Study of transverse-momentum spectrum of ultra-relativistic proton
projectile fragments in 60 A GeVOc
16O-emulsion interactions.
Evidence of a single temperature (*)
D. GHOSH, S. K. DASand K. GHOSHHigh Energy Physics Division, Department of Physics, Jadavpur University Calcutta 700 032, India
(ricevuto il 2 Luglio 1996; revisionato il 24 Aprile 1997; approvato il 18 Giugno 1997)
Summary. — This work reports a study of transverse-momentum distribution of
ultra-relativistic proton projectile fragments (Z 41) obtained from 16O-emulsion
interactions at 60 A GeVOc. This study, when compared with Maxwell-Boltzmann distribution, reveals the existence of a single temperature. This observation does not agree with the results obtained by a similar analysis with relativistic a-projectile fragments where there is an indication of two different temperatures. However this work supports the previous result obtained from relativistic proton PFs in
12C-emulsion interaction at 4 .5 A GeVOc.
PACS 25.75 – Relativistic heavy-ion collisions.
1. – Introduction
A large number of experiments have already been done to study the transverse-momentum distribution of relativistic a-PFs, whereas the number of similar experiments with relativistic proton PFs is small. Bhalla et al. [1], Baumgardt et al. [2], Aggarwal et al. [3] and Ghosh et al. [4]—all reported transverse-momentum
distribution of a-PFs and indicated the evidence of two different temperatures. These works are supported by Raha’s argument [5] and seemed to be an experimental signature of QGP. The analysis is based on participant-spectator concept [6] and simple fireball model [7]. It is assumed that the targets and the projectiles are spheres and they make cylindrical cut through each other, leaving target spectators and projectile spectators. Raha proposed that, while spectators separate from participants, there is some intercommunication between them, for which the spectators also get excited. They suggested that shear viscosity of nuclear fluid causes friction over the region of contact and work done against friction shows up as heat in the cut surface.
(*) The authors of this paper have agreed to not receive the proofs for correction.
The energy available to spectators produces particles emission in the fragmentation regions. If QGP is formed in the participant region, the coefficient of shear viscosity would be much reduced compared to the situation where no QGP is formed. Hence the existence of two different types of events and two different temperatures in the case of relativistic a-PFs. Ghosh et al. [8] reports a study of transverse-momentum distribution of relativistic proton PFs emerging from the interactions of12O with nuclear emulsion
at 4 .5 A GeVOc. When the PT distribution is compared with Maxwell-Boltzmann
distribution, contrary to the expectations, it gives the indication of a single temperature. This is against Raha’s proposal, which favours the existence of two different temperatures. This observation cannot be accounted properly by the existing theories. Therefore, further study on proton projectile fragments of different heavy-ion beam with increasing energy is solicited. We think the study would be of extreme intrinsic interest and would be important for better probing the dynamics of heavy-ion collisions. This compels us to take up the work. We, for the first time, studied the PT distribution of proton PFs obtained from 16O-emulsion interactions at 60A GeVOc.
We, also for the first time, make use of the technique of lacunarity (L) measurement to identify singly charged relativistic proton PFs for their PT-distribution study. The
method is very precise and yields an estimate of charges for relativistic PFs having 1 GZG3 with a standard deviation G 0.03e in the measured charge of each track.
2. – Experimental details
We have used a stack of ILFORD-K2 plates exposed to the 16O beam with the
average momentum 60 A GeVOc obtained from CERN, Geneva, Leitz-Metalloplan microscope with oil immersion objective having a magnification 100 3 and ocular lens 20 3, along with an image processor used for scanning. Data is taken with an ASM 68 K semi-automatic measuring system. SUSY system disk and a suitably developed programme is used to measure lacunarity (L) andOor opacity (f) of the track structure. We followed Bloomer et al. [9] to identify relativistic PFs having charge 1 GZG3. This technique is a very precise one and gives a charge precision of G 0.03e.
When a charged particle transverses a silver halide crystal of the nuclear emulsion, it deposits energy in the crystal by ionization. These excited crystals are converted into metallic silver by chemical reduction and the remaining AgBr crystals are then removed and the opaque silver grains form the structure of the track. Lacunarity (L) is defined as the fractional transparency of the track structure. For relativistic PFs, the charge ( 1 GZG3) of the ionizing particle is simply related to the L of its track by
Z 4K0(2ln L)1 O2,
(1)
where K0 is a proportionality constant that is most conveniently determined
empirically. The quantity proportional to Z is defined as
r 4 (2ln L)1 O24 [2ln ( 1 2 f) ]1 O2,
(2)
where f is defined as the opacity of the track structure. We have now the two ionization parameters L and f which are operationally well defined, easy to measure and related to charge by the simple relation Z 4K0r .
We have used a random subsample of 475 events from a bigger collection of events. Average multiplicity is found to be 3.5 considering all the charged PFs. Measurement of lacunarity (L) andOor opacity (f) is taken on 1500 mm of the linear track structure
for each track. It is seen that the lacunarity (L) obtained directly or calculated from the opacity (f) belongs to three distinct groups, which can be identified as Z 41, 2, 3 groups, respectively. Proton PFs are of interest here and 635 proton PFs are identified by this method.
Particles lying beyond the emission angle of 17 with respect to the incident beam direction are rejected deliberately as beyond this limit there is hardly any probability to have a PF for the present range of high-energy projectile. This angular cut also ensures no contamination with shower particles, as they do not get produced within this narrow cone of emergence. The proton PFs thus obtained possess velocity very close to that of the beam. Each event is scanned by two independent observers and the scanning efficiency turned out to be 98%.
3. – Analysis
Analysis is done within the framework of fireball model [10] of relativistic heavy-ion collision. It is assumed that when projectile and target nuclei collide with each other, a localisation of interaction of the two overlapping parts of the projectile and target nuclei takes place forming participants. The rest of the two nuclei remain relatively undisturbed forming spectators. The available energy in the centre of mass heats the swept-out nucleons leading to a quasi-equilibrium fireball. It is assumed that the fireball is formed by the nucleons in the swept-out region only. The large number of swept-out nucleons combined with an anticipated fairly large number of interactions per particle is presumably responsible for the quasi-equilibrated system, i.e. the fireball which can then be described in terms of mean values and statistical (Maxwell-Boltzmann) distribution. The transverse momentum of a projectile fragment is given by
PT4 Am0(g22 1 )1 O2sin u ,
(3)
where A 4mass number of the fragment, m04 the nucleon rest mass and g 4 the
Lorentz factor of the projectile. With the help of Bethe-Bloch formula the decrease in the kinetic energy of the oxygen projectiles on their way through the emulsion has been taken into account. As there is no contamination with the showers, uncertainty in the mass parameter of the proton PFs can be neglected. Assuming that the momentum of the proton PFs is Maxwell-Boltzmann distributed in the projectile rest frame with some temperature T, the integral frequency distribution of the transverse momentum per nucleon squared Q(4 P2
TOA2) is
ln F(DQ) 42 (AO2m0T ) Q .
(4)
If the plot is linear, then from the slope of the line we get a single characteristic temperature of the distribution.
Figure 1 shows the transverse-momentum (PT) distribution of relativistic
proton-PFs observed in all 475 events. The distribution shows a prominent peak at 0.30 GeVOc. Figure 2 shows a cumulative plot of ln F(D Q) as a function of Q for the experimental data. This plot gives a good linear fit with x2
Od.o.f. 4 0 .095 . An error bar is given in the figure to account for the statistical error. In this case of a single MB distribution, we get a temperature of 58 MeV.
Table I shows the results of some previous experiments, with the values of the two temperatures and the percentage of events of the two groups from the
transverse-Fig. 1. – Transverse-momentum (PT) distribution of the relativistic projectile-fragment (Z 41)
produced in16O-emulsion interaction at 60 A GeVOc. N4total number of proton PFs.
Fig. 2. – Cumulative plot of ln F(D Q) as a function of Q. Here Q is the transverse momentum per unit mass squared (P2
TABLE I. – Values of the two temperatures and percentage of events of the two groups from the transverse-momentum distributions of the a-PFs in different projectiles at several energies. Beam EnergyO momentum No. of events Cool temperature Hot temperature
Percentage of events Reference (Tc) MeV (Th) MeV in cold region in hot region 56Fe 56Fe 40Ar 56Fe 12C 0.9A GeV 1.7A GeV 2.0A GeV 1.9A GeV 4.5A GeVOc 900 423 975 368 1200 8 12 9 10 10 40 52 68 43 40 — — — 64 60 — — — 36 40 [3] [1] [3] [2] [4]
TABLE II. – Values of the single temperature from the transverse-momentum distributions of proton-PFs in two projectiles at two different energies.
Beam EnergyO momentum No. of events Single temperature Reference 12C
16O 4.5A GeVOc60A GeVOc
400 475 8 MeV 58 MeV [8] present work
momentum distributions of the a-PFs in different projectiles at several energies. It is very interesting to note that all the heavy-ion data with a-PFs speak in favour of the existence of two type of events, the so called cold and hot events. This observation was interpreted, following Raha et al. [5], as a possible signature for the production of QGP. Table II compares the present data with the previous data and shows the values of the single temperature from the transverse-momentum distributions of proton-PFs in two different projectiles at two different energies. Though both of the data favour the existence of a single temperature, its value for the present data is several times larger than the corresponding value for the previous data. Also, we see, the momentum of the projectile used in the present work is several times larger than the previous value. This indicates that the temperature of the fragmentation region increases with projectile momentum. These results do not agree at all with similar analysis for PT-distribution of a-PFs. Thus, Raha’s argument fails to explain such behaviour of proton PFs. However,
one may comment, the physical process involved in the behaviour of proton PFs must be different from the one we depicted from Raha’s hypothesis.
4. – Conclusion
We may now conclude the following: our new data on the transverse-momentum distribution of proton PFs of 16O-emulsion interaction at 60 A GeVOc indicate a single temperature in the fragmentation region. Previous data [8] on the PT-distribution of
proton PFs of12
C-emulsion interaction at 4 .5 A GeVOc support the present work with a difference in the temperature of the fragmentation region.
R E F E R E N C E S
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