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INCOMPLETE TRANSFER OF LINEAR MOMENTUM AND EXCITATION ENERGY
BETWEEN 20 AND 80 MeV/u
S. Leray
To cite this version:
S. Leray. INCOMPLETE TRANSFER OF LINEAR MOMENTUM AND EXCITATION ENERGY BETWEEN 20 AND 80 MeV/u. Journal de Physique Colloques, 1986, 47 (C4), pp.C4-275-C4-287.
�10.1051/jphyscol:1986432�. �jpa-00225798�
JOURNAL DE PHYSIQUE
Colloque C4, supplement au n° 8, Tome 47, aout 1986 C4-275
INCOMPLETE TRANSFER OF LINEAR MOMENTUM AND EXCITATION ENERGY BETWEEN 20 AND 80 MeV/u
S. LERAY
Service de Physique Nucléaire, Métrologie Fondamentale, CEN-Saclay, F-91191 Gif-sur-Yvette Cedex, France
Résumé - Une revue de résultats récents concernant les réactions entre ions lourds aux énergies intermédiaires est présentée. I l apparaît que le pour- centage de l'impulsion i n i t i a l e qui peut être transférée au système composé décroît régulièrement lorsqu'on augmente l'énergie incidente. I l semble y avoir une l i m i t e à l'impulsion par nucléon que Ton peut transférer, corres- pondant à environ 175 MeV/c. Avec des projectiles comme l"*°Ar au-dessus de 35 MeV/u, on semble atteindre l'énergie d'excitation par nucléon maximale que le système composé peut supporter, ce qui induit une disparition progressive du mécanisme de fusion incomplète.
Abstract - Recent results concerning intermediate energy heavy ion central collisions are reviewed. It appears that the amount of the initial linear mo- mentum that can be transferred to the composite system regularly decreases with increasing bombarding energy. There seems to be a limiting value near 175 MeV/c for the transferred linear momentum per nucleon. With "*0Ar projec- t i l e above about 35 MeV/u, the maximum energy per nucleon that a system can contain seems to have been reached, making quasi fusion process progressively vanishing.
I - INTRODUCTION
At low bombarding energies (< 10 MeV/u) central collisions between heavy ions lead to the fusion of the projectile and target into a fully equilibrated compound nu- cleus which decays either by light particle evaporation or by fission. This process is well understood and reflects the predominance of the mean field in this energy domain. At high energy (> 100 MeV/u) i t is known that nucleon-nucleon collisions prevail and that for head-on collisions the system completely explodes. We expect, therefore, the intermediate energy range, now accessible with the new accelerators, GANIL, SARA and MSU, to be of great interest since we should learn how the transi- tion between the two regimes occurs.
Many experiments /1-6/ have shown that when the incident energy exceeds 8-10 MeV/u fusion gives way to incomplete fusion in which only parts of the incoming ions merge into a quasi-compound nucleus and that the higher the bombarding energy, the more incomplete the fusion. An analysis of data obtained with light projectiles C*He to
20Ne) on 238U target / 7 / , referred to as Viola systematics, has suggested that the percentage of the initial linear momentum which is transferred to the composite sys- tem is independent of the nature of the projectile and decreases almost linearly with l/E/A where E/A is the bombarding energy per nucleon. Interesting questions are:
does the momentum transfer for systems involving different targets or heavier pro- j e c t i l e s s t i l l follow such an empirical law? How can we understand this behaviour?
What happens when the bombarding energy is increased even higher?
In connection with this l a t t e r question, there are now many theoretical calculations predicting that hot nuclei can no longer exist beyond certain critical values of
Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:1986432
C4-276 JOURNAL DE PHYSIQUE
temperature o r e x c i t a t i on energy because t h e sys tem m i g h t t o t a l l y evaporate 18-111 o r undergo mu1 t i f ragmentation 112-141. These c a l c u l a t e d c r i t i c a l values a r e a t t a i n a - b l e i n t h e i n t e r m e d i a t e energy range, thus w i t h measurements o f momentum t r a n s f e r we m i g h t expect t o see changes i n t h e r e a c t i o n mechanisms and perhaps determine t h e s t a b i l i t y l i m i t s o f h i g h l y e x c i t e d compound systems.
I 1 - EXPERIMENTAL METHODS
One way t o c h a r a c t e r i z e t h e degree o f "incompleteness" o f a f u s i o n r e a c t i o n i s t o measure t h e amount, p, o f t h e i n i t i a l l i n e a r momentum t r a n s f e r r e d (LMT) from t h e p r o j e c t i l e t o t h e quasi compound nucleus. p i s d e f i n e d as :
where pt, p i a r e r e s p e c t i v e l y t h e t r a n s f e r r e d and t h e i n i t i a l l i n e a r momentum. $t i s assumed t o be p a r a l l e l t o t h e beam d i r e c t i o n .
Depending on t h e f i s s i o n i b i l i t y o f t h e t o t a l system, one uses two d i f f e r e n t methods t o g e t i n f o r m a t i o n on p.
11.1 L i g h t systems
F o r 1 ig h t systems, t h e quasi compound nucleus mainly decays by p a r t i c l e evaporation.
According t o r e f s./15,3/, t h e l a b o r a t o r y v e l o c i t y spectrum o f t h e evaporation residues, ER, represented by t h e i n v a r i a n t cross s e c t i o n l / v 2 x d20/(&dv) should be a Gaussian c e n t e r e d on v = VR cose, where VR i s t h e v e l o c i t y o f t h e quasi f u s i o n nucleus from which t h e ER o r i g i n a t e and 8 t h e d e t e c t i o n angle i n t h e l a b o r a t o r y . Determining t h e v e l o c i t y spectrum o f ER by radiochemical t e c h n i c s o r w i t h a time o f
f l i g h t telescope one can t h e r e f o r e deduce t h e most probable value 7 o f t h e r a t i o
where VCN i s t h e v e l o c i t y o f t h e f u l l compound nucleus. An example i s given i n Fig.1 f o r t h e system 4 0 A r + 68Zn f o r which p = 0.73 ( f r o m r e f . / l 6 / ) .
Then, assuming t h a t t h e missing LMT
-
- 5
-el0 5 3 4 A E R 4 57 - ; = y AT ( 3 )
- AT + (1-7) Ap
4 b
N VFMT /Vp = 0.37 Fig. 1 - V e l o c i t y spectrum o f evapo-
'P 5
- - r a t i o n residues detected a t an an l e
a '.' 1' I e =5" f o r t h e r e a c t i o n '+OAr + ! Zn
N W
> ala#7.6 MeV. The b i g arrow i n d i c a t e s
: - - t h e c e n t r o i d Vfmt o f t h e d i s t r i b u t i o n
- - - i f f u l l LMT occurs. From ref./l6/.
0 I I I I A.r
0.0 0.1 0.2 0.3 0.4 0.5 0.6 'ER ' V~
I I I I I
' O A ~ + ''2"
E = 1102 MeV
€Ilab = s o
was c a r r i e d away by nucleons o f t h e p r o j e c t i l e t r a v e l l i n g a t t h e beam v e l o c i t y and t h a t t h e t a r g e t t o t a l l y p a r t i c i p a t e s ( i n case o f a p r o j e c t i l e 1 ig h t e r than t h e t a r g e t ) , i t i s pos- s i b l e t o c a l c u l a t e t h e most probable value, F , f o r p, through :
where A , AT a r e r e s p e c t i v e l y t h e p r o j e c t i l e and t a r g e t masses. These hypothesis i m p l y t R a t p i s s i m p l y t h e r a t i o o f t h e t r a n s f e r r e d p r o j e c t i l e mass A; = Ap-AA~ t o t h e i n i t i a l mass :
Ap - AAp
P = (4
AP
A A ~ being t h e p a r t o f t h e p r o j e c t i l e which does n o t p a r t i c i p a t e i n t h e fusion.
The e x c i t a t i o n energy, E*, i n t h e quasi-compound nucleus i s thus given by :
when t a k i n g i n t o account t h e mass balance, Q. Q i s c a l c u l a t e d supposing t h a t t h e m i s s i n g mass escapes as f r e e nucleons. The r o t a t i o n a l energy which would reduce t h e i n t r i n s i c e x c i t a t i o n energy i s neglected.
I I .2 Heavy systems
The p r i n c i p l e decay channel f o r a heavy composite system i s f i s s i o n . I n f o r m a t i o n about p can be provided by measurements o f t h e angular c o r r e l a t i o n between f i s s i o n f r a g m e n t (FF) p a r t n e r s . As shown i n Fig. 2, t h e f o l d i n g angle, efol , between t h e two FF increases w i t h decreasing LMT. From simple kinematics, one can ieduce a r e l a - t i o n s h i p between efold and p :
As Vs sinefOld P =
A, V1 sine, (6)
where Al, V a r e t h e mass and ve- l o c i t y o f t h e p r o j e c t i l e . As, V, those o f t h e FF b e f o r e evapora- t i o n . With t h e same hypothesis as made above and adding t h e assump- t i o n t h a t f i s s i o n i s symmetric and t h a t FF v e l o c i t i e s a r e given by t h e systematics o f r e f ./l7/, t h e measurement o f the most probable value o f t h e f o l d i n g angle d i s t r i - b u t i o n w i l l a l l o w t h e determina- t i o n o f t h e most probable value ;
o f p. I n Fig. 3, a f o l d i n g angle d i s t r i b u t i o n i s resented f o r t h e system 4 0 A r + 8 7 A ~ a t 20 MeV/u ( r e f . 1 1 8 1 ) . The peak around o f o l d
= 150" i s a t t r i b u t e d t o a sequen- t i a l f i s s i o n o f a quasi t a r g e t a f t e r a p e r i p h e r a l r e a c t i o n . The o t h e r peak g i v e s an evidence of g r e a t e r LMT b u t i t i s l o c a t e d a t a efol d v a l u e 1 a r g e r t h a n expected f o r f u l l LMT (arrow). I n t h i s case, i t corresponds t o 5 = 0,85.
Complete linear momentum I Incomplete linear momentum transfer - I transfer -
F i g . 2 - F o l d i n g angle, efold, between t h e two f i s s i o n fragment p a r t n e r s I n t h e case o f com- p l e t e and i n c o m p l e t e LMT. V i s t h e v e l o c i t y o f t h e compound n u c l e u s , v # h a t o f t h e quasi composite system.
JOURNAL DE PHYSIQUE
Fig. 3 - Folding angle d i s t r i b u t i o n for the system 40Ar + l g 7 ~ u a t 19.6 MeV/u. The arrow indicates the e f o l d value corresponding t o f u l l LMT. From ref ./l8/.
111 - ORIGIN OF THE MISSING LMT
To derive formulas ( 3 ) t o (6) we assumed, as i t i s usually done, t h a t the missing mass originates only from t h e p r o j e c t i l e ( i n the case of a l i g h t p r o j e c t i l e on a heavy t a r g e t ) . Indeed there a r e now many indications t h a t t h i s might be true. Fig. 4 shows ER spectra f o r three systems : '+OAr + 1 2 C , 40Ar + 40Ca, 2 0 ~ e + 2 7 ~ 1 from ref.
/19/. One can s e e t h a t f o r t h e symmetric system, the spectrum i s centered a t VR = V since there must be evidently the same number of p a r t i c l e s leaving the p r o j e c t i l e a
:
! t h e t a r g e t , while i n t h e asymmetric c a s e s , VR > V C N when the p r o j e c t i l e i s h e a v i e r than t h e t a r g e t and V < V i n the opposite case. This means t h a t i t i s always the l i g h t e r nucleus thatRlosesC!he most mass. Furthermore, a recent analysis of ER r e s u l t s by Nifenecker e t a1./20/ showed t h a t the hypothesis t h a t the heavier nucleus ( i n t h e i r case, the t a r g e t ) t o t a l l y p a r t i c i p a t e s t o the incomplete fusion, leads t o a b e t t e r agreement with the measured E R masses than other hypothesis. So i t seems t h a t , as soon as a system deviates l i t t l e from symmetry, one may safely assume t h a t the whole missing mass originates from the l i g h t e s t of the two ions.
Another question about the missing LMT concerns the nature and velocity of the par- t i c l e s escaping before the formation of the quasi-compound nucleus. Many coincidence experiments between FF produced in central c o l l i s i o n s and 1 ight p a r t i c l e s /21-24/
have shown t h a t incomplete LMT could be associated with prompt p a r t i c l e s emitted i n the early stages of the reaction i n the forward direction and t h a t the energy spec- t r a of these p a r t i c l e s are roughly centered around the beam energy per nucleon.
3- , , . . , . , . , , , . .-, Recently, in ref.1241, i t was shown
4 0 t h a t more than one t h i r d of the mis-
Ar + '*c sing LMT could be a t t r i b u t e d t o pre- equilibrium neutrons. This suggests t h a t mostly 1 i g t h p a r t i c l e s a r e res-
- ponsible f o r the missing LMT.
IV - LIMITATION TO THE TRANSFERRED LINtAR M O M t N IUM
Many data on the amount of l i n e a r mo- mentum t h a t can be transferred by
p r o j e c t i l e s ranging from '+He t o 58Ni
C5
t o the quasi-compound nucleus are now available. The most s t r i k i n g f a c t i s
z +Oe5 t h a t t h e q u a n t i t y a, whether i t i s
- , , l l , , ~ ~ . oextracted from ER o r FF measurements, ~ , ~ i s approximatly independent of the
< 4 - ''A, + 'OC~ - p r o j e c t i l e and t a r g e t and decreases roughly 1 i nearly with increasing re1 a- t i v e velocity of the two incoming
- ions, vrel. vrel i s defined as : Vrel = L/2(ECm - V C ) / ~ ( 7 )
N where E i s the center of mass ener-
s gy, V C i r e Coulomb b a r r i e r and p the
P
- reduced mass. Fig. 5 shows a compila- t i o n of recent r e s u l t s 12-5,16,18-22, 25-42/ f o r systems f o r which there is unambiguous evidence of incomplete fusion. The average behaviour of a l l
I I I these data can be parametrized by :
1 ON^ + 2 7 ~ 1 - - = 1 f o r vr,l/c < .1
p = - 1.904 vrel + 1.19 (8)
- f o r v r e l / c .1
- In f a c t , i t seems t h a t v i s a more relevant parameter than &. The de-
- crease of t h e percentage of LMT when the bombardi ng enefgy increases might
- be an indication t h a t the mean f i e l d i s no longer e f f i c i e n t enough t o trap
A a1 1 t h e nucleons. An estimation of the number of nucleons which can escape
V - VCN (cm / ns) from t h e mean f i e l d , based on phase space considerations was proposed in Fig. 4 - Velocity spectra of ER f o r three 1431 and reproduces the tendency of d i f f e r e n t s y s t e m s v e r s u s t h e d e v i a t i o n the data, while the preequilibrium mo- (V-VCN) from the f u l l compound nucleus velo- del of Bl ann 1441 seems t o f i t 40Ar c i t y . From ref ./l9/. and 58Ni r e s u l t s 1391. I t has been
s t r e s s e d t h a t the lowering of the pos- s i b l e LMT could be due t o the enhan- cement of the importance of nucleon-nucleon c o l l i s i o n s . A s a matter of fact, models including coll i sion terms such a s the intranuclear cascade calculation of 1451 or t h a t of Gregoire e t a1 ./46/ seems t o be able t o explain the data.
C4-280 JOURNAL DE PHYSIQUE
It was suggested a few years ago /6,4/, c o n s i d e r i n g experiments u s i n g 4 ~ e /6/ and 12C /4/ p r o j e c t i l e s , t h a t t h e LMT c o u l d s a t u r a t e near 180 MeV/c p e r i n c i d e n t nucleon when t h e bombarding energy increased. T h i s i d e a seems corroborated by r e s u l t s w i t h h e a v i e r p r o j e c t i l e s /28,33,36,39,42/. As an example one can l o o k a t Fig. 6 where t h e f o l d i n g angle d i s t r i b u t i o n f o r t h e system =*Ni + 232Th /39/ a t 20, 25 and 30 MeV/u i s presented. It appears t h a t t h e value o f t h e LMT stays constant over t h e t h r e e bombarding energies and corresponds here t o about 165 MeV/c p e r nucleon. However t h e r e a r e q u i t e i m p o r t a n t d e v i a t i o n s f o r t h e value o f t h e l i m i t i n g LMT per nucleon s i n c e i t v a r i e s from 165 t o 220 MeV/c ( r e f ./42/).
I n F i g . 7, ii v a l u e s measured f o r d i f f e r e n t systems are p l o t t e d ver- sus and compared t o a curve obtained assumi ns a 1 im i t i n s value f o r Pt/A o f 175 M ~ V / C . One can see that, except a t low energy where the l i m i t i s probably n o t y e t a t t a i n e d , t h e curve provides us w i t h a r a t h e r good f i t t o t h e data.
?a- -
Fig. 5 - Most probable value o f p ,
5, measured i n v a r i o u s r e a c t i o n s 0.5- 12c x
as a f u n c t i o n o f t h e r e l a t i v e ve- 14N v l o c i t y o f t h e incoming ions. Data -
a r e from refs./2-5, 16,18-22, 25- I60 .
42/, t h e l i n e corresponds t o t h e - 2 0 ~ e A
f i t given i n t h e t e x t ( f o r m u l a
(8) 1. - lo^, 0
- 5 8 ~ i +
V - LIMITS TO THE ENERGY DEPOSIT O.oI I t I t I I I I
I N A NUCLEUS 0.0 0.1 0.2 0.3 0.4
When p r o j e c t i l e s as heavy as 40Ar are used, t h e e x c i t a t i o n energy i n t h e quasi-compound nucleus can reach q u i t e h i g h values. Even i f t h e LMT i s l i m i t e d , t h e energy d e p o s i t goes on i n c r e a s i n g togeth- e r wi t h t h e bombarding energy.
Indeed, n e g l e c t i n g t h e Q-val ue, t h e e x c i t a t i o n energy p e r nucleon, e*, o f t h e incomplete f u s i o n nu- c l e u s i s r e l a t e d t o t h e i n c i d e n t 1 i near momentum, p i , by
w i t h t h e same assumptions and no- t a t i o n s as above. Therefore, i t i s p o s s i b l e t h a t we reach t h e l i m i t s o f s t a b i l i t y o f an e x c i t e d nu- cleus.
Fig. 6 - F o l d i n g angle d i s t r i b u - t i o n f o r t h e system 5 8 ~ i + 252Th a t 20, 25 and 30 MeVIu. The arrows correspond t o a c o n s t a n t value o f P f o r c e ' n t r a l a n d p e r i p h e r a l c h l i s i o n s . From r e f . /39/.
There i s now much evidence t h a t the l i m i t o f s t a b i l i t y o f excited nuclei may have been attained. The f i r s t i n d i c a t i o n o f the disappearance o f i ncompl e t e fusion was found i n the '+OAr + l g 7 ~ r , 2 3 8 ~ systems a t 44 MeV/u studied a t GANIL w i t h the angu- l a r c o r r e l a t i o n method /47/.
The same conclusions can be drawn from r e s u l t s obtained w i t h 40Ar p r o j e c t i l e s w i t h l i g h t e r targets. It appears t h a t one no longer observes ER formed i n c e n t r a l c o l l i - sions above about 35 MeV/u. As an example, Fig. 10 shows the v e l o c i t y spectra mea- sured w i t h radiochemical technics by Blachot e t a1 ./50/ f o r the system '+OAr + 1 2 Y n a t d i f f e r e n t energies. The 1 owest v e l o c i t y peak corresponds t o peripheral col 1 i sions w h i l e the highest one can be a t t r i b u t e d t o more c e n t r a l c o l l i s i o n s . One can see t h a t a t 35 MeV/u t h i s l a t t e r component begins t o disappear and has t o t a l l y vanished a t 44 MeV/u.
The same was found f o r ' + O A ~ + 68Zn /16/, ' + O A ~ + lo8Ag /32/ and '+OAr + 27A1 /30/.
Figs. 11 and 12 represent the r a t i o of the quasi f u s i o n t o the r e a c t i o n cross sec- t i o n f o r 68Zn and l o 8 ~ g targets respectively as a f u n c t i o n o f parameters r e l a t e d t o t h e amount o f energy d e p o s i t e d i n t h e system. I n both cases afuS/uR i s found t o reach zero f o r values corresponding t o about 35 MeV/u bombarding energy. For the system '+OAr + 27Al, Auger e t a1 ./30/ a l s o come t o the conclusion t h a t the ER compo- nent vanishes f o r beam energies i n excess o f 32-36 MeV/u.
It can be seen i n Fig.8d t h a t there i s no peak corresponding t o central c o l l i s i o n s w h e r e we would expect i t assuming
t h a t the system follows V i o l a systematics. The o n l y peak a p p e a c i ng around e f l d = 170 i s due t o tRe sequential f i s s i o n o f the target.
A s i m i l a r r e s u l t was ob- t a i ned w i t h a 232Th /48/
target. Other experi- ments were then perform- ed i n order t o determine the energy a t which the incomplete f u s i o n peak disa ears. For the '+OAr + 8 U system, Fig. 8 shows the f o l d i n g dis-
I I I I I I I I
- -
- -
- -
-
-
- -
-
2 4 10 t r i b u t i o n a t f o u r bom-
112 bardi ng energies between
& (PfeV/ul 20 and 44 MeV/u /47,49, 38,18/. A t 20 and 27 Fig. 7 - Most probable value of p versus f o r the MeV/u, the peak asso- same systems as i n Fig. 5. The l i n e corresponds t o pt/A = c i a t e d w i t h quasi-fusion
175 MeV/c. can c l e a r l y be i d e n t i -
f i e d while a t 35 MeV/u, a1 though there are s t i 11 events i n which f i s s i o n follows p a r t i a l fusion, i t i s d i f f i c u l t t o see a peak cor- responding t o central events. The same behaviour was found f o r the '+OAr + 232Th /36/
and 4 0 ~ r + 197Au /35/ systems f o r which the c e n t r a l c o l l i s i o n peak vanishes between 35 and 44 MeV/u.
The incomplete fusion cross sections measured by Conjeaud e t a1./36/ f o r the '+OAr +
* 3 2 ~ h r e a c t i o n (Fig. 9) present a gradual drop w i t h increasing .energy probably due t o the enhanced competition o f channels other than fusion.
0.0.
- 2 0 ~ e A -
- ''A, o -
- 5 a ~ i + -
I I I I I I I
JOURNAL DE PHYSIQUE
I 1 1 1 1 1 1
-
ul
C
1 1 1 , 1 1 1 ,
Y- 0 - +*\\ -
;L-
- .' I
@ E = 27 MeV/u
M.F. Rivet e t at, IPNO-ORE-84-32:
90 120 150 180 90 120 150 180
Fig. 8 - F o l d i n g angle d i s t r i b u t i o n f o r t h e Ar + U system a t d i f f e r e n t bombarding energies. a ) from ref./l8/, b ) from ref./38/, c ) from r e f . /49/, d) from ref./47/.
Fig. 9 - Estimated c r o s s s e c t i o n s f o r p e r i p h e r a l (-1 and c e n t r a l ( 0 ) c o l l i - sions versus bombarding energy. The cur- ve i s t h e r e a c t i o n c r o s s s e c t i o n calcu- 1 a t e d according t o /36/.
I n Fig. 13, as i n ref./31/ t h e e x c i t a - =
t i o n energy p e r nucleon, E * , i n t h e = 1000r
quasi-compound nucleus i s p l o t t e d versus b i t s mass, AR f o r d i f f e r e n t systems. For f u s i n g systems, E* i s c a l c u l a t e d accord- i n g t o formula (5) t a k i n g f o r ; t h e mea- sured value. For cases where f u s i o n was n o t observable ( f i l l e d c i r c l e s ) a LMT o f
I I I 1 I
- 'OAI- + 2 3 2 ~ h -
- m . . . % -
-
- -
- B small transfer large transfer
175 MeV/c p e r nucleon was supposed. H a l f 100 I I I I I f i l l e d c i r c l e s a r e f o r systems where i n - 30 35 d0 45 EAr (MeV/u) complete f u s i o n begins t o disappear. It
seems t h a t t h e reason f o r t h e disappea-
rance o f incomplete f u s i o n c o u l d be t h e reaching o f t h e h i g h e s t e x c i t a t i o n energy per nucleon t h a t t h e quasi-compound nucleus can c o n t a i n and t h a t t h e l i m i t i n g value depends on t h e mass of t h e nucleus, s i n c e i t v a r i e s f r o m about 5 MeV f o r l i g h t systems t o 3 MeV f o r heavy ones.
Fig. 10 - V e l o c i t y spectra o f ER f o r the system 4 0 A r + 124sn a t d i f f e r e n t i n c i d e n t energies o b t a i n e d by radiochemi c a l tech- n i c s i n /50/.
exc 1/2
T = [ E ~ ~ / ( A - / B ) ] (MeV) C N
I t can be n o t i c e d t h a t t h e h i g h e s t
E * values a t t a i n e d up t o now were achieved o n l y w i t h 40Ar p r o j e c t i l e s . T h i s explains, t h e r e f o r e , why no e x c i t a t i o n e n e r g y l i m i t a t i o n t o f u s i o n was observed w i t h l i g h t e r p r o j e c t i l e s . With = * ~ i , i t seems t h a t t h e bombarding energy was n o t h i g h enough t o reach t h e l i m i t s . I t c o u l d seem s u r p r i s i n g t h a t f o r a1 1 t h e systems where t h e p r o j e c t i l e i s '+OAr, q u a s i - f u s i o n disappears around the same i n c i d e n t energy per nucleon s i n c e t h i s should correspond t o d i f f e r e n t values o f e x c i t a t i o n energy. I n a r e c e n t work, Auger e t a1./30/ have p o i n t e d o u t t h a t t h e 1 aboratory energy per nucleon f o r which f u s i o n vanishes depends on t h e same time on t h e importance o f t h e LMT and on t h e l i m i t i n g temperature o f t h e formed nucleus. E s t i m a t i n g :
from V i o l a systematics /7/ and u s i n g t h e c a l c u l a t i o n o f L e v i t and Bonche
1111 t o determine t h e l i m i t i n g tem- eerature, they f i n d (Fig. 14) f o r
OAr p r o j e c t i l e a n e a r l y c o n s t a n t value o f about 35 MeV/u f o r t h e d i s - appearance of fusion.
The l i m i t a t i o n o f t h e e x c i t a t i o n energy per nucleon t h a t a nucleus can c o n t a i n as observed i n Fig. 13, can be understood w i t h a simple n a i v e model. One m i g h t expect a h i g h l y e x c i t e d nucleus t o completely evaporate i n t o i t s c o n s t i t u e n t s when t h e e x c i t a t i o n energy p e r nucleon i s o f t h e same o r d e r o f magnitude as t h e nucleon b i n d i n g energy, E , t h a t i s 7 o r 8 MeV. F o r n u c l e i wi!h mas- ses g r e a t e r t h a n 50 u, EB i s a de- c r e a s i n g f u n c t i o n o f t h e mass o f t h e nucleus, so we can p r e d i c t t h a t i n t e r m e d i a t e mass n u c l e i can c o n t a i n more e x c i t a t i o n energy per nucleon t h a t heavy ones.
Fig. 11 - R a t i o o f quasi f u s i o n c r o s s s e c t i o n by the r e a c t i o n cross s e c t i o n f o r t h e 40Ar + 68Zn system as a f u n c t i o n o f t h e temperature, T, o f t h e quasi compound nucleus. T i s d e f i n e d by t h e r e l a t i o n s h i p E*=a T2 w i t h a=A/8. From ref./l6/.
W i t h i n t h i s p i c t u r e , i s t o o h i g h compared t o experimental values. However, i t should be taken i n t o account t h a t very h o t n u c l e i can a l s o e m i t c l u s t e r s /25,52,53/.
I t was shown i n /49/ t h a t assuming a A;= dependence f o r t h e c l u s t e r emission pro- b a b i l i t y l e a d s t o €$,, i n q u i t e good agreement w i t h data. T h i s i s i l l u s t r a t e d on Fig. 15.
C4-284 JOURNAL DE PHYSIQUE
Fig. 12 - Ratio o f the quasi fusion cross
section by the r e a c t i o n cross section f o r nat
the system Ar + Ag versus the r e l a t i v e + Ag
velocity, V m . From r e f ./51/.
V I - LMT AND FISSION-EVAPORATION COMPETI- be - -
- ION \ %
0.4 - -
R i v e t e t a1 ./54/, i n a recent experiment, ba
found a d i f f e r e n c e i n the i j values dedu- -
ced from ER and FF measurements i n the 40Ar + l o 8 ~ g system a t 27 MeV/u, f o r
which both decay channels are opened. At 0.2 -
lower energies such a d i f f e r e n c e was not
noticed /51/ (Fig. 16). According t o the -
authors o f r e f ./54/ t h i s could be r e l a t e d
t o the enhancement o f p r e f i s s i o n evapora- 0.0 I
t e d when l a r g e temperatures are reached 0 1 2 3 4 S 1 6 7
/55,56/ : indeed i f the composite system
[ ( E ~ - V, ) / A ~ ] 1 / 2 loses too much mass due t o p r e f i s s i o n
evaporation, i t w i l l no more undergo f i s -
sion since f i s s i l i t y decreases s t r o n g l y w i t h the mass i n t h i s region o f nuclei and despite the decrease o f the f i s s i o n b a r r i e r due t o temperature and angular momentum /57/. This means t h a t only the heaviest nuclei, i.e. those produced through the l a r g e s t LMT w i l l de-excite by f i s s i o n .
Another i n t e r p r e t a t i o n can be suggested /51/ : i f we believe t h a t ER are formed i n the most c e n t r a l c o l l i s i o n s and t h a t f i s s i o n occurs f o r the most peripheral'of the c o l l i s i o n s leading t o fusion, the i n t r i n s i c e x c i t a t i o n energy, f o r a given p value, w i l l be lower f o r composite nuclei undergoing f i s s i o n than f o r those decaying by e v a p o r a t i o n due t o t h e r o t a t i o n a l energy. It i s thus possible t h a t ~ l f i ~ ~ i s reached f o r the most c e n t r a l c o l l i s i o n s and the highest p-value, making i j apparently smaller w h i l e the l i m i t a t i o n i s never a t t a i n e d f o r c o l l is i o n s leading f i s s i o n . However, based on the systematics discussed i n section V, i t seems u n l i k e l y t h a t such a l i m i - t a t i o n could be already reached a t 27 MeV/u.
V I I - CONCLUSION
The i n v e s t i g a t i o n o f central col 1 i sions a t intermediate energies was made possible by the new accelerators. We have learned t h a t f o r heavy i o n p r o j e c t i l e s the l i n e a r momentum t r a n s f e r t o a composite system seems t o be 1 i m i te d t o around 175 MeV/c per i n c i d e n t nucleon, a value which i s roughly independent o f the p r o j e c t i l e and target.
Furthermore, i t appears t h a t w i t h 40Ar o r heavier p r o j e c t i l e s , the energy deposit i n the system can reach the l i m i t i n g value above which the composite nucleus loses i t s cohesion, r e f l e c t e d i n the vanishing o f incomplete fusion process. Further expe- riments i n v o l v i n g l i g h t e r p r o j e c t i l e s a t higher energies than those used up t o now, o r heavier p r o j e c t i l e s , would be needed t o confirm t h i s hypothesis.
Several d i f f e r e n t models are available, a l l o f which reproduce the data reasonably well. Even so, many questions are s t i l l unanswered concerning the mechanisms respon- s i b l e f o r the 1 im i t a t i o n s i n l i n e a r momentum t r a n s f e r and e x c i t a t i o n energy, the processes which take the place o f fusion a t higher energies and the onset o f m u l t i - fragmentation.
I t i s a pleasure t o thank B. Borderie, A. Demeyer, D. Guinet, D. Jouan, J. Natowitz, C. Ng6. M.F. R i v e t and C. Volant f o r f r u i t f u l discussions and f o r permission t o use some r e s u l t s before publication.
Fig. 13 - E x c i t a t i o n energy per nucleon, c*, deposited i n a quasi compound nucleus o f mass AR. The f i l l e d c i r c l e s correspond t o systems /47,48,30,32,50/ where there was no f u s i o n . I n t h a t case e* i s c a l c u l a t e d assuming t h a t /A = 175 MeV/c. H a l f f i l l e d c i r c l e s are f o r systems /49,50/ f o r which fusion beglns t o disappear. The dashed area i n d i c a t e s the region where e* seems t o reach i t s 1 imi t i n g value.
Sym .
0 I I I I I
60 120 180 240
Composite nucleus mass ( u )
Fig. 14 - Laboratory energy per nucleon such t h a t the c r i t i c a l temperature i s reached f o r an e f f e c t i v e composite nucleus o f mass A. The f u l l l i n e i s f o r '+OAr induced reactions, the dashed l i n e f o r 1 * C induced reactions and the dot-dashed f o r symmetric systems. From r e f ./30/.
C4-286 JOURNAL D E PHYSIQUE
2
0 50 100 150 200 250
MASS [amu) 0.0
2 3 C 5 6 7 8 9 1 0
Fig. 15 - Maximum e x c i t a t i o n energy f o r ( MeV /u I " ~ n u c l e i along t h e beta s t a b i l i t y l i n e ,
c a l c u l a t e d assuming t h a t c l u s t e r s o f mass Fig. 16 - Most probable percentage o f A a r e formed w i t h a p r o b a b i l i t y Am'. The LMT as a f u n c t i o n o f fl~ f o r t h e Ar + c a l c u l a t i o n i s made f o r d i f f e r e n t T values Ag system, measured though ER v e l o c i t y ( from r e f . /49/). spectra (R) o r FF angular c o r r e l a t i o n (F) t h e l i n e corresponds t o V i o l a sys-
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