(Anti)proton and Pion Source Sizes and Phase Space Densities in Heavy Ion Collisions

NA44 has measured mid-rapidity deuteron spectra from AA collisions at √ snn ≈ 18 GeV at the CERN SPS. Combining these spectra with published p, p̄ and d̄ data allows us to calculate, within a coalescence framework, p and p̄ source sizes and phase space densities. These results are compared to π source sizes measured by Hanbury-Brown Twiss, HBT, interferometry and phase densites produced by combining pion spectra and HBT results. We also compare to pA results and to lower energy (AGS) data. The p̄ source is larger than the proton source at √ snn = 17.3 GeV. The phase space densities of π + and p are not constant but grow with system size. Both π and proton radii decrease with mT and increase with √ snn. Pions and protons do not freezeout independently. The nature of their interaction changes as √ snn and the π/p ratio increases. Relativistic heavy ion collisions provide a mechanism to heat and compress nuclear matter to temperatures and energy densities comparable to those of the early universe when it was still a plasma of quarks and gluons. Such a state may be fleetingly restored in these collisions where temperatures of T = 168±3 MeV and energy densities ǫ = 3 GeV/fm are observed [1, 2]. These values are close to those of the phase transition found in lattice calculations [3]. If such a hot and dense state were formed one would expect a large increase in entropy and possibly a saturation of the density of particles in phase space. The coalescence of nucleons into deuterons is sensitive to both their spatial and momentum correlations. In this paper we report p, p̄ and π source sizes measured by coalescence and interferometry, and combine these with single particle spectra to derive phase space densities. The phase space densities depend on temperature, chemical potentials, and velocity fields in the system. This description of the final hadronic state serves as a boundary condition for models of possible quark gluon plasma production. We vary the total size of the system by studying PbPb, SPb, SS and pPb collisions. We also compare our results to lower energy AGS data where the π/p ratio is much lower. This comparison shows that the freeze-out of pions and protons is coupled. NA44 is a focusing spectrometer that uses conventional dipole magnets and superconducting quadrupoles to analyze the momentum of the produced particles and create a magnified image of the target in the spectrometer [4, 5, 6, 7, 8, 9, 10]. The systematic errors on the deuteron yields range from 14% for SPb to 9% for PbPb. The p and p̄ spectra are corrected for feed-down from Λ and Σ decays using a GEANT simulation with the (Λ/p) and (Σ/p) ratios taken from the RQMD model [9, 10, 11]. The systematic error was estimated by varying these ratios by ±25%. These errors are slightly correlated for p and p̄. Fig. 1 shows NA44 deuteron spectra and previously published proton spectra at y = 1.9-2.3 as a function of mT /A [12]. The centrality is ≈ 10% for SS, SPb and PbPb. The spectra get flatter for the larger systems consistent with a higher temperture and/or stronger sidewards flow. As expected from coalescence, the slopes are similar for protons