Two-Component Statistical Model of a Nuclear Fireball in the Cooling Stage (Freezeout)

Abstract

The saddle point method is applied to the statistical integral of the Grand Canonical Ensemble for the cases of one-component and two-component van der Waals gas. This made it possible to obtain the state equation and corrections to the pressure and density of the final statistical system. These contributions, taking into account the realistic effective potential, make it possible to take into account the finite dimensions of the system and, as expected, can be used, in particular, in the case of a nuclear fireball that occurs in high-energy nucleus-nucleus collisions. The corrections depending on the size of the system were compared with the corresponding fluctuations. These corrections become insignificant at the thermodynamic boundary, where, according to statistical physics, the difference between the observed thermodynamic quantities obtained in different statistical ensembles disappears. Taking into account modern estimates of the sizes of mesons and nucleons, as well as realistic estimates for the potentials of their effective interactions, formulas for pressure with a transparent nonrelativistic constraint are obtained. It is expected that they can be used to analyze experimental data on the quantitative characteristics of the yield of particles of various types in the final state from the final stages of the freezeout and to determine the critical parameters of the system in high-energy nucleus-nucleus collisions.