- Email: [email protected]
nucleon Pb+Au two-body final-state reactions
NUCLEAR PH Y SICS A ELSEVIER
Nuclear Physics A 587 (1995) 499-512
Complete energy damping in 29 MeV/nucleon Pb+Au two-body final-state reactions * R. Bougault a, J.F. Lecolley a, M. Aboufirassi a, A. Badala a'a, B. Bilwes b, R. Brou a, j. Colin a, F. Cosmo h, D. Durand a, j. Galin c, A. Genoux-Lubain a, D. Guerreau c, D. Horn a,2, D. Jacquet d, J.L. Laville a,3 C. Le Brun a, E Lefebvres a, O. Lopez a, M. Louvel a, M. Mahi a, M. Morjean c, C. Paulot a, A. Peghaire c, G. Rudolf h, E Scheibling b, J.C. Steckmeyer a, L. Stuttg6 b, S. Tomasevic b, B. Tamain a a Laboratoire de Physique Corpusculaire Caen (IN2P3-CNRS/1SMRA et Universitd de Caen), BM Mardchal Juin, F-14050 Caen cddex, France b Centre de Recherches Nueldaires (IN2P3-CNRS/Universitd Louis Pasteur), B.P. 20, F-67037 Strasbourg cddex, France c GANIL (DSM-CEA/IN2P3-CNRS), B.P. 5027, F-14021 Caen cddex, France tl Institut de Physique Nucldaire (IN2P3-CNRS/Universitd Paris Sud), B.P. 1, F-91406 Orsay cddex, France Received 4 January 1995; revised 6 February 1995
Abstract Decay products emitted in highly dissipative P b + A u reactions at 29 M e V / n u c l e o n have been detected using a large area array. Multiplicities of fragments as large as 8 have been detected with a sizeable cross section. The m-fragment exit channels are fully compatible with the formation o f a transient excited dinuclear system formed in damped collisions. The excitation energy function shows that fully damped collisions are achieved even for m = 2 indicating that heavy nuclei are able to sustain high excitation energy and end up as evaporation residues. Keywords: NUCLEAR REACTIONS 197Au (Pb,X), E = 29 MeV/nucleon; measured fragment multiplicities; deduced transient excited dinuclear system formation evidence.
* Experiment performed at Ganil. 1 On leave from: INFN, Catania, Italy. 2 On leave from: CRL-AECL, Chalk River, Canada. 3 Present address : SUBATECH, Nantes, France. 0375-9474/95/$09.50 (~) 1995 Elsevier Science B.V. All rights reserved SSD1 0 3 7 5 - 9 4 7 4 ( 9 5 ) 0 0 0 4 1 - 0
500
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
1. Introduction Heavy-ion induced reactions in the Fermi energy domain (10-100 MeV/A) allow one to investigate the link between the different reaction mechanisms which occur at low and high bombarding energies. They remain a unique tool to study nuclear matter and for instance, the balance between the mean-field and the nucleon-nucleon interaction effects, the statistical mechanics applied to a finite ensemble such as the nucleus, the time scale for equilibration phenomena, the damping of energy and the role of the dynamics in the processes. In this paper, we focus on the study of the behaviour of heavy nuclei produced in very inelastic collisions for the system Pb+Au at 29 MeV/nucleon. At energies near the Coulomb barrier, the deep inelastic reaction mechanism [ 1-3] plays an important role in heavy-ion reactions. This process is still present at higher bombarding energies [4-7]. However, for very heavy systems and for a center-of-mass available energy of about 6 MeV/A, the full energy damping had not been demonstrated yet [8,9]. In a previous publication based on the same experiment [ 10], it has been shown that, for Pb+Au 29 MeV/nucleon, all collisions present a first step binary character irrespective of possible further disassembly of the two highly excited primary partners. There is no fusion. Furthermore, at an excitation energy of about 4.5 MeV/A, the most probable exit channel becomes the production of Intermediate Mass Fragments from the two primary partners [ 10,11]. Nevertheless we will see that the two-fragment exit channel leading to evaporation residues is still present at high excitation energies (6 MeV/nucleon). This last observation raises questions about the de-excitation scheme of a highly excited nucleus. After a rapid presentation of the experimental set-up and of the general trends of the detected events, we will focus on two-fold events. The goal of this study is to demonstrate that full energy damping has been achieved for the two-fragment exit channel. For this purpose, the excitation function has been extracted from the two-fold events using a background subtraction and taking into account for pre-equilibrium effects. Finally, the production cross section of such highly excited nuclei will be compared with the prediction of a statistical model.
2. Experimental description The experiment was performed at the GANIL facility in the Nautilus scattering chamber by bombarding a 500 /zg/cm 2 Au target with a one-particle nA Pb beam at 29 MeV/nucleon. Fragments were detected using the detectors Delf [12] and XYZt [ 13], while light charged particles were detected with the Mur [ 14] and the Tonneau [ 15]. Delf and XYZt are an ensemble of 30 position-sensitive parallel-plate avalanche counters (PPAC), each followed by an ionisation chamber. The covered angular range is from 3 ° to 150 ° with a 55% geometrical acceptance and full efficiency for atomic numbers equal to or larger than 8. The set-up has a low velocity threshold: 0.5 cm/ns (0.13 MeV/nucleon) for Delf (30°-150 °) and 2 cm/ns (2.07 MeV/nucleon)
501
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
Table 1 Multiplicity cross sections Multiplicity Cross section (mb)
2 4300
3 670
4 220
/> 5 56
for XYZt in the forward direction ( 3 ° - 3 0 ° ) . The fragment measured parameters are the atomic number Z, the velocity V and the angles with a resolution better than one degree. The Mur and Tonneau cover an angular range between 3 ° and 150 ° with about 50% geometrical acceptance and can detect light charged particles (up to Z = 6, but mainly Z = 1, 2) with a velocity threshold of about 2.2 cm/ns. The four types of detectors have an azimuthal symmetry. The Mur and the Tonneau were not used in the triggering condition which was decided among the 30 PPACs o f Delf and XYZt. In the here described experiment, the triggering condition was set to one detected fragment at least.
3. General trends of the detected events Coincidence events of n-fold have been detected with up to n = 8 fragments. The detected cross section represents about half the reaction cross section. Since the nfold measured events contain events with actual fragment multiplicity m 7> n, in order to infer the corrected multiplicity cross sections, we have proceeded as follows. We have retained events leading to the detection of more than 80% of both the available total parallel momentum and total charge ("well characterised" events). The measured values take into account fragments and light charged particles. The latter, which did not contribute to the triggering condition, were corrected by a factor of 2 to take into account the 50% geometrical acceptance of the Mur and Tonneau. Then each "well characterised" detected event has been used for generating an entire set of events by a random azimuthal-angle rotation of the experimental set-up. These generated events are then passed through a filter, which represents the experimental covered angles, to estimate the rate of m-type events on each n ~< m fold. It was then possible to extract the apparatus-corrected multiplicity cross sections. The result is presented in Table 1. The total corrected cross section represents about 5 / 6 of the reaction cross section with roughly 1 barn corresponding to more than two fragments in the exit channel. As mentioned previously, it has been shown [ 10] that all collisions leading to m fragments present a binary character in a first step. In Fig. 1, the distribution of detected light charged particles (Nlcp) for various values of the fragment multiplicity ("well characterised" events) are displayed. The pattern of the summed distribution is similar with what has been measured as a function o f neutron multiplicity for the same system at the same incident energy [ 11 ]. There is a large contribution at small Nlcp values associated with peripheral collisions and a shoulder around Nlcp = 8 associated with the largest fragment multiplicities and extending up to 15 detected LCP (recall that the average LCP detection acceptance is around 50%). As the fragment multiplicity increases, the detected LCP number
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
502
1°5I
~m=2 ]
~
Om=5 "~ m = 4
104 I
f
- .,.,e---e._._.~-~
,
,
Am-~5
10 2
10
1
0
2
4
6
8
10
12
14
16
Nlcp Fig. 1. Number of light charged particles, as measured, detected in coincidence with m fragments ("well characterised events"). The histogram represents the sum of the different spectra.
distribution evolves steadily towards a more symmetric distribution peaked around 8. For Nlcp larger than 8, the probability of finding large numbers of LCP does not depend strongly on the associated number of fragments. If we assume that the multiplicity of light particles is a good measure of the violence of a collision, then this is a first indication that violent collisions can lead to two-body in the final state. For such events, the extremely heated projectile- and target-like nuclei end up as evaporation residues. In the following we will focus on two-fragment production considering the entire set of two-fold coincidence data (i.e. no selection based on "well characterised" events).
4. Events with two detected fragments Fig. 2 presents the two-fold events as detected. The presented observables concern the detected fragments only. On the left part, the total detected charge as a function of the measured parallel momentum normalised to the entrance channel values is displayed. When detected light charged particles are taken into account the balances are better. A detected two-fold event can originate from events with a multiplicity (m) greater than or equal to 2. This is visible in Fig. 2-1eft, the bump corresponding to a balance of 1 for both observables originates from m = 2 (zone a) while the one lying on half atomic number and 1 momentum balance is related to the detection of only the two fission fragments of the projectile from m >~ 3 events (zone b). In order to extract observables concerning m = 2 events, we have proceeded in two steps. The procedure can be summarised as follows, (i) a primary selection has been made on the basis of an event by event analysis, (ii) a m ~> 3 event background subtraction has been performed on the spectra of the two-fold events retained after the first selection. From this procedure m = 2 event spectra have been obtained.
503
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
(IogorithrnTc
1.4
contour
lines)
10 4 lO 3
1.2
~9 102 10 1
1
0
.t_ 0.8 0.5
.-.t~ 0.6
105~
0.4
104~
)
0.2 0
1
I
=
i
I i ~ J 0.5
i
[ r I r
e
2
× (V(Iz) + v~Z))/(Vbeam/2) 7
~
I I/
H 10
1
(Z 1 X V~"))+ (Z 2X V~z))
~, -200
I
,
-100
f
0
,
i
100
,
~1
200
(012 - 180) (o)
Fig. 2. Characteristics of the two-fold events in the laboratory frame. The label (z) represents the beam axis, 1 and 2 refer to the two detected fragments. For the two-dimensional plot, atomic number and momentum balance are relative to the entrance channel (Zbeam, Zbeamx Vbeam)- The one-dimensionalspectra present the fragment-velocitycorrelation along the beam axis and on to tile planes perpendicular to the beam axis. The detailed description of the two-step procedure will now be explained but it has to be kept in mind that the consequence of the second step is the vanishing of the event by event analysis concept in our analysis. (i) In order to eliminate the two-fold detected events which clearly originate from m ~> 3 events (as the zone b o f Fig. 2-1eft), the primary step requires the momentum conservation in the beam direction and in the planes perpendicular to it. Since the studied system is almost symmetric and since the atomic number of the fragments are heavily affected by secondary evaporation, the method is based on the measured velocities which are, on the average, conserved in such a process rather than on the momenta. The filter consists of two conditions: to require that the laboratory center-of-mass velocity in the beam direction of the two detected fragments (the system is assumed to be symmetric) is equal to half the beam velocity (Fig. 2-right): 0.5 (gl (z) -~- V2(z)) = (1gbeam) + 2 5 % ;
(1)
- to require that the angle between the two fragment velocities projected on to the planes perpendicular to the beam direction is equal to 180 ° (Fig. 2-right): 012 = 180 ° -t- 25 °.
(2)
This first selection does not eliminate all the m >~ 3 events contained in the two-fold event sample. (ii) The second step is a background subtraction applied to the two-fold event spectra obtained after the first-step selection. The background represents the remaining
504
R. Bougault et aL /Nuclear Physics A 587 (1995) 499-512
m /> 3 event contained in the two-fold event spectra after the first selection. For this purpose we have used the method described in Ref. [ 16]. The method uses the three-fold coincidences, from which one detected fragment has been removed randomly ("three-fold minus one"), and a normalisation factor in order to described the two-fold m ~> 3 events. The observable used to deduce the background rate of the two-fold coincidences was the perpendicular center-of-mass velocity of the fragments (VcM±). This variable is defined as the projection on to the perpendicular planes relative to the beam axis of the fragment center-of-mass velocity. Furthermore, in order to deduce unambiguously the value of the normalisation factor, we have used VCM± spectra for both sets of two-fold and "three-fold minus one" events, not filtered by the first step selection. The VCM± spectra are presented in Fig. 3-1eft for the two-fold and the "three-fold minus one"events. These spectra are not filtered by the primary step selection and it is clear that the long tail (VcM± >7 1.5 cm/ns) for the two-fold coincidences corresponds to rn/> 3 events since those events are unable to achieve momentum conservation. This background is well reproduced by the "three-fold minus one" spectrum as soon as a factor of 1.35 is applied to it. This factor, deduced from the VCM± spectra, is explained by different geometrical efficiencies for m = 2 and 3 events. From the "well characterised" events we were able to measure the percentage of m = 2 events and m = 3 events detected as two-fold events, these percentages are respectively 51.4% and 38.1% leading to a ratio identical to the value of the correction factor. This method gives a universal way to subtract the background from all two-fold spectra. The result of the two-step method is presented in Fig. 3-right. This reconstructed figure is issued from (i) the primary selection on the two-fold events, (ii) a background subtraction with the 1.35 factor applied to the same spectra concerning "three-fold minus one" selected events. In the following all spectra and mean values of variables will be obtained through the above described procedure. Therefore, they will be labelled "reconstructed". In order to extract the excitation function, we will now characterise these events by studying their kinematics.
5. Energy balance For a two-body reaction, the energy balance of the system leads to E* = ECM - - TKE (MeV)
-
Epre,
(3)
where ECM is the available energy, TKE the total kinetic energy of the two partners just after separation (so before subsequent evaporation) and F-,pre the total energy removed by pre-equilibrium emission. All quantities refer to center-of-mass system. The pre-
505
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
10 5
1.4
10 4
1.2
(Iogorilhmic contour lines)
] 10 3
10 2
~
0.8
~
o.6 0.4
10 0.2 1
0
0
1
2
3
VcM ± (cm/ns)
I
0
,
.
.
0.5
.
.
~
1
(Z 1 × V~ )) + (Z 2 × V~z))
Fig. 3. Left: VCM.I_spectra for two-fold events (upper histogram) and for "three-fold minus one" events (hatched area). Right: same as Fig. 2-1eftafter event selection and background subtraction. equilibrium definition implies all particles which have been emitted before the separation of the projectile-like and the target-like nuclei. The total kinetic energy is given by TKE (MeV) = 1 Aprojeetile-likeAtarget-like Vr21" 2 Aprojectile-like"k- Atarget-fike
(4)
V~el is the relative velocity between the two partners and the mass numbers are referring to partner sizes before subsequent evaporation. With the only assumption that the preequilibrium particles are equally issued from the projectile and the target (symmetric system), i.e. Aprojeetile-like= Atarget-like, this leads to TKE (MeV/A) = 1~v,e~. 2
(5)
Since the sequential evaporation process does not affect the measured fragment velocities on the average, the T K E ( M e V / A ) can be used to characterise the damping of energy independently of any pre-equilibrium effect. Nevertheless, Epre has to be measured in order to deduce the excitation energy. This is achieved in the following section.
6. Pre-equilibrium particles In the Fermi energy region, the pre-equilibrium particle process can play an important role and the velocity of those particles can extend to values corresponding to several times that of their parent nucleus [ 17]. The energy carried away by these pre-equilibrium particles can prevent deposition of high excitation energy in a composite system [ 18 ] and
506
R. Bougault et a l . / N u c l e a r Physics A 5 8 7 (1995) 4 9 9 - 5 1 2
25
10 3 (Io9ofithmic z scole)
[] uQF1
noon° DOn•o••• on ~,nnnn• 17~17r70ooo nOD
r~ ,-,I
15
°
10 2 _
DO
•on•oDD
]
o0,
ODoo
7~ ,~
o
000
0
=o 10
r) i~-j
[_ ~ D D o D [] I_D_I_L~Di-'IDD D D n LDU_LLJDI-7D D n
10
.z
~D~I-313
0
5
....
10
ULl L~
~
1
O []
o r.r,--:,
\
e-
, ....
15
i
, ....
20
25
I~LCP " ~pLFI (cm/ns)
0
,
....
10
, ....
20
|,
30
VR12 (cm/ns)
Fig. 4. Reconstructed spectra of Z = 1 particles detected between 5 and 150 ° for TKE=4-5 MeV/A. A method to identify pre-equilibrium particles.
associated multiplicity seems to increase with decreasing impact parameter [ 19]. Several works related to the same system at the same bombarding energy [20,8,21] have shown that the neutron production can be explained through an equilibrated part and a weak nonequilibrium component. The equilibrated part is well reproduced by a parametrisation involving the PLF and TLF sources (the projectile-like and the target-like nuclei). The pre-equilibrium neutron emission is consistent with the Fermi-jet model [22] and corresponds to about 8 neutrons for dissipative detected events corresponding to a total kinetic energy of 3.7 M e V / A [8,23]. In order to measure the pre-equilibrium particle multiplicity, we have used their ability to achieve much larger velocities (Fermi jets) than evaporated particles. For the latter large velocities are only found as a tail in the spectra. The fast velocity component of LCP has not been extracted from absolute velocity spectra but rather by using the relative velocities between LCP and the two heavy partners (PLF and TLF). Reconstructed spectra of Z = 1 particles detected from 5 ° to 150 ° in coincidence with two fragments are presented in Fig. 4 for TKE(MeV/A) ranging from 4 to 5 MeV/A. The two-dimensional spectrum presents the relationship between the two abovementioned relative velocities. The spectrum on the right side of the picture corresponds to the projection on to the diagonal axis, i.e. the reconstructed spectrum of /
VRj2 = ~/IVlcp - VPLFI2 + ]V~p - VTLF[2.
(6)
The reconstructed data present two contributions. The most important one is related mainly to evaporated Z = 1 particles (small relative velocities in accordance with an evaporation scheme) and it seems possible to separate PLF and TLF sources from such a correlation. The second contribution is mainly visible at high relative velocities
507
R. Bougault et aL /Nuclear Physics A 587 (1995) 499-512
3°1
E
E
5
25
~
20
•
15
[]
DATA
"
i0
E, 0
~Jlr 0
1
2
3
4
5
6
7
8
T K E (MeV/A) Fig. 5. Multiplicity of pre-equilibrium nucleons versus the total kinetic energy (reconstructed correlation). The quoted impact parameter values refer to Landau-Vlasov calculations.
(Vm2 ~> 20 cm/ns), but it extends down also to smaller Vm2. It can be clearly associated with pre-equilibrium emission. A pure fraction of the pre-equilibrium particles can be selected with the condition VR12 >~ 20 cm/ns. This method presents two main advantages. The first one is its frame independence, the second is the possibility of using a unique selection value independent of TKE: for a prompt particle originating from the projectile-like nucleus, as TKE decreases [Vlcp - VpLFI will increase but IVlcp - VTLFI will decrease of the same amount and vice-versa for a prompt particle emitted by the target-like nucleus. These two points ensure a good selection independent of the energy damping. The selection method has been applied for several bins in TKE(MeV/A). For each bin, the reconstructed number of fast pre-equilibrium has been extracted with the reconstructed mean value of TKE(MeV/A). Nevertheless the pre-equilibrium multiplicity is not fully described by fast velocity Z = 1 particles. It implies neutrons and in addition this process contributes also to the first bump (low VR12 values) of Fig. 4 by interactions of nucleons emitted from one partner with the nucleons of the other one. So far the numbers of fast Z = 1 particles have been normalised to the value of neutron pre-equilibrium multiplicity (corrected by the ratio N/Z of the entrance channel) for the same system and for TKE=3.7 MeV/A [8,23]. This normalisation implies the assumption of a constant percentage between the number of fast velocity particles and the multiplicity of pre-equilibrium nucleons. We report on Fig. 5 the behaviour of the pre-equilibrium nucleon multiplicity as a function of TKE (black circles). In order to check our measurements, we have reported in the figure results obtained with dynamical calculations of the Landau-Vlasov type [24]. These calculations have been performed for the same system and the same bombarding energy (open squares) [20] (open triangles) [25]. Both calculations have been done with a soft Zamick effective interaction, the second one has taken into account the isospin dependence
508
R. Bougault et aL /Nuclear Physics A 587 (1995) 499-512
of the mean field. We see that the agreement is excellent. For head-on collisions, the calculations seems to indicate a saturation or a small decrease of the pre-equilibrium multiplicity (not reported in the figure). The semi-classical calculation of Ref. [25] gives a mean total energy removed by pre-equilibrium emission of 17 MeV/A (ranging from 17.9 to 16.4 M e V / A for an impact parameter ranging from 12 to 2 fm). The nonequilibrated part of the neutron spectra detected for the same system in Ref. [8] is well fitted by a volume emission from a "source at rest in the center of mass frame" parametrisation with a slope parameter ~- = 7 MeV [21]. This is consistent with a dominant low-velocity part of the pre-equilibrium particles and with the mean energy deduced from the semi-classical calculation when including the binding energy in the energy balance (27-+8 M e V / A ) . Therefore, for the energy balance, the pre-equilibrium nucleon multiplicity ( M p r e ) will be described by the line presented in Fig. 5 and the associated energy has been taken equal to 17 MeV/A. We now come to the determination of both the excitation energy and the temperature of the two-fragment events. Nevertheless, it has to be pointed out that the pre-equilibrium contribution to both energy balance and emitted nucleons is small for all impact parameters. For the energy balance, neglecting the pre-equilibrium emission would lead to an overestimation of about 0.5 MeV/nucleon of the excitation energy for the most dissipative events.
7. Excitation energy and temperature measurements
The excitation energy is now given by E*
= ECM
--
(405
-
Mpre) TKE (MeV/A) - 17Mpre
(7)
with Mpr e = Mpr e (TKE (MeV/A)) as obtained in the previous section. This excitation energy is shared among (405 - Mpre) nucleons, and the result is reported in Fig. 6. We recall that all figures (from Fig. 3-right to Fig. 6) are reconstructed spectra obtained with the procedure described in Section 4. The excitation function of the m = 2 events evolves from quasi-elastic processes to damped collisions. The shape of the spectra for the deep-inelastic collisions reflects a continuous decrease until the full energy damping is reached (around 6 M e V / A ) , for greater values of excitation energy the spectra falls off rapidly. Finally, we have compared the velocity, v, spectra of Z = 1 particles detected in coincidence with two fragments with a two moving source parametrisation (projectilelike and target-like nuclei):
The function 1/" describes a volume emission [26] and the Coulomb repulsion ( E c ) from the source has been included [27]. The pre-equilibrium emission has been neglected since it represents a small fraction of detected Z = 1 particles. Several bins in
509
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
10 s
10 4
*~
10 3
10 2
10 0
1
2
3
4
5
6
7
EXCITATION ENERGY (MeV/A) Fig. 6. Reconstructed excitation function for two-body final-state events. The full energy damping (around 6 MeV/A) is achieved.
T K E ( M e V / A ) have been investigated. For each bin, the source velocities (VpLF and Z=I
VTLF) and the angle between the source and the emitted particle velocities (0pLF and 0ZLFl) were set to the determined reconstructed mean values. The Coulomb repulsion and the normalisation factor (k) were left as free parameters but they were imposed to be identical for the two sources. The temperature, identical for the two sources, was restricted to values corresponding to the reconstructed mean excitation energy, for each T K E ( M e V / A ) bin, assuming a level density parameter ranging from a/8 to A/12. Therefore, properly speaking, the fit procedure is not a "best fit" procedure but rather an excitation energy verification procedure. The result is presented in Fig. 7 through reconstructed spectra of Z = 1 particles detected in the forward direction. Because the LCP spectra result from a long evaporation chain and are affected by pre-equilibrium emission, at the most, we were able to verify that the high-velocity (v ~> 7.5 cm/ns) part of them was compatible with our assumptions. Nevertheless, for a large emitting source the apparent temperature (slope of the spectra) value is close to the mean temperature of the emitting source [28]. For each experimental spectra, to indicate visually the error on the slope determination, we present three curves related to three temperatures (T, T - 1 and T + 1 MeV) with T cori:esponding to the fitting result. By comparing the experimental data and the curves, we are able to affirm that the excitation function presented in Fig. 6 is a thermal excitation function. The measured cross section for E* ~> 4.5 MeV/A is 9 mb, this corresponds to 0.53% of the surface of the excitation function spectra. This percentage leads to 23 mb with the help of Table 1 (0.53% of the total corrected cross section). This cross section raises several questions about the ability of a nucleus to sustain such excitation energy [29]. For an excitation energy above 4.5 M e V / A but less than the binding energy, in a multifragmentation scenario [30] and for a heavy nucleus, the dominant exit channel is
510
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
1 ~
_
T = 8 + l MeV
10 10-2 10
%
1
~
T = 6 + l MeV
101 lO
-1 -2
~
1 10
-2
+1 MeV
1
5
+
1
MeV
-1
10-2 7.5
10
12.5
v (cm/ns)
15
7.5
10
12.5
15
v (cm/ns)
Fig. 7. Reconstructed Galilei-invariant Z = 1 particle velocity distributions for a fragment multiplicity of two. The spectra are plotted versus laboratory particle velocity and correspond to particles emitted between 5 and 20 ° (laboratory). Four total kinetic energy selections are shown ( 1:TKE=0-2 MeV/A, 2:TK~2-3 MeV/A, 3:TKE=3-4 MeV/A, 4:TKE=4-5 MeV/A). The reconstructed mean excitation energy for each selection is: 5.2 MeV/A (1), 4.3 MeV/A (2), 3.4 MeV/A (3) and 2.5 MeV/A (4). The curves are fits to the data with a temperature of T, T -- 1 and T + 1 MeV. the production o f at least three fragments. This is the case in this experiment, were the dominant exit channel for E* > 4.5 M e V / A is the five-fold coincidences [ 10] (i.e. at least one partner o f the deep inelastic reaction has broken into three fragments). The statistical model o f multifragmentation predicts different final channels, especially the "evaporation" one (a single fragment). The probability for finding this "evaporation" partition simultaneously in the projectile-like and the target-like nucleus is the square o f the fraction predicted by the model for a single nucleus. By using the results presented in Ref. [30] for a gold nucleus we are able to compare our measurement with the prediction. For E* > 4.5 M e V / A the model predicts almost 0% o f evaporation event production. I f we assume a production o f this kind o f events (evaporation events with E* > 4.5 M e V / A ) over an impact parameter range between b = 10 and 0 fin, the percentage should be equal to 9% to reproduce the measured cross section ( ~ b 2 ( 9 % ) a = 2.3 fm2). Therefore, the statistical model o f Ref. [ 30] is unable to describe the measured rate o f single fragment events.
8. Conclusion In conclusion, we report results obtained from an exclusive experiment where fragments and light charged particle were detected from 3 ° to 150 ° . Large fragment multiplicities have been observed correlated with large light charged-particles multiplicities
17. Bougault et aL /Nuclear Physics A 587 (1995) 499-512
511
and large values of energy damping. From the overall set of data which shows a dominant binary character of the reaction for any n-fold exit channels, we have selected the two-fold events. A background subtraction was performed in order to extract the quantities and the spectra corresponding to true two-body final state collisions. The n u m b e r of fast pre-equilibrium nucleons was measured for all accessible total kinetic energy bins (i.e. impact parameters). This number, when normalised with an independent measurement for the same system, is fully compatible with a semi-classical calculation to represent the multiplicity of pre-equilibrium nucleons. The pre-equilibrium measurements have allowed us to present an accurate excitation function for the two-body final reactions. This spectrum implies that the two-body final state is still present in violent collisions corresponding to fully damped deep inelastic reactions which, for the present system, correspond to excitation energy values as high as 6 M e V / A . These excitation energy values were compared to LCP velocity spectra and they do correspond to thermal excitation energy values. Finally, we have compared the cross section of violent two-body final-state events within a statistical multifragmentation scenario. The model is unable to describe the measured values. This experimental result could be used to bound parameters in theoretical description of the exit channel in the de-excitation scheme of heavy-ion reaction mechanisms. But nevertheless, it shows that heavy nuclei are able to sustain high excitation energies.
Acknowledgements The authors want to thank P. Abgrall, S. Bresson, E Gulminelli and B.M. Quednau for discussions and for providing us calculated results.
References [ 1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [ 12] [13] [ 14] [15]
W.U. Schr6der and J.R. Huizenga,Ann. Rev. Nucl. Sci. (1977) 465. M. Lefort and C. Ngo, Ann. de Phys. 3 (1978) 5. T. Tanabe et al., Nucl. Phys. A 342 (1980) 194. R.J. Charity et al., Z. Phys. A 341 (1991) 53. D. Jouan et al., Z. Phys. A 340 (1991) 369. L. Stuttg6 et al., Nucl. Phys. A 539 (1992) 511. M.E Rivet et al., Proc. XXXI Int. Winter Meet. on nuclear physics (Bormio), ed. I. Iori (Universityof Milano, Italy, 1993) p. 92. B.M. Quednau et al., Phys. Lett. B 309 (1993) 10. B. Lott et al., Phys. Rev. Lett. 68 (1992) 3141. J.E Lecolley et al., Phys. Lett. B 325 (1994) 317. E. Piasecki et al., Phys. Rev. Lett. 66 (1991) 1291. R. Bougault et al., Nucl. Instr. Meth, A 259 (1987) 473. G. Rudolf et al., Nucl. Instr. Meth. A 307 (1991) 325. G. Bizard et al., Nucl, Instr. Meth. A 244 (1986) 483. A. Peghalre et al., Nucl. Instr. Meth. A 295 (1990) 365.
512
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
[16] G. Casini et al., Nucl. Instr. Meth. A 277 (1989) 445. [17] E. Gadioli and EE. Hodgson, Pre-equilibdum nuclear reactions, Oxford studies in nuclear physics, vol. 15 (Clarendon, Oxford, 1992). [18] O. Lopez et al., Phys. Lett. B 315 (1993) 34. [19] J. P6ter et al., Phys. Lett. B 237 (1990) 187. [20] S. Bresson, Thesis, Caen University (1993). [21] B.M. Quednau et al., Rochester Progress Report, Depamnent of Chemistry and Nuclear Research Laboratory (1992-1993)p. 51. [22] J. Randrup and R. Vandenbosch, Nucl. Phys. A 474 (1987) 219. [23] B.M. Quednan (GANIL), private communication. [24] P. Schuck et al., Prog. Part. Nucl. Phys. 22 (1990) 181. [25] P. Abgrall (LPN Nantes), private communication. [26] A.S. Goldhaber, Phys. Rev. C 17 (1978) 2243. [27] M. Gyulassy and S.K. Kauffmann, Nucl. Phys. A 362 (1981) 503. [28] E. Vient et al., Nucl. Phys. A 571 (1994) 588. [29] B. Borderie, Ann. de Phys. 17 (1992) 349. [30] D.H.E. Gross, Nucl. Phys. A 553 (1993) 175c.
Nuclear Physics A 587 (1995) 499-512
Complete energy damping in 29 MeV/nucleon Pb+Au two-body final-state reactions * R. Bougault a, J.F. Lecolley a, M. Aboufirassi a, A. Badala a'a, B. Bilwes b, R. Brou a, j. Colin a, F. Cosmo h, D. Durand a, j. Galin c, A. Genoux-Lubain a, D. Guerreau c, D. Horn a,2, D. Jacquet d, J.L. Laville a,3 C. Le Brun a, E Lefebvres a, O. Lopez a, M. Louvel a, M. Mahi a, M. Morjean c, C. Paulot a, A. Peghaire c, G. Rudolf h, E Scheibling b, J.C. Steckmeyer a, L. Stuttg6 b, S. Tomasevic b, B. Tamain a a Laboratoire de Physique Corpusculaire Caen (IN2P3-CNRS/1SMRA et Universitd de Caen), BM Mardchal Juin, F-14050 Caen cddex, France b Centre de Recherches Nueldaires (IN2P3-CNRS/Universitd Louis Pasteur), B.P. 20, F-67037 Strasbourg cddex, France c GANIL (DSM-CEA/IN2P3-CNRS), B.P. 5027, F-14021 Caen cddex, France tl Institut de Physique Nucldaire (IN2P3-CNRS/Universitd Paris Sud), B.P. 1, F-91406 Orsay cddex, France Received 4 January 1995; revised 6 February 1995
Abstract Decay products emitted in highly dissipative P b + A u reactions at 29 M e V / n u c l e o n have been detected using a large area array. Multiplicities of fragments as large as 8 have been detected with a sizeable cross section. The m-fragment exit channels are fully compatible with the formation o f a transient excited dinuclear system formed in damped collisions. The excitation energy function shows that fully damped collisions are achieved even for m = 2 indicating that heavy nuclei are able to sustain high excitation energy and end up as evaporation residues. Keywords: NUCLEAR REACTIONS 197Au (Pb,X), E = 29 MeV/nucleon; measured fragment multiplicities; deduced transient excited dinuclear system formation evidence.
* Experiment performed at Ganil. 1 On leave from: INFN, Catania, Italy. 2 On leave from: CRL-AECL, Chalk River, Canada. 3 Present address : SUBATECH, Nantes, France. 0375-9474/95/$09.50 (~) 1995 Elsevier Science B.V. All rights reserved SSD1 0 3 7 5 - 9 4 7 4 ( 9 5 ) 0 0 0 4 1 - 0
500
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
1. Introduction Heavy-ion induced reactions in the Fermi energy domain (10-100 MeV/A) allow one to investigate the link between the different reaction mechanisms which occur at low and high bombarding energies. They remain a unique tool to study nuclear matter and for instance, the balance between the mean-field and the nucleon-nucleon interaction effects, the statistical mechanics applied to a finite ensemble such as the nucleus, the time scale for equilibration phenomena, the damping of energy and the role of the dynamics in the processes. In this paper, we focus on the study of the behaviour of heavy nuclei produced in very inelastic collisions for the system Pb+Au at 29 MeV/nucleon. At energies near the Coulomb barrier, the deep inelastic reaction mechanism [ 1-3] plays an important role in heavy-ion reactions. This process is still present at higher bombarding energies [4-7]. However, for very heavy systems and for a center-of-mass available energy of about 6 MeV/A, the full energy damping had not been demonstrated yet [8,9]. In a previous publication based on the same experiment [ 10], it has been shown that, for Pb+Au 29 MeV/nucleon, all collisions present a first step binary character irrespective of possible further disassembly of the two highly excited primary partners. There is no fusion. Furthermore, at an excitation energy of about 4.5 MeV/A, the most probable exit channel becomes the production of Intermediate Mass Fragments from the two primary partners [ 10,11]. Nevertheless we will see that the two-fragment exit channel leading to evaporation residues is still present at high excitation energies (6 MeV/nucleon). This last observation raises questions about the de-excitation scheme of a highly excited nucleus. After a rapid presentation of the experimental set-up and of the general trends of the detected events, we will focus on two-fold events. The goal of this study is to demonstrate that full energy damping has been achieved for the two-fragment exit channel. For this purpose, the excitation function has been extracted from the two-fold events using a background subtraction and taking into account for pre-equilibrium effects. Finally, the production cross section of such highly excited nuclei will be compared with the prediction of a statistical model.
2. Experimental description The experiment was performed at the GANIL facility in the Nautilus scattering chamber by bombarding a 500 /zg/cm 2 Au target with a one-particle nA Pb beam at 29 MeV/nucleon. Fragments were detected using the detectors Delf [12] and XYZt [ 13], while light charged particles were detected with the Mur [ 14] and the Tonneau [ 15]. Delf and XYZt are an ensemble of 30 position-sensitive parallel-plate avalanche counters (PPAC), each followed by an ionisation chamber. The covered angular range is from 3 ° to 150 ° with a 55% geometrical acceptance and full efficiency for atomic numbers equal to or larger than 8. The set-up has a low velocity threshold: 0.5 cm/ns (0.13 MeV/nucleon) for Delf (30°-150 °) and 2 cm/ns (2.07 MeV/nucleon)
501
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
Table 1 Multiplicity cross sections Multiplicity Cross section (mb)
2 4300
3 670
4 220
/> 5 56
for XYZt in the forward direction ( 3 ° - 3 0 ° ) . The fragment measured parameters are the atomic number Z, the velocity V and the angles with a resolution better than one degree. The Mur and Tonneau cover an angular range between 3 ° and 150 ° with about 50% geometrical acceptance and can detect light charged particles (up to Z = 6, but mainly Z = 1, 2) with a velocity threshold of about 2.2 cm/ns. The four types of detectors have an azimuthal symmetry. The Mur and the Tonneau were not used in the triggering condition which was decided among the 30 PPACs o f Delf and XYZt. In the here described experiment, the triggering condition was set to one detected fragment at least.
3. General trends of the detected events Coincidence events of n-fold have been detected with up to n = 8 fragments. The detected cross section represents about half the reaction cross section. Since the nfold measured events contain events with actual fragment multiplicity m 7> n, in order to infer the corrected multiplicity cross sections, we have proceeded as follows. We have retained events leading to the detection of more than 80% of both the available total parallel momentum and total charge ("well characterised" events). The measured values take into account fragments and light charged particles. The latter, which did not contribute to the triggering condition, were corrected by a factor of 2 to take into account the 50% geometrical acceptance of the Mur and Tonneau. Then each "well characterised" detected event has been used for generating an entire set of events by a random azimuthal-angle rotation of the experimental set-up. These generated events are then passed through a filter, which represents the experimental covered angles, to estimate the rate of m-type events on each n ~< m fold. It was then possible to extract the apparatus-corrected multiplicity cross sections. The result is presented in Table 1. The total corrected cross section represents about 5 / 6 of the reaction cross section with roughly 1 barn corresponding to more than two fragments in the exit channel. As mentioned previously, it has been shown [ 10] that all collisions leading to m fragments present a binary character in a first step. In Fig. 1, the distribution of detected light charged particles (Nlcp) for various values of the fragment multiplicity ("well characterised" events) are displayed. The pattern of the summed distribution is similar with what has been measured as a function o f neutron multiplicity for the same system at the same incident energy [ 11 ]. There is a large contribution at small Nlcp values associated with peripheral collisions and a shoulder around Nlcp = 8 associated with the largest fragment multiplicities and extending up to 15 detected LCP (recall that the average LCP detection acceptance is around 50%). As the fragment multiplicity increases, the detected LCP number
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
502
1°5I
~m=2 ]
~
Om=5 "~ m = 4
104 I
f
- .,.,e---e._._.~-~
,
,
Am-~5
10 2
10
1
0
2
4
6
8
10
12
14
16
Nlcp Fig. 1. Number of light charged particles, as measured, detected in coincidence with m fragments ("well characterised events"). The histogram represents the sum of the different spectra.
distribution evolves steadily towards a more symmetric distribution peaked around 8. For Nlcp larger than 8, the probability of finding large numbers of LCP does not depend strongly on the associated number of fragments. If we assume that the multiplicity of light particles is a good measure of the violence of a collision, then this is a first indication that violent collisions can lead to two-body in the final state. For such events, the extremely heated projectile- and target-like nuclei end up as evaporation residues. In the following we will focus on two-fragment production considering the entire set of two-fold coincidence data (i.e. no selection based on "well characterised" events).
4. Events with two detected fragments Fig. 2 presents the two-fold events as detected. The presented observables concern the detected fragments only. On the left part, the total detected charge as a function of the measured parallel momentum normalised to the entrance channel values is displayed. When detected light charged particles are taken into account the balances are better. A detected two-fold event can originate from events with a multiplicity (m) greater than or equal to 2. This is visible in Fig. 2-1eft, the bump corresponding to a balance of 1 for both observables originates from m = 2 (zone a) while the one lying on half atomic number and 1 momentum balance is related to the detection of only the two fission fragments of the projectile from m >~ 3 events (zone b). In order to extract observables concerning m = 2 events, we have proceeded in two steps. The procedure can be summarised as follows, (i) a primary selection has been made on the basis of an event by event analysis, (ii) a m ~> 3 event background subtraction has been performed on the spectra of the two-fold events retained after the first selection. From this procedure m = 2 event spectra have been obtained.
503
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
(IogorithrnTc
1.4
contour
lines)
10 4 lO 3
1.2
~9 102 10 1
1
0
.t_ 0.8 0.5
.-.t~ 0.6
105~
0.4
104~
)
0.2 0
1
I
=
i
I i ~ J 0.5
i
[ r I r
e
2
× (V(Iz) + v~Z))/(Vbeam/2) 7
~
I I/
H 10
1
(Z 1 X V~"))+ (Z 2X V~z))
~, -200
I
,
-100
f
0
,
i
100
,
~1
200
(012 - 180) (o)
Fig. 2. Characteristics of the two-fold events in the laboratory frame. The label (z) represents the beam axis, 1 and 2 refer to the two detected fragments. For the two-dimensional plot, atomic number and momentum balance are relative to the entrance channel (Zbeam, Zbeamx Vbeam)- The one-dimensionalspectra present the fragment-velocitycorrelation along the beam axis and on to tile planes perpendicular to the beam axis. The detailed description of the two-step procedure will now be explained but it has to be kept in mind that the consequence of the second step is the vanishing of the event by event analysis concept in our analysis. (i) In order to eliminate the two-fold detected events which clearly originate from m ~> 3 events (as the zone b o f Fig. 2-1eft), the primary step requires the momentum conservation in the beam direction and in the planes perpendicular to it. Since the studied system is almost symmetric and since the atomic number of the fragments are heavily affected by secondary evaporation, the method is based on the measured velocities which are, on the average, conserved in such a process rather than on the momenta. The filter consists of two conditions: to require that the laboratory center-of-mass velocity in the beam direction of the two detected fragments (the system is assumed to be symmetric) is equal to half the beam velocity (Fig. 2-right): 0.5 (gl (z) -~- V2(z)) = (1gbeam) + 2 5 % ;
(1)
- to require that the angle between the two fragment velocities projected on to the planes perpendicular to the beam direction is equal to 180 ° (Fig. 2-right): 012 = 180 ° -t- 25 °.
(2)
This first selection does not eliminate all the m >~ 3 events contained in the two-fold event sample. (ii) The second step is a background subtraction applied to the two-fold event spectra obtained after the first-step selection. The background represents the remaining
504
R. Bougault et aL /Nuclear Physics A 587 (1995) 499-512
m /> 3 event contained in the two-fold event spectra after the first selection. For this purpose we have used the method described in Ref. [ 16]. The method uses the three-fold coincidences, from which one detected fragment has been removed randomly ("three-fold minus one"), and a normalisation factor in order to described the two-fold m ~> 3 events. The observable used to deduce the background rate of the two-fold coincidences was the perpendicular center-of-mass velocity of the fragments (VcM±). This variable is defined as the projection on to the perpendicular planes relative to the beam axis of the fragment center-of-mass velocity. Furthermore, in order to deduce unambiguously the value of the normalisation factor, we have used VCM± spectra for both sets of two-fold and "three-fold minus one" events, not filtered by the first step selection. The VCM± spectra are presented in Fig. 3-1eft for the two-fold and the "three-fold minus one"events. These spectra are not filtered by the primary step selection and it is clear that the long tail (VcM± >7 1.5 cm/ns) for the two-fold coincidences corresponds to rn/> 3 events since those events are unable to achieve momentum conservation. This background is well reproduced by the "three-fold minus one" spectrum as soon as a factor of 1.35 is applied to it. This factor, deduced from the VCM± spectra, is explained by different geometrical efficiencies for m = 2 and 3 events. From the "well characterised" events we were able to measure the percentage of m = 2 events and m = 3 events detected as two-fold events, these percentages are respectively 51.4% and 38.1% leading to a ratio identical to the value of the correction factor. This method gives a universal way to subtract the background from all two-fold spectra. The result of the two-step method is presented in Fig. 3-right. This reconstructed figure is issued from (i) the primary selection on the two-fold events, (ii) a background subtraction with the 1.35 factor applied to the same spectra concerning "three-fold minus one" selected events. In the following all spectra and mean values of variables will be obtained through the above described procedure. Therefore, they will be labelled "reconstructed". In order to extract the excitation function, we will now characterise these events by studying their kinematics.
5. Energy balance For a two-body reaction, the energy balance of the system leads to E* = ECM - - TKE (MeV)
-
Epre,
(3)
where ECM is the available energy, TKE the total kinetic energy of the two partners just after separation (so before subsequent evaporation) and F-,pre the total energy removed by pre-equilibrium emission. All quantities refer to center-of-mass system. The pre-
505
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
10 5
1.4
10 4
1.2
(Iogorilhmic contour lines)
] 10 3
10 2
~
0.8
~
o.6 0.4
10 0.2 1
0
0
1
2
3
VcM ± (cm/ns)
I
0
,
.
.
0.5
.
.
~
1
(Z 1 × V~ )) + (Z 2 × V~z))
Fig. 3. Left: VCM.I_spectra for two-fold events (upper histogram) and for "three-fold minus one" events (hatched area). Right: same as Fig. 2-1eftafter event selection and background subtraction. equilibrium definition implies all particles which have been emitted before the separation of the projectile-like and the target-like nuclei. The total kinetic energy is given by TKE (MeV) = 1 Aprojeetile-likeAtarget-like Vr21" 2 Aprojectile-like"k- Atarget-fike
(4)
V~el is the relative velocity between the two partners and the mass numbers are referring to partner sizes before subsequent evaporation. With the only assumption that the preequilibrium particles are equally issued from the projectile and the target (symmetric system), i.e. Aprojeetile-like= Atarget-like, this leads to TKE (MeV/A) = 1~v,e~. 2
(5)
Since the sequential evaporation process does not affect the measured fragment velocities on the average, the T K E ( M e V / A ) can be used to characterise the damping of energy independently of any pre-equilibrium effect. Nevertheless, Epre has to be measured in order to deduce the excitation energy. This is achieved in the following section.
6. Pre-equilibrium particles In the Fermi energy region, the pre-equilibrium particle process can play an important role and the velocity of those particles can extend to values corresponding to several times that of their parent nucleus [ 17]. The energy carried away by these pre-equilibrium particles can prevent deposition of high excitation energy in a composite system [ 18 ] and
506
R. Bougault et a l . / N u c l e a r Physics A 5 8 7 (1995) 4 9 9 - 5 1 2
25
10 3 (Io9ofithmic z scole)
[] uQF1
noon° DOn•o••• on ~,nnnn• 17~17r70ooo nOD
r~ ,-,I
15
°
10 2 _
DO
•on•oDD
]
o0,
ODoo
7~ ,~
o
000
0
=o 10
r) i~-j
[_ ~ D D o D [] I_D_I_L~Di-'IDD D D n LDU_LLJDI-7D D n
10
.z
~D~I-313
0
5
....
10
ULl L~
~
1
O []
o r.r,--:,
\
e-
, ....
15
i
, ....
20
25
I~LCP " ~pLFI (cm/ns)
0
,
....
10
, ....
20
|,
30
VR12 (cm/ns)
Fig. 4. Reconstructed spectra of Z = 1 particles detected between 5 and 150 ° for TKE=4-5 MeV/A. A method to identify pre-equilibrium particles.
associated multiplicity seems to increase with decreasing impact parameter [ 19]. Several works related to the same system at the same bombarding energy [20,8,21] have shown that the neutron production can be explained through an equilibrated part and a weak nonequilibrium component. The equilibrated part is well reproduced by a parametrisation involving the PLF and TLF sources (the projectile-like and the target-like nuclei). The pre-equilibrium neutron emission is consistent with the Fermi-jet model [22] and corresponds to about 8 neutrons for dissipative detected events corresponding to a total kinetic energy of 3.7 M e V / A [8,23]. In order to measure the pre-equilibrium particle multiplicity, we have used their ability to achieve much larger velocities (Fermi jets) than evaporated particles. For the latter large velocities are only found as a tail in the spectra. The fast velocity component of LCP has not been extracted from absolute velocity spectra but rather by using the relative velocities between LCP and the two heavy partners (PLF and TLF). Reconstructed spectra of Z = 1 particles detected from 5 ° to 150 ° in coincidence with two fragments are presented in Fig. 4 for TKE(MeV/A) ranging from 4 to 5 MeV/A. The two-dimensional spectrum presents the relationship between the two abovementioned relative velocities. The spectrum on the right side of the picture corresponds to the projection on to the diagonal axis, i.e. the reconstructed spectrum of /
VRj2 = ~/IVlcp - VPLFI2 + ]V~p - VTLF[2.
(6)
The reconstructed data present two contributions. The most important one is related mainly to evaporated Z = 1 particles (small relative velocities in accordance with an evaporation scheme) and it seems possible to separate PLF and TLF sources from such a correlation. The second contribution is mainly visible at high relative velocities
507
R. Bougault et aL /Nuclear Physics A 587 (1995) 499-512
3°1
E
E
5
25
~
20
•
15
[]
DATA
"
i0
E, 0
~Jlr 0
1
2
3
4
5
6
7
8
T K E (MeV/A) Fig. 5. Multiplicity of pre-equilibrium nucleons versus the total kinetic energy (reconstructed correlation). The quoted impact parameter values refer to Landau-Vlasov calculations.
(Vm2 ~> 20 cm/ns), but it extends down also to smaller Vm2. It can be clearly associated with pre-equilibrium emission. A pure fraction of the pre-equilibrium particles can be selected with the condition VR12 >~ 20 cm/ns. This method presents two main advantages. The first one is its frame independence, the second is the possibility of using a unique selection value independent of TKE: for a prompt particle originating from the projectile-like nucleus, as TKE decreases [Vlcp - VpLFI will increase but IVlcp - VTLFI will decrease of the same amount and vice-versa for a prompt particle emitted by the target-like nucleus. These two points ensure a good selection independent of the energy damping. The selection method has been applied for several bins in TKE(MeV/A). For each bin, the reconstructed number of fast pre-equilibrium has been extracted with the reconstructed mean value of TKE(MeV/A). Nevertheless the pre-equilibrium multiplicity is not fully described by fast velocity Z = 1 particles. It implies neutrons and in addition this process contributes also to the first bump (low VR12 values) of Fig. 4 by interactions of nucleons emitted from one partner with the nucleons of the other one. So far the numbers of fast Z = 1 particles have been normalised to the value of neutron pre-equilibrium multiplicity (corrected by the ratio N/Z of the entrance channel) for the same system and for TKE=3.7 MeV/A [8,23]. This normalisation implies the assumption of a constant percentage between the number of fast velocity particles and the multiplicity of pre-equilibrium nucleons. We report on Fig. 5 the behaviour of the pre-equilibrium nucleon multiplicity as a function of TKE (black circles). In order to check our measurements, we have reported in the figure results obtained with dynamical calculations of the Landau-Vlasov type [24]. These calculations have been performed for the same system and the same bombarding energy (open squares) [20] (open triangles) [25]. Both calculations have been done with a soft Zamick effective interaction, the second one has taken into account the isospin dependence
508
R. Bougault et aL /Nuclear Physics A 587 (1995) 499-512
of the mean field. We see that the agreement is excellent. For head-on collisions, the calculations seems to indicate a saturation or a small decrease of the pre-equilibrium multiplicity (not reported in the figure). The semi-classical calculation of Ref. [25] gives a mean total energy removed by pre-equilibrium emission of 17 MeV/A (ranging from 17.9 to 16.4 M e V / A for an impact parameter ranging from 12 to 2 fm). The nonequilibrated part of the neutron spectra detected for the same system in Ref. [8] is well fitted by a volume emission from a "source at rest in the center of mass frame" parametrisation with a slope parameter ~- = 7 MeV [21]. This is consistent with a dominant low-velocity part of the pre-equilibrium particles and with the mean energy deduced from the semi-classical calculation when including the binding energy in the energy balance (27-+8 M e V / A ) . Therefore, for the energy balance, the pre-equilibrium nucleon multiplicity ( M p r e ) will be described by the line presented in Fig. 5 and the associated energy has been taken equal to 17 MeV/A. We now come to the determination of both the excitation energy and the temperature of the two-fragment events. Nevertheless, it has to be pointed out that the pre-equilibrium contribution to both energy balance and emitted nucleons is small for all impact parameters. For the energy balance, neglecting the pre-equilibrium emission would lead to an overestimation of about 0.5 MeV/nucleon of the excitation energy for the most dissipative events.
7. Excitation energy and temperature measurements
The excitation energy is now given by E*
= ECM
--
(405
-
Mpre) TKE (MeV/A) - 17Mpre
(7)
with Mpr e = Mpr e (TKE (MeV/A)) as obtained in the previous section. This excitation energy is shared among (405 - Mpre) nucleons, and the result is reported in Fig. 6. We recall that all figures (from Fig. 3-right to Fig. 6) are reconstructed spectra obtained with the procedure described in Section 4. The excitation function of the m = 2 events evolves from quasi-elastic processes to damped collisions. The shape of the spectra for the deep-inelastic collisions reflects a continuous decrease until the full energy damping is reached (around 6 M e V / A ) , for greater values of excitation energy the spectra falls off rapidly. Finally, we have compared the velocity, v, spectra of Z = 1 particles detected in coincidence with two fragments with a two moving source parametrisation (projectilelike and target-like nuclei):
The function 1/" describes a volume emission [26] and the Coulomb repulsion ( E c ) from the source has been included [27]. The pre-equilibrium emission has been neglected since it represents a small fraction of detected Z = 1 particles. Several bins in
509
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
10 s
10 4
*~
10 3
10 2
10 0
1
2
3
4
5
6
7
EXCITATION ENERGY (MeV/A) Fig. 6. Reconstructed excitation function for two-body final-state events. The full energy damping (around 6 MeV/A) is achieved.
T K E ( M e V / A ) have been investigated. For each bin, the source velocities (VpLF and Z=I
VTLF) and the angle between the source and the emitted particle velocities (0pLF and 0ZLFl) were set to the determined reconstructed mean values. The Coulomb repulsion and the normalisation factor (k) were left as free parameters but they were imposed to be identical for the two sources. The temperature, identical for the two sources, was restricted to values corresponding to the reconstructed mean excitation energy, for each T K E ( M e V / A ) bin, assuming a level density parameter ranging from a/8 to A/12. Therefore, properly speaking, the fit procedure is not a "best fit" procedure but rather an excitation energy verification procedure. The result is presented in Fig. 7 through reconstructed spectra of Z = 1 particles detected in the forward direction. Because the LCP spectra result from a long evaporation chain and are affected by pre-equilibrium emission, at the most, we were able to verify that the high-velocity (v ~> 7.5 cm/ns) part of them was compatible with our assumptions. Nevertheless, for a large emitting source the apparent temperature (slope of the spectra) value is close to the mean temperature of the emitting source [28]. For each experimental spectra, to indicate visually the error on the slope determination, we present three curves related to three temperatures (T, T - 1 and T + 1 MeV) with T cori:esponding to the fitting result. By comparing the experimental data and the curves, we are able to affirm that the excitation function presented in Fig. 6 is a thermal excitation function. The measured cross section for E* ~> 4.5 MeV/A is 9 mb, this corresponds to 0.53% of the surface of the excitation function spectra. This percentage leads to 23 mb with the help of Table 1 (0.53% of the total corrected cross section). This cross section raises several questions about the ability of a nucleus to sustain such excitation energy [29]. For an excitation energy above 4.5 M e V / A but less than the binding energy, in a multifragmentation scenario [30] and for a heavy nucleus, the dominant exit channel is
510
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
1 ~
_
T = 8 + l MeV
10 10-2 10
%
1
~
T = 6 + l MeV
101 lO
-1 -2
~
1 10
-2
+1 MeV
1
5
+
1
MeV
-1
10-2 7.5
10
12.5
v (cm/ns)
15
7.5
10
12.5
15
v (cm/ns)
Fig. 7. Reconstructed Galilei-invariant Z = 1 particle velocity distributions for a fragment multiplicity of two. The spectra are plotted versus laboratory particle velocity and correspond to particles emitted between 5 and 20 ° (laboratory). Four total kinetic energy selections are shown ( 1:TKE=0-2 MeV/A, 2:TK~2-3 MeV/A, 3:TKE=3-4 MeV/A, 4:TKE=4-5 MeV/A). The reconstructed mean excitation energy for each selection is: 5.2 MeV/A (1), 4.3 MeV/A (2), 3.4 MeV/A (3) and 2.5 MeV/A (4). The curves are fits to the data with a temperature of T, T -- 1 and T + 1 MeV. the production o f at least three fragments. This is the case in this experiment, were the dominant exit channel for E* > 4.5 M e V / A is the five-fold coincidences [ 10] (i.e. at least one partner o f the deep inelastic reaction has broken into three fragments). The statistical model o f multifragmentation predicts different final channels, especially the "evaporation" one (a single fragment). The probability for finding this "evaporation" partition simultaneously in the projectile-like and the target-like nucleus is the square o f the fraction predicted by the model for a single nucleus. By using the results presented in Ref. [30] for a gold nucleus we are able to compare our measurement with the prediction. For E* > 4.5 M e V / A the model predicts almost 0% o f evaporation event production. I f we assume a production o f this kind o f events (evaporation events with E* > 4.5 M e V / A ) over an impact parameter range between b = 10 and 0 fin, the percentage should be equal to 9% to reproduce the measured cross section ( ~ b 2 ( 9 % ) a = 2.3 fm2). Therefore, the statistical model o f Ref. [ 30] is unable to describe the measured rate o f single fragment events.
8. Conclusion In conclusion, we report results obtained from an exclusive experiment where fragments and light charged particle were detected from 3 ° to 150 ° . Large fragment multiplicities have been observed correlated with large light charged-particles multiplicities
17. Bougault et aL /Nuclear Physics A 587 (1995) 499-512
511
and large values of energy damping. From the overall set of data which shows a dominant binary character of the reaction for any n-fold exit channels, we have selected the two-fold events. A background subtraction was performed in order to extract the quantities and the spectra corresponding to true two-body final state collisions. The n u m b e r of fast pre-equilibrium nucleons was measured for all accessible total kinetic energy bins (i.e. impact parameters). This number, when normalised with an independent measurement for the same system, is fully compatible with a semi-classical calculation to represent the multiplicity of pre-equilibrium nucleons. The pre-equilibrium measurements have allowed us to present an accurate excitation function for the two-body final reactions. This spectrum implies that the two-body final state is still present in violent collisions corresponding to fully damped deep inelastic reactions which, for the present system, correspond to excitation energy values as high as 6 M e V / A . These excitation energy values were compared to LCP velocity spectra and they do correspond to thermal excitation energy values. Finally, we have compared the cross section of violent two-body final-state events within a statistical multifragmentation scenario. The model is unable to describe the measured values. This experimental result could be used to bound parameters in theoretical description of the exit channel in the de-excitation scheme of heavy-ion reaction mechanisms. But nevertheless, it shows that heavy nuclei are able to sustain high excitation energies.
Acknowledgements The authors want to thank P. Abgrall, S. Bresson, E Gulminelli and B.M. Quednau for discussions and for providing us calculated results.
References [ 1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [ 12] [13] [ 14] [15]
W.U. Schr6der and J.R. Huizenga,Ann. Rev. Nucl. Sci. (1977) 465. M. Lefort and C. Ngo, Ann. de Phys. 3 (1978) 5. T. Tanabe et al., Nucl. Phys. A 342 (1980) 194. R.J. Charity et al., Z. Phys. A 341 (1991) 53. D. Jouan et al., Z. Phys. A 340 (1991) 369. L. Stuttg6 et al., Nucl. Phys. A 539 (1992) 511. M.E Rivet et al., Proc. XXXI Int. Winter Meet. on nuclear physics (Bormio), ed. I. Iori (Universityof Milano, Italy, 1993) p. 92. B.M. Quednau et al., Phys. Lett. B 309 (1993) 10. B. Lott et al., Phys. Rev. Lett. 68 (1992) 3141. J.E Lecolley et al., Phys. Lett. B 325 (1994) 317. E. Piasecki et al., Phys. Rev. Lett. 66 (1991) 1291. R. Bougault et al., Nucl. Instr. Meth, A 259 (1987) 473. G. Rudolf et al., Nucl. Instr. Meth. A 307 (1991) 325. G. Bizard et al., Nucl, Instr. Meth. A 244 (1986) 483. A. Peghalre et al., Nucl. Instr. Meth. A 295 (1990) 365.
512
R. Bougault et al./Nuclear Physics A 587 (1995) 499-512
[16] G. Casini et al., Nucl. Instr. Meth. A 277 (1989) 445. [17] E. Gadioli and EE. Hodgson, Pre-equilibdum nuclear reactions, Oxford studies in nuclear physics, vol. 15 (Clarendon, Oxford, 1992). [18] O. Lopez et al., Phys. Lett. B 315 (1993) 34. [19] J. P6ter et al., Phys. Lett. B 237 (1990) 187. [20] S. Bresson, Thesis, Caen University (1993). [21] B.M. Quednau et al., Rochester Progress Report, Depamnent of Chemistry and Nuclear Research Laboratory (1992-1993)p. 51. [22] J. Randrup and R. Vandenbosch, Nucl. Phys. A 474 (1987) 219. [23] B.M. Quednan (GANIL), private communication. [24] P. Schuck et al., Prog. Part. Nucl. Phys. 22 (1990) 181. [25] P. Abgrall (LPN Nantes), private communication. [26] A.S. Goldhaber, Phys. Rev. C 17 (1978) 2243. [27] M. Gyulassy and S.K. Kauffmann, Nucl. Phys. A 362 (1981) 503. [28] E. Vient et al., Nucl. Phys. A 571 (1994) 588. [29] B. Borderie, Ann. de Phys. 17 (1992) 349. [30] D.H.E. Gross, Nucl. Phys. A 553 (1993) 175c.