ЯДЕРНАЯ ФИЗИКА, 2004, том 67, № 2, с. 290-297
ЭЛЕМЕНТАРНЫЕ ЧАСТИЦЫ И ПОЛЯ
FLOW EFFECTS IN HIGH-ENERGY NUCLEUS COLLISIONS WITH Ag(Br) IN EMULSION
© 2004 M. I. Adamovich
N. P. Andreeva2), E. S. Basova3\ V. Bradnova4\ V. I. Bubnov2), M. M. Chernyavsky1), A. S. Gaitinov2), K. G. Gulamov5), M. Haiduc6),
D. Hasegan6), L. Just7), E. K. Kanygina2), S. P. Kharlamov1), A. D. Kovalenko4), S. A. Krasnov4), A. KravCakova8), V. G. Larionova1^ I. A. Lebedev2), O. V. Levitskaya9), N. S. Lukicheva5), A. K. Musaeva2), S. Z. Nasyrov3), V. S. Navotny5), G. I. Orlova1^ N. G. Peresadko1), L. N. Philippova2), V. A. Plyushchev10), V. V. Rusakova4),
N. Saidkhanov5), N. A. Salmanova1^ A. M. Seitimbetov2), M. I. Tretyakova
i)
T. P. Trofimova3), S. Vokai8), J. Vriakova8), P. I. Zarubin4), S. I. Zhokhova5)
Received April 10, 2002; in final form, January 16, 2003
Various flow phenomena observed by unique emulsion method are reviewed. The experimental data of the emission of projectile and target fragments and relativistic particles in collisions of 1—160-^ GeV/c 16O, 22Ne, 28Si, 32S, 84Kr, 197Au, and 208Pb nuclei with 108Ag (80Br) targets are investigated. The transverse-momentum approach, the flow-angle analysis using principal vectors, the azimuthal correlation functions, the method of the azimuthal correlations between the charged secondaries, and the method of the Fourier expansion of the azimuthal angle distributions are applied. The evidence of the directed flow of spectators has been obtained in the medium-impact nuclear interactions. In azimuthal distributions, with respect to the reaction plane, the signal of the elliptic flow of participants has been observed.
1. INTRODUCTION
Reactions between heavy nuclei at high energies have been investigated for a number of years at the Dubna, Brookhaven, and CERN accelerators. A characteristic feature of nucleus—nucleus collisions is that the direction of the outgoing particles projected onto the transverse plane is correlated with the orientation of the impact parameter. These azimuthal correlations are usually referred to as "collective flow" [1].
The directed fluid-like emission of nuclear matter in energetic collisions of two nuclei was first predicted by [2]. Then many experiments have been devoted
''Lebedev Institute of Physics, RAS, Moscow.
2)Energy Physics Institute, Almaty, Kazakhstan.
3)Institute of Nuclear Physics, Tashkent, Uzbekistan.
4) Joint Institute for Nuclear Research, Dubna, Russia.
5)Physical-Technical Institute, Tashkent, Uzbekistan.
6)Institution of Gravitation and Space Research, Bucharest, Romania.
7)Institute of Experimental Physics, Slovak Academy of Sciences, Kos ice.
8)Department of Nuclear Physics, S afa rik University, Kos ice, Slovakia.
9)Petersburg Nuclear Physics Institute, RAS, Gatchina.
10)Khlopin Radium Institute, St. Petersburg, Russia.
to the study of hydrodynamical behavior of nuclear matter in nucleus—nucleus collisions [3].
The first conclusive evidence of collective sideward flow was provided by heavy-ion experiments around
I A GeV/c [4]. Their 4n detectors were able to measure event-by-event the four-momenta of all particles.
This phenomenon was also observed at ultra-relativistic energies by E877 Collaboration in Au + + Au collisions at a beam momentum of about
II A GeV/c [5] and, only recently, in Pb + Pb collisions at 158 A GeV/c by NA49 and WA98 Collaborations [6]. One of the main motivations of such a study is that the experimental observation of asymmetries in azimuthal distributions for noncentral collisions at ultrarelativistic energies could be sensitive to the formation of quark—gluon plasma [7]. At intermediate energies, they yield information on the nuclear compressibility [8] and on the in-medium nucleon—nucleon cross section [9].
The quantifying of the collective flow in nucleus— nucleus collisions starts usually by determining an event plane which is strong correlated with the reaction plane which in turn is given by the directions of the impact parameter b and the beam.
Different aspects of flow phenomena have been observed: the bounce-off of the spectator fragments and the side splash of participant matter which occurs in the reaction plane and the squeeze-out of nucleons perpendicular to the reaction plane [ 10].
The goal of the present paper is to review the various flow phenomena observed by unique emulsion method at momenta between 1 and 160 A GeV/c.
2. EXPERIMENT
Stacks of NIKFI BR-2 nuclear emulsions were irradiated by 1.55-A GeV/c 84 Kr beam at SIS in Darmstadt, by 16O, 22Ne, 28Si, and 32S at Dubna synchrophasotron (4.1—4.5 A GeV/c), by 28 Si and 197Au beams at BNL AGS (14.6 and 11.6 A GeV/c) and by 208Pb beams at CERN SPS (158 A Gev/c). The details of the experiments can be found in previous papers of the Dubna [11], Krypton [12] and EMU01 [13] Collaborations and in the references therein. In some cases, the experimental data were compared with cascade calculations [14].
Secondary charged particles were classified into the following groups:
1. Projectile spectator fragments (PF) — with charges ZPF > 1 and ft & 0.98, emitted inside the fragmentation cone [15].
2. Target fragments (TF) — so-called h particles — consist of fast g particles, mainly recoil protons with velocity 0.23 < ft < 0.7, and slow b particles, target fragments with velocity ft < 0.23.
3. Relativistic s particles — fast singly charged particles with ft > 0.7.
For all particles the polar (0) and azimuthal emission angles have been measured and charges of multiply charged projectile fragments have been determined.
For the present analysis we selected events of inelastic interactions of the projectile nucleus with Ag(Br) target nuclei at medium impact parameters. Selected events, if not saying else, are characterized by the number of TFs NTF > 8 (representing interactions with Ag or Br targets) and NPF > 4, where NPF is the number of PFs (or Na > 3 in the case of197Au-induced interactions, Na is the number of projectile alpha fragments). In the last case these two criteria correspond approximately to an impact parameter cut at about 0.8(RAu + RAg(Br)) [13].
3. RESULTS
There are many methods which are ideally suited to study emission patterns and event shapes in relativistic nuclear reactions. For our analysis we adopted the transverse-momentum approach [16], the flow-angle analysis using principal vectors [17], the azimuthal correlation functions [18], the method of the azimuthal correlations between the charged secondaries [19], and the method of the Fourier expansion of the azimuthal angle distribution [7].
In the transverse-momentum analysis the reaction plane is defined by the direction of the incident nucleus and the plane vector R^, which is constructed individually for each PF from the transverse momenta PTj of all remaining PFs in the same event as R = E AjPTj, where j = i (i,j = 1,2,..., Npf) and Aj is the mass of the fragment. The definition of R ensures that the autocorrelations are removed by calculating R for each fragment separately from the transverse momenta of all remaining fragments, without including the fragment itself [16]. Assuming that each jth PF has the same longitudinal momentum per nucleon PL as the projectile nucleus, the transverse momentum per nucleon of the jth fragment is given by PTj = PLtan0j, where 0j is the emission angle of the jth fragment. Then we find the projection of PT, i onto the corresponding Ri by Pr,i = PT,i • Ri/|Ri|. The average values (Pr) for nuclear interactions on Ag(Br) targets (NTF > 8) are shown in Table 1 as a function of beam mass and momentum. Given in the Table 1 A characterizes effect of flow (see below). The mean value of PR is zero if PT,i is randomly distributed in the azimuthal plane and is nonzero if the energy flow of fragments deviates from the zero-angle direction, i.e., if bounce-off of PFs occurs. One observes that our data significantly differ from zero and display the bounce-off of the PFs.
To investigate if the obtained value represents a significant flow of transverse momenta, the same procedure has been applied to mixed events (ME) which lack a dynamic effect in the reaction plane. The ME have been generated from the original total sample of fragments randomly distributed in the new events. The results are shown in Table 1. The randomized events do not exhibit this bounce-off effect.
Also the plane vector R of the TFs has been constructed for each event according to previously used formula. The coefficient Aj = 1 and, instead of PTj, a unit vector of the azimuthal direction of ^j has been considered. The sum runs over all TFs in the given event. The distribution of the relative azimuthal angle (A^PF_TF) between "projectile" and "target" plane vectors (Fig. 1a) shows strong correlation between them. The average azimuthal angles between them are 112° ± 4° and 107° ± 3° for 84 Kr and
Table 1. The values of (PR)exp, (PR}me, and A for different projectile masses and momenta
Momentum, A GeV/c Beam (PR)exp,AMeV/f (PB)ME,iMeV/c A
1.55 84 Kr 23.6 ± 2.3* 0.6* 0.47 ±0.04
4.1 22 Ne 16.1 ±2.6 0.8 0.53 ±0.06
4.5 is o 12.8 ±2.8 -0.7 0.62 ±0.09
4.5 28 Si 6.1 ±2.3 0.1 0.39 ±0.10
4.5 32 s 18.4 ±2.1 1.3 0.54 ±0.06
11.6 197 Au 32.0 ± 1.8* -0.2* 0.41 ±0.02
14.6 28 Si 7.2 ± 2.5 0.5 0.43 ±0.10
Single-charged PFs are not included in NPF.
197Au primaries [12, 13]. The E877 Collaboration has previously reported [20] a corresponding pronounced event anisotropy.
In order to test the reaction plane determination the method proposed in [16] has been used. Each event was randomly divided into two parts and the reaction planes have been estimated separately for these subevents. The distribution of the differences between the azimuthal angles of the two constructed
Number of events 30 a
20
10
Number of events b
60
40
20
0 50 100 150
A^pf-tf, deg Number of fragments
c
ME
+++
50 100 150
AY, deg
120 80 40
0
Number of fragments 120
100 80 60
100
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