Volume 237, number 2 PHYSICS LETTERS B 15 March 1990

S T R O N G I M P A C T P A R A M E T E R D E P E N D E N C E O F P R E - E Q U I L I B R I U M PARTICLE E M I S S I O N IN N U C L E U S - N U C L E U S R E A C T I O N S AT I N T E R M E D I A T E E N E R G I E S ~r

J. PI~TER ", J.P. SULLIVAN h, D. CUSSOL ", G. BIZARD a, R. BROU a, M. LOUVEL a, j .p . PATRY ", R. R E G I M B A R T a, J.C. STECKMEYER a, B. T A M A I N a E. CREMA b.I, H. DOUBRE b, K. H A G E L b.2, G.M. JIN h.c, A. PI~GHAIRE b F. SAINT-LAURENT b y . CASSAGNOU d R. LEGRAIN d, C. LEBRUN ~, E. ROSATO r, R. M A C G R A T H 8, S.C. J E O N G h, S.M. LEE h, Y. N A G A S H I M A h, T. N A K A G A W A h M. O G I H A R A h, j . KASAGI i and T. MOTOBAYASHI a,~,o

• LPC Caen, ISMRA, IN2P3-CNRS, F-14032 Caen, France b GANIL, BP5027, F-14021 Caen, France

Institute of Modern Physics. P.O. Box 31, Lanzhou, P.R. China a DPhN/BE CEN. Saclay, F-91191 Gifsur Yvette. France • LPN. 2 Rue Houssinibre. F-44072 Nantes. Prance • Dipartimento di Scienze l"isiche. Universita di Napoli. 1-80125 Naples. Italy s SUNY. StonyBrook. NY 11794. USA

Institute of Physics. University of Tsukuba. Ibaraki-ken 350. Japan ' Department of Physics. Tokyo Institute of Technology. Meguro-ku. lokyo 158. Japan J Rikkyo University. Toshima-ku. Tokyo 171. Japan

Received 14 December 1989

Charged particles and fragments emitted in reactions between 4°Ar at 45 and 65 MeV/u and a n 27A1 target have been detected in a geometry close to 4n in the center of mass. A new global variable, the average parallel velocity, has been used to sort the events as a function of the impact parameter value. For particles with Z= 1 and 2, a pre-equilibrium component is present. Its multiplic- ity increases strongly when the impact parameter value decreases, and reaches 7 in head-on reactions.

The emission of nucleons and light clusters in the first steps of a nucleus-nucleus interact ion becomes more and more copious when the incident velocity reaches values comparable to the Fermi velocity. Some nucleons, ei ther isolated or clustered, may es- cape without suffering any collision in the par tner nucleus. In peripheral reactions, they form the pro- jecti le-l ike and target-like spectator nuclei [ 1 ]. In the case of pure Fermi jets [2] nucleons also fail to col- lide. Let us call them "no coll is ion" nucleons. An- other component of fast emit ted nucleons consists of nucleons which suffer one (or two) collisions during

Experiment performed at the GANIL facility. Permanent address: Instituto de Fisica, Universidade de Sao Paulo, CP 20516, Sao Paulo, Brazil.

-' Present address: Cyclotron Institute, Texas A&M University, College Station, TX 77843, USA.

the interaction. We call them " 'pre-equi l ibr ium" nu- cleons (PE) . Some authors define PE as the sum of both components above. Most exper imental data are inclusive or coincidence measurements of neutrons [3,4] and light charged particles [ 5]. In these stud- ies, average mult ipl ici t ies per collision have been ob- tained. It is highly desirable to know to which amount "'no coll is ion" and PE emissions occur in central re- actions and thus how they can l imit the excitat ion en- ergy of the incomplete fusion nucleus.

In order to measure the number of "no coll is ion" and PE nucleons, all or nearly all particles emit ted in each event must be measured. We have performed an exclusive exper iment in which the charge and veloc- ity of nearly all charged products were measured on an event by event basis. We chose the system 4°Ar+27Al which had been studied in several inclu-

0370-2693/90/$ 03.50 © Elsevier Science Publishers B.V. ( North-Holland ) 1 87

Volume 237, number 2 PHYSICS LETTERS B 15 March 1990

sive experiments between 15 and 45 MeV/u [6 -8 ] . The measurements have been made from 25 to 65 MeV/u in steps o f 10 MeV/u. The results obtained at 45 and 65 MeV/u are shown here.

In our reverse kinematics, two complementary multidetector systems which cover 2~z in the lab span nearly 4z~ in the center-of-mass. The forward angles between 3.2 ~ and 30: were covered by a plastic wall ( M U R ) [9]. All angles between 30 ° and 90: were covered using a spherical half-barrel (TONNEAU [10] ) . Elements were separated using the energy versus time of flight technique. All events with a mul- tiplicity larger than 1 were recorded. Very peripheral interactions do not bring an excitation energy suffi- cient to emit a charged particle and arc thus elimi- nated by the trigger condition.

The neutrons are not detected and (10-15%) of the charged products are missed due to narrow dcad areas between the detectors and to the absence of de- tectors 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 products was more than 65% of the projectile's linear momentum [ 11,12 ]. Since the grazing angle is close to 1 : and the min imum detection angle is 3.2 ~, many peripheral reaction events were eliminated when the projectile-like fragment is not kicked to more than 3.2 ° and most of the linear momentum is not mea- sured. The analysis keeps all central and intermedi- ate impact parameter reactions as well as a few well characterized peripheral reactions. Simulation cal- culations confirmed this picture [ 12 ].

The next step was to sort events according to their violence, which is assumed to increase when the im- pact parameter value b decreases. We use the fact that the "no collision" nucleons (or clusters, or frag- ments) issued from the target nucleus remain at rest in the lab and are not detected, due to the velocity threshold of the detectors. The violence of the reac- tion increases when the number of these "no colli- sion" target nucleons decreases. Whether these nu- cleons form a single fragment (target-like in peripheral reactions) or are separated (Fermi jets propagating undisturbed through the Ar nucleus [ 2 ] ) does not make any difference. We will show now that this number is directly related to the mass-weighted average parallel velocity of the detected products.

Let us assume we have a perfect detection system

which accurately measures the mass, direction and velocity of all final products, including neutrons, ex- cept the "'no collision" target nucleons. They carry the whole initial projectile linear momentum. The mass-weighted average parallel velocity of the de- tected nucleons is

'"" m, 7, I', cos 0, I ' . , = ~ ' = ' ( l ) ZI'_-, m,7,

where m, is the mass. V, is the laboratory velocity, O, the laboratory polar angle and 7, the relativistic pa- rameter o f each of the v detected products. 14d~ is sim- ply the velocity which, when multiplied by the de- tected mass, gives the parallel momentum detected in the event [numerator in ( l ) ] .

When the denominator varies from the projectile mass (in very peripheral reactions) to the total mass of the system (assumed to be central collisions), I'~,,, varies from the projectile velocity I/p down to the center-of-mass velocity V~.,,,. Thus, sorting events ac- cording to ¢~,, from V~,, to I/p is equivalent to sorting them according to the violence of the collision, i.e. to b going from 0 to the maximum interaction distance, even though fluctuations can weaken this corre- spondence. Note that V~m is reached only if all target nucleons have at least one collision. The correspond- ence between I'av and h depends on the system stud- ied: the cross section da for events with I/],v = I',..1 is attributed to impact parameter values ranging from 0 to h such that da=~rh 2. and so on for events at the next I,~d,. values.

This method is suited to reverse kinematics and to the low threshold of our dectectors (see fig. I ): with a higher threshold. I],v would no longer reflect the number o f " n o collision" target nucleons. In eq. ( 1 ), the errors in the numcrator and denominator due to the missed particles and neutrons cancel each other to a large extent. The uncertainty on V.d,. due to this effect as well as to other experimental uncertainties (charge-to-mass conversion, resolution on I~'] and 0,, missing 0> 90: , double hits) has been calculated via a complete simulation of the response of the detec- tors. A direct observation of the experimental reso- lution is given by events with t~,, slightly lower than V,.m. This resolution led us to divide the I~v distri- bution in I I bins. Other variables linked to the viol- ence of the reaction vary consistently: as I,;~,, de- creases from I,~ to I'~,,, the average multiplicity of

188

vii

. . . . F'T" "T ~ - - "

ZE 1,2

!

• " ~6 " I

• L NN CM P - ~

V / / ( c m ,' ns)

Ar + AI 45 MeV'u

l- Z= 6-8 Z>~9

" i i - ~ T - t ~ " - 1 i - " " 1 i

Z= 6-8 ~ Z>~9

, __ ~ , ~ - - ~ , -~ N ~ / ~ l ,It - ,~

800

Fig. 1. Ar on AI at 45 MeV/u. Invariant cross sections d2a/ V± dl," 1 dl/. of different panicles detected in two bins of events characterized by the value of their average parallel velocity I"~ v (see text ). Top: mid-peripheral collisions: V,v (shown by the black rectangle ) is slightly below the projectile velocity P. Bottom: cen- tral collisions: t',v is close to the projectile-target center-of-mass velocity CM. NN is the center-of-mass velocity of free projectile nucleon-target nucleon. The dashed line shows the detection ve- locity threshold.

detected products increases, the measured total charge increased from around 18 (Ar) to 31 ( A r + A 1 ) , and the average transverse momen tum and energy increase.

To help identify the processes and thcir evolution with Vav, we built, for each Vav bin, contour plots as in fig. 1. For mid-per iphera l reactions, i.e. large V,v (upper part of fig. 1 ), the invariant cross sections of heavy fragments (most ly Z>~9) and light charged particles exhibit circular contours centered close to lip: excited projecti le-l ike transfer products have iso- tropically evapora ted a few light panicles. For Z = 1 and 2, a weak component at l,'l, values below V~,,, is present. For central reactions, i.e. I/~v close to Vcm (lower part of fig. 1 ), the heavy fragments (most ly Z = 6 - 8 ) are the residues of equi l ibrated nuclei formed via fusion, which de-excited through iso- tropic emission of many particles and clusters. The velocities of the equil ibrated nuclei lie between I," o and Vcm, indicat ing that fusion is far from being com- plete. For Z = I and 2, in addi t ion to particles iso- tropically emit ted by the incomplete fusion nucleus, a component at VII values below l'~m is clearly seen. It does not show up for higher Z values (except, pos- sibly, for very few Z = 3 pan ic les ) .

This slow component is better seen in fig. 2, for bins 10, 8, 6, 4, 2 and 1, ranging from V,,. slightly below lip (upper left corner) down to Va~ just below Vcm (bot tom right) , i.e. from gentle mid-per ipheral to vi- olent central reactions. The values of I,'~ are shown as black rectangles.

This figure shows, in each bin. the parallel velocity spectra of light panic les ( Z = 1, 2) and heavy prod- ucts (Z>~ 6). The velocity of the equil ibrated nuclei is easily obtained from the 1/, d is t r ibut ion of heavy products which is narrow (due to phase space limi- ta t ions) and has no slow component . As in fig. 1, it coincides with the location of the high velocity peak for Z = 1 and 2. The equi l ibrated Z = I and 2 com- ponent is obta ined by symmetr iz ing its upper part around the velocity of the equil ibrated nuclei (dot- ted l ines). The remaining particles (dashed lines)

c 0 .1 .2 .3 .4 0 .1 .2 .3 C .4

1000

400

2OO

5 2000

1000 >

300{]

2 0 0 C

Volume 237, number 2 PHYSICS LETTERS B 15 March 1990

100C

0 NN CM P 0 NN CM P

V//

Fig. 2. Parallel velocity spectra of light charged particles (Z= 1 and 2, white area ) and heavy products (shaded area, on a differ- ent vertical scale). From the upper left corner to the bottom right corner one goes from mid-peripheral to central collisions. The light panicle spectra are split in two components: an equilibrated one (dotted line) and a pre-equilibrium one (dashed line). The average number of PE panicles in each bin is indicated.

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Volume 237, number 2 PHYSICS LETTERS B 15 March 1990

have a parallel velocity distribution centered below I"NN which corresponds to the center-of-mass of free projectile-nucleon and target-nucleon system (very close to ½ Vo). This is thc value expected if they are ejected after a single collision with a bound nucleon of the other nucleus, and this location is the same in all bins. Moreover, the transverse energy distribu- tions of the particles is identical in all bins. Thus, wc attribute them to PE emission after one or two collisions.

Could they originate from the de-excitation of a target-like nucleus? In this case, their source velocity and the slope o f their transverse energy distribution should increase from peripheral to central reactions, at variance with observation. A weak contribution from the target-like nucleus, however, cannot be excluded.

This component cannot originate from a hot par- ticipant zone either [ 13 ]. Indeed, the source velocity would lie between INN and V~ m and the cold projcc- tile fragment should be observed at V. close to l~, at variance with the many products ( ~ 12 in central re- actions) observed at V. between l'~m and V o.

Fig. 3 shows the variation of the averagc PE mul- tiplicity ( t )~) versus b. (t)p,) is very low in mid-pe- ripheral reactions and rises rapidly when b decreases. Head-on reactions (full overlap of Ar and AI) corrc- spond to less than 1 fm, i.c. 30 mb. Since l~v = V~.m, all or nearly all target nucleons experienced at least one collision and the total detected charge is indeed close to 31. There, surprisingly large PE multiplici- ties are reached: 7 particles, half of them with Z = 1 and the other half with Z = 2 , i.e. 10 charge units. Onc third o f the system is emitted before equilibration! Of course, this high ratio is favored by the small size of the nuclei. For such nuclei, fusion is very incom- plete. Note, however, that in each bin, there is a broad distribution of OpE values. Even in central collisions, ot,E = 1 or 2 are observed, i.e. nearly complete fusion occurred with cross section of several mb (as ex- pected, the residue velocity and the average parallel velocity of Z = I and 2 is close to V~.m for those events). The variation of the excitation cnergy, in the bombarding energy range 25 to 85 MeV/u, has been discussed in another paper [ 11 ].

Let us compare the PE multiplicities at 65 MeV/u to the number of nucleons contained in the overlap region [12]. At 7 fm, the multiplicity o f Z = 1 PE

A 4 -

, , 4 0 2 7 ' : ,, A r + A I

- i t _ _ ]

'. , - .- - 6 5 MeV. ' u 3 -

,, - - 4 5 M e V . ' u

^ , 2 ,I t , - - - ,

ui ~ / , Z = t

v

1 = ' : t ~ ' - - ' z - - ' , -',_ _.

L I - - I ~ - - L - k ~ _ _ ~ _ _ . - p ( J

. . . . . . . . . . . . . . . ( b ) 5 0 0 1 0 0 0 1 5 0 0 m _ b

Fig. 3. Average number of pre-equilibrium particles, versus the impact parameter value b. h=0 corresponds to r'~v=CM (see text). The widths of the 11 steps represent the cross sections of events detected in the 11 l'~v bins.

particlcs (average m a s s = l . 5 ) is lower than 0.1 whereas the numbcr of interacting nucleons is ~ 1. A multiplicity 1 needs an impact parameter ~ 5.5 fro, where 10 nucleons are in the overlap volume. The production of Z = 2 (mostly alpha particles) needs a larger overlap. At 3 fm, 36 nucleons interact during the first 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 = 1 and both elements reach a multiplicity value >i 3 in head-on collisions. Both the surprisingly large PE multiplicity of Z = 2 particles and its steep increase at low b could bc explained by the increase of the overlap region coupled with the presence of per- formed clusters in the nuclei. These features would be more easily understood in the hot participant zone picture. An alternative explanation could be the coa- lescencc process, which is favored by the larger num- ber of primary PE nucleons. The data shown here provide a good basis for such calculations.

Now, let us compare the 45 and 65 MeV/u data. At a fixed .b value, the multiplicity o f Z = 1 particles exhibits a distinct incrcase with energy, while the

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Volume 237. number 2 PHYSICS LETTERS B 15 March 1990

mul t ip l ic i ty of Z = 2 part icles increases slightly or re- ma ins constant . This difference has no obv ious ex- p lana t ion . Is it a clue that complex part icles and sin- gle nuc leons are due to different PE processes?

In conc lus ion , exclusive m e a s u r e m e n t s of charged

products ob ta ined in Ar on A1 react ions have been

performed. A me thod of sor t ing events has been de-

veloped: the value of the average parallel velocity of

detected products provides the impact pa ramete r

value. It al lowed us to show that the n u m b e r of par- ticles emi t t ed after one (or perhaps two) col l is ions

increases very, quickly when b decreases. Even in the most violent react ions, m a n y nuc leons do not suffer

enough collisions to allow for a full diss ipat ion of their

kinet ic energy. In head-on react ions at 45 and 65

M e V / u , all nuc leons have at least one coll ision, but

7 charged particles have suffered only one (or two)

collisions. Clusters like 4He are emi t t ed as f requent ly

as l ighter particles. This emiss ion of a large fract ion

of the system at the very, beg inn ing of the in te rac t ion severely l imi ts the exci ta t ion energy deposi ted in the

equi l ibra ted incomple te fus ion nuc leus which is sub-

scqucnt ly formed.

One o f us (E .C. ) thanks the F u n d a c a o de A m p a r o a Pesquisa do Estado de Sao Paulo for f inancia l support .

References

[ 1 ] J. Randrup and R. Vandenbosch, Nucl. Phys. A 474 ( 1987 ) 219.

[2] M.C. Robel, Ph.D. Thesis, LBL-8181 (1979). [3] E. Holubet al., Phys. Rev. C 33 (1986) 143. [4] J. Kasagi et al., Phys. Lctt. B 104 ( 1981 ) 434. [ 5 ] T.C. Awes et al., Phys. Rev. C 24 ( 1981 ) 89. [6] G. Augeret al., Phys. Left. B 169 (1986) 161. [ 7 ] R. Dayras et al., Nucl. Phys. A 460 ( 1986 ) 299. [ 8 ] E. Plagnol et al., Phys. Lett. B 221 ( 1989 ) 11. [9] G. Bizard et al., Nucl. Instrum. Methods A 244 (1986) 483.

[ 10 ] A. Peghaire et al., report GANIL p. 89-24, submitted to Nucl. Instrum. Methods.

[ I 1 ] K. Hagel et al., Phys. Lett. B 229 (1989) 20. [12] K. Hagel et al., Proc. XXVII Intern. Meeting on Nuclear

physics (Bormio, 1989). [ 13] See appendix in J. Gosset et al., Phys. Rev. C 16 (1977)

629.

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