ИЗВЕСТИЯ РАН. СЕРИЯ ФИЗИЧЕСКАЯ, 2010, том 74, № 4, с. 592-595
УДК 539.172.1
EMISSION TIME OF THE INTERMEDIATE MASS FRAGMENTS IN COLLISIONS OF RELATIVISTIC DEUTERONS WITH THE GOLD TARGET
© 2010 S. P. Avdeyev1, V. A. Karnaukhov1, H. Oeschler2, V. V. Kirakosyan1, P. A. Rukoyatkin1, A. Budzanowski3, W. Karcz3, E. Norbeck4, A. S. Botvina5
E-mail: avdeyev@netscape.net
The relative velocity correlation function of pairs of intermediate mass fragments has been studied for d + Au collisions at 4.4 GeV. Experimental correlation functions are compared to that obtained by multi-body Coulomb trajectory calculations under the assumption of various decay times of the fragmenting system. The combined approach with the empirically modified intranuclear cascade code followed by the statistical mul-tifragmentation model was used to generate the starting conditions for these calculations. The fragment emission time is found to be less than 40 fm • c-1.
INTRODUCTION
The main decay mode of very excited nuclei (E* > > 4 MeV/nucleon) is copious emission of intermediate mass fragments (IMF), which are heavier than a-par-ticles but lighter than fission fragments. An effective way to produce hot nuclei is reactions induced by heavy ions with energies up to hundreds ofMeV per nucleon. But in this case the heating ofthe nuclei may be accompanied by compression, rotation, and shape distortion, which can essentially influence the decay properties of hot nuclei. The picture becomes clearer when light relativistic projectiles (protons, antiprotons, pions) are used. In this case fragments are emitted by only one source — the slowly moving target spectator. Its excitation energy is almost entirely thermal. Light relativistic projectiles provide therefore a unique possibility for investigating thermal multifragmentation.
It has been found experimentally that the process is characterized by two volumes [1, 2]. The first one corresponds to the chemical freeze-out state when pre-fragments are formed, Vt = (2.6 ± 0.2) V0. The second one is reached by the nucleus after its descent from the top of the fragmentation barrier to the multi-scission point. It is called the kinetic freeze-out volume Vf= = (5.0 ± 0.5) V0.
The decay properties of hot nuclei are well described by statistical models of multifragmentation [3, 4] and this can be considered as an indication that the system is in thermal equilibrium or at least close to that.
The time scale of fragment emission is a key parameter for understanding the decay mechanism of highly excited nuclei. Is it sequential and independent evaporation of IMF's or is it a multibody decay mode with almost simultaneous emission of fragments gov-
Joint Institute for Nuclear Research, Dubna, Russia.
1
2 Institute für Kernphysik, Darmstadt University of Technology, Darmstadt, Germany.
H. Niewodniczanski Institute of Nuclear Physics, Cracow, Poland. 1 University of Iowa, Iowa City, USA. Institute for Nuclear Research RAN, Moscow, Russia.
erned by the total accessible phase space? As was suggested by D.H.E. Gross in ref. [5], "simultaneous" means that fragments are liberated during a time interval which is smaller than the Coulomb acceleration time tc, when the kinetic energy of fragments amounts to ~90% of the asymptotical value. According to [5], tc is estimated to be (400—500) fm • c-1. Fragments emitted within this time interval are considered being not independent as they interact via the Coulomb force while being accelerated in the electric field of the source. As a result, the yield of events with small relative velocities of the fragments (or small relative angle between them) is suppressed. The magnitude of this effect drastically depends on the emission time since the longer the time separation of the fragments, the larger their space separation and the weaker the mutual Coulomb repulsion. Thus, measurement of the IMF emission time Tem (the mean time separation between two fragment emissions in a given event) is a direct way to answer the question as to the nature of the multi-fragmentation phenomenon. In some papers, the mean lifetime of the fragmenting system t s is used to characterize the process of disintegration. There is a simple relation between these two quantities [6, 7]
M-1
Tem =Ts/(M -1)£ i.
(1)
n = 1
Both values are close to each other when the mean IMF multiplicity, M, is in the range 2-3, as in the case of the light relativistic projectiles.
The time scale for IMF emission is estimated by comparing the measured correlation function with the multibody Coulomb trajectory calculations with Tem as a parameter. There are two procedures to measure the emission time: analysis of the IMF-IMF correlation function of the relative angle or the relative velocity.
The first measurements of the time scale for the thermal multifragmentation were performed for 4He + Au collisions at 14.6 GeV by analyzing the IMF-IMF relative angle correlation [6, 7]. It was found that Tem is
EMISSION TIME OF THE INTERMEDIATE MASS FRAGMENTS
593
less than 75 fm • c-1. The same procedure was used by the FASA group in Ref. [8] for the p + Au interaction at 8.1 GeV when the emission time Tem < 70 fm • c-1 was found. A similar value was obtained by the ISiS collaboration for collisions of 4.8 GeV 3He with the gold target [9]. In this paper IMF-IMF relative velocity correlations were studied. A general overview of the experimental activity in this field can be found in review paper [10].
In the present paper the temporal characteristics of multifragmentation are investigated for the first time for interaction of 4.4 GeV deuterons with the Au target. For that purpose the IMF-IMF correlation function of the relative velocity was studied.
1. EXPERIMENTAL
The experiment has been performed with the 4n setup FASA [11, 12] installed at the external beam of the Dubna superconducting accelerator NUCLO-TRON. The FASA device consists of two main parts:
1) The array of thirty AE-E telescopes, which serve as triggers for the read-out of the whole FASA detector system. These telescopes allow measuring the fragment charge and energy. The spatial distribution of fragments is also obtained (with steps AG = 10°).
2. The fragment multiplicity detector (FMD) including 58 thin CsI(Tl) counters (with scintillator thickness around 35 mg • cm-2), which cover 81% of 4n. The FMD gives the number of IMF's in the event and their spatial distribution.
The fragment telescopes consist of a compact ionization chamber as the AE counter and a Si (Au) semiconductor detector as the E-spectrometer. Effective thickness of the E-detector was around 700^, which is enough to measure the energy spectra of all intermediate mass fragments. The ionization chambers have a shape of a cylinder (50 mm in diameter, 40 mm in height) and are made from polished brass. The entrance and exit windows are made from organic films (~100 ^g • cm-2) covered by a thin gold layer prepared by thermal evaporation. A gold wire 0.5 mm in diameter is used as the anode. The cathode (brass cylinder and mechanically supported thin entrance and exit windows) is surely grounded. Carbon fluoride CF4 at the pressure of 50 torr is used as a working gas.
A self-supporting Au target (~1.5 mg • cm-2) is located at the center of the FASA vacuum chamber supported by thin tungsten wires. The energy calibration of the counters was done periodically using a precise pulse generator and a 241Am alpha source. The beam intensity was around 1010 particles per spill. The beam spot was continuously controlled by two multiwire proportional chambers placed at the entrance and the exit of the FASA device. The beam intensity was measured by the special ionization chamber located 150 cm behind the target. The spill length was 1.5 s, the frequency of the beam bursts was 0.1 Hz.
Figure 1 gives an example of the AE-E plot measured by one of the telescopes for d +Au collisions at
dE, MeV 60 5O 4O 3O 2O 1O
0 20
.V\■ ■ ' . . ■■
~ ' * . -л-,' . . ' '
'««nvtfW* 1Г1-. . I .
60
100 140 180
E, MeV
Fig. 1. Multifragmentation in d(4.4GeV) + Au collisions, AE—E plot measured by one of the thirty telescopes of FASA set-up, total number of events detected is around 1.5 • 106.
d 2N/dEdQ 103
102 10 1
103 102 10 1
103 102 10 1
V
".........I.........I.........I.........I.........
Vt^u t
".........I.........I.........I........Il I I 11.....
i
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..........I.........I.........I I I I lllll ill I I.........
0
50
100
150 200 E, MeV
Fig. 2. Kinetic energy spectra of Be («-label), C (¿-label), Ne (c-label) measured by telescope located at polar angle 0 = 40°.
the beam energy 4.4 GeV. The energy is given for the fragment at the front of the telescope. It was obtained from the measured value by adding the energy absorbed on the way from the target to the E-detector. The loci for different intermediate mass fragments are
b
c
594
AVDEYEV et al.
dN/dured 103
102r
10 г
10 20 30 40 50 60 70 80
Ured * C-1 • 103
Fig. 3. The yield as a function of the reduced relative velocity of coincident IMFs. Histogram is for the mixed events.
well resolved in the range from lithium to silicon. The energy cutoff caused by adsorption of the low energy fragments before the Si(Au) detector increases with Z of fragments. Thus, Ne fragments with the energy lower than 25 MeV do not reach the E-counter.
2. RESULTS OF MEASUREMENTS
Examples of kinetic energy spectra of Be, C and Ne measured by one of the telescopes are given in fig. 2. They are well described by the combined model which includes the intranuclear cascade step, the thermal expansion of the hot residual nucleus and the statistical multifragment decay [13, 14]. We used a refined version of the intranuclear cascade model (INC) [15] to describe the fast stage of the reaction and to get the N, Z and the excitation energy distributions of the target spectators. The mean excitation energy of the target spectator is (150-200) MeV accordi
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