t r o n g a b s o r p t i o n r a d i u s (6.2 fm) and reaches even t h e sum o f t h e n u c l e a r charge r a d i i (4.8 fml. T h i s e f f e c t has a l s o been observed f o r o t h e r heavy systems such as 12c + 12c /9-13/ and 160 + 28Si /14,15/. The e v o l u t i o n o f t h e sensi- t i v e r a d i u s as a f u n c t i o n o f energy i s shown i n f i g . 2 f o r t h e system l 6 0 + 28Si.

The s o l i d l i n e corresponds t o t h e middle of t h e domain where t h e nuclear p o t e n t i a l i s determined by t h e e l a s t i c angular d i s t r i b u t i o n whereas t h e dashed 1 in e s i n d i c a t e r o u g h l y t h e w i d t h o f t h i s r e g i o n as o b t a i n e d by a n o t c h t e s t /14,15/. Between t h e b a r r i e r r e g i o n and 60 MeV/n t h e c e n t e r o f t h e s e n s i t i v e r e g i o n has moved inward by r o u g h l y 2 fm o r 25 %. I t s w i d t h seems a l s o t o increase a t h i g h energy.

T h i s behavior has two main explanations. F i r s t a t h i g h energy the n u c l e i become more t r a n s p a r e n t and t h e s t r o n g a b s o r p t i o n r a d i u s Rl12 decreases (see f i g s . 2 and 3). A t very low energy, near t h e b a r r i e r , R / 2 decreases because t h e maximum o f t h e poten- t i a l b a r r i e r f o r t h e g r a z i n g p a r t i a t wave moves inward. However a t h i g h e r energy, t h e pocket disappears i n t h e t o t a l n u c l e a r p o t e n t i a l and t h e e v o l u t i o n o f Rl12 re- f l e c t s m a i n l y t h e exponential decrease o f t h e n-n c r o s s s e c t i o n up t o Ec

.

MeVIn. T h i s has been shown t o lead, i n r e l a t i v e l y l i g h t heavy-ion sys'teins, t o a r e d u c t i o n i n t h e r e a c t i o n cross s e c t i o n a t h i g h energy /12,20/.

A t h i g h energy, we a r e a l s o more s e n s i t i v e t o t h e i n t e r i o r o f t h e nucleus because t h e f a r s i d e amplitude becomes more i m p o r t a n t i n t h e angular d i s t r i b u t i o n s . T h i s c o n t r i b u t i o n which i s associated w i t h n e g a t i v e angl e s c a t t e r i n g has i t s o r i g i n mai n- l y i n t h e a t t r a c t i v e nature o f t h e n u c l e a r p o t e n t i a l and Goldberg and Smith /21/

have shown how t h e appearance o f t h i s f a r s i d e c o n t r i b u t i o n helps t o r e s o l v e a m b i g u i t i e s i n t h e i o n - i o n p o t e n t i a l .

As t h e energy increases s e m i c l a s s i c a l concepts o r WLB approximations should work r a t h e r w e l l . The n o t i o n o f t r a j e c t o r y and impact parameter a r e b e t t e r j u s t i f i e d because o f t h e reduced wavelength as are a l s o the concepts o f t u r n i n g p o i n t and d e f l e c t i o n f u n c t i o n (and i t s associated phenomena such as rainbow, g l o r y , i n t e r - ference...). I n t h e present energy domain s e m i c l a s s i c a l method can p r o v i d e very p r e c i s e and u s e f u l d e s c r i p t i o n o f heavy-i on s c a t t e r i n g /13,22/.

Hussein and McVoy /23/ have discussed t h e dynamical aspects o f t h e nearside and f a r s i d e decomposition f o r t h e s c a t t e r i n g o f n u c l e i which a r e n e i t h e r pure absorber n o r pure r e f r a c t o r . They show t h a t t h e increased importance o f t h e f a r s i d e amplitude a t h i g h energy i s mainly due t o s m a l l e r d e f l e c t i o n from t h e Coulomb f i e l d which a c t s as a d i v e r g i n g l e n s ( o r i n f a c t as two f l a t prisms i f we consider o n l y t h e edge o f t h e nucleus) and s h i f t s t h e f a r s i d e and nearside amplitude r e l a t i v e t o each o t h e r by 291/4.

Due t o t h e a t t r a c t i v e nature o f t h e nuclear i n t e r a c t i o n , t h e f a r s i d e amplitude has always a f l a t t e r slope than t h e nearside amp1 i t u d e so t h a t a t any energy i t should e v e n t u a l l y dominate a t s u f f i c i e n t l y l a r g e angle. The cross-over angle becomes much s m a l l e r a t h i g h energy.

R ( f m)

Fig. 1 - ^{a ) 160 + 12C} e l a s t i c angular distribution a t EL = 94 MeV/n. The l i n e s are optical model f i t s /a/. b) Real part of the Woods-Saxon optical potentials which f i t

the ¹⁶⁰ + 1 2 C data. The insert shows the results of a notch text /15/.

C4-144 JOURNAL DE PHYSIQUE

Fig. 4 presents the nearside

10 - _I - f a r s i d e decomposition o f the

160 + 2 8 ~ i ¹⁶⁰ e l a s t i c angular d i s t r i bu- t i o n on various targets a t

- _{EL =} 94 MeV/n 1151. One ob- serves t h a t as the charge o f

8- the t a r g e t (and as a conse-

112 ^quence el,,) increases the

f a r s i de ampl i tude becomes

7- 1 ess prominent.

Various reduced r a d i i deduced

6 - \ - from these data are shown i n

\ f i g . 5. For 208Pb which s t i l l

\ a t the present energy pre-

5 ^I I I I 1 1 1 1 1 I I I I l ~ ~ ~ l \ sents a pure Fresnel-type an-

10 lo2 lo3 gul a r d i s t r i b u t i o n the center

o f t h e s e n s i t i v e region ( r S )

Ec.M.(M~V) where the nuclear p o t e n t i a l i s best determined ' i s very close t o the strong absorp- Fig. 2

-

l60 + 28Si /14,15/. s e n s i t i v e radius moves i n s i d e

t h e strong absorption radius

I I and f o r the 1 2 C t a r g e t appro-

aches the sum o f the nuclear

R112 r a d i i (rCo).

subject o f much discussion Fig. 3

-

radius f o r the 160 + 4 0 ~ a and 160 + 208Pb systems

/15,17 ,la/. The l i n e s are p r e d i c t i o n s o f energy I n previous studies o f heavy- independent p o t e n t i a l which f i t s low energy data. i o n e l a s t i c s c a t t e r i n g i t had

been suggested thas the ob- servation o f an exponential fa1 1 - o f f f o l 1 owing the nearside-farside Fraunhijfer i n t e r f e r e n c e p a t t e r n (see f i g . 4a) was a signature o f a nuclear rainbow 19-111. As shown i n ref.1251 a smooth expo- n e n t i a l f a l l - o f f i s simply the manifestation o f the far-side t a i l and i s n o t s u f f i - c i e n t t o confirm the presence o f a nuclear rainbow. It i s suggested t h a t the only c l e a r signature o f the rainbow i s the observation o f the interference produced by the two branches o f the d e f l e c t i o n function on each side o f the nuclear rainbow. As shown i n f i g . 6b f o r the system 12c + 12C a t EL = 289 MeV such interference appears i n the f a r s i d e ampl i t u d e i n c a l c u l a t i o n which neglects absorption. These calcula- t i o n r e s u l t s i n a k i n d o f A i r y p a t t e r n s i m i l a r t o t h a t observed near the Coulomb rainbow. I n t e r f e r e n c e o f t h i s type (and thus a c l e a r signature o f a nuclear rainbow) has been c l e a r l y evidenced only i n 1 ig h t p a r t i c l e s c a t t e r i n g 126,281. As shown

*

*

- -

. . . .

A 160+40ca ^a

160+208pb -

I I 1 1 1 1 1 1 I I 1 1 1 1 1 1

I I n I .2 the Nuclear energy rainbow range discussed here, a l l reasonably a t t r a c - t i v e p o t e n t i a l s such as those obtained from microscopic o r f o l d i n g model (50 < V < 300 MeV) r e s u l t i n a 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 present- i n g a nuclear rainbow and the reduced absorption may be s u f f i c i e n t t o reveal it. This

5 10 50 f)o could f u r t h e r constrain the

%,I ~ ( M e V l u ) p o t e n t i a1 1241. The evidence f o r such rainbow has been the

e ~ . ~ . ( d e g . )

Fig. 4 - Nearsi de-f arsi de decomposition of 60 el a s t i c scattering angular di s t r i bu- tions a t 94 MeV/n on various targets /8,15/.

The evolution of the farside amplitude with the absorption has been studied for an analytic case in ref./26/. The result i s shown in fig. 7. I t i s expressed in terms of reduced variables : 9~ i s the rainbow angle, q i s the curvature of the deflection function a t the rainbow, and a i s a parameter related to the absorption. The open c i r c l e s correspond t o 12c + 1 2 C e l a s t i c scattering data a t EL = 86 MeV/n / I l l . For moderate absorption (small a 1, the nuclear rainbow s t i l J manifests i t s e l f , even when there i s no interference l e f t , by a change in the slope of the farside amplitude when we reach the shadow region a t 9 > OR. Strong evidences for such an effect are presented in ref. 1131 for the system 12c + 12c and 12c + 13c a t EL = 20 MeV/n.

I t i s thus possible that many high energy heavy-ion data are influenced by the presence of a nuclear rainbow (even i f not clearly evidenced in the data) and that such rainbow has contributed to better constrain the potential deduced from the data.

JOURNAL DE PHYSIQUE

Fig. 5 - Target mass dependence o f various reduced r a d i i f o r I 6 0 s c a t t e r i n g a t 94 MeV/n. A r e shown, t h e Coulomb rainbow (rCR), t h e Coulomb b a r r i e r (RCB), t h e s t r o n g a b s o r p t i o n (rlI2), t h e p o t e n t i a l s e n s i t i v e ( r S ) , and t h e sum o f t h e charge d e n s i t y

(RCDl r a d i i .

11.3 Nuclear p o t e n t i a l s

I t i s o f t e n d i f f i c u l t t o compare p o t e n t i a l s obtained i n d i f f e r e n t works o r f o r d i f - f e r e n t systems s i n c e i t i s n o t always c l e a r which r e g i o n o f t h e p o t e n t i a l should be compared o r how t o take i n t o account the s c a l i n g between systems. The simple compa- r i s o n o f p o t e n t i a l parameters i s r a r e l y i n s t r u c t i v e . The double-folding model /29/

o f f e r s such a p o s s i b i l i t y since i t i s expected t o g i v e a good d e s c r i p t i o n o f t h e po- t e n t i a l geometry, a t l e a s t i n t h e t a i l , and i t uses r e a l i s t i c d e n s i t y d i s t r i b u t i o n s which should a l l o w p o t e n t i a l s deduced f o r d i f f e r e n t systems t o be compared.

The f a c t o r by which t h e r e a l p a r t o f t h e double-folded p o t e n t i a l has t o be renorma- 1 iz e d t o f i t t h e data i s shown as a f u n c t i o n o f energy i n f i g . 8 f o r t h e systems 12C

+ 1 2 ~ /9,30/, 160 + 12C /8,31,32/ and 160 + 208Pb /15,33/. A l l t h e c a l c u l a t i o n s were done w i t h t h e M3Y i n t e r a c t i o n /29,33/ which contains already a weak l i n e a r energy dependence which reduces the volume i n t e g r a l o f t h e i n t e r a c t i o n by roughly 30 %, a t 100 MeV/n. The r a p i d increase o f t h e p o t e n t i a l near t h e b a r r i e r f o r t h e 160 + 208Pb system i s due t o t h e rapi'd v a r i a t i o n o f W a t t h r e s h o l d which a f f e c t s t h e deduced r e a l p o t e n t i a l through d i s p e r s i o n r e l a t i o n /34/. Above t h e b a r r i e r r e g i o n one obser- ves a decrease o f t h e nuclear p o t e n t i a l w i t h energy which i s comparable f o r a l l systems w i t h i n t h e experimental e r r o r s .

There i s a t present no evidence t h a t t h e n o r m a l i z a t i o n f a c t o r depends on t h e t a r e t mass ( f i g . 9 ) o r on t h e p r o j e c t i l e since 4 0 ~ r s c a t t e r i n g a t 44 MeV/n on 60Ni, l2 3 Sn and 208Pb leads t o n o r m a l i z a t i o n f a c t o r o f = 0.7, i n good agreement w i t h t h e values shown i n f i g . 8. The energy v a r i a t i o n o f t h e p o t e n t i a l i s i n good agreement w i t h t h a t obtained from t h e s c a t t e r i n g o f p a r t i c l e s from 208pb /35/. Due t o Paul i b l o - c k i ng e f f e c t s , d i f f e r e n c e s should e x i s t between l i g h t i o n and heavy-ion p o t e n t i a l s , i n t h e present energy-range. The s c a t t e r i n g o f t h e experimental p o i n t s i n f i g . 8 shows t h a t these d i f f e r e n c e s w i l l o n l y be evidenced by more systematic and p r e c i s e data as w e l l as by a more c o n s i s t a n t analysis.

Fig. 6 - Nearside-farside decompo- s i t i o n o f t h e 1 2 C + ^{1 2 C} e l a s t i c s c a t t e r i n g angular d i s t r i b u t i o n a t EL = 289 MeV f o r a p o t e n t i a l which f i t s t h e data /9/ (upper p a r t ) and assuming no a b s o r p t i o n ( 1 ower p a r t ) /25/.

I t i s puzzl i ng t h a t t h e observed energy dependence o f t h e nuclear i n t e r a c t i o n i s c l o s e t o t h a t pre- d i c t e d by a simple e i k o n a l appro- x i m a t i o n which does n o t t a k e i n t o account Paul i b l o c k i n g e f f e c t s /12,36/ whereas more microscopic c a l c u l a t i o n s /1-4/ p r e d i c t t h a t t h e i n t e r a c t i o n should be weak a t

14

c - NEAR ... 1

F A R ---

l o w energy and should i n c r e a s e up G

W=O ^TOTAL -

t o EL= 50-100 MeV/n. NEAR .. ...

E x c e l l e n t f i t s a r e obtained a t a l l Fa(X) energies o f one uses i n s t e a d a re-

normal i r e d f o l d e d p o t e n t i a l based on an energy and d e n s i t y dependent i n t e r a c t i o n such as t h e DDM3Y i n - t e r a c t i o n /33,37/. For d e s c r i b i n g a s c a t t e r i n g data i t i s necessary t o renormal i z e t h e p o t e n t i a l by a c o n s t a n t f a c t o r o f = 1.3 a t a l l energies. However, when a p p l i e d t o heavy-ion systems t h e DDM3Y i n t e r - a c t i o n g i v e s a c o n f u s i n g p i c t u r e . For 160 s c a t t e r i n g a t 94 MeV/n i t r e s u l t s i n n o r m a l i z a t i o n f a c t o r c l o s e r t o 1 (and l a r g e r than w i t h

t h e M3Y i n t e r a c t i o n ) b u t which 0 1 -

seems t o vary smoothly w i t h t h e x =(e-le,l)/q1/3

mass o f t h e t a r g e t (see f i g . 9). Fig. 7 - E v o l u t i o n w i t h a b s o r p t i o n o f t h e f a r - On t h e c o n t r a r y a t l o w energy and s i d e amplitude produced by a n u c l e a r rainbow

f o r ' + O A ~ s c a t t e r i n g a t 44 MeV/n /26/. The open p o i n t s correspond t o 1 2 c + 1 2 c t h e n o r m a l i z a t i o n f a c t o r s a r e re- e l a s t i c s c a t t e r i n g data a t 86 MeV/n /11/.

duced r e l a t i v e t o those obtained

w i t h t h e M3Y i n t e r a c t i o n /33/. T h i s would i n d i c a t e t h a t t h e geometry r e s u l t i n g from t h e DDM3Y i n t e r a c t i o n i s n o t q u i t e r i g h t p a r t i c u l a r l y i n t h e t a i l .

A t l o w energy, renormal i z e d f o l d e d FAR - - - -

p o t e n t i a l s based i n t h e M3Y nucle- on-nucleon i n t e r a c t i o n succeed t o d e s c r i b e very w e l l the e l a s t i c an- g u l a r d i s t r i b u t i o n s mainly because such data a r e s e n s i t i v e o n l y t o

t h e t a i l o f t h e nuclear p o t e n t i a l . 0 - .. ... .... -

A t h i g h e r energy when we probe a .'... '....

more i n t e r i o r region, i t i s impos- I . . , ^I I . ^{p ... . 1} , . I . I I I . . . .~

s i b l e t o o b t a i n an as good des- 0 20 4 0 6 0 8 0 100 c r i p t i o n o f t h e data because the Bc M (deg I

M3Y i n t e r a c t i o n r e s u l t s i n a too l a r g e c e n t r a l depth.

JOURNAL DE PHYSIQUE

The energy dependence o f the absorb- t i v e p o t e n t i a l i s n o t as well deter- mined as t h a t of the r e a l interac- t i o n . Whereas a t high energy the e l a s t i c angular d i s t r i b u t i o n s seem t o determine the r e a l p o t e n t i a l over a large r a d i a l domain ( f i g s . 1 and 91, the imaginary p o t e n t i a l i s well defined only near the strong absorp- t i o n radius. Thus the p o i n t where the imaginary p o t e n t i a l i s measured moves w i t h energy as R ( f i g s . 2 and 3) and i t i s d i f f c u f C 2 t o separa- t e which p a r t o f t h i s energy depen- dence i s associated w i t h the geome- t r y o f the p o t e n t i a l and which p a r t corresponds t o a v a r i a t i o n o f i t s strength. The l i n e s i n f i g . 3 are the p r e d i c t i o n s f o r R1 o f energy independent p o t e n t i a l s # r t t e d t o the e l a s t i c data a t E < 20 MeV/n. The measured value o f k

,,

The parameter which i s best determi- Fig. 8 - Normalization f a c t o r o f double-folded ned by the data i s the r a t i o o f the

o t e n t i a l s which f i t the 1 2 C + 12c /30,9,15/, imaginary p o t e n t i a l t o the r e a l po- P60 + 12C /8,30,32/ and 160 + ,OePb /15,33/ t e n t i a l near the strong absorption e l a s t i c angular d i s t r i b u t i o n s . The l i n e s are radius. 160 data a t 94 MeV/n /9/ and t o guide the eyes. 1 2 C + 1 2 C data a t 86 MeV/n /12/ give r a t i o o f 0.8 + ^0.1. Between 10 and 100 MeV/n t h i s r a t i o seems t o increase s l i g h t l y w i t h energy /9,12,31/. It i s i n t e r - e s t i n g t o note that, as f o r the r e a l p o t e n t i a l , t h i s behavior i s very s i m i l a r t o t h a t observed i n a p a r t i c l e s c a t t e r i n g /35/. The observed energy dependence seems t o be much weaker than predicted by microscopic c a l c u l a t i o n s /2,3,38/.

111. INELASTIC SCATTERING

Heavy-ion i n e l a s t i c s c a t t e r i n g a t high energy i s p a r t i c u l a r l y favourable f o r study- i n g high l y i n g states. This i s the realm o f g i a n t resonances which i s the subject o f a t a l k a t t h i s conference /39/. Concerning i n e l a s t i c e x c i t a t i o n o f more standard low l y i n g states two i n t e r e s t i n g aspects have been addressed recently.

The increased s e n s i t i v i t y t o the i n t e r i o r o f the n u c l e i discussed above should a l l o w a b e t t e r t e s t o f the form f a c t o r used i n the c a l c u l a t i o n o f i n e l a s t i c e x c i t a t i o n . Usually c o l l e c t i v e form f a c t o r s are simply taken as the f i r s t d e r i v a t i v e o f the nuclear p o t e n t i a l . As long as the s c a t t e r i n g i s s e n s i t i v e only t o the exponential t a i l o f the nuclear i n t e r a c t i o n data cannot be very s e n s i t i v e t o d e v i a t i o n from t h a t p r e s c r i t i o n . Recently i t was observed /13/ t h a t i n e l a s t i c angular d i s t r i b u t i o n s i n 2C + P2C and 1 2 C + 1 3 C s c a t t e r i n g a t EL = 20 MeV/n d i d n o t show, a t l a r g e angles, the r e f r a c t i v e peak associated w i t h inner p a r t i a1 waves and the nuclear rainbow ( f i g . 10a). Coupled-channel calcul ations p r e d i c t t h a t t h i s peak which i s c l e a r l y seen i n the e l a s t i c and sing1 e nucleon t r a n s f e r angular d i s t r i b u t i o n s shoul d a1 so appear i n the i n e l a s t i c d i s t r i b u t i o n s . This r e s u l t means t h a t f o r some reason ine- l a s t i c e x c i t a t i o n i s reduced i n the i n t e r i o r . The best d e s c r i p t i o n o f the data was obtained by reducing considerably the 2+ form f a c t o r f o r radius R < 4.5 f m ( f i g . l o b ) . To obtain more precise information on t h i s subject i t i s important t o f i n d the conditions where the experimental signature o f the i n n e r c o n t r i b u t i o n i s maximum.

The highest energy may n o t always be the most favourable f o r such a study /10,13/.

Optical model analysis o f h i g h energy e l a s t i c s c a t t e r i n g data seems t o provide us w i t h precise information on the nuclear i n t e r a c t i o n . I n such an analysis, however,

.... 03M3Y N=1,19

-.- M3Y N=0.68

-.- M3Y N=0,62

Fig. 9

-

n. The arrows indicate the center of the sen- s i t i v e region as ob- tained by a notch t e s t

9 10 11 12

~ [ f ~ ) I t , i s assumed that a l l the inelas- t i c channels (including a1 l the complex channels) contribute only t o the imaginary part of the inter- action and have l i t t l e influence on the real potential. The influence of each s t a t e even those closely related to the ground s t a t e (including the low lying collective s t a t e s which play an important role a t low energy) i s expected t o decrease a t h i g h energy because each s t a t e contributes in general less to the reaction cross section ( f i g . 11). I t was suggested that for a collective s t a t e such as the 2' s t a t e of 12C

C4-150 JOURNAL DE PHYSIQUE

I I I

"C +"c , 20 MeVIN

r " "

Elastic Scatter~ng Elas:~c Scatter~ng

lnelast~c Scattering lnelast~c Scatter~ng

Bc M ldeg )

0 10 20 30 40 50 60 70

Bc ^{M (deg} l

Fig. 10 - a) E l a s t i c and i n e l a s t i c angular d i s t r i b u t i o n s f o r 12c + 13C a t 20 MeV/n.

S o l i d 1 ines are t h e r e s u l t s o f coup1 ed-channel calculations; The dash-dotted 1 ines are obtained by removing c o n t r i b u t i o n s from p a r t i a l waves L c 28 /13/. b) Same as a) but f o r 12c * ^12C. The l i n e s correspond t o coupled-channel c a l c u l a t i o n s using the standard i n e l a s t i c form f a c t o r (dash-dotted) o r a modified form f a c t o r ( s o l i d l i n e ) (see i n s e r t ) . The dashed l i n e s include the c o n t r i b u t i o n from mutual e x c i t a t i o n . t h i s reduction o f the cross section i s a measu- r2+' ^!

rement o f the increased predominance o f the n-n m b . \

i n t e r a c t i o n over the nucl eus-nucl eus one-body I2c +12c

i n t e r a c t i o n a t high energy /12/.

!\\it

'

20 Fig. 11 - Energy dependence o f the cross section f o r the 4.4 MeV 2* s t a t e i n the ~ Z C + ^1% reac-

t i o n /12/.

G2+ -

The i n f l u e n c e o f i n e l a s t i c states on the deduced Oi o p t i c a l p o t e n t i a l has been studied i n refs./lO, 31,40/ f o r the s c a t t e r i n g o f 12C on 12C, 13C and 160 a t energies between 10 and 20 MeV/n. It i s 0.02-

shown i n f i g . 12 t h a t even i f each i n e l a s t i c s t a t e i s weak, coupled channel e f f e c t s c o n t r i - bute very s i g n i f i c a n t l y t o the r e s u l t i n g e l a s t i c ^O.O1 angular d i s t r i b u t i o n . Even unbound 3-a break-up channels have very sizable e f f e c t s . These data

-

'.

'"-k

I I , , , , I

\

-

i\!+,

\ '\

'9-.

- $ P * - - - - q

:

L

.

can be f i t t e d very well w i t h a unrenormalized ^{10 50 100}

E[,~/A ( M ~ v )

Fig. 12

-

( ~ ~ ' 1 ) f o l ded p o t e n t i a l i f the i n e l a s t i c channels are included e x p l i c i t l y . Equiva- l e n t f i t t o the data i n a one channel approximation necessitates a renormalization o f the r e a l p o t e n t i a l by a factor 0.84 1311. The i n e l a s t i c states introduce a dyna- mica1 p o l a r i z a t i o n p o t e n t i a l which has a repulsive r e a l p a r t ( f i g . 12b) which i s on average compensated by reducing the strength o f the p o t e n t i a l i n a one channel cal- culation. Fig. 12b i n d i c a t e s that, contrary t o the behavior o f the imaginary poten- t i a l 1411, the r e a l p a r t of the dynamical p o l a r i z a t i o n p o t e n t i a l i s unexpectedly l a r g e r a t 20 MeV/n t h a t a t 10 MeV/n.

I t i s c l e a r l y important t o pursue such a work a t higher energy i f one wants t o as- c e r t a i n our conclusion on the evolution w i t h energy o f the nuclear i n t e r a c t i o n . I n p a r t i c u l a r i t would be i n t e r e s t i n g t o obtain data on a l l the states which should be introduced i n the coup1 ed-channel analyses.

I V . TRANSFER REACTIONS

'Heavy-ions induced t r a n s f e r reactions t o i n d i v i d u a l states i s re1 a t i v e l y we1 1 under- stood a t low e n e r g and has been shown t o give precise and valuable spectroscopic information. Near or above the Fermi energy ( i .e. high v e l o c i t y ) nucleon t r a n s f e r between low l y i n g d i s c r e t e states becomes determined mainly by recoi 1 e f f e c t s i .e.

the dynamics 1421. A t these energies, mass t r a n s f e r i s associated w i t h l a r g e moment- um transfer. This means t h a t such reactions w i l l p r e f e r e n t i a l l y populate unbound states corresponding t o l a r g e Q values. For low l y i n g d i s c r e t e states, however, the t r a n s f e r happens only between the high momentum t a i l s o f the incoming and ougoing t r a n s f e r r e d p a r t i c l e wave function. This r e s u l t s i n a roughly exponential decrease o f the t r a n s f e r cross section w i t h energy r e f l e c t i n g the shape o f these high moment- um t a i l s ( f i g . 13). The slope of the energy dependence o f the cross section depends on the t r a n s f e r r e d angular momentum, being much f l a t t e r f o r t r a n s f e r t o high spin states 1431. Single nucleon t r a n s f e r a t high energy could thus be a s e n s i t i v e t e s t o f a p a r t i c u l a r p a r t o f the nuclear wave function. It i s n o t clear, however i f heavy i o n i s the best probe f o r such studies since the high momentum component o f the wave

C4-152 JOURNAL DE PHYSIQUE

Fig. 13 - Calculated integrated cross section f o r the neutron t r a n s f e r reac- tion '2C(13C,12C)13C*. The points a r e f i n i t e range DWBA calculations /42/.

The dynamical c o n s t r a i n t s imposed by mass t r a n s f e r a r e evidently more severe when we t r y t o t r a n s f e r more t h a n . one nucleon. Above t h e Fermi energy the cross section f o r t r a n s f e r t o low lying bound s t a t e is very small. Such data could, however, be of great i n t e r e s t since population of the highest a1 igned spin configuration shoul d be strong1 y favoured. T h i s has been s t r i k i n g l y de- monstrated r e c e n t l y i n t h e r a c t i o n 4 2 ~ a ( 4 8 ~ i ,46Ti ) 4 4 ~ a a t 8 MeY/n 1471 ( f i g . 14). Below t h e grazing angle the 4 6 ~ i s p e c t r a show a s i n g l e peak a t EX = 17.8 MeV which has been interpreted as r e s u l t i n g from t h e (f7/2)-: S t a t e i n 4 6 ~ i a t 3.3 MeV coupled t b t h e (g9/2)::

o r ( g 9 / 2 , ~ d 5 / 2 ) ~ + neutron s t a t e r n 4 4 ~ a . Data a t h i g h & energy should dis- criminate between these two possibili- t i e s since they correspond t o d i f f e r e n t t r a n s f e r r e d angular momenta.

Fig. 14 - Spectra of the two-neutron stripping reaction 48Ti + 42Ca + 4 6 ~ i +

Arrows i n d i c a t e s the position of predicted bjgh spin configurations : -2

a ) ( f 1 / 2 ) 6 + (f512 g9/2)7- ; b) ( f i / 2 ) 6 + (99/2):+ ; C ) f 1 1 ~ ) ' ~ (9912 d512) /47/

6+ 6+

function i s mainly in t h e i n t e r i o r , of t h e nucleus /44/ so t h a t the r e s u l t i n g cross section can be strongly influenced by the not so well determined absorption.

As the above remarks indicate, high ener- gy favours high angular momentum t r a n s f e r /45/. Another advantage of high energy i s t h a t as i n e l a s t i c s c a t t e r i n g angular d i s t r i b u t i o n s , t h e Coulomb e f f e c t de- creases and eventually a l l the t r a n s f e r angular d i s t r i b u t i o n s evolve from be1 1 shape t o being forward peaked. In such case the shape of t h e angular distribu- t i o n near 0" contains in general a signa- t u r e not only of the transferred angular momentum but a l s o of the spin. This s i - gnature i s , however, apparent only i n the f i r s t o s c i l l a t i o n of the angular d i s t r i - bution. This requires measurements inside e = (1 ,,,i 1-I : a r a t h e r d i f f i c u l t task. I nt3resting p o s s i b i l i t y i s t o use such reactions t o reach high-lying s t a t e s based on high j o r b i t a l s . The d i f f e r e n t spin and transferred angular momentum s e l e c t i v i t y of heavy-ion induced reactions may render such data complemen- t a r y t o what i s obtained from l i g h t ions /46 /

.

-

1

LOO

600

I

0 5 10 15 20 25

Ex ( MeV

Most o f the high spin nuclear spectroscopy which has generated so much i n t e r e s t i n the l a s t few years i s based on our understanding o f such aligned configurations. May be t r a n s f e r data can b r i n g new informations t o t h a t f i e l d p a r t i c u l a r l y on the struc- t u r e o f wave functions which cannot be reached by simple y-spectroscopy.

The use o f heavy-ions f o r studying charge exchange r e a c t i o n i s also very promising.

They o f f e r several p o t e n t i a l advantages over l i g h t ions f o r the study o f s p i n and i s o s p i n t r a n s i t i o n i n nuclei. One i s the p o s s i b i l i t y t o study from a nucleus o f i s o s p i n T, T > = To, To > both the t r a n s i t i o n s To + 1, To + 1 > i n the nucleus w i t h Z-1 ( e q o i v a f e n t t o (n,p) r e a c t i o n ) and the t r a n s i t i o n s t o Ti, To - ^{1 >} (Ti = To ,

To -+ 1 ) i n t h e nucleus w i t h charge Z+l (equivalent t o (p,n)). Probably more impor- t a n t i s the p o s s i b i l i t y by changing the p r o j e c t i l e - e j e c t i l e choice t o have some s e l e c t i v i t y on the spin t r a n s f e r channel. These p o s s i b i l i t i e s are demonstrated i n two c o n t r i b u t i o n s a t t h i s conference 148,491.

Recent data on the 12C(12C,12N)12E r e a c t i o n show t h a t even a t 35 MeVIn, heavy-ion induced charge reaction i s s t i l l dominated by Sequential transfer. The s i t u a t i o n seems more favourabl e f o r 1 i ghter p r o j e c t i 1 es 1491. However the sequential process should decrease r a p i d l y w i t h energy and as shown i n f i g . 15 above 60 MeVIn the one-

step t r a n s f e r should c l e a r l y dominate

I ' - . . I . . " I . . " J t h i s reaction. This i s a l s o i n t h i s

\ 12 12 12

x C( C, N)'~B,,

:

10-2

-

*,

V. CONCLUSION

o 20 40 60 00 The f i e l d o f heavy-ion induced e l a s t i c Eh, [MeV/nucleon] and quasi-elastic reactions above 30

MeVIn i s s t i l l h i g h l y unexplored. Up t o Fig. 15 - Estimated trend o f the sequen- now, the bulk o f the experiments have t i a l and one-step t r a n s f e r cross section addressed the dynamical aspects o f f o r the charge exchange reaction 12c(12C, these reactions. The few examples pre-

1501. sented here c l e a r l y show t h a t t h i s type o f r e a c t i o n o f f e r s new and i n t e r e s t i n g p o s s i b i l i t i e s both i n the study o f r e a c t i o n mechanism and nuclear spectroscopy. The recent and f u t u r e a v a i l a b i l i t y o f high r e s o l u t i o n spectrometers a t intermediate energy f a c i l i t i e s i s t h e c a t a l y s i s needed t o f u l f i l successfully such a program.

Many o f the r e s u l t s presented here are from the t h e s i s o f P a t r i c i a Roussel, whom I wish t o thank a l s o f o r valuable discussions and h e l p f u l remarks concerning t h i s paper.

REFERENCES

/1/ Sartor, R. and Stancu, F l

.

.

/21 Faessler, A. e t a1 . , ^Nucl

.

I 3 1 Trefz, M. e t al., Nucl . Phys. ~ 4 4 m 9 8 5 ) 499.

I 4 1 Brink, D.M. and Stancu, Fl., Phys. A243 (1975) 175.

I 5 1 Faessler, A., Proceedings o f t h i s conference.

161 Satchler, G.R., Proc. I n t e r . Conf. On r e a c t i o n between complex nuclei, Nashvil- l e (Tenn. (North Holland, Amsterdam, 1974) p. 171.

/7/ Christensen, P.R. and Winther, A., Phys. L e t t . 658 (1976) 19.

C4-154 JOURNAL DE PHYSIQUE

/8/ Roussel, P. e t al., Phys. Rev. L e t t . 54 (1985) 1779.

/9/ Brandan, M.E., Phys. Rev. L e t t . 49 (1V82) 1132.

/lo/ Bohlen, H.G. e t al., Z. Phys. A 3 m (1982) 121.

/11/ Buenerd, M. e t al., Phys. Rev.= (1982) 1299.

/12/ Bwnerd, M. e t al., Nucl. P h y s . T Z 4 (1984) 313.

/13/ Bohlen, H.G. e t al., Z. Phys. A3-1985) 241.

/14/ Cramer, J.G. and DeVries, R.~.,Phys. Rev. C22 (1980) 91.

/15/ Roussel , ^P., These, U n i v e r s i t 6 Paris-Sud ( 1 m .

/16/ Roussel, P. e t al., C o n t r i b u t i o n t o t h i s conference, vol. 1.

/17/ Olmer, C. e t a1

.

/18/ Vigdor, S.E. e t al., Phys. ~ e r C 2 0 (1979) 2147.

/19/ Alamanos, N. e t a1 . , Proc. ~ e c o n n n t e r . Conf. on nucleus-nucleus c o l l i s i o n s , vol. I, (ed. Jakobsson, B and A l e k l e t t , K. 1, p. 36.

/20/ DeVries, R.M. and Peng, J.C., Phys. Rev. C22 (1980) 1055.

/21/ Goldberg, D.A. and Smith, S.M., Phys. R e v x e t t . 33 (1974) 715.

/22/ F r o b r i c h , P. and Kaufmann, P., Phys. L e t t . 1548 ( m 8 5 ) 24.

/23/ Hussein, M.S. and McVoy, K.W., Proc. i n P a r n u c l . Phys. 12 (1984) 103.

/24/ Goldberg, D.A. and Smith, S.M., Phys. Rev. L e t t . 29 (1975)TOO.

/25/ McVoy, K.W. and Satchler, G.R., Nucl. Phys. A417 77384) 157.

/26/ Da S i l v e i r a , R. and L e c l e r c q - W i l l a i n , Ch., . J Phys. C6 (1984) 395.

/27/ S a t c h l e r , G.R. e t al., Phys. L e t t . 1288 (1983) 147. -

/28/ Da S i l v e i r a , R. and L e c l e r c q - W i l l a i m h . , Z. Phys. A314 (1983) 63.

/29/ Satchler, G.R. and Love, W.G., Phys. Rep. 55 (1979) /30/ Stokstad, R.G. e t a1

.

/31/ Sakuragi, Y. and Kamimura, M., P h y n e t t . 149B (1984) 307.

/32/ Brandan, M.E. e t al., B.A.P.S. 31 (1986) 8 3 V ,

/33/ El-Azab F a r i d , M. and S a t ~ h 1 e r ~ T . R . . Nucl. Phys. A438 (1985) 525.

/34/ Nagarajan, M.A. e t al., Phys. Rev. L e t t . 54 (1985)=6.

/35/ Bonin, B. e t al., Nucl. Phys. A445 (19851381.

/36/ Chauvin, J. e t al., Phys. R e v . m (1983) 1970.

/37/ Kobos, A.M. e t al., Nucl. P h y s . T 8 4 (1982) 65.

/38/ Bonin, B., p r i v a t e c o m m u n i c a t i o n 7 /39/ Chomaz, P., Proceedings o f t h i s conference.

/40/ Kubqno, S. e t al., Phys. l e t t . 1638 (1985) 75.

/41/ Kubo, K.I. and Hodgson, P.E., W Phys. A366 (1981) 320.

/42/ Yon Oertzen, W., Phys. L e t t . 1518 (1985) 9 5 ,

/43/ Kurihara, T. and Sakai, M., PK L e t t . 1338 (1983) 157.

/44/ Durand, M. e t al., Phys. L e t t . 113B ( 1 9 8 m 1 6 . /45/ Mermaz, M.C. e t a1

.

/46/ Gales, S., Proc. o f t h e I n t e r n . Symp. on h i g h l y e x c i t e d s t a t e s and nuclear s t r u c t u r e , J. Phys. 45, C4 (1984) 39.

/47/ Brendel, C. e t al., miys. L e t t . 171B (1986) 28.

/48/ Bohlen, H.G. e t al., C o n t r i b u t e w e r s t o t h i s conference, p. 12 and t h i s v o l ume.

/49/ W i n f i e l d , J.S. e t al., C o n t r i b u t e d paper t o t h i s conference, p. 14.

/50/ W i n f i e l d , J.S. e t a1 ., Phys; Rev. C33 (1986) 1333.