Multicomponent van der Waals Model of a Nuclear Fireball in the Freeze-Out Stage

Abstract

A model of a two-component van der Waals gas is proposed to describe the hadronic stages of nuclear fireball evolution during the cooling phase. During the initial stage of hadronization, when mesons are dominant, a two-component meson model (π0 and π+ mesons) with an effective two-particle interaction potential in the form of a rectangular well is suggested. In the later stages of hadronization, when almost all mesons have decayed, a two-component nucleon model consisting of protons and neutrons is proposed, incorporating the corresponding effective rectangular nucleon potential. The saddle point method has been utilized for analytical computations of the partition function. This approach has facilitated the consistent derivation of analytical expressions for both pressure and density, considering the finite dimensions of the system, as well as analytical expressions for chemical potentials. It is envisaged that the proposed models and resulting equations can be employed for analyzing experimental data related to the quantitative attributes of particle yields of various types in the final state arising from the hadronic stages of nuclear fireball evolution. Additionally, these models can aid in determining the critical parameters of the system during high-energy nucleus-nucleus collisions. It is demonstrated that in the single-component case, the model’s results for the baryonic chemical potential correlate with calculations by other authors.

Keywords

• multicomponent hadron gas, fireball, freeze-out, van derWaals equation, effective nuclear capability, grand canonical ensemble, pressure fluctuation, quark-gluon plasma, experimental data