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Strong impact parameter dependence of pre-equilibrium particle emission in nucleus-nucleus reactions at intermediate energies
Volume 237, number 2
PHYSICS LETTERS B
15 March 1990
STRONG IMPACT PARAMETER DEPENDENCE OF PRE-EQUILIBRIUM PARTICLE EMISSION 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. S U L L I V A N h, D. C U S S O L ", G. B I Z A R D a, R. B R O U a, M. L O U V E L a, j . p . PATRY ", R. R E G I M B A R T a, J.C. S T E C K M E Y E R a, B. T A M A I N a E. C R E M A b.I, H. D O U B R E b, K. H A G E L b.2, G.M. JIN h.c, A. PI~GHAIRE b F. S A I N T - L A U R E N T b y . C A S S A G N O U d R. L E G R A I N d, C. LEBRUN ~, E. R O S A T O 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°Arat 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 multiplicity increases strongly when the impact parameter value decreases, and reaches 7 in head-on reactions.
The emission o f nucleons and light clusters in the first steps o f a nucleus-nucleus interaction becomes more and more copious when the incident velocity reaches values c o m p a r a b l e to the Fermi velocity. Some nucleons, either isolated or clustered, may escape without suffering any collision in the partner nucleus. In peripheral reactions, they form the projectile-like and target-like spectator nuclei [ 1 ]. In the case of pure Fermi jets [2] nucleons also fail to collide. Let us call them " n o collision" nucleons. Another c o m p o n e n t o f fast emitted 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-equilibrium" nucleons ( P E ) . Some authors define PE as the sum o f both c o m p o n e n t s above. Most experimental data are inclusive or coincidence measurements o f neutrons [3,4] and light charged particles [ 5]. In these studies, average multiplicities per collision have been obtained. It is highly desirable to know to which amount "'no collision" and PE emissions occur in central reactions and thus how they can limit the excitation energy o f the incomplete fusion nucleus. In order to measure the n u m b e r o f " n o collision" and PE nucleons, all or nearly all particles emitted in each event must be measured. We have performed an exclusive experiment in which the charge and velocity o f 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 )
187
Volume 237, number 2
PHYSICS LETTERS B
sive experiments between 15 and 45 M e V / u [ 6 - 8 ] . The measurements have been made from 25 to 65 M e V / u in steps o f 10 MeV/u. The results obtained at 45 and 65 M e V / 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 ( T O N N E A U [ 1 0 ] ) . Elements were separated using the energy versus time of flight technique. All events with a multiplicity larger than 1 were recorded. Very peripheral interactions do not bring an excitation energy sufficient to emit a charged particle and arc thus eliminated by the trigger condition. The neutrons are not detected and ( 1 0 - 1 5 % ) of the charged products are missed due to narrow dcad 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 m o m e n t u m of all detected products was more than 65% of the projectile's linear m o m e n t u m [ 11,12 ]. Since the grazing angle is close to 1 : and the m i n i m u m 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 m o m e n t u m is not measured. The analysis keeps all central and intermediate impact parameter reactions as well as a few well characterized peripheral reactions. Simulation calculations confirmed this picture [ 12 ]. The next step was to sort events according to their violence, which is assumed to increase when the impact parameter value b decreases. We use the fact that the "no collision" nucleons (or clusters, or fragments) 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 reaction increases when the number of these "no collision" target nucleons decreases. Whether these nucleons 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 188
15 March 1990
which accurately measures the mass, direction and velocity of all final products, including neutrons, except the "'no collision" target nucleons. They carry the whole initial projectile linear momentum. The mass-weighted average parallel velocity of the detected nucleons is I ' . , = ~'"" ' = ' m, 7, I', cos 0,
(l)
ZI'_-, m,7, where m, is the mass. V, is the laboratory velocity, O, the laboratory polar angle and 7, the relativistic parameter o f each of the v detected products. 14d~is simply the velocity which, when multiplied by the detected mass, gives the parallel m o m e n t u m 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 according 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 correspondence. Note that V~m is reached only if all target nucleons have at least one collision. The correspondence between I'av and h depends on the system studied: 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 detectors. A direct observation of the experimental resolution is given by events with t~,, slightly lower than V,.m. This resolution led us to divide the I~v distribution in I I bins. Other variables linked to the violence of the reaction vary consistently: as I,;~,, decreases from I,~ to I'~,,, the average multiplicity of
Volume 237, number 2
PHYSICS LETTERS B
Ar + AI
45 MeV'u
l-
Z= 6-8
vii . . . .
F'T"
"T ~
--""
i
i
-
~T
- t ~
Z= 6-8
ZE 1,2
" -
~
Z>~9
1
i-
" " 1
i
Z>~9
!
•"
~6 "
I
•
L NN CM
P-~
, __ N~/~l V//(cm
,It
~
-,~
, ~ - - ~ ,-~
,' ns)
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: central 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 velocity threshold.
15 March 1990
This slow component is better seen in fig. 2, for bins 10, 8, 6, 4, 2 and 1, ranging from V,,. slightly below lip ( u p p e r left corner) down to Va~ just below Vcm ( b o t t o m right), i.e. from gentle mid-peripheral to violent central reactions. The values o f I,'~ are shown as black rectangles. This figure shows, in each bin. the parallel velocity spectra o f light panicles ( Z = 1, 2) and heavy products (Z>~ 6). The velocity o f the equilibrated nuclei is easily obtained from the 1/, distribution of heavy products which is narrow (due to phase space limitations) and has no slow component. As in fig. 1, it coincides with the location o f the high velocity peak for Z = 1 and 2. The equilibrated Z = I and 2 component is obtained by symmetrizing its upper part around the velocity of the equilibrated nuclei (dotted lines). The remaining particles (dashed lines)
0
.1
.2
.3
c
.4
0
.1
.2
.3 C .4
1000 800
detected products increases, the measured total charge increased from around 18 ( A r ) to 31 ( A r + A 1 ) , and the average transverse m o m e n t u m 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-peripheral reactions, i.e. large V,v ( u p p e r part o f fig. 1 ), the invariant cross sections o f heavy fragments (mostly Z>~9) and light charged particles exhibit circular contours centered close to lip: excited projectile-like transfer products have isotropically e v a p o r a t e d a few light panicles. For Z = 1 and 2, a weak c o m p o n e n t at l,'l, values below V~,,, is present. For central reactions, i.e. I/~v close to Vcm (lower part o f fig. 1 ), the heavy fragments (mostly Z = 6 - 8 ) are the residues o f equilibrated nuclei formed via fusion, which de-excited through isotropic emission of many particles and clusters. The velocities o f the equilibrated nuclei lie between I,"o and Vcm, indicating that fusion is far from being complete. For Z = I and 2, in a d d i t i o n to particles isotropically emitted by the incomplete fusion nucleus, a c o m p o n e n t at VIIvalues below l'~m is clearly seen. It does not show up for higher Z values (except, possibly, for very few Z = 3 p a n i c l e s ) .
400 2OO
5
>
2000
1000
300{]
200C
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 different 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. 189
Volume 237, number 2
PHYSICS LETTERS B
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 ½Vo). 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 distributions 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 participant zone either [ 13 ]. Indeed, the source velocity would lie between INN and V~m and the cold projcctile fragment should be observed at V. close to l~, at variance with the many products ( ~ 12 in central reactions) observed at V. between l'~m and Vo. Fig. 3 shows the variation of the averagc PE multiplicity ( t ) ~ ) versus b. (t)p,) is very low in mid-peripheral reactions and rises rapidly when b decreases. Head-on reactions (full overlap of Ar and AI) corrcspond 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 multiplicities 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 incomplete. 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 expected, 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 M e V / u , has been discussed in another paper [ 11 ]. Let us compare the PE multiplicities at 65 M e V / u to the number of nucleons contained in the overlap region [12]. At 7 fm, the multiplicity o f Z = 1 PE 190
15 March 1990
A 4-
, ,
'
40
: ,,
-
+
AI
it__]
'.
3-
,
- .- -
6 5 MeV.' u
,,
- -
45 MeV.' u
^ 2 ui
27
Ar
,I ~
, ,---,
t /
,
Z=t
v 1
z
=':
t~
' --'
--', L I-
-I
-',_ _.
~--L-
. . . . . . . . . . . . . . . 500 1000
_ _
k~~_ _ .
-
1500
p(J
(b) 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'~vbins. 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 performed clusters in the nuclei. These features would be more easily understood in the hot participant zone picture. An alternative explanation could be the coalescencc process, which is favored by the larger number of primary PE nucleons. The data shown here provide a good basis for such calculations. Now, let us compare the 45 and 65 M e V / u data. At a fixed .b value, the multiplicity o f Z = 1 particles exhibits a distinct incrcase with energy, while the
Volume 237. number 2
PHYSICS LETTERS B
m u l t i p l i c i t y o f Z = 2 particles increases slightly or rem a i n s constant. T h i s difference has no o b v i o u s exp l a n a t i o n . Is it a clue that c o m p l e x particles a n d single n u c l e o n s are due to different PE processes? In c o n c l u s i o n , exclusive m e a s u r e m e n t s o f charged products o b t a i n e d in Ar on A1 reactions have been performed. A m e t h o d o f sorting e v e n t s has been developed: the value o f the average parallel velocity of detected products provides the i m p a c t p a r a m e t e r value. It allowed us to show that the n u m b e r of particles e m i t t e d after o n e (or perhaps two) collisions increases very, quickly w h e n b decreases. Even in the most violent reactions, m a n y n u c l e o n s do not suffer enough collisions to allow for a full dissipation of their kinetic energy. In h e a d - o n reactions at 45 a n d 65 M e V / u , all n u c l e o n s have at least one collision, but 7 charged particles have suffered o n l y one (or two) collisions. Clusters like 4He are e m i t t e d as frequently as lighter particles. T h i s e m i s s i o n o f a large fraction o f the system at the very, b e g i n n i n g of the i n t e r a c t i o n severely limits the excitation energy deposited in the e q u i l i b r a t e d i n c o m p l e t e fusion n u c l e u s which is subs c q u c n t l y formed.
15 March 1990
O n e o f us ( E . C . ) t h a n k s the F u n d a c a o de A m p a r o a Pesquisa do Estado de Sao Paulo for financial 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.
191
PHYSICS LETTERS B
15 March 1990
STRONG IMPACT PARAMETER DEPENDENCE OF PRE-EQUILIBRIUM PARTICLE EMISSION 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. S U L L I V A N h, D. C U S S O L ", G. B I Z A R D a, R. B R O U a, M. L O U V E L a, j . p . PATRY ", R. R E G I M B A R T a, J.C. S T E C K M E Y E R a, B. T A M A I N a E. C R E M A b.I, H. D O U B R E b, K. H A G E L b.2, G.M. JIN h.c, A. PI~GHAIRE b F. S A I N T - L A U R E N T b y . C A S S A G N O U d R. L E G R A I N d, C. LEBRUN ~, E. R O S A T O 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°Arat 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 multiplicity increases strongly when the impact parameter value decreases, and reaches 7 in head-on reactions.
The emission o f nucleons and light clusters in the first steps o f a nucleus-nucleus interaction becomes more and more copious when the incident velocity reaches values c o m p a r a b l e to the Fermi velocity. Some nucleons, either isolated or clustered, may escape without suffering any collision in the partner nucleus. In peripheral reactions, they form the projectile-like and target-like spectator nuclei [ 1 ]. In the case of pure Fermi jets [2] nucleons also fail to collide. Let us call them " n o collision" nucleons. Another c o m p o n e n t o f fast emitted 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-equilibrium" nucleons ( P E ) . Some authors define PE as the sum o f both c o m p o n e n t s above. Most experimental data are inclusive or coincidence measurements o f neutrons [3,4] and light charged particles [ 5]. In these studies, average multiplicities per collision have been obtained. It is highly desirable to know to which amount "'no collision" and PE emissions occur in central reactions and thus how they can limit the excitation energy o f the incomplete fusion nucleus. In order to measure the n u m b e r o f " n o collision" and PE nucleons, all or nearly all particles emitted in each event must be measured. We have performed an exclusive experiment in which the charge and velocity o f 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 )
187
Volume 237, number 2
PHYSICS LETTERS B
sive experiments between 15 and 45 M e V / u [ 6 - 8 ] . The measurements have been made from 25 to 65 M e V / u in steps o f 10 MeV/u. The results obtained at 45 and 65 M e V / 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 ( T O N N E A U [ 1 0 ] ) . Elements were separated using the energy versus time of flight technique. All events with a multiplicity larger than 1 were recorded. Very peripheral interactions do not bring an excitation energy sufficient to emit a charged particle and arc thus eliminated by the trigger condition. The neutrons are not detected and ( 1 0 - 1 5 % ) of the charged products are missed due to narrow dcad 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 m o m e n t u m of all detected products was more than 65% of the projectile's linear m o m e n t u m [ 11,12 ]. Since the grazing angle is close to 1 : and the m i n i m u m 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 m o m e n t u m is not measured. The analysis keeps all central and intermediate impact parameter reactions as well as a few well characterized peripheral reactions. Simulation calculations confirmed this picture [ 12 ]. The next step was to sort events according to their violence, which is assumed to increase when the impact parameter value b decreases. We use the fact that the "no collision" nucleons (or clusters, or fragments) 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 reaction increases when the number of these "no collision" target nucleons decreases. Whether these nucleons 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 188
15 March 1990
which accurately measures the mass, direction and velocity of all final products, including neutrons, except the "'no collision" target nucleons. They carry the whole initial projectile linear momentum. The mass-weighted average parallel velocity of the detected nucleons is I ' . , = ~'"" ' = ' m, 7, I', cos 0,
(l)
ZI'_-, m,7, where m, is the mass. V, is the laboratory velocity, O, the laboratory polar angle and 7, the relativistic parameter o f each of the v detected products. 14d~is simply the velocity which, when multiplied by the detected mass, gives the parallel m o m e n t u m 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 according 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 correspondence. Note that V~m is reached only if all target nucleons have at least one collision. The correspondence between I'av and h depends on the system studied: 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 detectors. A direct observation of the experimental resolution is given by events with t~,, slightly lower than V,.m. This resolution led us to divide the I~v distribution in I I bins. Other variables linked to the violence of the reaction vary consistently: as I,;~,, decreases from I,~ to I'~,,, the average multiplicity of
Volume 237, number 2
PHYSICS LETTERS B
Ar + AI
45 MeV'u
l-
Z= 6-8
vii . . . .
F'T"
"T ~
--""
i
i
-
~T
- t ~
Z= 6-8
ZE 1,2
" -
~
Z>~9
1
i-
" " 1
i
Z>~9
!
•"
~6 "
I
•
L NN CM
P-~
, __ N~/~l V//(cm
,It
~
-,~
, ~ - - ~ ,-~
,' ns)
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: central 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 velocity threshold.
15 March 1990
This slow component is better seen in fig. 2, for bins 10, 8, 6, 4, 2 and 1, ranging from V,,. slightly below lip ( u p p e r left corner) down to Va~ just below Vcm ( b o t t o m right), i.e. from gentle mid-peripheral to violent central reactions. The values o f I,'~ are shown as black rectangles. This figure shows, in each bin. the parallel velocity spectra o f light panicles ( Z = 1, 2) and heavy products (Z>~ 6). The velocity o f the equilibrated nuclei is easily obtained from the 1/, distribution of heavy products which is narrow (due to phase space limitations) and has no slow component. As in fig. 1, it coincides with the location o f the high velocity peak for Z = 1 and 2. The equilibrated Z = I and 2 component is obtained by symmetrizing its upper part around the velocity of the equilibrated nuclei (dotted lines). The remaining particles (dashed lines)
0
.1
.2
.3
c
.4
0
.1
.2
.3 C .4
1000 800
detected products increases, the measured total charge increased from around 18 ( A r ) to 31 ( A r + A 1 ) , and the average transverse m o m e n t u m 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-peripheral reactions, i.e. large V,v ( u p p e r part o f fig. 1 ), the invariant cross sections o f heavy fragments (mostly Z>~9) and light charged particles exhibit circular contours centered close to lip: excited projectile-like transfer products have isotropically e v a p o r a t e d a few light panicles. For Z = 1 and 2, a weak c o m p o n e n t at l,'l, values below V~,,, is present. For central reactions, i.e. I/~v close to Vcm (lower part o f fig. 1 ), the heavy fragments (mostly Z = 6 - 8 ) are the residues o f equilibrated nuclei formed via fusion, which de-excited through isotropic emission of many particles and clusters. The velocities o f the equilibrated nuclei lie between I,"o and Vcm, indicating that fusion is far from being complete. For Z = I and 2, in a d d i t i o n to particles isotropically emitted by the incomplete fusion nucleus, a c o m p o n e n t at VIIvalues below l'~m is clearly seen. It does not show up for higher Z values (except, possibly, for very few Z = 3 p a n i c l e s ) .
400 2OO
5
>
2000
1000
300{]
200C
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 different 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. 189
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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 ½Vo). 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 distributions 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 participant zone either [ 13 ]. Indeed, the source velocity would lie between INN and V~m and the cold projcctile fragment should be observed at V. close to l~, at variance with the many products ( ~ 12 in central reactions) observed at V. between l'~m and Vo. Fig. 3 shows the variation of the averagc PE multiplicity ( t ) ~ ) versus b. (t)p,) is very low in mid-peripheral reactions and rises rapidly when b decreases. Head-on reactions (full overlap of Ar and AI) corrcspond 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 multiplicities 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 incomplete. 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 expected, 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 M e V / u , has been discussed in another paper [ 11 ]. Let us compare the PE multiplicities at 65 M e V / u to the number of nucleons contained in the overlap region [12]. At 7 fm, the multiplicity o f Z = 1 PE 190
15 March 1990
A 4-
, ,
'
40
: ,,
-
+
AI
it__]
'.
3-
,
- .- -
6 5 MeV.' u
,,
- -
45 MeV.' u
^ 2 ui
27
Ar
,I ~
, ,---,
t /
,
Z=t
v 1
z
=':
t~
' --'
--', L I-
-I
-',_ _.
~--L-
. . . . . . . . . . . . . . . 500 1000
_ _
k~~_ _ .
-
1500
p(J
(b) 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'~vbins. 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 performed clusters in the nuclei. These features would be more easily understood in the hot participant zone picture. An alternative explanation could be the coalescencc process, which is favored by the larger number of primary PE nucleons. The data shown here provide a good basis for such calculations. Now, let us compare the 45 and 65 M e V / 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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m u l t i p l i c i t y o f Z = 2 particles increases slightly or rem a i n s constant. T h i s difference has no o b v i o u s exp l a n a t i o n . Is it a clue that c o m p l e x particles a n d single n u c l e o n s are due to different PE processes? In c o n c l u s i o n , exclusive m e a s u r e m e n t s o f charged products o b t a i n e d in Ar on A1 reactions have been performed. A m e t h o d o f sorting e v e n t s has been developed: the value o f the average parallel velocity of detected products provides the i m p a c t p a r a m e t e r value. It allowed us to show that the n u m b e r of particles e m i t t e d after o n e (or perhaps two) collisions increases very, quickly w h e n b decreases. Even in the most violent reactions, m a n y n u c l e o n s do not suffer enough collisions to allow for a full dissipation of their kinetic energy. In h e a d - o n reactions at 45 a n d 65 M e V / u , all n u c l e o n s have at least one collision, but 7 charged particles have suffered o n l y one (or two) collisions. Clusters like 4He are e m i t t e d as frequently as lighter particles. T h i s e m i s s i o n o f a large fraction o f the system at the very, b e g i n n i n g of the i n t e r a c t i o n severely limits the excitation energy deposited in the e q u i l i b r a t e d i n c o m p l e t e fusion n u c l e u s which is subs c q u c n t l y formed.
15 March 1990
O n e o f us ( E . C . ) t h a n k s the F u n d a c a o de A m p a r o a Pesquisa do Estado de Sao Paulo for financial 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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