GIANT RESONANCES IN HEAVY ION COLLISIONS

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GIANT RESONANCES IN HEAVY ION COLLISIONS

Ph. Chomaz

To cite this version:

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JOURNAL DE PHYSIQUE

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

GIANT RESONANCES IN HEAVY ION COLLISIONS

Ph. CHOMAZ

Division de Physique ~ h e o r i q u e * , Institut de Physique Nucleaire, F-91406 Orsay Cedex, France

Resume

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Dans c e t a r t i c l e nous discutons l e s progres apportes par l e s ions

E i K E dans l a connaissance des resonances geantes. Cette discussion s'appuie sur l a description de t r o i s r e s u l t a t s recents e t s u r l a cornparaison de ces r e s u l t a t s avec l e s predictions des modeles microscopiques (RPA, quasi-boson e t multiphonon ...). Nous montrons comment l e s mesures de decroissance par r a i e s y sont un t e s t de la structure des resonances geantes e t nous decrivons des experiences qui ont mis en evidence s o i t des resonances de t r e s haute energie s o i t des e t a t s de multiphonons b a t i s sur l e s resonances geantes I

2 fiu dd'nergie d ' e x c i t a t i o n . Nous abordons aussi l e r d l e des resonances geantes dans l e s reactions par ions lourds e t I l a lumiere des nouveaux r e s u l t a t s presentes nous mettons l ' a c c e n t s u r l'importance de l ' e x c i t a t i o n des multiphonons dans l e s mecanismes de reactions par ions lourds.

Abstract

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This paper presents some of the new r e s u l t s on giant resonances obtained using heavy ion p r o j e c t i l e s . I t i s shown t h a t t h e microscopic s t r u c t u r e of g i a n t s t a t e s can be probed using y coincidence measurements. An example of the search f o r high lying s t a t e s with l i g h t "heavy ion" probes a t high incident energy i s given and, the investigation of multiphonon exci- t a t i o n using heavier ions a t intermediate energy i s discussed. These experimental r e s u l t s a r e compared with the theoretical predictions of the multiphonon model. The r o l e of giant resonances i n heavy ion reactions i s discussed and i n the l i g h t of the new experimental r e s u l t s the importance of the multiphonon excitation f o r t h e heavy ion dynamics i s emphasized.

I

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INTRODUCTION

Since t h e discovery of the g i a n t dipole resonance GDR in photoabsorption reactions in1947 /1/ a considerable amount of experimental and theoretical e f f o r t s have been devoted t o the study of g i a n t resonances / 2 / . In p a r t i c u l a r , during the l a s t decade numerous vibrational modes have been observed and studied by means of i n e l a s t i c s c a t t e r i n g of electrons and hadrons ( p , d , 3He, 4He). These modes are seen t o be a general property of nuclei, they a r e coupled t o the ground s t a t e by strong electro-magnetic matrix elements, t h e i r e x c i t a t i o g fjnergies and widths vary smoothly with the nuclear mass A ( i .e. l i k e ~ - 1 1 3 and A- respectively). Giant resonances are expected t o play a dominant role in many nuclear reactions. For example the e x c i t a t i o n of c o l l e c t i v e s t a t e s in heavy ion reactions i s now well established /3-5/. The purpose of t h i s paper i s t o study, on the one hand, the role of giant resonances i n heavy ion c o l l i s i o n mechanisms and, on the other hand, the way i n which heavy ion c o l l i s i o n s can enhance our knowledge of g i a n t resonance s t a t e s . A complete review of these two points i s nearly an impossible task and t h u s I shall r e s t r i c t myself t o the discussion of a few selected aspects. After a rapid introduction on the nature of giant resonances I s h a l l touch in section I1 upon the r o l e of giant resonances i n heavy ion collisions. Then in section I11 I shall

'~aboratoire associe au CNRS

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C4-156 JOURNAL DE PHYSIQUE

discuss recent o r future studies on giant resonances performed with heavy ion probes :

subsection 111.1 will be devoted t o the study of g i a n t s t a t e decay whereas subsection 111.2 will describe the observation of new g i a n t s t a t e s a t high excitation energy. The implications of t h i s new information on the r o l e of giant s t a t e s i n heavy fon dynamics lirill then be stressed and conclusions will be drawn i n the l a s t section.

I1

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ROLE OF GIANT RESONANCES 11.1.

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Generalities.

In the liquid-drop model giant resonances are interpreted as co7fective vibrations of the nucleus. For example, the monopole resonance i s a compression mode whereas the other modes a r e associated with nuclear surface deformations /6/.

In e l e c t r i c i s o s c a l a r vibrations a l l nucleons vibrate i n phase, conversely i n isovector modes protons and neutrons vibrate out of phase a s do spin-up and spin- down nucleons in magnetic resonances.

Ina microscopic description, giant resonances can be seen as coherent exci- t a t i o n s of elementary particle-hole t r a n s i t i o n s i n a s h e l l model. Hence the proper- t i e s of the resonance : the multipolarity, the strength, the spin and isospin t r a n s f e r s are defined by the under1 ying article-hole structure. This structure i s often described by the Random Phase Approximation (R.P.A).

In f a c t the two previous descriptions of giant s t a t e s are complementary and i t i s often useful t o consider both i n order t o get a b e t t e r understanding of giant resonance properties.

11.2.

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Zero point motions.

Fig. 1

Giant resonances induce zero point motion i n the collective coordinate q.

Indeed, a g i a n t resonance can be considered a s a quantum harmonic o s c i l l a t o r in the coordinate q. Fiaure 1 presents the t h r e e f i r s t s t a t e s i n a parabolic potential together with t h e i r wave function. The extention i n q of the wave function of the first s t a t e i 1 l u s t r a t e s the zero point motion of the nucleus in i t s ground s t a t e . The two other s t a t e s are respectively the one-phonon ( i .e. the giant resonance i t s e l f ) and the two phonon excitations. This zero point motion induces fluctuations of the i n i t i a l conditions i n heavy ion c o l l i s i o n s . For example, the fluctuations associated w i t h isovector dipole resonance account f o r the i s o b a r i c d i s t r i b u t i o n s measured i n f i s s i o n o r fragmentation processes /7/.

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11.3.

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Heavy ion dynamics.

The existence of giant resonances which are strongly couoled t o the ground s t a t e i s of great importance f o r the description of heavy ion dynamics. For instance, Fig. 2 presents a heavy ion reaction calculated i n the Copenhagen model 181 which e x p l i c i t l y takes i n t o account giant s t a t e degrees of freedom. In these calculations the excitation of giant resonances induces deformations of the nuclei and d i s s i p a t i m of k i n e t i c energy and angular momentum. Hence, giant resonances a c t as doorway s t a t e s f o r thermalization.

Fig. 2

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See r e f . /8/

The complete understanding of the role of giant resonances i n heavy ion reactions implies a more profound knowledge of t h e i r properties and excitation mechanisms.

I11

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NEW STUDIES ON GIANT RESONANCES

In t h i s section I shall survey the s p e c i f i c i t i e s , advantages and disadvantages of heavy ions i n comparison with other hadronic o r electromagnetic probes.

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JOURNAL DE PHYSIQUE Fig. 3 ORNL-DWG83-14678 E460= 400 MeV 1 100% E W S R ' 0, , ( d e g l Fig. 4

-

See r e f . / l o /

threshold (e.g. 170,

ON^).

Another disadvantage of heavy ions associated w i t h the p a r t i c l e decay of the e j e c t i l e i s the pick-up-break-up background. In t h i s process the p r o j e c t i l e picks-up one o r more nucleons from the t a r g e t while being excited and then decays i n f l i g h t be reemiting the same p a r t i c l e s . The r e s u l t i n g fragment i s miss detected as a scattered p r o j e c t i l e . This process i s the most important contribution t o the background but can be calculated using Monte Carlo methods /9/.

This background i s found t o be smooth i n most cases and strongly dependent on t h e incident energy.

The l a s t disadvantage of heavy ion probes i s the absence of signature of the multipolarity of the t r a n s i t i o n . This feature i s c l e a r l y i l l u s t r a t e d i n the

D.W.B.A. calculation shown on Fig. 4 which shows the similarity of the angular d i s t r i b u t i o n s f o r a l l m u l t i p o l a r i t i e s in the 160 + * 0 8 ~ b case a t 400 MeV.

Heavy ion probes also present numerous advantages f o r g i a n t resonance studies. These advantages can be separated i n t o two categories : advantages f o r coincidence experiments and advantages f o r the search of new s t a t e s .

Advantages f o r Coincidence Experiments :

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Fig. 5

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See r e f . / 1 1 / Fig. 6

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DWBA calculation f o r the incident energy dependence of the d i f f e r e n t i a l cross-section of the f i r s t maximum of angular d i s t r i b u - t i o n in the case of a L = 2 s t a t e (100% EUSR 18 MeV) in 4 0 ~ a excited by an 4 0 ~ r p r o j e c t i l e .

Advantages f o r the Search of New States :

Several f a c t s a r e i n favour of the search of new giant s t a t e s w i t h heavy ion probes :

i ) The f i e l d s involved i n kavy ion reactions are so strong that strong excitations of the nuclei may be expected.

i i ) As discussed before, the background i s small, smooth and calculable.

i i i ) The large variety of p r o j e c t i l e - e j e c t i l e couples allows t o s e l e c t p a r t i c u l a r spin and isospin transfers.

i v ) Finally, the heavy ions bring large angular momenta i n t o the system and thus can t e s t high multipolarity strength d i s t r i b u t i o n s .

111.2.

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Decay studies.

In thi section I s h a l l discuss coincidence experiments i n the l i g h t of the r e s u l t s on 20QPb described in r e f . 110, 121. Figure 7 displays the most important l e v e l s i n 208pb and 207pb relevant f o r the decay studies.

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JOURNAL DE PHYSIQUE Fig. 7

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See r e f . /12/ BEAM Fig. 8 ORNL-DIG 83-17418 I I I I I I - 2 0 0 ~ b GAMMA-RAYS - v 2 0 ---- V Z 0.98 - - - - 0 5 I0 15 20 25 30

SUM GAMMA ENEROI { M e V )

Fig. 9

-

See ref. /12/

of the y branching r a t i o t o the ground s t a t e gives the B(E ) value of the excited s t a t e . The branching r a t i o s t o excited s t a t e s y i e l d information on the underlying microscopic structure of giant s t a t e s and may be helpful i n

the extraction of high multipolari t y strength. Moreover the angular d i s t r i

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butions of neutrons and y ' s associated with a d i r e c t decay t o the ground s t a t e give access t o the multipolarity of the excited mode. Finally, the detailed analysis of energy spectra and of angu- l a r correlations are a way t o separate d i r e c t decay from spreading decay.

Figure 8 shows a schematic view of the experimental s e t up used in the experiment of reference /12/. The ejec- t i l e s are detected i n 8 AE. E telescopes whereas y ' s and neutrons a r e measured i n a array of NaI detectors which covers a large s o l i d angle (a 4 ~ ) . This device

separates y ' s from neutrons and yields energies and m u l t i p l i c i t i e s on an event by event basis. Thus the measured q u a n t i t i e s are : i ) the k i n e t i c energy of the ejec- t i l e s ( i . e . 170 i n the case of r e f s .

/ l o , 12/ equivalent t o the E* of the t a r g e t , i i ) The energies of y ' s and neutrons, i i i ) The y and neutron multi- p l i c i t i e s . In what follows I shall only discuss y ray decay.

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4 8 12 16 EXCITATION ENERGY (MeV)

Fig. 10

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See r e f . /1/ -12.2 MeV "10.6 MeV 2 . 6 MeV G . S . Fig. 11

-

r

width f o r L = 2 s t a t e s i n 208pb see r e f . /14/

In f a c t , much more information can be extracted from such experiments. For instance, the branching r a t i o t o a l l low lying s t a t e s may be measured. Figure 10 gives some examples of branching

r a t i o s : i ) t o the ground s t a t e ( p a r t a ) ;

i i ) t o the c o l l e c t i v e 3- s t a t e a t 2.61 MeV ( o a r t b) ; i i i ) t o the c o l l e c t i v e 2+ s t a t e a t 4.08 MeV and i v ) t o the particle-hole

3- s t a t e a t 4.97 MeV. These four spectra appear t o be very d i f f e r e n t : whereas the

GQR bump i s c l e a r l y v i s i b l e in the f i r s t one, i t disappears completely i n the second and t h i r d ones. These r e s u l t s are a strong t e s t of. the theoretical description of giant s t a t e s and in f a c t a r e i n remarkable agreement with the recent calculations of Bortignon e t a1

.

/13/. Moreover, i n Fig. 10d, a strong decay y i e l d i s observed around 10 HeV. This feature together with the s i m i l a r r e s u l t s obtained f o r the 5-

s t a t e a t 3.9 MeV seem t o indicate the existence of high spin strength underlying the GQR.

In Figure lob, i t must be noted t h a t the strong peak a t 5.2 MeV might be the f i r s t experimental signature of the existence of a two phonon s t a t e ( i . e . of the second excited s t a t e of a vibrational band) b u i l t on the low lying 3- s t a t e .

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111.3.

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Search o f new s t a t e s .

From a t h e o r e t i c a l p o i n t o f view numerous y e t unobserved g i a n t s t a t e s are p r e d i c t e d ( f o r i n s t a n c e : h i g h m u l t i p o l a r i t y s t r e n g t h , h i g h energy resonances, i s o v e c t o r modes,

. .

.) /16-19/. I would l i k e t o r e p o r t here t h e main r e s u l t s o b t a i n e d i n t h e multiphonon c a l c u l a t i o n o f r e f s /19, 20/. I n references /19, 20/ the

response o f t h e t a r g e t nucleus t o t h e e x t e r n a l f i e l d c r e a t e d by t h e p r o j e c t i l e i s c a l c u l a t e d m i c r o s c o p i c a l l y i n t h e quasi-boson approximation ( i .e. t h e RPA f o r the f i r s t phonon). On t h e o t h e r hand the n u c l e i are assumed t o f o l l o w c l a s s i c a l t r a j e c t o r i e s . T h i s view p o i n t i s v e r y close t o the TDHF approximation /19/ o r t o the Copenhagen model /21/ except f o r t h e microscopic treatment o f t a r g e t e x c i - t a t i o n s .

The c a l c u l a t i o n o f a heavy i o n r e a c t i o n i n t h i s model must be performed i n two steps. The f i r s t s t e p c o n s i s t s o f t h e microscopic d e s c r i p t i o n o f t h e t a r g e t response t o the e x t e r n a l f i e l d c r e a t e d by t h e p r o j e c t i l e . F o r example, the c o n t i - nuous p a r t o f t h e RPA s t r e n g t h d i s t r i b u t i o n i n l e a d e x c i t e d by an argon

p r o j e c t i l e i s p l o t t e d i n F i g . 12a. We have solved the RPA equation i n coordinate r e p r e s e n t a t i o n w i t h t h e Skyrme i n t e r a c t i o n S G I I i n o r d e r t o o b t a i n a good descrip- t i o n o f g i a n t resonances t o g e t h e r w i t h a f u l l treatment o f continuum e f f e c t s / l 9 , 20/. I n t h i s f i g u r e t h e d i s c r e t e s t a t e s are n o t displayed. The f i r s t peak correspotids t o the GQR b u t an another bump i s v i s i b l e around 35 MeV. For comparison t h e usual d i s t r i b u t i o n associated w i t h t h e r t o t h e power L e x c i t a t i o n o p e r a t o r i s d i s p l a y e d i n Fig. 12b. I n t h a t case no h i g h l y i n g resonances are e x c i t e d . T h i s i l l u s t r a t e s the f a c t t h a t a r e l i a b l e microscopic d e s c r i p t i o n o f t a r g e t e x c i t a t i o n s i s a c r u c i a l p o i n t i n such c a l c u l a t i o n s .

Before concluding t h a t new h i g h l y i n g resonances are e x c i t e d i n heavy i o n r e a c t i o n s , one must f i r s t go t h r o u g h t the dynamics o f these r e a c t i o n s . The main e f f e c t o f t h e dynamics i s t o weight t h e s t r e n g h t d i s t r i b u t i o n by a k i n e m a t i c a l c u t o f f f a c t o r /19-20/. The r o l e o f t h i s f a c t o r i s v e r y important and i s i l l u s t r a t e d i n Fig. 13 which g i v e s t h e one phonon e x c i t a t i o n p r o b a b i l i t y f o r the argon on l e a d r e a c t i o n a t 11 MeV p e r nucleon. As you can see, the c u t o f f f a c t o r suppresses

h i g h energy t r a n s i t i o n s because t h e i r p u l s a t i o n i s missmatched w i t h t h e r e a c t i o n time.

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dz1135frn - d=1135frn -

50 1 W 50 100 50 _loo_E_(MeV)

Fig. 14

The r e s u l t s of the multiphonon excitation calculation are ummar'zedon Fig. 14 which shows the t a r g e t e x c i t a t i o n spectrum (thick l i n e ) of the 3 9 ~ r + 3 0 8 ~ b reaction a t three incident energies and f o r two distances of c l o s e s t approach around t h e grazing. The monophonon d i s t r i b u t i o n ( t h i n l i n e ) i s a l s o displayed.

A t low incident energy the i n e l a s t i c spectrum shows s t r u c t u r e s due t o the multiple e x c i t a t i o n of the 2 hw g i a n t s t a t e s . These multiphonon s t a t e s are more strongly excited below the grazing distance of c l o s e s t approach which i s around 12 fm. On the other hand the monophonon d i s t r i b u t i o n dominates the i n e l a s t i c (spectra a t high energy. Structures a r e a l s o v i s i b l e up t o 40 o r 50 MeV but, here,

they are due t o high lying giant s t a t e e x c i t a t i o n . These monophonon s t a t e s a r e not excited a t low incident energy because of the missmatch of t h e i r pulsation w i t h the reaction time. A complete study shows t h a t heavier p r o j e c t i l e s favour multiphonon excitation whereas l i g h t e r p r o j e c t i l e s strongly e x c i t e high lying monophonons /19/.

In conclusion f a s t l i g h t heavy ions must allow t o observe the high lying g i a n t resonances and slower heavier ions the multiphonons b u i l t w i t h 2 hw resonances.

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C)

Ex~srl~!t~-w!th-!e~!!~-~se_aY-i0!l~_at-moderate-l!clde_!t~en_er9~

Comparison between theory and experiment a t low incident energy (E/A 10 MeV1 An i l l u s t r a t i o n of theoretical predic-

. , , . - t i o n s concerning the excitation of multi-

13 i phonons i s given by the high energy structures

(aunts .

i

Y

:

observed in heavy ion reactions a t low energy.

~ 0 3 1

,

; j f

:<

. In references /19, 20/ i t . i s shown t h a t the

G M R + GaR + GHR... G5R

J multiphonon model provides an adequate explaination f o r the positions and the

'

widths of the observed s t r u c t u r e s and t h e shapes and the angular evolution of the

.. spectra. An example of t h i s agreement i s

. displayed on Fig. 16 which compares

-

on the one hand, the t o t a l excitation probability, as i n Fig. 14

-

and, on the other hand, the measured spectra ( t h i s figure displays a t r a n s f e r channel which allows a c l e a r observation of the angular evolution because of the Fig. 15

-

See r e f . /24/ absence of the t a i l of the e l a s t i c peak.

Nevertheless the e s s e n t i a l features are the same a s i n the i n e l a s t i c channel. This means t h a t the t r a n s f e r reaction leads only t o a small additional e x c i t a t i o n on the multiphonon excitation of the core. The remarkable feature i s t h e s t r i k i n g s i m i l a r i t y between the calculation and the data both i n shape and in evolution. For impact parameters l a r g e r than the grazing only the monophonons are predicted t o be excited whereas strong p r o b a b i l i t i e s t o e x c i t e mu1 tiphonon are found f o r small distances of c l o s e s t approach. Likewise i n the experimental spectra, only the f i r s t s t r u c t u r e s are observed a t the grazing angle whereas the deeper ones become predominant a t smaller angles.

New intermediate energy r e s u l t s /22/

The new r e s u l t s obtained a t the GANIL national f a c i l i t y i n Caen have shed l i g h t on the multiphonon excitation process. These r e s u l t s a t intermediate energy

a r e important because i ) the variation i n incident energy allows t o distinguish between the pick-up-break-up process and the t a r g e t excitation i i ) t h e quasi-boson calculation predicts the optimal incident energy f o r t h e multiphonon excitation t o be around 30 t o 40 MeV/nucleon.

Figure 17 presents the most complete s e t of data which was obtained f o r the 4 0 ~ r

+

90zr reaction a t 44 MeV/nucleon. A t angles close t o the grazing bumps are c l e a r l y v i s i b l e up t o 60 MeV excitation energy. The cross section decreases rapidly with angle and only a smooth background remains above 3.8". The bumps appear even more c l e a r l y on the p a r t i a l sums displayed on Fig. 18. In t h i s representation a t l e a s t three bumps a t 50, 58 and 66 MeV a r e observed, the positions of which a r e independent of angle.

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Fig. 16a F i g . 16b

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Fig. 17

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I n e l a s t i c spectra of

4 0 ~ r

+

a t 44 MeVIn see

r e f . I221

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Fig. 19 Fig. 20

the f a c t t h a t the s t r u c t u r e s show up a t the same e x c i t a t i o n energy i n a l l t h e spectra, except above 3.8" where only a smooth background was observed i n the original spectra.

Influence of the incident velocity

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JOURNAL DE PHYSIQUE I 1000

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500- €lL zL.6" mr ** ,

***.

0 1 . " Ex (MeV) 70 56 30 Fig. 2 1

Influence of the t a r g e t nucleus

In f a c t , the s t r u c t u r e s only depend on the t a r g e t nucleus. In Fig. 22 are displayed four i n e l a s t i c spectra obtained b

bombard? ng four d i f f e r e n t t a r g e t s IOca, 3 0 ~ r , 1 2 0 ~ n and 2 0 8 ~ b with an 40Ar beam a t 44

MeV/nucleon. These four spectra were measured around the respective grazing angles of the considered reaction. For the lower spectrum the pick-up-break-up background i s drawn

w i t h a thin l i n e . For the three others only the centroid of t h i s contribution i s indi- cated by arrows since the shapes of the four contributions are the same /9, 22/.

In the four spectra, the s t r u c t u r e s a r e observed a t d i f f e r e n t excitation energies. The heavier the t a r g e t , the more numerous and the narrower the bumps.

This evolution i s q u a n t i t a t i v e l y i l l u s t r a t e d i n Fig. 23 which presents the positions of t h e s t r u

_{9 Y}

r e s as a function of the t a r g e t mass A-

.

The s t r a i g h t l i n e s passing through four data points and through t h e o r i g i n c l e a r l y show t h a t t h e positions of t h e s t r u c t u r e s follow a A - ~ D law. This i s known t o be a c h a r a c t e r i s t i c property o f g i a n t resonance s t a t e s . For instance, the slooes of t h e three f i r s t l i n e s corresoond t o 'the low e x c i t a t i o n octupole resonance

I

Ln Ln (LEOR), t o the GQR and t o the high excitation

octupole resonance (HEOR) respectively. The

3

0 others are not known but two of them could u 0 correspond t o two already predicted /17/ and

t e n t a t i v e l y observed /24/ giant resonances a t high energy. The others are i n good agreement with what i s expected from the multiphonon model : Approximately two and three times the GQR slope f o r the two f i r s t

im- l i n e s .

Role of multiphonons i n heavy ion reactions As we have seen, the new GANIL r e s u l t s have confirmed the predictions of the mu1 t i

-

p h o n model. Plultiphonons seem t o be strongly excited i n heavy ion reactions between 10 and 50 MeV/nucleon. This i s an important feature f o r the heavy ion dynamics. Indeed,

,250 multiphonons appear t o be the preferential

way of dissipating energy and angular momen- t u m in the f i r s t stages of the collision and i n f a c t they can be thought of a s doorway s t a t e s f o r thermal ization. Accordingly, t o

I I

O

' Ex (Mev)80 70 &I50 LO 3b 20

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i

I

1

3L M ~ v / A - " ~ 62 10L 128 156 186 221 LO I 10 20 30 50 60 70 Ex (MeV) Fig. 23 IV

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CONCLUSION

I r w s p e c t i v e of some important disadvantages heavy ions have brought and will continue t o bring new information about g i a n t resonances.

In t h i s paper I have described three examples of new r e s u l t s , f i r s t , the study of the microscopic s t r u c t u r e of g i a n t s t a t e s using y coincidence measurements, second, the search of high lying s t a t e s with l i g h t "heavy ion" probes a t high incident energy, and t h i r d , the investigation of mu1 tiphonon excitation using heavier ions a t intermediate energy. I have a l s o discussed the r o l e of giant resonances i n heavy ion reactions and I have emphasized the importance of multiphonons i n the dynamics of these c o l l i s i o n s . Indeed these multiple phonon s t a t e s could be the doorway towards thermalization. Moreover the deformations they induce in and ff spaces should have important consequences on the measured observables

i n many heavy ion reactions. Acknowledgements

I wish t o acknowledge my colleagues 3. Barrette, J.C. Jacmart, B. Fernandez, J.P. Garron, J . Gastebois, W. r l i t t i g and p a r t i c u l a r l y Y. Blumenfeld, N . Frascaria, P a t r i c i a Roussel and J .C. Roynette f o r many stimulating discussions and f o r a1 loding me t o use some of our unpublished r e s u l t s . Special thanks are due t o Y. Blumenfeld and N. Frascaria f o r t h e i r help during the elaboration of t h i s paper. Discussions w i t h H. Flocard, Nguyen Van Giai, D . Vautherin and M. VGneroni are g r a t e f u l l y acknowledged.

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