Nuclear Physics A519 (1990) 127c-140c 127c North-Holland

EXCLUSIVE STUDY OF NUCLEUS-NUCLEUS REACTIONS AT INTERMEDIATE ENERGIES :

IMPACT PARAMETER DEPENDENCE OF PRE-EQUILIBRIUM EMISSION, COLLECTIVE FLOW AND HOT NUCLEI FORMATION

J. P6ter a, j.p. Sullivan a, D. Cussol a, G. Bizard a, R. Brou a, M. Louvel a, j.p. Patry a, R. Regimbart a, J.C. Steckmeyer a, B. Tamain a, E. Crema b-l, H. Doubre b, K. Hagel b-f, G.M. Jin b-h, A. Peghaire b, F. Saint-Laurent b, y . Cassagnou c, R. Legrain c), C. Lebrun d, E. Rosato e, R. MacGrath g, S.C. Jeong i, S.M. Lee i, y . Nagashima i, T. Nakagawa i, M. Ogihara i, j . Kasagi i-j, T. Motobayashi a-b-k

a) LPC Caen (France), b) GANIL Caen (France), c) DPhN/SEPN CEN Saclay (France), d) LPN Nantes (France), e) Dipart. di Scienze Fisiche Univ. di Napoli (Italy), f) Present address : Cyclotron Institute Texas A & M Univ. (USA), g) SUNY Stony Brook (USA), h) Inst. of Modern Physics Lanzhou (China), i) Inst. of Physics Univ. of Tsukuba (Japan), j) Dept. of Physics Tokyo Inst. of Technology (Japan), k) Rikkyo Univ. Tokyo (Japan), 1) Permanent address : Inst. di Fisica Univ. de Sao Paulo (Brazil).

Charged particles and fragments emitted in reactions between 40Ar at energies ranging from 25 to 85 MeV/u and an 27A1 target have been detected in a geometry close to 4~ in the center of mass with the 4~ array MUR + TONNEAU. A new global variable, the average parallel velocity, has been used to sort the events as a function of the impact parameter value.

The multiplicity of particles emitted from the interaction region increases strongly when the impact parameter value decreases, and reaches 7 in head-on reactions.

The flow of these particles is attributed to scattering at negative angles. When the energy increases, compression gradually opposes this negative scattering, until the flow fails to zero. This is obtained at a beam energy in the range 70-80 MeV/u for impact parameters below 2 fm and increases with the impact parameter.This study as a function of the impact parameter and the energy should allow information both on the nucleon-nucleon cross section in medium and the EOS of nuclear matter to be obtained.

In central reactions, incomplete fusion nuclei are formed at all incident energies. Their excitation energy increases with the incident energy. Above 36 MeV/u no heavy residue is left, the multiplicity of final products increases as well as the emission probability of several heavy fragments.

1. INTRODUCTION

Complete fusion ceases to be the dominant reaction mechanism in nucleus-nucleus collisions

having projectile bombarding energies larger than 10 to 15 MeV/u . The incomplete fusion

reaction, which occurs even in central collisions, is characterized by a measurement of the mass and

recoil velocity of the remaining heavy residue 1). The cross section of fusion residues in the case of

40Ar projectiles decreases strongly between 35 and 45 MeV/u. This vanishing can be explained in

several ways. One possibility could be an entrance channel effect of strong preequilibrium particle

emission. Another possibility could be an exit channel effect caused by the high temperature of the

0375-9474/90/$03.50 © 1990 - Elsevier Science Publishers B.V. (North-Holland)

128c J. PFter et al. / Exclusive study of nucleus-nucleus reactions

compound system which results in the evaporation of heavy clusters or in the onset of

multifragmentation. In the second case, no heavy residue is left and the final products are particles

and fragrnents emitted isotropically in the frame of the fusion nucleus. The simultaneous detection

of all products is then necessary in order to reconstruct the mass and velocity of the initial fusion

nucleus and to see the amount of preequilibrium emission.

Another issue which has been studied in the same experiment is the value of the collective

transverse momentum. It has been studied mostly at energies above 200 MeV/u. For the particles

emitted from the interaction region at the beginning of the collision (participants), a specific analysis

method 2) allowed the component of their transverse momentum Pt on the reaction plane (px) to be

obtained, the so-called sidewards flow 3). At these high energies, the interaction is dominated by

two-body collisions and the flow is attributed to a repulsive momentum transfer in the compressed

interaction region. Conversely, at a few tens of MeV/u, the interaction is dominated by the

attractive mean field. There, fragments have been shown to be deflected to negative angles 3). The

continuous evolution from negative to positive flow values as a function of incident energy has

been studied with the Boltzmann equation 4). The flow values strongly depend on the incident

energy and on the impact parameter. Different compressions are reached at different impact

parameters, leading to different distances between nucleons in the interaction region. The values are

sensitive both to the nucleon-nucleon cross section aNN in the nuclear medium and to the equation

of state through the compressibility factor K. In order to disentangle the respective influences of

two parameters (~NN and K) by comparing the results of such calculations to experimentally

determined flow values, the flow should be measured as a function of two variables, namely the

incident energy and the impact parameter.

We have designed and performed an exclusive experiment in which the charge and velocity of

nearly all charged products were measured on an event by event basis. The charge of each fragment

gave us an estimate of the mass and therefore, with the velocity, an estimate of the momentum.

Auger et al have studied the production of fusion residues in the 40Ar + 27A1 system in an

inclusive experiment 4). They showed that the cross section of fusion residues vanishes between

32 and 36 MeV/u. We have performed an exclusive measurement of charged products on the same

system from 25 to 65 MeV/u in steps of 10 MeV/u. The 36Ar + 27A1 system was also measured

with low statistics at 85 MeV/u.

Before undertaking any data analysis, a way of sorting the events as a function of their impact

parameter had to be devised. On the basis of simulations, the global variables used at relativistic

energies do not give here a sufficient accuracy. Another variable, the average parallel velocity of the

detected nucleons, has been built and found to give a better information.

This sorting allowed to determine that a large number of nucleons is emitted in the first stages

of the reaction, i.e. after 1 or 2 collisions. These preequilibrium nucleons-also called participants -

have a transverse momentum due to the collective flow of nuclear matter. This flow varies strongly

as a function of the impact parameter and the incident energy. This variation is related to the values

of the nucleon-nucleon cross section in medium and to the compressibility of nuclear matter.

J. P#ter et a L / Exclusive study of nucleus-nucleus reactions 129c

In central reactions, we observe that fusion nuclei are indeed formed after the residues have

disappeared. We also have some information on the excitation energy of these nuclei. The question

o f whether the deexcitation process is sequential evaporation or multifragmentation will be

discussed in a forthcoming paper as more detailed analysis is necessary.

2. EXPERIMENTAL SET-UP

Almost all particles are focused in the forward hemisphere in a reverse kinematics system such

as ours. We were therefore able to cover nearly 4~ in the center of mass by using two

complimentary multidetector systems which covered nearly 2~. The forward angles between 3.2

and 30 degrees were covered by 96plastic scintillators arranged in 7 concentric rings located 210

cm from the target. A detailed description of this plastic wail (MUR) is found in reference 5). All

angles between 30 and 90 degrees were covered using the spherical half-barrel (TONNEAU 6))

which was located 80 cm from the target. Each of the 36 half-staves had an azimulthal coverage of

10 °. One photomultiplier at each ene of the half-stave allowed to determine the polar angle, 0 , with

a resolution of 6 °. All events with multiplicities larger than 1 were recorded in order to avoid an

uncontrolled bias on the reactions. Elements were separated using the energy vs time of flight

technique.The resolution, threshold, and geometry of the experimental set up have been taken into

account in the analysis.

//./

F I G U R E 1 : ,~0" ~.

Experimental set-up

The neutrons are not detected and 10-15 % of the charged products are missed due to narrow

dead areas between the detectors and to the absence of detectors at backward and very forward

angles. The first step in the event by event analysis was to demand that the total parallel momentum

of all detected prducts was more than 65 % of the projectile's linear momentum. Since the grazing

angle is close to 1 ° and the minimum detection angle is 3.2 ° , many peripheral reaction events

were eliminated when the projectile-likke fragment is not kicked to more than 3.2 ° and most of the

130c J. Pdter et a L / Exclusive study of nucleus-nucleus reactions

linear momentum is t/ot measured. The analysis keeps all central and intermediate impact parameter

reactions as well as a few well characterized peripheral reactions.

3. IMPACT PARAMETER DETERMINATION

In analyzing the data, the events have to be sort~ according to their impact parameter value

b 7). The basic assumption is : the larger the violence of the collision, the larger the interaction

volume of the two nuclei, i.e. the smaller the impact parameter. Once the events axe sorted

according to the violence of the collision, their cross sections give b via da = 2xb, b -- 0

corresponding to the most violent event. The violence of the collision is expressed through the

value of a global variable.

Several global variables have been used in the study of reactions induced by relativistic heavy

ions. We have tested them by means of simulated events, produced by a code which simulated the

reaction mechanisms. Each event is filtered through a software replica of the detection set-up, to

take into accound all the actual detector limitations. The quality of the impact parameter

determination is expressed by the correlation between the real b value and the "experimentally"

determined value. Figure 2 shows that this correlation is broad with the multiplicity, the total

detected charge and the total transverse momentum. The mid-rapidity charge gives a similar result.

We looked for a global variable more adapted to incident energies below 100 MeV/u. We

found it in the average (mass-weighted) parallel velocity. It is based on linear momentum

conservation and geometry. After the collision, the projectile momentum Pproj is found in the sum

of the parallel momenta of all final particles. The average (mass-weighted) of these particles is : v v

Vav = ~ miTiV~cos0i/~ miT i (1) i = l i = l

Vav is simply the velocity which, when multiplied by the detected mass (denominator in I), gives

the parallel momentum detected in the event (numerator).

If all particles, including neutrons, were measured, the numerator would be the total mass of

the system and Vav would be nothing but the center-of-mass velocity Vcm, for any event. To get

a variation of Vav with b , we make use of the fact that the target nucleons not located in the

interaction region ("spectators") have a very low velocity. In the analysis of the simulated data, an

artificial velocity threshold eliminates these nucleons. Whether they are isolated or form a target-like

product does not make any difference. The remaining nucleons are all the projectile nucleons and

the target nucleons which were in the interaction region. The maximum value of Vav is Vp,

obtained in very peripheral reactions where the denominator is the projectile mass. Its minimum

value is reached in head-on collisions. In reverse kinematics, the whole target nucleus is involved in

the interaction (no "spectator target nucleons"), this minimum value is Vcm • With the real detector

Mur + Tonneau, the velocity threshold which eliminates the "spectator target nucleons" is due to the

aluminum foil which is used to prevent the detection of electrons.

J. Pdter et a L / Exclusive study of nucleus-nucleus reactions 131 c

The sorting is made by attributing the minimum values of Vav to the most central reactions.

The correlation, bexp versus breal, is better than with the other global variables. The reason is that,

in equation (1), the errors in the numerator and the denominator due to the missed particles cancel

each other to a large extent. We have thus used this method for impact parameter sorting.

7 6

5

4

3

2

1 0 7 6

5

4

3

2

1

0

31

V

O"~eal 05 283 503 785 1131 1540 2010

°00

~0~0 oO00o

* o O O O o

0 0 0 0 °

a O o a I [ l l l l

2Z ooOO

°o000 oo0½0

,oO00o °oOOo

aOOo O O O

12345878

b real

0

0

O'Teal 31 95 283 503 785 1131 1540 2010

2 p j . o o 0 [ ~ I-I

o o 0 o o o 0 0

o o o o o

I T I I ~ I

Vav oO

o [ ] o o[]o

= O D O o [ ] O O 0 0

f l i T 1

1 2 3 4 5 6 7 8

b real

FIGURE 2

m

~exp

1131

785

503

283

95

31

Simulated data Ar + A1 at 45 MeV/u. Correlation between bexp (vertical axis) and breal (horizontal axis) obtained in simulated reactions sorted according to th-e value of a global variable. The area of each square is proportional to the cross section of events ; the scale is given by the area of the square in the right-bottom comer, equal to 300 mb. The cross sections xb 2 corresponding

to b=l,2,.., fm are indicated in mb. The global variables are the multiplicity ~ , the total detected

charge ,~,Z, tho total measured transverse momentum ~ and the average parallel velocity Vav of the detected products.

4. PRE-EQUILIBRIUM AND EQUILIBRIUM EMISSIONS

To help identify the processes and their evolution with b , we built contour plots as in figure 3.

For mid-peripheral reactions (upper part), the invariant cross sections of heavy fragments (mostly

Z > 9) and light charged particles exhibit circular contours centered close to Vp : excited projectile-

like transfer products have isotropically evaporated a few light particles. For Z = 1 and 2, a weak

component at V// values below Vcm is present. For central reaction (lower part of Fig. 1), the

heavy fragments (mostly Z = 6-8) are the residues of equilibrated nuclei formed via fusion, which

132c J. Pdter et aL / Exclusive study of nucleus-nucleus reactions

de-excited through isolxopic emission of many particles and clusters. The velocities of the

equilibrated nuclei lie between Vp and Veto, indicating that fusion is far from being complete. For

Z = 1 and 2 , in addition to particles isotropically emitted by the incomplete fusion nucleus, a

component at V// values below Vcm is clearly seen. It does not show up for higher Z values

(except, possibly for very few Z = 3 particles).

10

vi

10

Z = 1 - 2

I I I

-' Z = 1 - 2

1

! ! 0 NN CM i~ 10"-

Ar + AI 45 MeV/u

Z = 6-8 Z>~9

Z = 6-8

I I I I I I

Z~>9

I I / ] O r I I / 1 0 r NN cM p NN o

V/ / (cm / ns)

FIGURE 3 Invariant cross sections d26/V dV dV/[ of different particles detected in two bins of events characterized by the value of their average parallel velocity Vav (shown by the black rectangle). Top : mid-peripheral collisions (b ~ 6 fm). Bottom : central collisions (b < 2 fm). NN is the center-of-mass velocity of free projectile nucleon-target nucleon. The dashed line shows the detection velocity threshold.

By looking at the projections of this figure on the parallel velocity axis, one easily sees that the

slow component is centered around VNN which corresponds to the center-of-mass of free nucleon-

nucleon system (very close to Vp/2) 12). This is the value expected if they are ejected after a single

collision with a nucleon of the other nucleus, and this location is the same in all bins. Moreover, the

transverse energy distributions of the particles is identical at all impact parameters. Thus, we

attribute them to pre-equilibrium emission from the interaction region, i.e. the so-called participants

at high energies.

Z P ~ t e r e t a L / E x c l u s i v e s t u d y o f n u c l e u s - n u c l e u s r e a c t i o n s 133c

Figure 4 shows the variation of the average P.E. multiplicity < ~pe > versus b . < ~ e > is

veery low in mid-peripheral reactions and rises rapidly when b decreases. Head-on reactions (full

overlap of Ar and A1) correspond to less than 1 fm, i.e. 30 mb. Since Vav = Vcm, all or nearly

all target nucleons experienced at least one collision and the total detected charge is indeed close to

31. There, surprisingly large P.E. multiplicities are reached : 7 particles, half of them with Z = 1

and the other half with Z = 2 , i.e. 10 charge units. One third of the system is emitted before

equilibration ! Of course, this high ratio is favored by the small size of the nuclei. At these energies,

fusion is very incomplete.

A u.i 2 ,~,

> V

1

I I

I t - ~ 1

l l ' I

I

z = 2

4 ° A r + 27AI

. . . . 65 MeV/u

45 MeW u

I

- - - I Z = l

1 9

I I I ~ - - - , I I

I - - I ' ~ ' ' ' ' ' ' ' ' ' ' ' ' ' (mb~~Y) FIGURE 4 :

0 500 1000 1500 Average number of pre-equilibrium , _ b particles, versus the impact parameter 1 ~ 3 ~ ~ 6 ÷-(fro/ value b.

Let us compare the P.E. multiplicities at 65 MeV/u to the number of nucleons contained in the

overlap region 8). At 7 fm, the multiplicity of Z=I PE particles (average mass = 1.5) is lower

than .1 whereas the number of interacting nucleons is - 1. A multiplicity 1 needs an impact

parameter ~ 5.5 fm, where 10 nucleons are in the overlap volume. The production of 7_,=2 (mostly

alpha particles) needs a larger overlap. At 3 fm, 36 nucleons interact during the fin'st steps of the

reaction and 1 alpha is emitted, in addition to 3 hydrogen particles. At lower b values, the increase

of the Z=2 yield is steeper than that of Z=I and both dements reach a multiplicity value > 3 in

head-on collisions.Both the surprising large P.E. multiplicity of Z--2 particles and its steep

increase at low b could be explained by the increase of the overlap region coupled with the

presence of preformed clusters in the nuclei. An alternative explanation could be the coalescence

process, which is favored byk the larger number of primary P.E. nucleons. The data shown here

provide a good basis for such calculations.

134c J. Pdter et aL / Exclusive study of nucleus-nucleus reactions

Now, let us compare the 45 and 65 MeV/u data. At a fixed b value, the multiplicity of Z = 1

particles exhibits a distinct increase with energy, while the multiplicity of Z=2 particles increases

slightly or remain constant. This difference has no obvious explanation. Is it a clue that complex

particles and single nucleons are due to different P.E, process ?

5. FLOW AND EQUATION OF STATE

These nucleons emitted from the interaction region (pre-equilibrium or participant nucleons) are

sensitive to the flow of nuclear matter during the reaction. This flow can be studied through the

value of the transverse momentum Pt. More precisely, we study the projection pX of Pt on the

reaction plane. For the particles issued from the projectile (i.e. with a rapidity larger than the cm

rapidity Ycm) pX has a direction opposed to the direction of particles issued from the target nucleus

(below Ycm) : Figure 5.

-¢

X

~zPt Jz

FIGURE 5 Flows of nuclear matter. Left : before the collision, Right : after the collision, at Einc > Ebal (b), i.e. scattering of projectile nucleons to positive angles. The transverse momentum, of a particle Pt and its projection on the reaction plane, pX, are also shown.

The direction t~ of the reaction plane and the value of pX are calculated using a slight

modification 9) of the methods originally described by Danielewicz and Odyniec 2) : the weight of

each particle i is taken to be Yi-Ycm, where Yi is the rapidity of the particle 13).

J. P~ter et aL / Exclusive study of nucleus-nucleus reactions 135c

Figure 6 shows a series of plots of pX/A versus the particle rapidity (y), obtained at 45 MeV/u

for Z=2 at impact parameter values centered at 6, 4.5, 2.6 and 1.6 fm with a FWHM ~ 1 fm 3).

The rapidities of the projectile, yp, the center-of-mass, Ycm, and the nucleon-nucleon center-of-

mass YNN = yp/2, are shown by arrows. The location of the "spectator" equibrated nuclei is

shown by a rectangle. At 5 and 1.6 fm, the rapidity distribution of Z=2 particles is shown -

helping to see where participants and "spectators" contribute.

"0

~,-40 <p_x_x> o 6 fm . . . . . .

A flow --t" - 2 °

YNN YCM Yp

_40 0

0

-20

-40

0

-20

-4O

"0

Z 2~

o.1 0.2 0;..5 o.4 2'. '6 fm ' ~ - 'L~-~- -F -[

/ . . . . . . . . . . . ,.., ~,.,>,.-,-.,,..~ ~ ÷+

. . . . t , ,

YNN YCM Yp

FIGURE 6 45 MeV/u Ar on A1. Measured mean transverse momentum per nucleon projected into the reaction plane as a function of the particle (Z=2) rapidity. 4 impact parameter bins, 1 fm wide, are shown. At 6 and 1.6 fm, the distribution of Z=2 particles dN/dy is also shown, allowing two sources to be located • pre-equilibrium ("participants") around the nucleon-nucleon rapidity and particles emitted from the equilibrated nuclei ("spectators") whose rapidity is indicated by rectangle (see figure 3). The flow parameter of the participants is shown at 6 fro. Here, the rapidity is very close to the parallel velocity in c units (~//).

Around YNN the participants clearly exhibit the linear increase of pX/A versus the rapidity

which characterizes directed collective motion. At large y values, particles emitted by the

"spectator" equilibrated nucleus constitute the main contribution 8). Their transverse momentum is a

complex combination of sidewards flow, bounce-off and a large thermal motion. Their interference

with participant particles causes the slope of pX versus y to decrease. A similar effect has been observed at higher energies 3,9,10).

136c J. P#ter et aL / Exclusive study of nucleus-nucleus reactions

As in ref. 11), the flow parameter of the participants is the slope multiplied by (Yp-YNN). This is

shown in figure 6 at 6 fm. The variation of the flow versus b is plotted in figure 7 at 55 MeV/u,

for Z=I and Z=2. A small number of Z=3 participants are also seen in central reactions. 25 MeV/u

is similar to 36 MeV/u, 55 MeV/u is intermediate between 45 and 65. The flow at 36 MeV/u does

not depend as strongly on b as at the other energies and has the largest observed values. In central

collisions, at 45 MeV/u, some compression is reached. Inside the interaction region, where

nucleons get closer, the potential is less attractive and the flow falls to smaller values. At higher

energies, this effect becomes stronger. Larger flow values are observed for Z=2 than for Z=I. This

effect has already been observed 10) and is not clearly understood.

40-

t -

O 30 ¸

F I G U R E 7 : Flow as a function of the '- experimentally determined impact parameter value (bexp),

20 for Z=I and Z=2 particles. > Ar+AI at 55 MeV/u. Error bars indicate the uncertainties in getting the slopes(see figure 6). Theses values axe not corrected _o

" 10 for the difference between the true and measured reaction plane and are thus lower limits.

55 MeV / u

Z=2

+÷÷ z__,

. . . . 5 6 o . . . . l o ' . . . . . " O" O0 (rnb) 1500

bexp (fm)

There is some uncertainty in determining the reaction plane from experimental data in each

event. Then, the experimentally determined value of the the flow must be multiplied by a correcting

factor 2) whose value is subject to a large uncertainty. This difficulty can be avoided by looking at

the energy Ebal where the attractive and repulsive parts of the potential balance each other. There,

the flow is zero and no correcting factor is needed.

We see in figure 8 the flow measured at different energies for bexp = 3 fm. According to

figure 2, the average value of b is equal to bexp and the FWHM is 1 fm. Ebal (3fm) appears to

lie in the range 90-100 MeV/u. Ebal (1.6 fm) is located in the range 70-80 MeV. At 5 fm, the

uncertainties on the data are large. Nevertheless, Ebal (5fm) is larger than Ebal (3 fm). This

increase of Ebal with b is in agreement with the prediction 4).

J. Pdter et al. / Exclusive study of nucleus-nucleus reactions 137c

The data in figure 8, when compared to the calculations in reference 4), are not consistent with

the calculations which assume GNN -- 20 m b . They agree much better with the (~NN = 41 mb

calculations, but do not exclude slightly smaller values of (~NN • The data can not be used to

distinguish between the two values of K at b = 3 fm since the calculated curves lie so close to

each other. Clearly, detailed measurements should be up to 150 MeV or more. On the theoretical

side, detailed calculations should be made on the system Ar + AI at all impact parameter values.

F I G U R E 8 40- Flow for Z = 1 and 2 particles as a function of beam energy for impact parameter 3 0 b=3_+0.5 fm. The ~ " calculated values c o at 60, 100 and 200 MeV/u fortbe "~ 20 neighbouring system r- . 40+40 are indicated. =. They show the expected ~. 1 0 - variation in the flow for different values o

of ONN and constant K. ~ 0 The experimental data show positive flow .,-, values since the analysis method gives only the ~ -10 - absolute value of the o flow. The experimental 14. values are not corrected -20 - for the difference between the true and measured reaction plane. The solid lines are to guide the eye. -30

b = 3 f m

~ , ~NN= 41 mb / I ~ 1 - , , , . K = 2 o o . o

i i i J i i , r ~ l i I I • ' 1 i i j - ~ t ' ° l i •

50 .', 1 0 0 . ' 150"" 2 0 0 ,', . " E i n c ( M e V / u ) • El o "

CJ ' * "

an"

~N= 20 mb • K = 2 0 0 [] K = 3 7 5

f oO

6. FORMATION OF HOT EQUILIBRATED NUCLEI

We have seen already in figure 3 that, in addition to pre-equilibrium emission from the

interaction zone, light particles and fragments are issued from a source the velocity of which is

located between the projectile and center-of-mass velocities. Figure 9 bottom shows the light

particles distributions for peripheral (b - 6-7 fm) and central (b < 3 fm) reactions. The circular

shape of cross section contours indicates isotropic emission from an equilibrated source. In

peripheral reactions, this source is a projectile-like product, whose residue is also detected. In

central reactions, these circles are slightly deformed at low V// values, due to a small PE

contribution ; the source velocity is located slightly above Veto, indicating that this source is a

nearly complete fusion nucleus (remember the system is in reverse kinematics), which is consistent

with the small PE component.

138c J. Pgter et aL / Exclusive study of nucleus-nucleus reactions

CF

d

0 2 4 6

E* / A MeV

do-

db

250 mb

11 J

1.11.o. I E*/A ( M e V ) / ~ ~ dateetasl

1 2 3 4 5 6 7 8 b frn

5

E*/A= 5.4 - 6 MeV

, , . . . . . , , ,

0 ! 10 V m V/ / c m / n s

E* /A= 1.2 MeV

\ i i i

t 10 Vproj

F I G U R E 9 Ar + AI at 25 MeV/u . Top left : excitation energy distribution of the equilibrated nuclei ; CF indicates the value obtained for complete fusion. Top r ight : excitation energies versus impact parameter. Bo t tom : invariant cross sections (arbitrary units) for light particle (Z--- 1 and 2) as a function of their velocity components parallel and perpendicular to the beam direction left : central collisions (high excitation energies) r ight : peripheral collisions.

Similar features are observed at higher energies. When the energy increases, fusion becomes

more and more incomplete. The charge of the fusion nucleus is obtained, event by event, by adding

the charges of its products (after removing the P.E. particles, located mostly at V//< Vcm ). At 25

MeV/u, it is close to the total charge of the system, 31, whereas at 65 MeV/u it reaches only 20-21

(in agreement with 10 units emitted in PE). Consistently, its velocity moves further above Vcm.

Isotropic particle emission is a signature of the independence between the entrance and exit

channels. It is then the f'trst requirement for a thermally equilibrated nucleus. We therefore checked

it. In addition to observing circular contour levels, we used a momentum tensor analysis of the

emitted particles (after removing the PE particles). In the reference frame located at the nucleus

velocity, the eccentricity is low ; the polar angle cosine of the direction of its largest axis, is equally

distributed from 0 to 1. That means the ellipsoid which represents the momenta is nearly a sphere

(it can never be a sphere, due to the finite number of products) with no preferential direction.

The excitation energy of this nucleus can be determined experimentally event by event. It is the

J. Pdter et aL / Exclusive study of nucleus-nucleus reactions 139c

sum of 3 terms : 1) the kinetic energies of the products in the nucleus reference frame, 2) the mass

balance between the fusion nucleus and the final products, 3) the energy removed via neutron

emission, estimated form the number of protons and the N/Z ratio.

In central reactions, the excitation energy nearly reaches 6 MeV/nucleon (complete fusion) at

25 MeV/u : figure 9 top. This value increases with the incident energy, but it increases much less

than the available energy, since the larger P.E. emission removes a larger amount of energy. At

65 MeV/u, E*/A reaches - 9 MeV/u whereas complete fusion would lead to 15.6 MeV. The

distribution of E*/A values tends to become flat when the incident energy increases.

0 2 5 M e V / u • 3 6 M e V / u

A 4 5 M e V l u • 5 5 M e V / u [ ] 6 5 M e V / u 10 2

" ' - 101 X

E N • ---." O0

151 0

b < 2 f m

o 0 U I A - '~0 0

A [~A A O 0 O 0 ~e • rflA A 0

0 • 6 ~A A •

2 4 6 8 10 12 14 16 18 20 22 24

Z max FIGURE 10

Distributions of the heaviest fragment (Zmax) for central collisions (b<2fm) of Ar+AI at 25, 36, 45, 55 and 65 MeV/u.

These larger excitation energies brought in the incomplete fusion nuclei at larger incident

energies manifest themselves in the larger multiplicities of final particles and fragments : the average

values are 7, 9, 10, 11, 11.5, 12 at 25, 36, 45, 55, 65 and 85 MeV/u respectively 11). In agreement with this observation, the charge of the heaviest fragment decreases when the

energy increases : figure 10 (in contrast, the charge of the heaviest fragment in peripheral reactions

remains close to that of the projectile). This charge distribution has an immediate consequence on

the identification of fusion nuclei. In inclusive experiments, the fusion cross section was taken as

the cross section of slow residues with Z>16 4). We see in figure 10 that this leads to miss a large

part of events at energies below -35 MeV/u. Above this energy, it is quite misleading. Incomplete

fusion does not disappear at energies around 40 MeV/u, as inclusive measurements seemed to

indicate. It just becomes more and more incomplete, and de-excitation leads to a large number of

particles and fragments. Initial fusion nuclei can be reconstructed only through an exclusive

140c J. Pdter et al. / Exclusive study of nucleus-nucleus reactions

measurement of all final charged products.

Is the de-excitation process still sequential evaporation or does fast multifragmentation start

playing a role ? This is another question which requires a specific analysis.

REFERENCES

1) J. P6ter and B. Tamain, Proc. Riken-IN2P3 Symposium on Heavy Ion collisions, Shimoda, october (1987).357 and references therein.

2) P. Danielewicz and G. Odyniec, Phys. Lett. 157B (1985) 146 P. Danielewicz, H. Strt~bele, G. Odyniec, D. Bangert, R. Bock, R. Brockrnann, J.W. Harris, H.G. Pugh, W. Ranch, R.E. Renfordt, A. Sandoval, D. Schall, L.S. Schroeder and R. Stock Phys. Rev. C38 (1988) 120

3) K.G. Doss, H.A. Gustafsson, H. Gutbrod, J.W. Harris, B.V. Jacak, K.H. Kampert, B. Kolb, A.M. Poskanzer, H.G. Ritter, H.R. Schmidt, L. Teitelbaum, M. Tincknell, S. Weiss and H. Weiman - Phys. Rev. Lett. 59 (1987) 2720

4) G. Auger, E. Plagnol, D. Jouan, C. Guet, D. Heuer, M. Maurel, H. Nifenecker, C. Ristori, F. Schussler, H. Doubre and C. Gr6goire - Phys. Lett. 169B (1986) 161

5) G. Bizard, A. Drouet, F. Lefebvres, J.P. Patty, B. Tamain, F. Guilbault and C. Lebrun Nucl. Inst. & Meth. A244 (1986) 483

6) A. Peghaire, B. Zwieglinski, E. Rosato, G.M. Jin, J. Kasagi, H. Doubre, J. P6ter, Y. Cassagnou, R. Legrain, F. Guilbault and C. Lebrun - to be published in Nucl. Inst. & Meth.

7) J. P6ter, D. Cussol, G. Bizard, R. Brou, M. Louvel, J.P. Patry, R. Regimbart, J.C. Steckmeyer, J.P. Sullivan, B. Tamain, E. Cr6ma, H. Doubre, K. Hagel, G.M. Jin, A. Peghaire, F. Saint-Laurent, Y. Cassagnou, R. Legrain, C. Lebrun, E. Rosato, R. MacGrath, S.C. Jeong, S.M. Lee, Y. Nagashima, T. Nakagawa, M. Ogihara, J. Kasagi and T. Motobayashi LPC Caen report LPCC 90-03 (march 1990), submitted to Nucl. Phys. A

8) See appendix in : J. Gosset et al, Phys. Rev. C16 (1977) 629

9) J. Gosset, O. Valette, J.P. Alard, J. Augerat, R. Babinet, N. Bastid, F. Brochard, N. De Marco, P. Dupieux, Z. Fodor, L. Fraysse, P. Gododetzky, M.C. Lemaire, D. L'H6te, B. Lucas, J. Marroncle, G. Montarou, M.J. Parizet, J. Poitou, C. Racca, A. Rahmani, W. Schimmerling and Y. Terrien - Phys. Rev. Lett. 62 (1989) 1251

10) J.M. Harris, B.V. Jacak, K.H. Kampert, G. Claesson, K.G.R. Doss, R. Ferguson, A.I. Gavron, H.A. Gustafsson, H. Gutbrod, B. Kolb, F. Lefebvres, A.M. Poskanzer, H.G. Ritter, H.R. Schmidt, L. Teitelbaum, M. Tincknell, S. Weiss, H. Wieman and J. Wilhelmy Nucl. Phys. A471 (1987) 241c

11) K. Hagel et al Phys. Lett. B229 (1989) 20 and B324 (1990) 541

12) J. P6ter et al Phys. Lett. B237 (1990) 187

13) J.P. Sullivan et al - LPC Caen report 90-04 submitted to Phys. Lett. B