Multicomponent Van der Waals model of a nuclear fireball in the freeze-out stage

TL;DR

This paper introduces a two-component van der Waals model for describing the hadronic stages of a nuclear fireball's evolution, providing analytical formulas for pressure, density, and chemical potentials to analyze experimental data.

Contribution

It develops a novel two-component van der Waals model with analytical solutions for the hadronic stages of a nuclear fireball, applicable to high-energy collision data analysis.

Findings

Analytical expressions for pressure and density derived.

Model accounts for finite system dimensions.

Potential to analyze particle yields in experiments.

Abstract

A two-component van der Waals gas model is proposed to describe the hadronic stages of the evolution of a nuclear fireball in the cooling stage. At the first stage of hadronization, when mesons dominate, a two-component meson model ($\pi^0$ and $\pi^+$ -mesons) with an effective two-particle interaction potential of a rectangular well is proposed. At the late-stage hadronization, when almost all mesons have decayed, a two-component nucleon model of protons and neutrons is proposed with the corresponding effective rectangular nucleon potential. The saddle point method has been applied for analytical calculations of the partition function. This made it possible to uniformly obtain analytical expressions for both the pressure and density, taking into account the finite dimensions of the system, and the analytical expressions for chemical potentials. It is assumed that the proposed models and derived formulas can be used to analyze experimental data connected to the quantitative characteristics of the particle yields of different types in the final state from the hadronic stages of the evolution of a nuclear fireball, as well as to determine the critical parameters of the system in high-energy nucleus-nucleus collisions.