LIGHT-PARTICLE EMISSION AT HIGH ANGULAR MOMENTUM

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LIGHT-PARTICLE EMISSION AT HIGH ANGULAR

MOMENTUM

J.P. Wurm

To cite this version:

J.P. Wurm.

LIGHT-PARTICLE EMISSION AT HIGH ANGULAR MOMENTUM. Journal de

Physique Colloques, 1980, 41 (C10), pp.C10-200-C10-216.

�10.1051/jphyscol:19801021�.

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JOURNAL DE PHYSIQUE CoZZoque CIO, suppl6ment au n012, Tome 41, dgcembre 1980, page< ,C10-200

LIGHT-PARTICLE EMISSION AT HIGH ANGULAR MOMENTUM

J.P. Wurm.

~ a s c - ~ z m c k Institut fiir Kernphysik, HeideZberg, R.F.A.

1. Introduction

Emission of light particles from nuclear species at high angular momentum and excitation is a topic of long standing; yet, the

L.

discovery of deep-inelastic collisions has given a reviving impact to it as a possible

1 probe of nuclear equilibration phenomena

.

Dissipation seems to start as soon as the two ions collide and may or may not result in a compound nucleus in which all degrees of freedom, including the shape, are in a state of thermal equilibrium.

It might be worthwile to recall that o u ~ knowledge on nuclear behaviour at high angular momentum has almost entirely been col- lected by spectroscopy of cool nuclei. The 1

highest levels from which transitions are resolved in y spectra are within a very few MeV of the yrast line. Continuum y rays go up to and somewhat beyond the partic& bin- ding above yrast. So, the interesting physics as far as experimentally accessible dwells in a narrow region above the yrast line where the lifetimes are long and measure by picoseconds. By all standards, such nuclei are in a state of perfect equilibrium with respect to energy, angular momentum of their constituent nucleons, and also with respect to their shape.

.

'

In contrast, particles are being emitted

,

from regions tens Of MeV above yrast where nuclear behaviour is described without gross inaccuracies by models which are either classical' (Liquid Drop Model), or simple (Fermi Gas Modgl)

-

which merely states our yet insufficient knowledge. Trying to gain new experience, particle studies are done now at many laboratories, 'investigating the decay modes af nuelear systems with excitation energy aboua,l00 Mev and 'at angular momenta approaching the "l,Mit of their stabiiity.

Emission times for the first steps in the cascade are short enough to encounter nuclear systems remote from equilibrium. To give an example: at sufficiently high excitation, a damped binary system presumably undergoes particle decay faster than it takes to equilibrate its shape, so that there is the intriguing possibility to study the nascent, superdeformed2 stage of what will develop into a compound nucleus eventually.

The various stages of particle emission accompanying the evolution of the heavy-ion collision are sketched in Fig.1. Facing a highly complex situation, it is an all important question to which extent the experiment can provide us unique sign tures. Such is probably the case for some of the very early stages, and as I shall show below, for the late stages: break up, of the projectile, at the very beginning, and decay from equilibrated fragments at the very end, both established by fragment-particle correlation experiments. In between, the formation of Volcovs di-nuclear system (DNS) due to friction, as a quasi-stationary point

, ig

.

1

.

View of particle emission along the evolution of the heavy-ion collision. For other reviews see note at end of reference list.

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in the evolution, might provide us with a meaningful distinction into

(i) emission during the approach phase til, say, the DNS has been formed with considerable equilibration regarding the N/Z ratio, the energy, the angular momentum, e.g., and (ii) emission accompanying either the further evolution of the DNS into a compound nucleus (shape equilibration), or accompanying its fragmentation into deep-inelastic fragments and evaporation thereafter.

The first category comprises break up of the projectile with varying amount of partici- patiod of the targdt3,

.

including "deep-inelastic break upn4 and "pre-emission"5 as well as "promptly emitted particles"(~~~)', "Fkrmi jetsn7 as a physical consequence of two interpenetrating Fermi gas containers, or potential wells8. Experimental evidence of these mechanisms is still in debate. The same is true for emission from "hot spotsw 9 or hot zones -presumably on the borderline of categories (i) and (ii)- despite the fact that this concept has found a remarka- ble echo in a number of studiesi0. Category (ii) comprises the recently proposed1' "pre- equilibrium evaporation" of the DNS, scission a's and evaporation from fragments.

In passing through this vocabulary, it appears that the role of high angular momentum being of collective nature, is restric- ted to the later stages. However, high angular momentum and pre-equilibrium emission might not be antagonistic concepts altogeth- er, and following a suggestion of the organ- izers of this Conference,

I

shall try to elaborate somewhat on this interesting per- spective.

To be specific, I have chosen three chapters for my talk. The first deals with particle evaporation from deep-inelastic fragments, to determine their spin and spin alignment, and it is based on measurements, a good part o f which were done.here in Stras- bburg in collaboration with Dr. Scheibling

an'd t i i s group. A mo*e sketchy discussion of pre-equilibrium emission follows. In view of the sfrong.demand for experimental time scales, the third part reports on an experiment designed to measure emission times for a highly excited compound nucleus, using particle-particle correlations.

2. Particle Evaporation from Deep-Inelas- tic Fragments: Spin and Alignment I shall restrict the presentation of data to two systems: the light system 96 MeV

1 6 0 + 5 8 ~ i studied at Strasbourg and Heidel- berg 12,13 and thoroughly investigated also by y cicular polarization14 and fragment- neutron coincidence experiments15; and the system 400 MeV ' O A ~ + ~ ~ N ~ studied at ~ ~ 1 1 9 , 2 7 .

A measurement of the intrinsic angular momenta of the fragments requires that

(i) the source is unique and identified, (ii) the source is in thermal equilibrium. The sources are identified by the velocities of the particles detected at various detec- tion angles, for fixed deep-inelastic binary Q value, mass or Z and angle of the light fragment detected in coincidence. An example

Fig.2 Velocity diagram for the 400 MeV ' O ~ r i ~ ~ ~ b reaction, Q=-160 MeV, together with velocity spectrum of a particles detected at -480

is given in Fig.2 showing a clean separati,hn of a's from the fast-moving Ar-type fragmelirt and f r o m the slower Nb-type fragment.

. .

Because of the presence of pre-equilb- b r i m emission .at forward angles (see beiow) spin determinations have to be don,e,:in. the backward hemisphere. Once the source ;has,

.

been identified, some necessary. coh9Stions for' equilibration can'be tested by' traqdfop-

. ,

ming yields and ene'rgies event by eventl+int0

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JOURNAL DE PHYSIQUE

4

Fig.3. Differential a multiplicity dM/dR, the most-probable energy

!&,

and a shape parameter T describing the fall-off in the a spectra, in the rest frame of the heavy fragment

At backward angles opposite to the light- fragment detector (Ar type), a particles originate entirely from the heavy fragment

(Nb type), and constancy of yield and shape of the spectra for @a> 60° (80° lab) indicates equilibration. The energy well agrees with Coulomb repulsion for Nb-fragment decay (the corresponding velocity is that of the upper circle in Fig.2) and the shape parameter T is also consistent with this assumption (Fig.3).

When describing the decay of equilibrated fragments in analogy to CN evaporation, an important difference is evident. It arises from the fact that DIC are mainly binary reactions and conservation laws do not -as in fusion reactions- play a decisive role. Rath- er, the sharing of energy, angular momentum and its substate population are the result of the very nature of the dissipative collision process implying fluctuations around average values.

The average angular momentum of the fragments can be classically considered to be induced by tangential friction forces with the tendency to reach rigid rotation, a concept which is also quantum mechanically meaningfLl as it 'marks the state of maximum level density1 for frozen shape of the DNS. This "sticking limit" of the fragment spins

is given by the moments of inertia 0 and the initial (and usually total) angular momentum Ri as

for fragment no. I, and pR2 denotes the rela-

tive moment of inertia of the two fragments in the di-nuclear configuration.

The particle decay from a fragment with its spin Jo pointing in the direction normal to the reaction plane will display an anisotropy in yield with respect to this axis. The physical reason of this anisotropy is the tendency towards maximum level density in the residual nucleus. Because of the ex- ponential decrease of the density with spin, stretched transitions with

Ia

1 1

So

will be the most probable ones, and peaking therefore will occur in a plane orthogonal to 50, in the reaction plane(Fig.4).

The problem has been treated in the spi- rit of the statistical model in, a semi-classical manner by Ericson and Strutinski back in 195816. A result more useful for coincidence studies where Jo points in a fixed direction has been given by Th. ~ d s s i n g l ~ :

describes the angular distribution of the particles at angle 8 with respect to the spin axis of

So,,

and th,e, temperature, T ,and moment of inertia O refer to the residual nucleus. The expression is recognized as a

Boltzmann factor in the rotational energy of the particle at geographical latitude 8 18 on \he surface O F the spinning nucleus

.

For practical purposes it should be noted that parameters O,T in a formally identical expression for a rotating Maxwell gas refer instead to the decaying nucleus.

Geometry of particle decay. Spin

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Let us see then the results of fragment- light-particle correlation experiments, in which the particle telescopes are moved out of the reaction plane (Fig.5). For the

Resct~on Plane heavy -I

F,ig. 5 Typical geometry for out-of-plane cbrrelation measurements .between a moving light-particle detector and a fixed fragment detector (for O+ Ni).

400 MeV Ar+ Nb reaction, the coincident out- of plane yield for a's and protons is displayed in Fig. 6.

O ~ , P = 90' denotes the reaction plane. Proton distributions are con- siderably flatter than those of a particles, which is expected from eq.(l), but in addi-

Fig.6 a and proton out-of-plane distributions for three in-plane angles

@.

400 MeV 4 0 ~ r + ' = ~ b . Ref. 19.

Fig.7. Data of Fig.6, summed over the three in-plane angles.

tion, protons come from all stages of the cascade, while a's are dominantly first chance. As there is no significant dependence on the in-plane angle, the data is summed, Fig.7, and displays more clearly the small proton anisotropy.

Results for the 160+ 58Ni reaction, at 96 MeV, are shown in Fig.8, protons and a's were detected in coincidence with C ,N,O . ' ,

fragments at deep-inelastic Q values.

Fig. 8

.

Out-of-plane distributions of a's and ;pro-

tons in coincidence with d.i. C ,N,O frag-

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C10-204 JOURNAL DE PHYSIQUE Our c o n s i d e r a t i o n s o f t h e p a r t i c l e de- c a y up t o now were b a s e d on a f i x e d s p i n a x i s . I f t h e s p i n s a r e d i s t r i b u t e d i n d i - r e c t i o n , a s a r e s u l t o f s p i n f l u c t u a t i o n s , a p p l i c a t i o n o f e q . ( l ) t o d a t a w i l l y i e l d v a l u e s ' o f Jo t o o s m a l l . L e t ' s f i r s t s e e t h e p h y s i c s o f t h e s e f l u c t u a t i o n s and t h a n l o o k f o r a n improved v e r s i o n o f e q . ( l ) . D i s s i p a t i o n , we a r e t a u g h t by s t a t i s t i - c a l mechanics

,

necessarily i n t r o d u c e s f l u c - t u a t i o n s i n t h e q u a n t i t y c o n s i d e r e d . Ndren- b e r g and Wolschin h a v e a p p l i e d s u c h a t r a n s p o r t d e s c r i p t i o n o f d e e p - i n e l a s t i c c o l - l i s i o n s a l s o t o a n g u l a r momentum20. Micros- c o p i c a l l y , f l u c t u a t i o n s seem t o a r i s e , a t e n e r g i e s below 20 MeV/u, n o t s o much by n u c l e o n - n u c l e o n c o l l i s i o n s , b u t r a t h e r by n u c l e o n s exchange.@ t h r o u g h t h e window o f t h e c o n t a c t zone between t h e i - n t e r p e n e t r a - t i n g i o n s which t h e n c o l l i d e w i t h t h e i r ad- d i t i o n a l momentum w i t h t h e boundary o f t h e p a r t n e r 2 1 . O t h e r t h e o r i e s a r e r e v i e w e d i n R e f . 1 . I m e n t i o n t h i s t o u n d e r l i n e t h a t o u r u l t i m a t e aim i n m e a s u r i n g m a c r o s c o p i c quan- t i t i e s l i k e a v e r a g e f r a g m e n t s p i n and align-

-- ment i s t o learn about t h e m i c r o s c o p i c , o r c o l l e c t i v e p r o c e s s e s , by which c o l l i d i n g i o n s d i s s i p a t e r e l a t i v e a n g u l a r momentum. A more p e d e s t r i a n view o f s p i n f l u c t u a t i o n s i s d e p i c t e d i n F i g . 9 . F i g . 9 . ,View o f e l e m e n t a r y a n g u l a r momentum t r a n s f e r s , a d d i n g up i n a more ' c o o p e r a t i v e ( a ) , o r more random way

( b ) .

' T o a c c o u n t f o r t h i s composite of c o r r e l a t e d g r a n s f e r and, random walk i n t h e p a r a m e t r i - z a t i o n o f d a t a , w e c h o o s e a v e c t o r s p i n d i - , s t r i b u t i o n c o n s i s t i n g o f a "macroscopic1' s p i n Jo a l i g n e d a1orig.th.e .normal t o t h e re- & t i o n p l a n e a n d . $ ' f ~ u c t u a t i ' n ~ s p i n v e c t o r a s a g a u s s i a n random v a r , i a b l e . w i t h z e r o mean a n d v a r i a n c e 05. The a v e r a g e s p i n t h e n i s e q u a l t o J o , and t h e r e s u l t i n g s p i n d i s - t r i b u t i o n i s F o l d i n g W(B) o f e q . ( l ) w i t h t h i s s p i n v e c - t o r d i s t r i b u t i o n r e s u l t s i n a n e x p r e s s i o n f o r t h e o u t - o f - p l a n e d i s t r i b u t i o n w(8;u3+o) i n which t h e e x p o n e n t i n e q . 1 i s m o d i f i e d b y a f a c t o r A f i n i t e

03,

o r i n c o m p l e t e a l i g n m e n t , w i l l d e c r e a s e t h e a n i s o t r o p y W ( 90' ) /w(o0 )

,

a s e x p e c t e d i n t u i t i v e l y . We a r e now i n n e e d o f a n a d d i t i o n a l p i e c e o f i n f o r m a t i o n s i n c e Wfe) i s n o t s u f - f i c i e n t t o d e t e r m i n e b o t h Jo a n d 0 g . A somewhat l u c k y e s c a p e f r o m t h i s dilemma, f o r t h e d a t a o f F i g . 7 , i s d e m o n s t r a t e d i n F i g . 1 0 . I n v o k i n g t h a t Jo c a n n o t e x c e e d t h e l o a-particies

-11

F i g . 1 0 . Region i n t h e { J o , 0 3 } p l a n e as d e f i n e d by t h e a d a t a o f F i g . 7 , w i t h s t a t i s t i c a l e r r o r s . Sticking l i m i t o f Jo i s i n d i c a t e d . s t i c k i n g l i m i t , we d e r i v e a m e a n i n g f u l up- p e r l i m i t a j

s

1 2 TI. C o n v e r s e l y , a lower! l i m i t o f J ~ & 2 8 h c o r r e s p o n d s t o c o m p l e t e

a l i g n m e n t , u;7= 0 . The p r o t o n d a t a are con- s i s t e n t r e g a r d i n g Jo, b u t much less c o n c l u - s i v e r e g a r d i n g

03.

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moments of the y multiplicity12. I have no time to enter the discussion of the somewhat tedious procedure to relate the multiplicity moments to those of the primary spin dis- tribution13. It is important

,

however, to re-

alize that the width o of the primary

I

J I

distribution of spin magnitudes, as derived from the variance of M ,relates to spin

Y

Eluctuations only for light systems, like 0 + Ni at 6 MeV/u where the Ri window for deep-inelastic collisions is presumably very small. The multiplicity measurements are shown in Fig. 11.

1

O 0 10 20 30 40 - Q (MeV)

Fig.11. Average value and width of the

y multiplicity for the system

96 MeV ' 6 0 + 5 s ~ i , in coincidence with carbon ( 8 ) and oxygen (0) fragnents.

The combined analysis of particle and y data for 0t Ni uses a quantum mechanical expression for W(B) devised by Ddssing and described in Ref.13. The density matrix is assumed to be diagonal and given again by the spin distribution of eq.(2). The spin dependence of the a decay probability is taken from a statistical model calculation. The results are displayed in the (Jo, aj} plane in Fig.12. Three types of trajectories corresponding to the three experiments can be distinguished: the measured a out- of-plane anisotropy-A

,

with its errors, defines a band swinging to the right and up for larger

UZ.

The average of the spin magnitude <

131

>

,

derived from <M > ,decreases

Y

first slowly, then rapidly with 03. The

Fig. 12. Trajectories for combined analysis of particle and y data, see text. 96 MeV '60+ " ~ i . a parti-

cles.and y rays coincident with oxygen fragments.

experimental errors here are negligable, the uncertainties in deriving the primary spin considerable (hatched field). The widths of the spin magnitude distribution, from U Y'

yield trajectories running almost vertical- ly. Only the region between the inner two lines is due to the experimental error.

The result is not very comforting as the cores of the three branches dont overiap. Although, I think, the uncertainties which come especially into the y data analysis have been generously assessed, the poor con- sistency might just point to them. A more interesting version is given below.

An equivalent description of the spin distribution is provided by the alignment parameter 18

expressing the semi-classical tilt angle. The PZZ values for the data presented range

between 0.65 and 0.8.

It is interesting which equilibrium, or long-time limit,is .to be expected for UJ.

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c10-206 JOURNAL DE PHYSIQUE

separation into the fragments. A simple equipartition estimate, assuming 3 indepen- dent rotational degrees of freedom, yields a$= 30T, which amounts to OJ= 8.811 and 175 for Ni an Nb, respectively. A probably much better assumption is that the fragments in equilibrium form a rigid rotor which ad- justs to a statistical K distribution. The spin distribution of the fragments is then

composite system fragment

Fig. 13. K distribution of the DNS in equilibrium ( a and resulting fragment spin distribution after scission along the synanetry axis (b).

obtained by use of the standard23 assumption that the complex scissions along the symmetry axis. An elaborate discussion of the long-time limit of a 3 involving various collective degrees of freedom, like bending and wriggling modes, has been given by Moretto and ~ c h m i t t ~ ~ . These modes result in additional spin fluctuations.

I have the strong impression that an important dynamical aspect has been neglected so far. Within the rotating DNS, the fragments are exposed to a large inertial or centrifugal force which tends to disrupt the system in a direction perpendicular to

a

the rotation axis (J or z axis in Fig.13).

In consequence, the fragment spin distribution, after separation of the complex, will be re-aligned. Such an effect is of mere academic interest for low-energy fission, and not mentioned i n the book23; stili - small for sequential fission of deep-indas- tic- fragments, it gr0w.s to size for the large aggular domenta of a DNS, as a simple consideration of the balance of forces (Fig.14) shows: For the example of the- 400 MeV ~ r + Nb reaction, a DNS formed by .

Ri=

120% (20.8% ) and assumed to carry an

gr

alignment of PZZ= 0.6 (zBrms= 30') only, will by centrifugal re-alignment result in a h%ghly . aligned , ,fragment spin distribution,

I \

Fig.14. Centrifugal re-alignment by which the 8 distribution in the DNS is focused into a sharper 8' distribution of the fragments. Scission as-

sumed in direction of the combined force.

with PZZ= 0.9

(=qms=

16'). I note here in parenthesis that the combined experimental results analyzed in Fig.12 might be taken as evidence that the x,y components of 05 are significantly smaller than its z component, due to this effect.

The experimental determination of the size of spin fluctuations and the question of their physical origin is an important matter. I have to conclude that it remains completely open today, whether measured variances, including those from sequential fission studies25, correspond to equilibration in some way or the other, with regard to which collective degrees? Or whether variances are enlarged by non-equilibrium con- tributions and quantum fluctuations. Anyway, progress apparently needs'both, improving ' our experimental skill and further theoreti- cal guidance.

3. Fast Particle Emission: A Consequence of High Angular Momentum ?

The idea is not as curious as it might appear, as we are aware that deep-inelastic collisions themselves proceed faster than compound-nucleus formation due to lack of stability for high partial waves

(J. ~ i l c z ~ n s k i ~ ~ ) . Why should we not encounter similar physics in particle emission? I like to present some evidence that we actually do.

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brium pattern as it is observed in collisions with sufficiently fast projectiles, again for the example of 400 MeV 4 0 ~ r + 9 3 ~ b , Ref.27, which is shown in Fig.15 for a particles in coincidence with Ar-type fragnents-:

0.6 400 MeV + 9 3 ~ b

-

in plane angular

t

correlat~on ~ ( ' ~ 0 ) = 1 0 1 MeV

I

101 M e V " O + L 8 ~ i C - a Coinc. eL,,(c) = 30°

-7

6; (degrees)

Fig.15. In-plane correlation of a particles with light fragments detected well behind the grazing angle at position labeled H.I. 8 = 0 refers to recoil direction of heavy fragment; angleand yield in this rest frame.

Events are deep-inelastic (Q" -160 MeV) and

originate from Nb-type fragments, with some uncertainty close to the beam direction. The a channel seems to be the most favoura- ble one to observe pre-equilibrium emission, as there is little multiplicity from later, equilibrated stages of the cascade.

This pre-equilibrium emission has many sjmilarities .to the one observed in -the

8 8

96 ' M ~ V 04 Ni system 'which, was inierpre?ed

by Ho et a1. as evidence for emission

from a hot zone. There is considerable interest to look for a "shadow" in the angular correlation, on the side of the light- fragment detector, as this is considered to be a strong evidence for a hot spot me- chanism2*. Possibly, such a shadow has been observed for the 101 MeV 160+ " ~ i system by the Strasbourg group29, and I like to

Fig.16. Carbon-a correlation for 101 MeV l60+"~i, as presented in a Contri- bution to this Conference ,Ref. 29.

show their data in Fig.16. The correlation is for a selection of deep-inelastic events for which the 160 excitation remains below the effective a threshold. If substantiated, the shadow is indeed remarkably deep and sharp.

I like to convince you now, that we observe two different mechanisms in the Ar+ Nb reaction. Evidence for a "direct" component evolves from close inspection of a velocity spectra taken at forward lab angles. where a shoulder emerges which has about beam velocity (Fig.17). Gating on the

"direct" a's does not change the energy distribution of the coincident projectile-like fragments in a significant way. This invites to interprete these a's as being emitted prior to deep-inelastic scattering of the remainder of the projectile27. Much further support to this conjecture is given by a- light fragment correlation experiments pro7

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JOURNAL DE PHYSIQUE

Fig. 17

.

Coincident a velocity spectra at 4 lab angles revealing a "direct" component of about beam velocity (full line). 400 MeV "Art 93Nb, geometry as in Fig.2. Coulomb escape velocity from Nb-like fragment is also shown (dashed line).

Fig. 18. In-plane correlation of a particles with various light fragments for the system 148 MeV "N+ '@Ni. Solid curves are derived from singlesa an@= distributions.

Frwn

Ref.30.

that the a particles are emitted at an early stage, prior to the formation of the deep-inelastic fragments.

Fig.19 depicts the concept of what might be called the "incomplete collision": the emission of an a particle with momentum

"masswe transfer" incomplete fusion

Fig. 19. The incomplete collision, a concept linking break up and incomplete fu- s ion.

close to what it was inside the projectile precedes the scattering -or fusion- of the remainder of the projectile. While the a particle is more of a spectator, the projectile residue experiences various degrees of energy and angular momentum dissipation. The incomplete fusion, observed already by Sikkeland et al.31, has recently come intense- ly into discussion, stimulated by very in- formative experiments 32. At the early side, quasi-elatic brek-up has also been studied recently by correlation experiments, as mentioned above.

Its direct character quite obviously established by the large forward momentum, it is interesting to regard the fast a ,emission from a phase space point of view. Re- garding the DNS as a stationary- point in the evolution, its available level density is the this Conference., and part of the data is

larger, the smaller the amount of energy'is shown in Fig.18. The authors show that the

which is tied up in collective rotation., c.oincident crass section for a particles

Fast a emission, removing a large amount of

well factori,ze~ into a product of the sing-

angular momentum from the system, is there- les cross section

for

,a emission and the

fore statistically favored. To show that it s-ingles, heavy-ion cross ,section. They infer

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potential diagram (Fig.20) for the somewhat simplistic configuration of an a particle riding on the outer tip of the rotating di- nuclear system. It is apparent that the a

1 ;

-@&BE

(MeV)

F:g. 20. Potential diagram for an a par- tical in configuration depicted for a grazing orbit, Coulomb and centrifugal potentials superim- posed in the upper curve. Sketch of situation for 400 MeV 40Art 9 3 ~ b .

becomes unbound already by the Coulomb potential of the nearby target, but even more so due to the large centrifugal potential felt in its orbit around the common centre of mass. The centrifugal potential probably builts up very rapidly as soon as contact foqces between th& holliding partners

' become effective, much earlier than rigid rotation sets in. A rough estimate for this case, o f t h e relative a escape probability as a function of the angular'momentum brought into the collision, is given in Fig. 21.

Despite their simplicity,these argu-

, ments were given in order to show that "direct"

emission patterns might a180 evolve from a statistical and dynamical consideration of the very specific initial configuration encountered in deep-inelastic collisions being characterized by very high angular. momentum and highly non-spherical boundaries.

Maybe, a "constrained phase-space anlysis" as very successfully applied33to direct multi- nucleon transfer reactions, could provide a sound basis.

Fig.21. Estimate of relative a escape probability, combining pase space

(dashed) and barrier penetration, as funcion of R. Relates to Fig.20.

It is very interesting to follow this concept alongside the evolution of the DNS. Because of large viscosity, its shape ad- justs only slowly ( T ?hapel 2. . 4 x _s

,

Ref.1) -if at all- to the potential miaimum

/

of equilibrium shape of the compound nhcle- us, at given angular momentum.

In Fig.22,I show a schematic diagram of two Yrast lines, .one fdr the di-nuclear system, and one for the compound nucleus, sup- posedly in its equilibrium shape. The two

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yrast lines are displaced by an amount Q become effective can be imagined than the

which is the energy set free -for the DNS, in thermal or angular momentum equi-

light system under consideration- when the librium or not, but prior to shape equili-

two ions at contact are fused into a sphe- bration.

rical, non-rotating compound-nucleus. The arrow in Fig.22 indicates, that particle emission again is favoured by phase space, and that it is expected to strongly enhance

(incomplete) fusion of high partial waves. PUhlhofer has recently discussed his evaporation residue data for the reaction

MASS NUMBER

Fig.23. Mass distributions of evaporation residues for the reaction

it

''M~+ ''~e \at three energies

C

histogram ) dc- to CASCADE calculations without defdrmation,

(heavy lines )

.

From Ref. 34.

Tit Mg in terms of "pre-equilibrium evaporation", i.e. for the rotating, highly defor- med DNS. Such, he seems to explain the the large yield for multiple a emission which cannot be accounted for by evaporation calculations wiThout gross deformation.

Supkrdeformation of compound nuclei induced'and together with high angular momentum, eventually, has been shown by Blann et al. 35 to enhance

a'

emission over fission; and the results of the calculations for l b 9 ~ b compound nuclei are shown in Fig.24. No better conditions for such mechanisms to

Fig. 24. Partial decay probabilities for a, n, p and including fission ( f ) , for

"

9 ~ b at 120 MeV df excitation, as function of I. Calculations for spherical (full) and defomd nuclei (bm- ken). k o m Ref.35.

On occasion of this Conference, I tried to put the discussion of the high-angular momentum aspect in pre-equilibrium particle emission into the foreground; a ground not always quite firm is probably typical of a novel and exciting field.

Two-Particle Correlations: A Method to Measure Compound-Nucleus Emission Times ?

As the importance of time scales all along the heavy-ion colllsipn is quite evident, I like to close my talk by presenting an experiment which is devised to measure

, , emission times for a highly excited CN, in the range below 10-*~s.

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particles in coincidence from

an incoherent source (CN). It turned out, however, that the final-state interaction (FSI) between, say, two a particles or two protons, is by far dominant, and the quantum interference was not observed.

FSI

might not at all turn out to be in- ferior as a, tool to measure lifetimes: it is the effective distance r12 between the particles in the neighbourhood of the source which decides upon whether the interaction between the particles V(r12), Coulomb and nuclear, is effective in distorting particle spectra and yields. For a CN of lifetime T , and assuming here that T is the

same for the daughter nucleus, the mean separation is equal to the distance travelled by the first particle during T

Denoting the coincidence yields, or spectra, by CI2 and C13, respectively, CN symmetry

asserts that C = C

-

in the centre

of mass, and therefore C12= C13 in the la- boratory system. The last relation does not

_-

hold exactly since the recoil of the daughter nucleus enhances the solid angle for pair (1,3) by a small amount over that of pair (1,2) in the centre of mass. The detector assembly actually used in the experiment

The experiment was done at the Heidel- berg post-accelerator38 by choosing the reaction 144 MeV 1 9 ~ t 5 ' ~ + ''~e, achieving 122 MeV of excitation in this CN.

Fig. 25. Geometry chosen to detect interference or FSI effects in 2-ppr- ticle correlations from CN decay showing up in detector pair (1,2) while pair (1,3 ) is for comparison.

It is essential in such an experiment to supply simultaneously a .measurement of two-particle spectra undistorted by the effect to be observed, under otherwise identical conditions. For CN decay, the geometry shown schematically in Fig.25 comes close to this ideal. Detectors are arranged on a cone of constant scattering angle 0 ,assu- ring identical singles spectra; the "signal" expected to show up in the close pair (1,2) may be compared to the "background" in pair

Fig .2 6

.

Assembly of Si detectors. Flower and single detector on opposite sides of beam. Centres of closest neigh- bors are separated by A $ = 4'.

is shown in Fig.26. Particles were identified by their time of flight (pulsed beam), to have precise energy calibration.

Fig. 27. Difference-energy spectra of aa coincidences for the far geometry

A$- 1 7 6 h e f t : true coincidences Right: random coincidences for different beam pulses.:

The two-particle spectra are displayed as a function of the difference energy

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c10-212 JOURNAL DE PHYSIQUE

totally random spectrum (right) reveals better than any calculation that a compound nucleus at such high excitation energy behaves in the first place like an oven. So, Fig. 27

,

left, provides the reference or background spectrum, and it originates apparently from a highly statistical source. In Fig.28 two difference-energy spectra measured in close geometries are shown in comparison. The dominant feature are two peaks symmetric to zero difference energy, which originate from break up of *~e(~.s). Due to the long-lived ground state and the sm-all Q value of 92 keV, these peaks move as a function of A + in a very distinctive way, and disappear for A $ > 30'.

,Fig

.'

28. aa' dif f erence-energy spectra for two close geometries (top and middle), together with reference spectrum. Arrows label peak in. ~ ~ ~ ( 1 7 6 ~ ) for comparison of relative cross sections.

Fig.29. Plot of the quantity SI2(AE), de- fined in text, for aa and pp cor-

0

relations in 4 geometry. Offset merely to avoid neg. numbers.

Before returning to the possible origin of ,the 'Be(g.s.) events, the smooth part of the

spectea under the peaks deserves a closer inspection. TQe data of Fig.28 show that the absolute yield

'cI2

(4' ) is only about half of CI3(176O ) at AEe '0,. despite the tails- from the Be peaks.

In order to do a close comp'arison in- dependent from possible normalization'errors and derive the "signal" from the "noise", we use the quantity

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The o b s e r v e d e f f e c t s a r e by f a r t o o l a r g e , and o f wrong AE dependence, t o be ac- c o u n t e d f o r by r e c o i l e f f e c t s . The d e p l e t i o n o f , t h e s m a l l - a n g l e a a c o r r e l a t i o n , c l e a r l y , i s j u s t o p p o s i t e t o a c o n s t r u c t i v e boson i n - t e r f e r e n c e .

We a r e n o t aware o f any o t h e r example o f a s t a t i s t i c a l n u c l e a r r e a c t i o n i n which e f - f e c t s o f t h e mutual i n t e r a c t i o n between two emerging p a r t i c l e s have been o b s e r v e d . On t h e o t h e r hand, t h e environment o f a CN e m i t t i n g , even a t v e r y h i g h e x c i t a t i o n e n e r - g y , p a r t i c l e s w i t h s m a l l k i n e t i c e n e r g i e s from i t s s u r f a c e , f a v o u r s t h e low r e l a t i v e momenta a t which t h e a t t r a c t i v e s-wave nuc- l e a r i n t e r a c t i o n dominates. Here, ' ~ e ( ~ . s . ) comes i n t o p l a y , i n a t w o f o l d way: f i r s t , G . ~ e r t s c h ~ ' , and t h e c a l c u l a t e d f o r m a t i o n p r o b a b i l i t y f o r Be, g i v e n e l s e w h e r e 3 6 , a r e c o n s i s t e n t w i t h t h e l i f e t i m e s e s t i m a t e d below. Here, I l i k e t o g i v e o n l y a l i n e of t h o u g h t , r a t h e r t h a n p r e c i s e r e s u l t s , how t h e l i f e t i m e can be d e r i v e d from t h e measu- r e d d e p l e t i o n p a t t e r n , along with questions

( i ) and ( i i ) . ( i ) For c o a l e s c e n c e t o o c c u r , t h e t w o a par- t i c l e s must e n t e r a s p h e r e o f r a d i u s RBe. For t h i s t o happen, t h e f i r s t - e m i t t e d p a r - t i c l e i s a l l o w e d t o t r a v e l a t most a d i s t a n - ce R ~ e b e f o r e t h e second i s e m i t t e d . Deno- t i n g t h e a v e r a g e v e l o c i t y a t t h e s u r f a c e by < u > , T 6 RBe/<u>, and s i n c e t h e a v e r a g e k i n e t i c e n e r g y a t t h e s u r f a c e i s e q u a l t o T, we o b t a i n f o r RBe= 4fm and T= 3 . 5 MeV

-r 3 . 1 x 10-22s. synthesis of Corresponds to momentum distribution SO MeV/c wide decay of 8 ~ e g , , .

F i g ; 30.. View o f s y n t h e s i s and decay o f ' ~ e ( ~ . s . ) from two a particles. i t s f o r m a t i o n due t o r e s o n a n t s-wave i n t e r - a c t i o n i n t h e n u c l e a r h a l o d e p l e t e s t h e smooth background o f a a e v e n t s .

Second, i t s decay some 1 0 - ' ~ s l a t . e r a d d s two d i s t i n c t peaks i n t h e s m a l l - a n g l e AE s p e c t r a

( F i g . ?o,).:

Two q u e s t i o n s have '

primarily'

t o be an- swered: how does t h e l i f e t i m e o f t h e CN i n - f l u e n c e ( i ) t h e p r o b a b i l i t y o f c o a l e s c e n c e , and ( i i ) the, a c c e p t a n c e o f aa r e l a t i v e momenta i n t o ' ~ e ( ~ . s . ) and t h e d e p l e t i o n p a t - t e r n i n consequence ? The u l t i m a t e answer t o t h e s e q u e s t i o n s c a l l s f o r a quantum m e c h a n i c a l c a l c u l a t i o n w i t h i n c l u s i o n o f Coulomb e f f e c t s i n t h e 3-body problem, a t l e a s t i n an approximate way. A

similar problem h a s been t r e a t e d t o d e s c r i b e

pp and nn c o r r e l a t i o n s f r o m r e l a t i v i s t i c heavy-ion c o l l i s i o n s 39. Our problem was' con-

s i d e r e d i n an i n c o h e r e n t s o u r c e model by

F i g . 31. Schematic view o f acl r e l a t i v e wave f u n c t i o n i n and o u t s i d e ' ~ e ( e . s . ) . Before t r y i n g t o answer ( i i ) , l e t us l o o k a t t h e ' ~ e ( ~ . s . ) wave f u n c t i o n i n F i g . 31. It i s l a r g e i n s i d e RBe and v e r y s m a l l o u t s i d e , i n r e s p o n s e t o t h e e x t r e m e l y n a r - row r e s o n a n c e w i d t h o f 6 . 8 e v o l t 4 ' . The s t r o n g r i s e o f 4 ( r ) towards t h e i n t e r i o r r e s u l t s i n a momentum d i s t r i b u t i o n _Ap _z

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C10-214 JOURNAL DE PHYSIQUE

less than the range in AE over which depletion of the smooth aa background is observed (Fig. 29 ,top).

So far, in discussing an answer to (ii), we have neglected the finite lifetime of the CN. Adtually, when we observe two particles with energies EA and EB in the Si detectors, their energies at the nuclear surface are not known exactly, but described by a random probability distribution, presumably a Lorentzian of width

r

= * / T

.

Such, as the short-lived nucleus emits wave packets of width I'

,

formation of Be is enhanced

,

because the interval of difference energies which are acceptable 'to the momentum condition spreads out to the order of

r

(Fig.

3 2 ) . Correspondingly, the depletion pattern

widens.

Fig.32. Particles detected with energies EA

,

E B have identical energies at the

nuclear surface to the extent their wave packets overlap, which depends on the lifetime T = 5 of theCN.

Let us interprete the aa data in this way and obtain a second estimate of the lifetime. The two probability distributions of Fig.32 have to be,folded with the momentum distribution i n 'Be(.g.s.) -the Fourier 'transform of 4 (r) in Fig. 31

-

and averaged

over and weighted by the the evaporation spectra at the nucleus. Then, one obtains a window W of difference energies allowed by,the momentum condition Aprel< 50 MeV/c, as a function of

r

, Although straight- forward,, it, cannot be done in a closed ex- .-pression- even for gaussians

.

' A reasonable

estimate probably is W 3r

.

With W 2 8

MeV, from Fig. 29' we obtain

The lifetime estimates should be taken with some caution as the inter-particle Coulomb effects,especially, have been neglected. However complicated a full analysis of such measurements eventually will turn out, it wi.11 be essentially model-indepen- dent and (only) be the necessary and highly desired means to translate measured correlation spectra into lifetimes. Actually, even the measurement of decay curves can be envisioned, as the depletion spectrum, and its dependence on A $ , contains much more information, than just the mean lifetime. I am optimistic that this aim will be achie- ved, but ti1 then, the question mark in the heading to this section, better remains.

5. Conclusion

It is probably fair to state'that particle emission is a tool well chosen to study angular momentum effects as well as charac- teristic time scales in the evolution of heavy-ion collisions. Some of it is promise, other parts have already come under detail- ed investigation. In both repects, a lot remains to do. For topics to which I had either no time or no experience to turn to, I like to refer the reader of this volume to the talks of Dr. D. Guerreau and Dr. F. Plasil.

Acknowledgements

The author is indebted to F. Piihlhofer

for providing his results prior to publica- tion, and to M. Blann for his permission'to~ use Fig.24; to my experimental colleagues, especially Hans Ho-and Wolfgang KCihn, for the fruitful collaboration. It is also a pleasure to acknowledge fruitful discussions with Th. Ddssing (sect.2) and G.F. Bertsch,

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