Quantum statistics effects and fluctuations of particle numbers near the critical point of nuclear matter

TL;DR

This paper derives quantum statistical corrections to the equation of state for nuclear matter near the critical point, analyzing particle fluctuations and effects of interactions using an analytical approach that aligns well with numerical results.

Contribution

It introduces a first-order quantum-statistics correction to the van der Waals equation for nuclear matter, including particle fluctuations and impurity effects.

Findings

Quantum corrections modify the nuclear matter equation of state.

Particle number fluctuations are analytically related to isothermal in-compressibility.

Impurities have minimal impact on symmetric nuclear matter results.

Abstract

Equation of state with quantum statistics corrections is derived for a multi-component gas of particles interacting through the repulsive and attractive van der Waals (vdW) forces up to first few orders over a small parameter $\delta \approx \hbar^3 n(mT)^{-3/2}[g(1- bn)]^{-1}$, where $n$ and $T$ are the particle number density and temperature, $m$ and $g$ the particle mass and degeneracy factor. The parameter $b$ corresponds to the vdW excluded volume. For interacting system of Fermi nucleon and Bose $\alpha$ particles, a small impurity of $\alpha$ particles to the nucleon system at leading first order in both $\alpha $ particle and nucleon small parameters $\delta $ does not change much the basic results for the symmetric nuclear matter. The particle number fluctuations $\omega$ determined by the isothermal in-compressibility $\mathcal{K}(n,T)$ can be obtained analytically at the same first order quantum-statistics approximation for symmetric nucleon matter. Our approximate analytical results appear to be in good agreement with the accurate numerical calculations.