Chemical potential of a hadronic fireball in the freeze-out stage

TL;DR

This paper models the chemical potential of a hadronic fireball during freeze-out using a van der Waals gas approach, comparing analytic results with QCD-based numerical data for different hadronization stages.

Contribution

It introduces a two-stage van der Waals gas model for hadronic fireball evolution, providing analytic expressions for pressure and chemical potentials and analyzing effective chemical potential applications.

Findings

Analytic expressions for pressure and chemical potentials derived.

Model results compared with QCD numerical data.

Effective chemical potential applicability discussed.

Abstract

This article explores the van der Waals gas model proposed to describe the hadronic stages of nuclear fireball evolution during the cooling stage. Two different models were proposed for the early and late stages of hadronization. At the initial stage, a two-component meson model consisting of $\pi^0$ and $\pi^+$ mesons was suggested, and at the later stage, a two-component nucleon model consisting of protons and neutrons was proposed. The interaction potential for both models was represented by a rectangular well, and the statistical sum was calculated using the saddle-point method. The analytic expressions for pressure and chemical potentials obtained from the model were compared with the corresponding numerical results of other authors obtained earlier using quantum chromodynamics (QCD) methods. The possibility of applying and using the effective chemical potential is also analyzed.