Quantum statistics effects near the critical point in systems with different inter-particle interactions

TL;DR

This paper derives quantum statistical corrections to the equation of state for Fermi and Bose systems with van der Waals and Skyrme interactions, analyzing effects near the critical point and validating results against numerical calculations.

Contribution

It provides analytical expressions for quantum corrections in systems with different interactions, extending the understanding of quantum effects near phase transitions.

Findings

Quantum corrections are derived analytically for Fermi and Bose systems.

Impurity of alpha particles minimally affects nuclear matter properties.

Analytical results agree well with numerical calculations.

Abstract

Equation of state with quantum statistics corrections is derived for systems of the Fermi and Bose particles by using their van der Waals (vdW) and effective density-dependent Skyrme mean-field interactions. First few orders of these corrections over the small quantum statistics parameter, $\varepsilon \approx \hbar^3 n(mT)^{-3/2}g^{-1}$, where $n$ and $T$ are the particle number density and temperature, $m$ and $g$ the mass and degeneracy factor of particles, are analytically obtained. For interacting system of nucleon and $\alpha$ - particles, a small impurity of $\alpha$ - particles to a nucleon system at leading first order in both $\alpha $-particle and nucleon small parameters $\varepsilon$ does not change much the basic results for the symmetric nuclear matter in the quantum vdW consideration. Our approximate analytical results for the quantum vdW and Skyrme mean-field approaches are in a good agreement with accurate numerical calculations.