LOW AND INTERMEDIATE ENERGY HEAVY ION COLLISIONS IN THE SEMI-CLASSICAL MICROSCOPIC DESCRIPTION

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LOW AND INTERMEDIATE ENERGY HEAVY ION

COLLISIONS IN THE SEMI-CLASSICAL

MICROSCOPIC DESCRIPTION

C. Gregoire, B. Remaud, F. Sebille, L. Vinet, D. Jacquet

To cite this version:

C. Gregoire, B. Remaud, F. Sebille, L. Vinet, D. Jacquet. LOW AND INTERMEDIATE ENERGY

HEAVY ION COLLISIONS IN THE SEMI-CLASSICAL MICROSCOPIC DESCRIPTION.

Interna-tional Workshop on Semiclassical and Phase Space Approaches to the Dynamics of the Nucleus, 1987,

Aussois, France. pp.C2-203-C2-209, �10.1051/jphyscol:1987229�. �jpa-00226496�

JOURNAL DE PHYSIQUE

Colloque C2, suppl6ment au n o 6, Tome 48, juin 1987

LOW AND INTERMEDIATE ENERGY HEAVY ION COLLISIONS IN THE SEMI-CLASSICAL MICROSCOPIC DESCRIPTION

C. G R ~ G O I R E , B. REMAUD*, F. S~BILLE", L. VINET"* and

D.

JACQUET'

GANIL, BP 5027, F-14021 Caen Cedex, France

~ I R E S T E , 3, rue du Marechal Joffre, F-44041 Nantes Cedex 01,

France

**Universit6 de Nantes, 2, rue de la HoussiniBre, F-44072 Nantes,

France

" " ~ a w r e n c e Berkeley Laboratory, Nuclear Science Division,

Berkeley, CA 94720, U.S.A.

'Institut de Physique Nucleaire, BP 1, F-91406 Orsay Cedex, France

Resume : C e t t e c o n t r i b u t i o n e s t consacr6 8 l a d e s c r i p t i o n des c o l l i s i o n s c e n t r a l e s e t i p h 6 r i q u e s

1

l ' a i d e d'une dynanique Landau-Vlasov. Pour l e s c o l 1 is i o n s

peripheriques aux energies i ntermediai res, l e s c o r r 6 l a t i o n s masse-masse, l e s energies moyennes des q u a s i - p r o j e c t i l e s e t l e s d i s t r i b u t i o n s a n g u l a i r e s s o n t obtenues e t compares avec l e s donnees experimentales. Pour l e s c o l l i s i o n s centrales, on montre que l a fenEtre de f u s i o n de TDHF

2

basse Energie d i s p a r a i t avec l ' i n t r o d u c t i o n d'une i n t g r a c t i o n r g s i d u e l l e . Au-del6 de 20 MeV/u, l a f u s i o n incomplete e s t d e c r i t e avec l e t r a n s f e r t d'impulsion e t l e s ddformations

n u c l e a i r e s associees. Le couplage aux e t a t s du continuum e s t analyse dans l e s dynaniques Vlasov e t Landau-V1 asov. L ' i n t 6 r a c t i o n Coul ombienne &ant incorporee, nous presentons des r e s u l t a t s sur l e t r a n s f e r t d ' i s o s p i n e t l ' e x c i t a t i o n du mode dip01 a i r e i s o v e c t o r i e l au v o i sinage e t au-dessus de l a b a r r i e r e Coulombienne. Quelques perspectives pour l ' e t u d e d'observables physiques'sont finalement trac6es.

A b s t r a c t : It i s shown how p e r i p h e r a l and c e n t r a l heavy-ion c o l l i s i o n s can be described by Landau-V1 asov dynamics. For p e r i p h e r a l c o l l i sions a t i n t e r m e d i a t e energies, mass-mass c o r r e l a t i o n s , e j e c t i l e mean energies and angular d i s t r i b u t i o n s a r e obtained and compared w i t h fragmentation data. For c e n t r a l c o l l i s i o n s , one shows t h a t the c o l l i s i o n term destroys t h e TDHF p r o p e r t y o f transparency a t low impact parameters f o r c o l l i s i o n s c l o s e from t h e Coulomb b a r r i e r . Above 20 MeV/u incomplete f u s i o n i s described w i t h associated l i n e a r momentum t r a n s f e r and n u c l e a r deformations. One e x h i b i t s how c o u p l i n g t o t h e continuum i s obtained i n Vlasov and Landau-Vlasov dynamics. Coulomb i n t e r a c t i o n b e i n g taken i n t o account, we present a l s o r e s u l t s concerning t h e i s o s p i n t r a n s f e r and t h e e x c i t a t i o n of the i s o v e c t o r d i p o l e mode near and w e l l above the Coulomb b a r r i e r . Some p e r s p e c t i v e s t o f u r t h e r s t u d i e s o f p h y s i c a l observables are f i n a l l y drawn.

I n t r o d u c t i o n

The n u c l e a r Vlasov and Landau-Vlasov equations have been introduced i n o r d e r t o f o l l o w t h e t i m e e v o l u t i o n o f the microscopic one body d i s t r i b u t i o n f u n c t i o n f ( t , b l i n t h e phase space symplectic m a n i f o l d d e f i n e d a t the Hartree-Fock and extended Hartree-Fock l e v e l . P r o p e r t i e s and procedures f o r t h e determination of

approximate s o l u t i o n s have been w i d e l y discussed d u r i n g t h i s conference,

e s p e c i a l l y i n t h e B. Remaud's t a l k . I n t h e t a b l e I, we sketch t h e s a l i e n t f e a t u r e s c h a r a c t e r i z i n g t h e two main approches t o these nuclear k i n e t i c equations a v a i l a b l e i n the l i t e r a t u r e . A n i c e d e r i v a t i o n o f these equations can be found, on t h e o t h e r hand, i n R. M a l f l i e t ' s c o n t r i b u t i o n and i n reference [l]. It t u r n s o u t t h a t t h e r e a l and imaginary p a r t s o f the g-matrix e n t e r i n the mean f i e l d term and t h e c o l l i s i o n term r e s p e c t i v e l y . The energy and density dependence o f t h e e f f e c t i v e nucleon-nucl eon i n t e r a c t i o n f i n d s t h e r e i t s j u s t i f i c a t i o n when one deals w i t h t h e Landau-Vlasov equation.

Table I

-

Approaches t o the nuclear k i n e t i c equation : approximate s o l u t i o n s , i n g r e d i e n t s and a p p l i c a t i o n s .

LANDAU-VLASOV (Ref. [2,3,4.5,6,7,18])

Decomposition o f one-body d i s t r i b u t i o n f u n c t i o n on a movinq coherent s t a t e

Neutrons and protons ; Coulomb i n c l u - ded

.

s i m p l i f i e d Skyrme i n t e r a c t i o n s r2. 61 BOLZMANN-UEHLING-UHLENBECK (Ref. [8,9,10,11,12]) o r VLASO1'-UEHLING-UHLENBECK P a r a l l e l ensembles o f pseudo-parti- c l e s (nucleons) basis I n i t i a l n u c l e i i n t h e i r ground state, each o f them being an exact s t a t i o n - nary s o l u t i o n o f t h e Vlasov equation ( i n i t i a l s e l f - c o n s i s t e n t procedure)

b l s i n i e r a c t i o n ( l o n g range c o r r e l a -

I

t i o n s ) [ I ]

average over ensembles

Simpl i f i e d Skyrme i n t e r a c t i o n

Momentum dependent f o r c e [ l 3 1

Uehl ing-Uhlenbeck c o l l i s i o n term w i t h : unn (energy, density, i s o s p i n ) continuous r e l a x a t i o n

Slabs [ 5 ]

Spherical symmetry [ 3 ] 3D

-

d e s i n t e g r a t i o n [ 6 ] Intermediate and low energy heavy i o n c o l l is i o n s [4,18]

Uehl ing-Uhlenbeck c o l l i s i o n term w i t h : an,, = constant

continuous o r f l u c t u a t i n g [ l 4 1 re1 a x a t i o n

Intermediate and re1 a t i v i s t i c heavy i o n c o l l i s i o n s [8,9,10,11,12]

r and y emission [ l 5 1 Mu1 t i f r a g m e n t a t i o n [ l 4 1

The Vlasov equation i s w i d e l y used i n plasma physics where the mean-field i s e s s e n t i a l l y g i v e n by the electromagnetic l o n g range i n t e r a c t i o n . I n our c o n t e x t ( t h e heavy i o n c o l l i s i o n s ) , we note t h a t t h e dominant term derives from the s h o r t range s t r o n g i n t e r a c t i o n , a l l o w i n g a determination o f t h e s o l u t i o n which i s much more stable. I n t h i s c o n t r i b u t i o n , we r e p o r t on a few s i t u a t i o n s where these s o l u t i o n s were used i n o r d e r t o c a l c u l a t e physical observables and t o c h a r a c t e r i z e c o l l i s i o n processes. The f r a g ~ n e n t a t i o n mechanism i n i n t e r m e d i a t e energy heavy i o n c o l l i s i o n s i s analyzed ( s e c t i o n 1). The occurence o f f u s i o n - l i k e processes i s discussed i n s e c t i o n 2. P a r t i c u l a r a t t e n t i o n i s p a i d t o p a r t i c l e emission i n t h e continuuln i n s e c t i o n 3. I n s e c t i o n 4, we mention some r e s u l t s concerning t h e e x c i t a t i o n of i s o v e c t o r modes i n heavy i o n c o l l i s i o n s near the Coulomb b a r r i e r .

l

-

Fragmentation mechanism

As revealed by Landau-V1 asov c a l c u l a t i o n s f o r c o l l is i o n s above 30 MeV/u, t h e main p a r t o f t h e r e a c t i o n cross s e c t i o n goes i n t o t h e p r o j e c t i l e fragmentation cross section. As a m a t t e r of fact, t h e p a r t i a l waves corresponding t o deep i n e l a s t i c processes a t low energy c o n t r i b u t e a t i n t e r m e d i a t e energy t o an a b r a s i o n - l i k e mechanism. However d i f f e r e n t hebaviour i s found i n h i g h energy fragmentation

[l63

t h a t has l e d t o a model discussed i n r e f . 17. T h e f i g u r e 1

sketches t a r g e t - l i k e mass versus p r o j e c t i l e - l i k e mass c o r r e l a t i o n s f o r the k O A r

reduced r a d i u s ro = 1.36 Fm which f i t s the data ( r e f . 16) shows t h a t t h e

microscopic d e s c r i p t i o n accounts p r o p e r l y f o r the main c o r r e l a t i o n c h a r a c t e r i z i n g a fragmentation process. The t a r g e t - l i ke r e c o i l angle ( i n absolute values) versus p r o j e c t i l e - l i k e mass c o r r e l a t i o n a t 44 MeV/u i n c i d e n t energy i s described by t h e dashed area i n f i g u r e 2 f o r the experimental data and by the f u l l l i n e f o r the c a l c u l a t i o n s .

-GEOMETRICAL ro r L36 ABRASION

-LANDAU.VLASOV

F i g u r e 1 : T a r g e t - l i k e versus p r o j e c - F i g u r e 2 : Absolute value o f t h e t i l e - l i k e mass c o r r e l a t i o n i n fragmen- t a r g e t - l i ke r e c o i l angle versus t h e

t a t i o n r e a c t i o n s i n the geometrical p r o j e c t i l e - l i k e mass i n 40Ar (44 MeV/u) abrasion model ( f u l l l i n e ) and i n - t h e

+

27A1 r e a c t i o n s . The Landau-V1 asov Landau-V1 asov c a l c u l a t i o n (dashed l i n e ) c a l c u l a t i o n ( f u l l l i n e ) i s compared f o r t h e "0Ar (35 MeV/u)

+

2 7 ~ 1 r e a c t i o n . w i t h t h e d a t a o f r e f [ l 6 1 (dashed

area).

The d i p o f the c a l c u l a t e d curve corresponds t o a d e f l e c t i o n towards negatiue angles. The o r b i t i n g has a t w o f o l d o r i g i n : f i r s t t h e a t t r a c t i v e nucleus-nucleus f o r c e generated by t h e mean f i e l d ; secondly the one-body d i s s i p a t i o n (nucleon exchanges) on t h e one hand and t h e two-body d i s s i p a t i o n ( c o l l i s i o n term) on t h e o t h e r hand. For such p e r i p h e r a l reactions, i t i s worth mentioning t h a t t h e nucleon-nucleon c o l l i s i o n s a c t s t r o n g l y a t t h e surfaces o f the i n t e r a c t i n g n u c l e i i n order t o damp t h e r e l a t i v e motion. The apparent discrepancy between data and c a l c u l a t i o n s i n f i g u r e 2 c o u l d f i n d i t s o r i g i n i n t h e s t r e n g t h o f t h e two-body c o l l i s i o n term as f a r as very p e r i p h e r a l r e a c t i o n s are concerned (A

-

40).

Consequently, i t seems r e l e v a n t t o ask f o r a d d i t i o n a l experimental 8ata f o r a more p r e c i s e a n a l y s i s o f t h i s strength. For t h e mean energies o f fragmentation

products, one can mention t h a t the agreement between theory and experiments i s reasonable f o r t h e p e r i p h e r a l c o l l i s i o n s . We r e f e r t h e reader t o t h e reference

[ l 8 3 f o r d e t a i l S.

2

-

F u s i o n - l i k e processes

A comparison between V1 asov and Landau-Yl asov c a l c u l a t i o n s should answer t h e q u e s t i o n d e a l i n g w i t h t h e low l-window obtained so f a r i n TDHF c a l c u l a t i o n s (see r e f . [19]). A renewal o f t h i s question was r e c e n t l y given by t h e experimental observation o f a p o s s i b l e transparency i n 28Si

+

28Si r e a c t i o n s a t 12.4 MeV/u

( r e f . [20]). The c a l c u l a t e d time e v o l u t i o n o f t h e r e l a t i v e d i s t a n c e R 1 2 between t h e r e a c t i o n p a r t n e r s i n Vlasov dynamics i n d i c a t e s t h a t such transparency c o u l d be present i n absence o f r e s i d u a l i n t e r a c t i o n (Fig. 3). Nevertheless, t h e same c a l c u l a t i o n performed i n Landau-Vlasov dynamics shows t h a t t h i s e f f e c t i s j u s t an a r t e f a c t o f t h e TDHF approximation, as already mentionned by Tohyama e t a l . ( r e f . [21]) f o r t h e 160 t 160 system.

T I M E (frn/c)

-

m 20 U

z

3

m 15-

-

I n f a c t , t h e f u s i o n process i s very l i k e l y even a t h i g h bombarding energies (see t h e c o n t r i b u t i o n of M. P i i n t h i s conference), a t l e a s t f o r medium and heavy systems. For very l i g h t systems l i k e 40Ar t 27Al a transparency i s found again above 30 MeV/u as discussed i n t h e r e f . [ 4 ] and [12]. For t h e 40Ar (27 HkV/u)

+

23% r e a c t i o n , f o r instance, i t i s found t h a t l a r g e deformations o f t h e composite system (incomplete compound systern) are induced f o r a l o n g tirne l a g . This f e a t u r e (Fig. 4 ) combined w i t h a reasonable e s t i m a t i o n o f t h e l i n e a r and o r b i t a l momentum t r a n s f e r s ( r e f . [22]) provides us some confidence i n our microscopic d e s c r i p t i o n o f f u s i o n i n t h i s energy domain.

I c u l a t i o n s f o r t h e t i m e depen-

dence o f the r e 1 a t i v e distance between i n t e r a c t i n g n u c l e i shows t h a t the transparency i n 28Si (12 MeV/u) + 28Si w i t h a c e n t r a l impact parameter b = 1 Fm i s destroyed by t h e r e s i d u a l i n t e r a c t i o n . 0 1CC 200 300 400 500 600

-

2 8 ~ i (12 M~V/U) + 2 8 ~ i ,#(LASOV

-

b - l f m ,c' , / , / 3

-

P a r t i c l e emission i n t o t h e continuum F i g u r e 3 : A comparison between V l i d a s h e d l i n e ) and Landau-V1 asov ( f u l l l i n e ) c a l - Q

V1 asov and Landau-Vlasov dynamics a1 low a d i r e c t coup1 i ng i n t o continuum states, as soon as l a r g e c o l l e c t i v e motions a r e involved. It can be seen by a determination o f t h e f l u x o f p a r t i c l e s (neutrons and protons) c r o s s i n g a sphe- r i c a l surface surrounding t h e nuclear system. For n u c l e a r r e a c t i o n s l i k e the 'OAr (27 MeV/u)

+

27Al f o r example, the f l u x e x h i b i t s two components when t i m e increases :

F i g u r e 4 : Time dependence o f t h e r a t i o between major a x i s f o r t h e composite sys- tem formed i n t h e '+OAr (27 MeV/u)

+

238U

head-on c o l l i sion. Landau-V1 asov c a l c u l a t i o n s ( f u l l l i n e ) are compared w i t h data o f

l t o l ~ ~ ~ r e f . [22] dashed l i n e . ~ t ~ ~ ~ ~ l ~

(r 100 20 0 300 I f m / c j TIME

a p r e e q u i l i brium component ( l a r g e ani sotropy and k i n e t i c energy o f the e m i t t e d p a r t i c l e s ) d u r i n g t h e f i r s t stages o f t h e c o l l i s i o n and an evaporation component ( i s o t r o p i c and thermal k i n e t i c energy o f t h e p a r t i c l e s ) . For t h e decay o f a h o t nucleus ( r e f .

[23]),

a b u r s t o f e m i t t e d p a r t i c l e s i s obtained d u r i n g the f i r s t

4 x 10-22s ( f o r t h e 4oCa nucleus a t 15 MeV temperature i n the case o f the f i g . 6 ) .

0 30 60 W 120 150 WO 210 NO

TIME I f m / c )

F i g u r e 5 : ( a ) For a c e n t r a l c o l l i s i o n , time e v o l u t i o n f o r t h e nucleon emission f l u x ( r i g h t scale) and o f the t o t a l number o f e m i t t e d p a r t i c l e s ( l e f t scale), r e s p e c t i v e l y protons, neutrons and both.

$

'\

G I !\-a I l I l

1 8

d

60 90 120 150 183 210 2LO 270 300

TIME f m / c )

F i g u r e 5 : ( b ) For t h e same c o l l i - sion, time e v o l u t i o n o f the i n s t a n - taneous mean energy ( l e f t scale) and o f t h e a n i s o t r o p y f a c t o r ( r i g h t scale) o f t h e e m i t t e d ' nucleons.

5

-

I s o s p i n t r a n s f e r

--.

F i g u r e 6 : Decrease o f t h e e x c i t a t i o n

_S

energy per nucleon (upper p a r t ) and o f

,,,

The r o l e o f t h e i s o v e c t o r g i a n t resonance o f t h e composite system f o r t h e char- ge e q u i l i b r a t i o n d u r i n g heavy i o n c o l l i s i o n s was p o i n t e d o u t by t h e observation of t h e i s o b a r i c d i s t r i b u t i o n s i n deep i n e l a s t i c r e a c t i o n s ( r e f . [251 )

.

I t s e x c i t a t i o n i s revealed by TDHF c a l c u l a t i o n s ([26,271 ) . I n f i g u r e 7, the time e v o l u t i o n o f the s c a l a r p r o d u c t between t h e v e c t o r j o i n i n g t h e neutron and p r o t o n c e n t e r o f mass r e s p e c t i v e l y and an u n i t a r y v e c t o r along t h e l i n e j o i n i n g the c e n t e r o f mass of the t h e r e s i d u a l mass ( l o w e r p a r t ) o f a

_S

h°Ca nucleus i n i t i a l l y heated up t o a

temperature o f 15 MeV ( f u l l l i n e s ) and

'$

6.

' I " ' I ' I ' L

:',

40

-",

Ca

-

simultaneously compressed (dashed l i n e s ) . _-

C 41-2. ,

-.

-

-

-

, 3 ~ ' l ' l s ~ s

-

The mass o f t h e r e s i d u a l nucleus - decreases smoothly a f terwords

,

as

obtained r e c e n t l y i n s p h e r i c a l TDHF

-

c a l c u l a t i o n s ( r e f . [24

1.

The two

1

previous s i t u a t i o n s il u s t r a t e t h a t LU 20.

-

'\

- c o u p l i n g i n t o t h e continuum i s v, W n a t u r a l l y contained i n o u r d e s c r i p t i o n , a l l o w i n g p r e d i c t i o n s

3

'"

-

\.

_{----_}

---

---

_-_--_-_

__. _-

:

concerning l i g h t p a r t i c l e emissions I , I I , ! ,

r e a c t i o n p a r t n e r s i s drawn f o r t h e 160 (5.5 MeV/u)

+

4 0 ~ a r e a c t i o n where t h e impact parameter b i s equal t o 6 Fm. The l o n g i t u d i n a l i s o v e c t o r d i p o l e mode i s e x c i t e d i n Landau-Vlasov as w e l l as i n Vlasov dynamics. A time s h i f t between t h e two c a l c u l a - t i o n s i s due t o t h e surface c o l l i s i o n s which favour t h e e x c i t a t i o n f o r a smaller o v e r l a p o f t h e n u c l e a r d e n s i t i e s i n the Landau-Vlasov c a l c u l a t i o n than i n t h e Vlasov case. These c a l c u l a t i o n s , p o s s i b l e o n l y because our d e s c r i p t i o n accounts f o r t h e Coulomb i n t e r a c t i o n , c o n f i r m t h a t a c o l l e c t i v e mode whose c h a r a c t e r i s t i c s have been c a l c u l a t e d i n r e f . [ 2 8 1 i s very l i k e l y responsible f o r t h e charge e q u i l i b r a t i o n , a t l e a s t d u r i n g t h e f i r s t 5.10-22s ( i . e . 150 Fm/c). - . 7 L d 100 ZOO 300

TiME

Ifm/c) .9 - 8 .7 Conclusion I . - . ' r ' - ' . I a ' ' . a ' * ' 8 -- .. .. 160

(5.5

M ~ V / U ) +"CO

We have shown, w i t h t h e h e l p o f a few examples, t h e richness o f the

semi-classical microscopic d e s c r i p t i o n f o r many physical s i t u a t i o n s occuring i n low and i n t e r m e d i a t e heavy i o n c o l l i s i o n s . F u r t h e r s t u d i e s are i n progress ; they concern g i a n t resonances a t zero and f i n i t e temperature, t h e implementation o f t i e momentum dependent Gogny e f f e c t i v e i n t e r a c t i o n , the f i s s i o n process a t f i n i t e temperature, t h e gamma and p i o n production, t h e f l u c t u a t i o n s around mean val;es o f observables. This general p r o j e c t i s i n s p i r e d by an u t t e r a n c e from Gandhi : My quest f o r t r u t h t a u g h t me t h e beauty o f compromise".

Acknowledgments

F i g u r e 7 : E x c i t a t i o n o f t h e l o n g i t u d i n a l i s o v e c t o r d i p o l e mode i n 160

+

40Ca

-

.3 .. r e a c t i o n s near t h e Coulomb b a r r i e r . The

-.

4 - o s c i l l a t i o n s are obtained as w e l l i n

The authors a r e very g r a t e f u l t o t h e i r colleagues f o r t h e i r encouragements and f o r very f r u i t f u l discussions. We thank e s p e c i a l l y P. Schuck, M. Di Toro, J. De, J. Galin, E. Suraud and M. Pi. S. Geswend i s acknowledged f o r having made q u i c k l y t h i s manuscript i s proper shape.

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