FRAGMENTATION OF THE PROJECTILE NEAR THE FERMI ENERGY

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FRAGMENTATION OF THE PROJECTILE NEAR THE FERMI ENERGY

R. Dayras

To cite this version:

R. Dayras. FRAGMENTATION OF THE PROJECTILE NEAR THE FERMI ENERGY. Journal

de Physique Colloques, 1986, 47 (C4), pp.C4-13-C4-28. �10.1051/jphyscol:1986402�. �jpa-00225765�

JOURNAL DE PHYSIQUE

Colloque C4, suppl6ment au n o 8, Tome 47, aoQt 1986

FRAGMENTATION OF THE PROJECTILE NEAR THE FERMI ENERGY

R. DAYRAS

Service d e Physique Nucleaire, Basse Energie, CEN-Saclay, F-91191 Gif-sur-Yvette Cedex, France

Resume

-

Nous passons en revue l e s donnges experimentales r e l a t i v e s

i

l a f r a g m e n t a t i o n du p r o j e c t i l e au voisinage de 1 ' g n e r g i e de Fermi. Dans une corn- p a r a i s o n avec l e s r g s u l t a t s obtenus aux basses energies d'une p a r t e t aux energies r e l a t i v i s t e s d ' a u t r e p a r t c e t t e r e g i o n a p p a r a i t b i e n comme une rE- g i o n de t r a n s i t i o n . Les mecanismes dominEs p a r l e champ moyen aux basses energies csdent peu S peu l e pas aux c o l l is i o n s i n d i v i d u e l l e s n-n. Dans l e cas p r k e n t , c e t t e t r a n s i t i o n se t r a d u i t e n t r e a u t r e s par une d i m i n u t i o n ra- p i d e des r g a c t i o n s de t r a n s f e r t au p r o f i t du processus de fragmentation. Une d e s c r i p t i o n cohcrente des r e s u l t a t s observes nEcessite l a p r i s e en compte

i

l a f o i s des e f f e t s de champ moyen e t des c o l l i s i o n s i n d i v i d u e l l e s n-n.

A b s t r a c t

-

The experimental data about p r o j e c t i l e fragmentation around t h e m e r g y a r e reviewed. Comparisons w i t h l o w and h i g h energy data suggest t h a t t h i s energy domain i s indeed a t r a n s i t i o n region. Reaction mechanisms dominated by t h e mean f i e l d a t low energy p r o g r e s s i v e l y g i v e way t o i n d i v i - dual n-n c o l l i s i o n s . I n t h e p r e s e n t case, t h i s t r a n s i t i o n manifests i t s e l f by a r a p i d decrease o f t r a n s f e r r e a c t i o n s f o r t h e b e n e f i t o f fragmentation pro- cesses. A coherent d e s c r i p t i o n o f t h e observed r e s u l t s r e q u i r e s t o t a k e i n t o account mean f i e l d e f f e c t s as w e l l as I n d i v i d u a l n-n c o l l i s i o n s .

I

-

INTRODUCTION

U n t i l r e c e n t l y , f o l l o w i n g t h e developments i n heavy i o n a c c e l e r a t o r technology, heavy i o n induced r e a c t i o n s have been e x t e n s i v e l y s t u d i e d f o r p r o j e c t i l e s w i t h ener- g i e s l e s s than

-

20 MeV/n ( n f o r nucleon) /1,2/ o r g r e a t e r than

-

100 MeV/n /3,4/.

I n t h e low energy regime, i n t e r a c t i o n times are l a r g e compared t o t h e nucleon r e l a x - a t i o n time. As a r e s u l t , low energy heavy i o n induced r e a c t i o n s are dominated by c o l l e c t i v e e f f e c t s . Experimental observations a r e we1 1 accounted f o r i n t h e frame- work o f s t a t i s t i c a l e q u i l i b r i u m t h e o r i e s /5/ and o f mean f i e l d t h e o r i e s

161.

On t h e o t h e r hand, f o r bombarding energies E/A 2

-

200 MeV/n, i n t e r a c t i o n times become s h o r t e r than t h e r e l a x a t i o n time o f t h e various i n t r i n s i c degrees o f freedom. The reduced wavelength o f a nucleon o f t h e p r o j e c t i l e ( o r t a r g e t ) becomes s h o r t e r than t h e i n t r a n u c l e o n i c distance. One-body d i s s i p a t i o n gives way t o n-n c o l l i s i o n s . The main f e a t u r e s o f t h e data a r e s u c c e s s f u l l y described e i t h e r i n t h e framework of p a r t i c i p a n t s p e c t a t o r models /7/ o r i n terms o f f r e e n-n c o l l i s i o n s as i n i n t r a - n u c l e a r cascade c a l c u l a t i o n s /8,9/.

Only r e c e n t l y , w i t h t h e advent of new heavy-i on f a c i 1 i t i e s , t h e i n t e r m e d i a t e energy range (10 MeV < E/A < 100 MeV) has been opened up t o e x p e r i m e n t a l i s t s . T h i s energy regime i s f a s c i n a t i n g from several aspects : i ) T h i s i s a t r a n s i t i o n r e g i o n

/lo/

where c o l l e c t i v e beaviour dominated by one-body type c o l l i s i o n s i s expected t o g i v e way t o r e a c t i o n mechanisms determined by n-n c o l l i s i o n s . i i ) I n t e r a c t i o n times be- come comparable t o o r even s h o r t e r than r e l a x a t i o n times o f i n t r i n s i c degrees of freedom. Thus, n o n - e q u i l i b r i u m phenomena are expected t o i n c r e a s e i n importance.

iii ) The v e l o c i t y o f t h e p r o j e c t i l e becomes comparable o r g r e a t e r than c h a r a c t e r i s-

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986402

C4-14 JOURNAL DE PHYSIQUE

t i c v e l o c i t i e s i n t h e nucleus such as t h e sound v e l o c i t y /11/ (E/A = 18 FleV) and t h e Fermi v e l o c i t y (E/A = 30 MeV). By going over those d i f f e r e n t thresholds, q u a l i t a t i - v e l y new mechanisms may be expected t o occur.

F i r s t i n d i c a t i o n s o f a r a p i d change i n the r e a c t i o n mechanism came from t h e measure- ments o f t h e momentum w i d t h of p r o j e c t i l e - l i k e fragments i n t h e r e a c t i o n 160 + 2 0 8 ~ b a t E/A = 20 MeV/n /12/ causing a f l u r r y o f experimental works i n t h e i n t e r m e d i a t e energy domain.

From sub-Coul omb energies t o re1 a t i v i s t i c energies, fragmentation o f t h e p r o j e c t i l e i s a pervasive phenomenon i n n u c l e a r r e a c t i o n s i n v o l v i n g composite p r o j e c t i l e s from deuteron t o heavy ions. Here, "fragmentation" i s used as a generic term which describes i n n u c l e a r r e a c t i o n s , t h e p r o d u c t i o n o f a c h a r a c t e r i s t i c group o f f r a g - ments w i t h masses l e s s than t h e p r o j e c t i l e one and w i t h v e l o c i t y mean value c l o s e t o t h e beam v e l o c i t y . Production o f such fragments i s a w e l l known process i n l i g h t - i o n induced r e a c t i o n . F o r instance, t h e deuteron break-up i s q u i t e an o l d and common method f o r neutron beam p r o d u c t i o n /44/ w i t h a narrow energy spread around an energy En = Ed/2.

I n t h e n e x t section, we w i l l review the p o s s i b l e mechanisms f o r p r o d u c t i o n o f pro- j e c t i l e - l i k e fragments. I n s e c t i o n s I 1 1 and I V we w i l l u n d e r l i n e t h e b a s i c f e a t u r e s and our c u r r e n t understanding o f p r o j e c t i l e fragmentation i n t h e low and t h e h i g h energy domains r e s p e c t i v e l y . I n s e c t i o n V, we w i l l consider t h e d i f f e r e n t aspects o f p r o j e c t i l e fragmentation i n t h e i n t e r m e d i a t e energy regime more thorougly. I n sec- t i o n V I we s h a l l t r y t o draw some conclusions and t o emphasize t h e basic questions n o t y e t answered.

I 1

-

POSSIBLE MECHANISMS FOR THE PRODUCTION OF PROJECTILE-LIKE FRAGMENTS

Many d i f f e r e n t types of i n t e r a c t i o n s between p r o j e c t i l e and t a r g e t can produce pro- j e c t i l e - l i k e fragments. Two b a s i c scenarios a r e d e p i c t e d i n f i g . 1. Each o f them can then be subdivided. I n case l a ) ,

a f t e r i n e l a s t i c s c a t t e r i n g o r a f t e r picking-up few nucleons from t h e t a r g e t T (which may be e x c i t - ed), t h e p r o j e c t i l e P i s e x c i t e d

t o a continuum s t a t e which decays

& ^{@ !}

subsequently ( s e q u e n t i a l break- up). I n case l b ) , a s u b s t r u c t u r e

"a" ( t h e " p a r t i c i p a n t " ) o f t h e

@ ^s,

p r o j e c t i l e i n t e r a c t s w i t h t h e t a r - g e t whereas t h e remaining p a r t "A"

( t h e "spectator") o f t h e p r o j e c t i - l e misses t h e t a r g e t . The specta-

t o r "A", almost unperturbed w i l l

&B

c o n t i n u e i t s way i n t h e forward d i r e c t i o n w i t h approximately t h e beam v e l o c i t y superimposed by ;he

Fermi motion o f s u b s t r u c t u r e A" Fig. 1

-

Basic scenarios f o r p r o j e c t i l e f r a g - i n s i d e t h e p r o j e c t i l e

P.

The sub- mentation.

s t r u c t u r e "a" can e i t h e r be elas-

t i c a l l y s c a t t e r e d by t h e t a r g e t ( e l a s t i c break-up) o r i t can undergo any k i n d of i n t e r a c t i o n s w i t h t h e t a r g e t i .e. from compound t o d i r e c t r e a c t i o n processes. T h i s p a r t i c i p a n t - s p e c t a t o r d e s c r i p t i o n o f t h e fragmentation processes i s a t t h e o r i g i n of t h e geometrical model o f Serber /45/ and c o n s t i t u t e s t h e u n d e r l y i n g p i c t u r e o f many r e c e n t t h e o r e t i c a l approaches 146-531. A t r e l a t i v i s t i c energies, t h e Coulomb f i e l d can be s t r o n g enough f o r i n d u c i n g an electromagnetic d i s s o c i a t i o n o f t h e p r o j e c t i l e /54/. I n p r i n c i p l e , a l l the above mechanisms can c o n t r i b u t e t o t h e measured y i e l d s of p r o j e c t i l e - l i k e fragments. However, one may expect t h e dominant process t o change d r a s t i c a l l y w i t h t h e p r o j e c t i l e energy. I n t h e n e x t sections, we w i l l t r y t o f o l l o w t h e e v o l u t i o n o f t h e fragmentation process w i t h bombarding energy.

PROJECTILE FRAGMENTATION AT

LOW

BOMBARDING ENERGIES

For incident energies not too f a r from the Coulomb b a r r i e r , production of projecti- l e - l i ke fragments with v e l o c i t i e s close t o the beam velocity i s 1 imi ted t o a narrow s t r e t c h of p a r t i a l waves near the grazing angular momentum.

For l i g h t p r o j e c t i l e s (from deuteron t o lithium) Baur e t a1 ./51/, using the p a r t i c i - pant-spectator approach have performed an extensive s e r i e s of

DWBA

calculations and have been successful in reproducing both singles and coincidence data. From t h i s analysis they conclude t h a t e l a s t i c break-up which leaves the t a r g e t i n i t s ground s t a t e does not contribute s i g n i f i c a n t l y t o the y i e l d of p r o j e c t i l e fragments.

For heavier projecti 1 e s , recent coincidence experiments /46 ,55,56/ have shown t h a t many processes can contribute to t h e p r o j e c t i l e fragmentation

:

i ) Fusion of the p a r t i c i p a n t with the t a r g e t (incomplete fusion, massive t r a n s f e r , etc.. .

⁾

.

^{i i )}

^Exci-

t a t i o n of the p r o j e c t i l e i n t o the continuum followed by sequential decay (sequential break-up). i i i ) Pick-up of a few nucleons by t h e p r o j e c t i l e which decays subsequent- l y . The existence of the two l a s t processes i s c l e a r l y i l l u s t r a t e d i n f i g . 2. taken from ref./52/. In f i g . 2a, a

9

MeV/n 2 0 ~ e ion s c a t t e r s inelas- t i c a l l y from a

12c

t a r g e t l e f t i n i t s ground s t a t e . The pro- j e c t i l e i s excited t o unbound d i s c r e t e s t a t e s which decay

3WC

LC

i n t o an 160 nucleus i n i t s

+

C

ground s t a t e and an

a

p a r t i c l e .

3

In f i g . 2b, the

9

MeV/n 160

8 p r o j e c t i l e picks-u f i r s t a

bl

tooc

t r i t o n from t h e

P 2 ~

t a r g e t

@ .

I

(leaving a

^9~

nucleus i n i t s

73 U

round s t a t e ) , i t produces a

G

0 P9F

nucleus, excited t o unbound

u

s t a t e s , which then decays i n t o

a

1 5 N

nucleus i n i t s ground

1m

s t a t e and an

a

p a r t i c l e .

The competition between trans- f e r and sequenti a1 break-up seems strongly correlated with E

:

: (channels) the binding energy of the par-

t i c i p a n t and the spectator i n

Tr~ton pickup react~on

-

alpha decoy

t h e p r o j e c t i l e 1461. Sequential break-up i s favoured

b

; ^small

binding energies. The 0 ener-

LPN + a } detected gy

spectra resulting from the

break-up of 13 MeV/n 2 0 ~ e pro- j e c t i l e bombarding a 4 0 ~ a t a r - g e t a r e well reproduced by

DWBA

c a l c u l a t i o n s t a k i n g i n t o account t r a n s f e r and e l a s t i c

b) break-up of t h e p r o j e c t i l e

/46/.

Such calculations made over a wide range of energy would be most valuable.

E x "F = €,,I ("N

-

^{0 ) + 4 014MeV}

Fig. 2 - a ) Relative k i n e t i c energy of

a

p a r t i c l e s and 160 ions in t h e sequential

break-up of *ONe. b) Relative k i n e t i c energy of

a

p a r t i c l e s and

1 5 N

ions i n the

break-up of

1 9 ~

formed by a t r i t o n pick-up by the 160 p r o j e c t i l e . Ref ,1521.

JOURNAL DE PHYSIQUE

A n o t h e r i n t e r e s t i n g

aspect o f t h e data i n

600 -

t h i s energy domain i s

-

t h e i n c r e a s e o f t h e

momentuln d i s p e r s i o n o f 4 0 0

- E 2 0 N e = 'OMeV

t h e p r o j e c t i l e - l i k e

5 O 0

f r a g m e n t s w i t h t h e

energy o f t h e p r o j e c -

200 - ¹⁶⁹

t i l e . T h i s f e a t u r e i s ⁷

i l l u s t r a t e d i n f i g . 3 1 I I

1

I

where a r e shown t h e

600 -

energy spectra o f 160 fragments from a 2 0 ~ e p r o j e c t i l e bombarding an l g 7 A u t a r g e t i n t h e energy range 7.5 MeV/n t o 20 MeVIn /15/. The w i d t h o f these spectra taken near t h e g r a z i n g angle increases great- l y w i t h b o m b a r d i n g energy.

T h i s increase i n mo- mentum d i s p e r s i o n w i t h bombarding energy was imputed by McVoy and Nemes 1471 t o t h e com- p e t i t i o n between two p r o c e s s e s n a m e l y t r a n s f e r and e l a s t i c break-up. I n t h e f i r s t process which should dominate a t low ener- gy, t h e p a r t i c i p a n t i s captured by t h e t a r - get. I n t h i s case mo- mentum c o n s e r v a t i o n r e d u c e s t h e p h a s e soace a v a i l a b l e t o t h e spectator, producing

fragments w i t h a nar- F i g . 3

-

Laboratory ener spectra o f 160 fragments from t h e row momentum width. I n i n t e r a c t i o n o f %Ne w i t h l . 7 ~ ~ . Ref .Ill/.

t h e second p r o c e s s

expected t o dominate a t h i g h energy, t h e p a r t i c i p a n t does n o t i n t e r a c t w i t h t h e t a r - g e t and t h e momentum w i d t h o f t h e s p e c t a t o r i s given by t h e w i d t h o f i t s Fermi mo- mentum d i s t r i b u t i o n i n s i d e t h e p r o j e c t i l e . Except f o r sequential break-up which happens f a r from t h e t a r g e t , t h e Coulomb b a r r i e r i n t h e entrance channel i s expected t o reduce t h e momentum w i d t h f o r b o t h t r a n s f e r and break-up processes 147, 49,501.

Taking an approach s i m i l a r t o S e r b e r ' s 1451, Friedman I 4 9 1 and Utsunomiya 1501 em- phasize t h e p e r i p h e r a l n a t u r e o f t h e fragmentation process by assuming t h a t t h e s p e c t a t o r "A" misses t h e t a r g e t whereas t h e p a r t i c i p a n t "a" s t r i k e s and i n t e r a c t s i n a l l k i n d s o f way. The i n t r i n s i c momentum d i s t r i b u t i o n o f "A" i n t h e p r o j e c t i l e

P

i s governed by t h e square o f the F o u r i e r t r a n s f o r m o f t h e r e l a t i v e wave f u n c t i o n o f "a"

and "A" i n s i d e

P,

-

P r

$ 1

^a f o r r 2 RC

,

w i t h ^p = m / . K where mr and Es a r e r e s p e c t i v e l y t h e reduced mass and t h e sepa- r a t i o n energyrofs"a' and "AU ; Rc i s a c r i t i c a l distance. F o r s e p a r a t i o n distances r

<

RC, t h e c l u s t e r s "a" and "A" loose t h e i r i n d i v i d u a l i t y . F o r t h e s p e c t a t o r "A" t o

s u r v i v e t h e c o l l i s i o n , t h e r e l a t i v e separation r should be g r e a t e r than Rc. Thus t h e momentum d i s t r i b u t i o n o f "A" depends d i r e c t l y on t h e separation energy ES r a t h e r than on t h e Fermi energy. W i t h i n t h i s approach, t h e i n c r e a s i n g w i d t h o f t h e momentum d i s t r i b u t i o n of t h e p r o j e c t i l e - 1 i ke fragments w i t h bombarding energy does n o t r e s u l t from a c o m p e t i t i o n between two mechanisms b u t i s s o l e l y due t o t h e decreasing impor- tance o f t h e Coulomb b a r r i e r r e l a t i v e t o t h e i n c i d e n t energy. The success o f t h i s model f o r l i g h t p r o j e c t i l e s up t o Ne, from low energies t o r e l a t i v i s t i c energies i s impressive 1491. However i t f a i l s t o describe t h e fragmentation o f heavier p r o j e c t i - l e s such as Ar.

r l I I I I I l I _

- a Thus, several possi b i l i t i e s e x i s t

- 1 0 t o e x p l a i n t h e increase o f t h e

momentum w i d t h o f p r o j e c t i l e - 1 i k e fragments w i t h bombarding energy.

-

-2 On t h e b a s i s o f t h e e x i s t i n g data

i t i s n o t p o s s i b l e y e t t o choose between t h e d i f f e r e n t models.

I V

-

PROJECTILE FRAGMENTATION AT HEH ~NERGIES

The concept o f p r o j e c t i l e fragmen- t a t i o n was f i r s t i n t r o d u c e d t o cha- r a c t e r i z e f r a ments from re1 a t i v i s- t i c 12C and

B

0 p r o j e c t i l e s imping- i n g on v a r i o u s t a r g e t s 1571. I n c o n t r a s t w i t h low energy data where p r o j e c t i l e - 1 i k e fragments a r e l i m i - t e d t o few masses around t h e pro-

?

^(MeV/c) j e c t i l e mass, fragments w i t h beam

I . ~ . . I ~ . . . I - ' . v e l o c i t y were observed down t o pro-

b)

tons. These fragments are e m i t t e d

i n t h e beam d i r e c t i o n w i t h a vel o-

2 0 0

-

c i t y s l i g h t l y smaller than t h e beam

v e l o c i t y . I n t h e p r o j e c t i l e frame, t h e momentum d i s t r i b u t i o n s o f t h e fragments ( f i g . 4a) c o u l d be des- c r i b e d by Gaussian d i s t r i b u t i o n s :

=

c

exp(-

A) P*

exp[-

dp3

2 4

( 1 )

F i g . 4

-

a) P r o j e c t i l e - f r a m e p a r a l - l e l -momentum d i s t r i b u t i o n f o r l O ~ e fragments from

12c

a t 2.1 GeV/n on a Be t a r g e t . b) P a r a l l e l momentum

o 5 1 0 15 w i d t h ol o f f r a g m e n t s f r o m a 2.1

GeVIn 16b p r o j e c t i l e . From r e f .I571

FRAGMENT MASS (AMU)

where C i s a n o r m a l i z a t i o n c o n s t a n t . P,, and P a r e t h e f r a g m e n t momenta i n t h e d i r e c t i o n s p a r a l l e l and perpendicular t o t h e beam r e s p e c t i v e l y . The associated variances a r e a,, and ol. Po i s t h e average momentum s h i f t i n t h e p r o j e c t i l e frame. A good f i t t o t h e d a t a c o u l d be o b t a i n e d assuming a = ell. When t h e widths all a r e p l o t t e d versus the fragment mass ( f i g . 4b), they d i s h a y a p a r a b o l i c dependence on t h e fragment mass which can be parameterized as

all = K

I/-

JOURNAL DE PHYSIQUE

where K i s a n o r m a l i z a t i o n c o n s t a n t and Ap and AF a r e t h e masses o f t h e p r o j e c t i l e and o f t h e fragment r e s p e c t i v e l y .

These experiments were t h e s t a r t i n g o f t h e o r e t i c a l i n t e r p r e t a t i o n s /58, 59/ which a r e a t t h e o r i g i n of more s o r h i s t i c a t e d w d e l s . I n one approach /58/, t h e t a r g e t a c t s o n l y t o i n j e c t energy i n t h e p r o j e c t i l e , making i t explode. The fragment momen- tum i s then given e s s e n t i a l l y by t h e momentum i t had r e l a t i v e t o t h e c e n t e r o f mass o f t h e p r o j e c t i l e p r i o r t o t h e c o l l i s i o n . I n h i s s t a t i s t i c a l approach t o fragmenta- t i o n , Go1 dhaber /59/ assumes t h a t random nucleons are suddenly abraded from t h e p r o j e c t i l e ( f a s t - f ragmentation hypothesis

1.

Applying momentum conservation t h e f o l - l o w i n g r e l a t i o n i s d e r i v e d :

A (A -A )

.2= F P F $

" Ap-1 0 (2

where Ap and AF a r e t h e masses o f the p r o j e c t i l e and o f t h e fragment r e s p e c t i v e l y whereas a0 i s r e l a t e d t o t h e Fermi momentum PF o f t h e .nucleons i n s i d e t h e projec- t i l e :

p t

u2 =-•

0 5

Thus t h e p a r a b o l i c law found e m p i r i c a l l y /57/ i s recovered. Hence, i n p r i n c i p l e , r e l a t i o n (21 can be used i n order t o determine t h e Fermi nucleon momentum i n s i d e t h e p r o j e c t i l e . Using t h e value P = 250 l.leV/c deduced from e l e c t r o n s c a t t e r i n g measure- ments one gets a, = 112 ~eveY/F which agrees f a i r l y w e l l w i t h t h e experimental value o f s 90 MeVlc. However, t h i s agreement may be f o r t u i t o u s . Indeed, i n t h i s compari- son, t h e p r o j e c t i l e fragments a r e assumed t o emerge from t h e c o l l i s i o n s w i t h l i t t l e e x c i t a t i o n energy i n o r d e r f o r evaporation n o t t o p e r t u r b e t h e momentum width.

Taking i n t o account Paul i c o r r e l a t i o n s , Bertsch 160/ has shown t h a t f o r 4 0 ~ r , t h e uo value should i n f a c t be reduced by

-

^{20 %,} i n agreement w i t h t h e measured value /13/. However, i n a r e c e n t c a l c u l a t i o n Murphy /61/ shows t h a t phase-space con- s t r a i n t s , when taken i n t o account i n c o n j u n c t i o n w i t h Paul i c o r r e l a t i o n s , r e s u l t i n a r e d u c t i o n o f t h e value o f a, by more than a f a c t o r o f 2 f o r an ' + O A ~ p r o j e c t i l e . Thus, i n t h e l i g h t o f these c a l c u l a t i o n s , t h e simple i n t e r p r e t a t i o n o f a,, as re- f l e c t i ng d i r e c t l y t h e Fermi momentum d i s t r i b u t i o n o f t h e nucleons i n s i d e t h e nucleus i s c a l l e d i n question.

The s l i g h t down-shift o f the fragment v e l o c i t y r e l a t i v e t o t h e beam v e l o c i t y has been s u c c e s s f u l l y e x p l a i n e d /62/, assuming t h a t successive removal o f bound nucleons from t h e p r o j e c t i l e r e s u l t s i n a f r i c t i o n a l f o r c e which slows down t h e p r o j e c t i l e . The measured mass y i e l d s are w e l l accounted f o r by t h e f a s t abrasion mechanism /63- 651. I n t h i s p u r e l y geometrical p i c t u r e , i t i s assumed t h a t t h e o v e r l a p r e g i o n be- tween t a r g e t and p r o j e c t i l e i s sheared away t o form a h o t zone o f n u c l e a r matter, :he " p a r t i c i p a n t s " , whereas t h e remaining p a r t s o f t h e p r o j e c t i l e and t a r g e t , t h e

spectators" are o n l y s l i g h t l y perturbed. The abraded p r o j e c t i l e almost preserves i t s i n i t i a l d i r e c t i o n and v e l o c i t y and c a r r i e s a r e l a t i v e l y small amount o f e x c i t a - t i o n energy which i s p r o p p r t i o n a l t o t h e d i f f e r e n c e i n surface energy between t h e deformed abraded nucleus and a s p h e r i c a l nucleus o f same volume. The e x c i t a t i o n energy o f t h e fragments i s then d i s s i p a t e d by nucleon evaporation ( a b l a t i o n stage).

I s o t o p i c d i s t r i b u t i o n s o f the fragments can be reproduced q u i t e w e l l i f proton-neu- t r o n c o r r e l a t i o n s a r i s i n g from t h e z e r o p o i n t v i b r a t i o n o f t h e g i a n t d i p o l e resonan- ce a r e taken i n t o account 113,651.

As we w i l l hear a t t h i s conference, t h e geometrical aspect o f t h e abrasion model i s a t t h e o r i g i n o f several more s o p h i s t i c a t e d approaches t o p r o j e c t i l e fragmentation /66,67/.

THE INTERMEDIATE

ENERGY

REGIME

: A

TRANSITION REGION V . l Introduction

The dramatic change in the production of p r o j e c t i l e - l i k e fragnents with bombarding e n e r v i s well i l l u s t r a t e d in f i g .

5.

In f i g . 5a, a 6.75 MeVIn 'OAr beam impinges on a

l o

Mo t a r g e t /68/. Fragments with beam velocity a r e limited t o few masses around t h e p r o j e c t i l e whereas the bulk of the cross section i s dominated by deep i n e l a s t i c c o l l i s i o n s . In f i g . 5b, a 27.5 MeV/n

' + O A ~

beam h i t s a 68Zn t a r g e t 1271. As a t rela- t i v i s t i c energies, the masses of fragments with approximately beam velocity extend down t o the l i g h t e s t elements. However, one s t r i k i n g difference

w i t h

r e l a t i v i s t i c fragmentation i s immediately apparent in f i g . 6 1401. The fragment velocity spectra ( f i g . 6 a ) , peaked a t v e l o c i t i e s s l i g h t l y smaller than the beam velocity, are asymme- t r i c

w i t h

a low velocity t a i l . This t a i l i n g i s c l e a r l y seen i n the contour p l o t s of t h e i n v a r i a n t c r o s s s e c t i o n i n t h e p a r a l l e l

V

and transverse VI-velocity plane ( f i g . 6b). I t may indicate the action of dissipakive forces not present a t r e l a t i - v i s t i c energies.

E

(MeV

Fig.

5

- P l o t of mass versus energy f o r a ) the reaction

' + O A ~ +

loOMo a t 7 MeVIn 1681 and b) the reaction *OAr

+

68Zn a t 27 MeVIn 1271.

In the following sub-sections, we will review the properties of the p r o j e c t i l e frag- mentati on i n t h e intermediate energy regime.

V.2 Fragment y i e l d s

The cross sections f o r production of p r o j e c t i l e - l i k e fragments from an

'+OAr

projec-

t i l e have been measured f o r various t a r g e t s a t bombarding energies ranging from 27

MeV/n t o 213 MeVIn /13,21,27,31,40/. Elemental d i s t r i b u t i o n s i n t e rated over angles

a r e shown i n f i g . l a up t o Z=l7. Except f o r t h e 41 IleV/n

+ O A ~ +

q2C reaction, they

display quite simi 1 a r behavi our, with t h e same odd-even s t r u c t u r e and an enhancement

around

Z=6.

The magnitude of the cross sections increases regularly with the t a r g e t

size. For the 44 MeV/n

'+OAr + 1 2 C

reaction, the Z-distribution shows a strong enhan-

cement around Z=14. This was successfully interpreted 1311 a s the r e s u l t of an in-

complete fusion of t h e p r o j e c t i l e with the t a r g e t , followed by evaporation. Then, i t

may seem surprising t h a t t h e 27.6 MeVIn

' + O A ~ +

'j8Zn data I271 behave l i k e those from

the 213 MeVIn '+OAr

+ 1 2 C

reaction 1131. This would tend t o indicate t h a t a s long as

t h e t a r g e t i s s u f f i c i e n t l y heavy, the production of fragments from an

' + O A ~

projecti-

l e has already reached i t s asymptotic value a t 27.5 MeVIn. The d i f f e r e n t behaviour

of the 44 MeVIn '+OAr

+ 1 2 C

data suggests t h a t the beam velocity i s not a s u f f i c i e n t

criterium f o r describing t h e onset of the fragmentation process.

A

b e t t e r parameter

C4-20 JOURNAL

DE

PHYSIQUE

seems t o be t h e v e l o c i t y o f t h e p r o j e c t i l e pr r e l a t i v e t o t h e v e l o c i t y o f t h e c e n t e r o f mass. The v e l o c i t p (expressed i n u n i t o f c ) i s q u i t e low, 0.071 f o r a 44 MeV/n ' + O A ~ impinging on a 13C Farget whereas i t reaches 0.153 f o r 27.6 MeV/n * O A ~ on 6 8 ~ n , a value which i s reached by 213 MeV/n '+OAr on 12C. Except f o r t h e 44 MeV/n '+OAr +

1 2 ~ r e a c t i o n , t h e c r o s s s e c t i o n s c a l c u l a t e d w i t h t h e abrasion-abl a t i o n model a r e i n s a t i s f a c t o r y agreement w i t h t h e data. The geometrical aspect o f t h e fragment produc- t i

?

n i s supported b f i g . 7b where t h e r a t f o s o f t h e mass y i e l d s between t h e

7

' + O A ~ + na T i a n d ' + O A ~ + A1 a r e r e p o r t e d as a f u n c t i o n o f t h e fragment mass. The decrease o f these r a t i o s w i t h t h e fragment mass i s q u i t e w e l l reproduced by an abrasion c a l - c u l a t i o n .

Fig. 6

-

a) V e l o c i t y spectra f o r few fragments produced a t 2.5' i n t h e r e a c t i o n '+OAr + 27A1 a t 44 MeV/n. The arrows i n d i c a t e t h e beam v e l o c i t y . b ) I n v a r i a n t cross sec-

t i o n c o n t o u r - p l o t s i n t h e VI, Vn-plane f o r t h e same fragment /40/.

/

0.05

V.3 I s o t o p i c d i s t r i b u t i o n s o f t h e fragments

-t,)

^{I + 2 7 ~}

'

^~

Eiab=1760

MeV

A t h i g h bombarding energies (> 100 MeV/n), t h e measured i s o t o p i c d i s t r i b u t i o n s o f t h e p r o j e c t i 1 e-1 i ke fragments a r e independent o f t h e t a r g e t and merely r e f 1 e c t t h e composition o f t h e p r o j e c t i l e . T h i s i s expected i n a f a s t fragmentation process i n which t h e t a r g e t j u s t a c t s t o i n j e c t energy i n t h e p r o j e c t i l e . On t h e o t h e r hand, from measurements a t much lower energy (- 10 MeY/n), t h e

N/Z

r a t i o i s one o f t h e degrees o f freedom which e q u i l i b r a t e s t h e most r a p i d l y . Fig. 8 shows t h e v a r i a t i o n w i t h Z o f t h e cN>/Z r a t i o o f t h e p r o j e c t i l e - 1 i k e fragments f o r 27 MeV/n ( f i g . 8a) and 44 MeV/n ( f i g . 8b) 40Ar p r o j e c t i l e impinging on v a r i o u s t a r g e t s /21,40,42/. The

F i g . 7

-

a) E f f e c t o f t h e t a r g e t on t h e ele- mental d i s t r i b u t i o n s o f fragments from an '+OAr p r o j e c t i l e a t v a r i o u s energies. b ) R a t i o s o f t h e mass y i e l d s between t h e 4 0 ~ r + T i and ' O A ~

+

2 7 ~ 1 reactions. The s o l i d curve i s t h e p r e d i c t i o n o f t h e c l e a n - c u t abrasion model

1401.

C

2.0

-

^Exp.

more neutron r i c h t h e t a r g e t , t h e more neutron r i c h the fragments.

T h i s e f f e c t seems t o be s t r o n g e r a t 27 MeV/n than a t 44 MeVIn. Before g i v i n g any i n t e r p r e t a t i o n o f t h i s e f f e c t , i t should be noted t h a t t h e fragments may be e x c i t e d and t h a t sequential decay may s i g n i f i c a n t l y modify t h e i n i t i a l i s o t o p i c d i s t r i - b u t i ons. However r e c e n t measure- ments /39,69/ seem t o i n d i c a t e t h a t indeed t h e primary fragments c a r r y 1 i t t l e e x c i t a t i o n energy. Thus t h e measured i s o t o p i c d i s t r i b u t i o n s should be c l o s e t o t h e primary ones.

..--.

+

Q

5

-

\

.-

1.0

The dependence o f t h e cN>/Z r a t i o upon t h e t a r g e t might be an i n d i c a - t i o n o f t h e p e r s i s t e n c y o f mean f i e l d e f f e c t s l e a d i n g t o a few- nucleon exchange between p r o j e c t i l e and t a r g e t . As i t i s observed, t h i s e f f e c t i s supposed t o decrease w i t h i n c r e a s i n g bombarding energy. The presence o f fragments h e a v i e r than t h e p r o j e c t i l e /27, 40,43/ which a r e more abundantly produced a t 27 MeVIn than a t 44 MeVIn a t t e s t s o f t h i s exchange process.

-Abrasion -

" 5 :

_*...

-

: 1

1 I 1

A q u i t e d i f f e r e n t e x p l a n a t i o n i s brought o u t by Harvey 1661. He suggests t h a t t h e increase o f t h e

<N>/Z r a t i o o f t h e fragments f o r neutron r i c h t a r g e t i s n o t due t o a fragment enrichment i n neutrons b u t r a t h e r t o a d e p l e t i o n i n protons.

T h i s comes about from t h e energy dependence o f t h e n-n cross sec- t i o n s . Below

-

500 MeV, onp i s

-

³

t i m e s l a r g e r than u o r oPp. Thus f o r a t a r g e t w i t h

fl

^{> 2,} r o t o n s from the p r o j e c t i l e a r e more l i k e l y t o be s c a t t e r e d from t a r g e t nucle- ons than p r o j e c t i l e neutrons are.

10 20 3 0 G 0

The above mentioned processes can i n f a c t compete. The f i r s t one i s expected t o dominate a t low energy whereas t h e second one should increase w i t h bombarding ener- gy. I t would be i n t e r e s t i n g t o determine a t which energy t h e <N>/Z r a t i o reaches i t s s a t u r a t i n g value.

V.4 Momentum d i s t r i b u t i o n s o f t h e fragments : evidences f o r competing mechanisms A t h i g h energy, t h e w i d t h o f t h e momentum d i s t r i b u t i o n o f a given fragment ( f o r a g i v e n p r o j e c t i l e ) i s independent o f t h e i n c i d e n t energy, whereas a t low bombarding energy, i t increases w i t h bombarding energy /12,15,16/. The momentum w i d t h o f t h e fragments i s u s u a l l y determined by a f i t o f t h e i r energy s p e c t r a through t h e r e l a - t i o n :

EFsi n2e

E ~ c o s ~ c I - z ( E ~ E ) ~ / ~

COSB+E)~

*

^{= NO} (AFEF)1/2 exp

[ -

AF

(-

+ ( 3 )

dE

dsZ 4 4

CP-22 JOURNAL DE PHYSIQUE

A f t e r i n t e g r a t i o n over energy, r e l a t i o n ( 3 ) can be used t o f i t t h e fragment angular d i s t r i b u t i o n s and t o e x t r a c t values o f t h e momentum w i d t h ol perpendicular t o t h e beam d i r e c t i o n . The values o f al t h u s e x t r a c t e d as a f u n c t i o n o f t h e fragment mass a r e shown i n f i g . 9b f o r t h e r e a c t i o n 44 MeV/n '+OAr

+

2 7 ~ 1 . I n c o n t r a s t w i t h t h e r e 1 a t i v i s t i c e n e r g y d a t a , t h e values o f ol a r e much l a r g e r than t h e values of a

.

Such a d i f f e r e n c e has already been noted i n t h e fragmentation o f an 160 p r o j e c t i f e /14/ a t 90 and 120 MeV/n and o f a 12c p r o j e c t i l e /18/ a t 86 MeV/n. T h i s d i f f e r e n c e between al and a , has been i m p u t e d t o t h e d e f l e c t i o n o f t h e p r o j e c t i l e i n t h e

which i s j u s t t h e conversion ^I

i n t h e Laboratory frame o f t h e

l ^a)

momentum d i s t r i b u t i o n found 2 7 ~ e ~ / u ''A,

a t r e l a t i v i s t i c energy and g i v e n by r e l a t i o n

(1).

I n

t h i s expression, No i s a nor- 120

-

ma1 i z a t i o n c o n s t a n t , A t h e mass o f t h e f r a g m e n t ,

4

^it2

laboratory k i n e t i c energy, E i t s m o s t p r o b a b l e k i , n e t i c energy,

e

i s t h e l a b o r a t o r y

d e t e c t i o n angle and al and al

>

^11s-

are t h e momentum widths i n t h e d i r e c t i o n p a r a l l e l and

"

p e r p e n d i c u l a r t o t h e beam r e s p e c t i v e l y . However, as

mentioned e a r l i e r , t h e energy

.

^'"AU

s p e c t r a a t low and interme-

d i a t e bombarding e n e r g i e s 0 1 0 3 ~ h

p r e s e n t low energy t a i 1 s which cannot be f i t t e d by eq.3. It i s u s u a l l y assumed t h a t o n l y t h e h i g h energy p a r t o f t h e

.

^{! I}

\ I

.

"NI

$ 1

$1

s p e c t r a m i g h t have i t s o r i g i n 10s. 1 . I . I .

i n a fragmentation process. ^{5 10 15} Z

Thus t h e momentum w i d t h all i n t h e beam d i r e c t i o n i s e x t r a c t - 1.20 ed from r e l a t i o n ( 3 ) by fit- t i n g o n l y t h e h i g h energy p a r t o f t h e energy spectra. The momentum w i d t h a o f fragments

-

-

197

^b) - -

.

^Au

-

_{58 .}

-

o NI

from a 44 MeV/n I 0 A r p r o j e c t i -

-

nat

-

l e bombarding an 2 7 ~ 1 t a r g e t 1.15- A Ti

/40/ a r e shown as a f u n c t i o n o f t h e mass o f t h e fragments r-'

i n f i g . 9a. The average t r e n d

,;

o f t h e data i s w e l l reproduced by Go1 dhaber' s parabol i c law

r a b l e t o t h e l i m i t i n g value ( r e l a t i o n ( 2 ) ) w i t h a value o f oO = 87 MeV/c which i s compa- obtained a t much h i g h e r ener- g i e s /13 57/. Except f o r t h e 40Ar + r e a c t i o n /31/, a l l

a v a i l a b l e 44 MeV/n '+OAr data "05-

-

g i v e s s i m i l a r r e s u l t s /22,40/ ^{I 1} I 1 1 I \ I

8 10 12 16

independently o f t h e t a r g e t . 16

The same value o f o i s a l s o

Atomic number

obtained w i t h a 27 #ev/n pro- Fig. 8

-

I n f l u e n c e o f t h e target-neutron excess on j e c t i l e f o r fragments l i g h t e r t h e <N>/Z r a t i o o f t h e p r o j e c t i l e fragments i n '+OAr than s u l f u r . Thus i t seems induced r e a c t i o n s a t a) 27 I.(eV/n and b ) 44 MeV/n.

t h a t a l r e a d y a t 27 MeV/u, a, has reached i t s asymptotic value f o r an 4 0 ~ r p r o j e c t i l e .

A ( a.m.u.1

1 1 1 1 / I I l I I l l I l l l I I

0 12 13

LOO

E,,,=1760 M e V 300 -

Fig. 9

-

P a r a l l e l and transverse momentum widths o f p r o j e c t i l e - l i k e fragments i n the r e a c t i o n 4 0 ~ r +

2 7 ~ 1 a t 44 !,leV/n /40/.

nuclear and Coulomb f i e l d s o f t h e t a r g e t p r i o r t o fragmenta- t i o n . Such an e f f e c t i s expec- t e d t o become more important a t l o w e r energy. An o t h e r e f f e c t n o t i c e a b l e i n f i g . 9b i s , f o r a g i v e n fragment mass, a small b u t systematic increa- se o f t h e variances a: as the chdrge ndmber i n c r r d s ~ s . Tne opposi t e e f f e c t was observed i n t h e fragmentation o f 160 and 4 0 ~ r p r o j e c t i l e s /19/ a t

-

100 FleV/n. T h i s was a t t r i b u t e d /19/ t o a Coulomb f i n a l s t a t e i n t e r a c t i o n between t h e frag- ments and t h e protons disso- c i a t e d from t h e p r o j e c t i l e . Both e f f e c t s , d e f l e c t i o n o f t h e p r o j e c t i l e and f i n a l s t a t e i n t e r a c t i o n have been used t o generate t h e curves shown i n f i g . 9b which come s h o r t t o e x p l a i n t h e data. Recently, A .J

.

Cole /67/ was successful 1 i n reproducing t h e angular d i s t r i b u t i o n s o f t h e p r o j e c t i - 1 e-1 i ke fragments observed i n the r e a c t i o n 4 0 ~ r + 68Zn /27/.

I n h i s model, t h e r e a c t i o n mechanism i s g i v e n b y t h e number o f n u c l eon-nucl eon c o l l i s i o n s i n t h e o v e r l a p r e g i o n between t h e t a r g e t and t h e p r o j e c t i l e . Angular d i s - t r i b u t i o n s a r e o b t a i n e d as t h e c o n v o l u t i o n o f d i s t r i b u t i o n s due t o d e f l e c t i o n by t h e ion- p o t e n t i a l and r e c o i l e f f e c t s due t o t h e change i n mass.

I n a n a l y s i n g t h e momentum w i d t h o f t h e p r o j e c t i l e f r a g - ments from t h e 27 MeV/n 4 0 ~ r + 68Zn r e a c t i o n Rami e t a1 ./27/

found t h a t fragments 1 ig h t e r t h a n AF = 3 5 h a d a r e d u c e d momentum w i d t h 5, = 85 MeV/c whereas f o r h e a v i e r fragments a, = 50 MeV/c. T h i s suggests two d i f f e r e n t o r i g i n s f o r t h e p r o d u c t i o n o f t h e fragments. F o l l o w i n g McVoy and Nemes /47/ one i s tempted t o a t t r i b u t e t h e h e a v i e s t fragments w i t h the s m a l l e s t reduced momentum w i d t h a, t o t r a n s f e r r e a c t i o n s and t o a t t r i b u t e t h e l i g h t e r ones heaving t h e l a r g e s t values o f a, t o p r o j e c t i l e fragmentation. Using t h i s o p e r a t i o n a l d i s t i n c t i o n between t r a n s f e r and fragmentation, B o r r e l e t a1 ./42/ have undertaken a systematic study o f t h e c o m p e t i t i o n between these two processes using an 4 0 ~ r p r o j e c t i 1 e on v a r i o u s t a r g e t s . They found t h a t t h e reduced momentum w i d t h a, f o r t r a n s f e r products increases from 45 MeV/c t o 60 MeV/c between 27 MeV/n t o 44 MeV/n i n c i d e n t energies whereas f o r fragmentation products a, remained constant a t

-

90 MeV/c. A c o m p i l a t i o n o f t h e measured reduced w i d t h

IJ,

as a f u n c t i o n o f t h e bombarding energy EL, /A i s presented i n f i g . 10a f o r 2 0 ~ e and *OAr induced reactions. The values o? a, imputed t o t r a n s f e r r e a c t i o n s (eppty squares) i n t h e case o f 4 0 A r f o l l o w s t h e systematic t r e n d observed f o r 2 0 ~ e fragments. However, one may wonder why i n t h e r e g i o n o f overlap

JOURNAL DE PHYSIQUE

between 27 MeV/n and 44 MeV/n, t h e fragmentation l i m i t o f

-

⁹⁰

MeV/c reached by t h e '+OAr f r a g - ments remote by more t h a t 5 mass u n i t s from t h e r o j e c t i l e i s never reached by RNe frag- ments. I s i t due t o s p e c i a l s t r u c t u r e o f t h e 20Ne nucleus?

I n f i g . l o b i s r e p o r t e d the ra- t i o of t h e t r a n s f e r 'to t h e fragmentation component /42/

f o r Z=16 and Z=17 isotopes from t h e fragments o f an ' + O A ~ pro- j e c t i l e a t 27 MeV/n and 44 MeV/n. The t r a n s f e r component decreases s h a r p l y w i t h bombard- i n g energy.

An o t h e r evidence f o r t h e per- s i s t e n c y o f d i r e c t s u r f a c e t r a n s f e r r e a c t i o n s a t interme- d i a t e energy comes from t h e observation o f fragments w i t h masses o r charges g r e a t e r than those o f t h e p r o j e c t i l e /27, 40,43/. T h i s prompted Mermaz /36,43/ t o analyse t h e energy s p e c t r a o f t h e fragments c l o s e t o t h e p r o j e c t i l e i n t h e frame- work o f a d i f f r a c t i o n a l model i n c l u d i n g p o p u l a t i o n o f c o n t i - nuum states. It i s assumed i n t h e c a l c u l a t i o n than t h e obser- ved fragments a r e t h e primary ones ( e x c i t a t i o n energy

<

15 MeV) whereas t h e e x c i t a t i o n energy o f t h e t a r g e t - 1 i k e frag- ments i s o n l y l i m i t e d by energy conservation. The main i n g r e - d i e n t i n t h e model i s t h e use o f W i l l i a m ' s p a r t i a l l e v e l d e n s i t i e s . Agreement w i t h t h e data i s q u i t e s a t i s f a c t o r y f o r fragments c l o s e t o t h e p r o j e c - t i l e .

V.5 E x c i t a t i o n energy o f pro- j e c t i l e - 1 i k e fragments I n t h e previous discussion, t h e d i s t i n c t i o n between t r a n s f e r and f r a g m e n t a t i o n p r o c e s s e s has been based e s s e n t i a l l y on the shape o f t h e energy spec- t r a o f t h e fragments. More d i - r e c t evidences are now coming from e x c l u s i v e experiments i n which p r o j e c t i l e - 1 i k e fragments are detected i n coincidence e i t h e r w i t h l i g h t p a r t i c l e s o r w i t h more massive fragments /15,25,29,30,34,37, 39,69-72/. 0

Fig. 10

-

a) Reduced momentum widths f o r 2 0 ~ e ( @ , A ) /15,32,41/ and '+OAr

(a,-)

/22,27,40,42/. For 20Ne, o n l y 12C and 160 fragments were considered. F o r '+OAr, t h e open squares correspond t o t h e t r a n s f e r channel o n l y /41/. b) R a t i o o f t h e t r a n s f e r t o t h e fragmentation component f o r Z=16 and 17 isotopes i n t h e ' + O A ~ + 5 8 ~ i r e a c t i o n a t 27 MeV/n and 44 MeV/n

/41/.

ne e s s e n t i a l f e a t u r e o f these data (which w i l l be

t r e a t e d in d e t a i l by Bizard) i s the low m u l t i p l i c i t y of f a s t charged p a r t i c l e s asso- c i a t e d t o the p r o j e c t i l e fragments. Thus, these fragments must emerge from the ini- t i a l c o l l i s i o n with a small amount of excitation energy. This r e s u l t i s confirmed by a recent measurement of the l i f e t i m e s of the primary fragments from a 44 MeV/n 40Ar projecti 1 e bombarding a Ge c r i s t a l , using the blocking technique /73/. The measured l i f e t i m e s

^T = ( 2 f

1 ) 1 0 - 1 8 ~ e ~ f o r a l l fragments ( f i g .

11)

a r e compatible with prima- ry mass and excitation energy d i s t r i b u t i o n s as given by an abrasion calculation. In order t o f i t the data t h e excitation energies as predicted by the abrasion model had t o be increased by - ^{10 MeV.}

I l CALC

Fig. 11 - Lifetimes of the primary frag- ments from a 44 MeV/n 40Ar p r o j e c t i l e bom- barding a Ge c r i s t a l . The histograms are t h e r e s u l t s of a c a l c u l a t i o n assuming excitation energies as given by the abra-

sion model plus 10 MeV /73/.

where

V.6 Energy damping of the fragments As noted previously (see f i g .

61, the

projecti 1 e fragments undergo an energy damping which increases as the mass of the fragments decreases. The average v e l o c i t y

V F

of t h e fragments has been successfully /22,27,42/ parametrized

where

A

and

AF

a r e the masses of the p r o j e c t i q e and of t h e fragment respec- t i v l e y

; V

i s t h e v e l o c i t y of t h e p r o j e c t i l e grid E i t s k i n e t i c energy

: Es

i s t h e energy Recessary t o s p l i t the p r o j e c t i l e i n t o i t s p a r t i c i p a n t and spectator parts and i s given by the abrasion model.

An

other approach /40/

i s t o modify the abrasion model i n order t o include kinematical e f f e c t s . In the center of mass frame, energy and momentum conservation provides the r e l a t i o n s

:

AK[ +

AK; +

AK[

=

sp

⁺

ST and

P [ + P ; + P ~ = o ,

a r e

t h

k i n e t i c energy losses f o r the p r o j e c t i l e and t a r g e t spectators respectively

~

and

A K C

i s t h e change i n k i n e t i c energy of the f i r e b a l l made up of the p r o j e c t i l e and t a r g e t participants. The projecti 1 e and t a r g e t separation energies are given by Sp and ST.

T h

l i e a r m Y e n t a of t h e p r o j e c t i l e and t a r g e t spectators and of the f i r e b a l l a r e P%, PI ^{and PC} respectively. I t i s assumed furthermore t h a t the k i n e t i c energy losses

^0%

the p r o j e c t i l e r g e t spectators a r e i n the r a t i o of t h e sepa- r a t i o n e n e r g i e s

Sp

and S

: A K ~ ; A K ~ =

Sp/ST The observed energy damping i s well reproduced by such a calcuration /27,40/. An important f e a t u r e of the model i s the prediction of a change i n the reaction mechanism from massive t r a n s f e r (from the

1

i g h t t o t h e heavy nucleus) t o abrasion a s the bombarding energy increases. In f i g . 12, the prediction of the model a r e compared with recent coincidence data between r o j e c t i l e - l i k e and target-1 i k e fragments /38/ from the reaction '+OAr

+

27Al a t 44 Rev/n. Also shown in f i g . 12a (dashed curve) i s the

projectile-like/target-like mass

c o r r e l a t i o n predicted by GrZgoire e t a1./74/ using the Landau-Vlasov equation.

Although these data a r e consistent with the formation of a f i r e b a l l , there a r e not

y e t c l e a r evidences of such a phenomenon in t h e intermediate energy regime. Taking a

somewhat d i f f e r e n t approach, Bondorf e t a1 ./75/ assume t h a t the nucleons in the

f i r e b a l l r e s u l t i n g from the overlap between t a r g e t and p r o j e c t i l e a r e i s o t r o p i c a l l y

emitted. Those directed towards t h e spectators will contribute t o t h e i r excitation

energy and wi 11 communicate t o them recoil momenta, determining t h e i r kinematical

properties. Within t h i s picture, s t a t i s t i c a l fluctuations play an important role i n

t h e various c o r r e l a t i o n s between t a r g e t and p r o j e c t i l e spectators.

JOURNAL DE PHYSIQUE

Fig. 12

-

a) Target m a s s - p r o j e c t i l e mass c o r r e l a t i o n i n t h e r e a c t i o n 40Ar + 2 7 ~ 1 a t 44 MeV/n. b ) Average r e c o i l v e l o c i t y o f t h e t a r g e t fragments as a f u n c t i o n o f t h e i r mass. c ) Average r e c o i l angle o f t h e t a r g e t fragments as a f u n c t i o n o f t h e mass o f t h e p r o j e c t i l e fragments. The f u l l curves are t h e p r e d i c t i o n s o f an extended abra- s i o n model (see t e x t ) . The dashed curve i n fig. 12a i s t h e r e s u l t o f a c a l c u l a t i o n

i n t h e framework o f t h e Landau-Vlasov equation /74/.

F o r heavy p r o j e c t i l e such as Kr, t h e p r o d u c t i o n o f p r o j e c t i l e - 1 i k e fragments i s even more i n t r i c a t e d /75,77/. I n ref./76/, t h e authors assume t h a t under t h e e f f e c t o f t h e mean f i e l d , t h e h i g h l y e x c i t e d p a r t i c i p a n t zone may s t i c k e i t h e r t o t h e p r o j e c - t i l e o r t h e t a r g e t . However, l i k e i n a c l a s s i c a l c a l e f a c t i o n phenomenon, a gas o f nucleons a t the i n t e r f a c e between the h o t p a r t i c i p a n t zone and t h e c o l d s p e c t a t o r i n h i b i t s h e a t exchange and t h e p a r t i c i p a n t zone w i l l reseparate before thermal equi- l i b r i u m i s reached. T h i s p i c t u r e seems t o account f o r t h e p r o d u c t i o n o f low energy fragments c l o s e t o t h e p r o j e c t i l e charge i n t h e r e a c t i o n s K r + Au and K r + Mo a t 22 MeV/n /76/.

V I. SUMMARY

A f t e r t h i s quick survey o f t h e data on p r o j e c t i l e fragmentation a t i n t e r m e d i a t e energies, i t appears t h a t t h i s energy regime i s indeed a t r a n s i t i o n r e g i o n where l o w and h i g h energy mechanisms s t r o n g l y compete.

P r o j e c t i l e fragmentation which a t f i r s t glance seemed a very simple process i s i n f a c t very i n t r i c a t e d and i n v o l v e s several mechanisms. F o r t h e most p e r i p h e r a l c o l l i - sions, d i r e c t surface t r a n s f e r r e a c t i o n s s t i l l c o n t r i b u t e t o t h e y i e l d o f t h e f r a g - ments c l o s e t o t h e p r o j e c t i l e b u t t h e i r importance decreases r a p i d l y w i t h i n c r e a s i n g bombading energy. For these fragments, does t h e increase o f t h e reduced momentum w i d t h Go w i t h bombarding energy merely r e f l e c t t h e sagging o f Coulomb e f f e c t s o r does i t r e s u l t from a growth o f t h e a v a i l a b l e phase s p a c e A comprehensive descrip- t i o n o f t h e a v a i l a b l e data should answer t h i s question.

F o r fragments more remote from t h e p r o j e c t i l e , t h e s i t u a t i o n i s even l e s s c l e a r as t h e s t r u c t u r e o f t h e p r o j e c t i l e seems t o p l a y an i m p o r t a n t r o l e . F o r Ar p r o j e c t i l e s , the reduced w i d t h a. seems t o have already reached i t s s a t u r a t i n g value a t 27 MeV/n, whereas f o r l i g h t e r p r o j e c t i l e s such as Ne, t h i s value i s n o t y e t reached a t 44 MeV/n. I n a l l cases, t h e low energy t a i l observed i n t h e energy spectra a t t e s t s o f mean f i e l d e f f e c t s and t h e regime o f s t a t i s t i c a l fragmentation may n o t have been reached. I n any case, t h e ,significance o f t h e reduced w i d t h a,, and i t s l i n k w i t h t h e Fermi momentum i n s i d e t h e p r o j e c t i l e i s n o t c l e a r .

Although some data a r e c o n s i s t e n t w i t h t h e formation o f a f i r e b a l l , no d i r e c t e v i - dences o f such a process are a v a i l a b l e .

Some e x c l u s i v e experiments have already been performed and many more a r e i n pro- gress. Such experiments should h e l p t o answer t h e above questions and have already shown t h a t p r o j e c t i l e fragments c a r r y a r e l a t i v e l y reduced amount o f e x c i t a t i o n

energy. A t t h e same time, more m i c r o ~ c o p i c models i n c l u d i n g mean f i e l d e f f e c t s and n-n c o l l is i o n s /74,78/ should shed some 1 i g h t on t h e c o m p e t i t i o n between t h e v a r i o u s mechanisms involved.

ACKNOWLEDGEMENTS

I wish t o thank a l l my colleagues which have c o n t r i b u t e d unpublished data t o t h i s review, G. Bizard, J.L. Charvet, N. Frascaria, B. Heusch, D. Guerreau, C. ~ g 6 and many others.

I

am g r a t e f u l t o C. Gregoire and M. Di Toro f o r e n l i g h t e n i n g discussions on t h e o r e t i c a l aspects.

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