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

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, $\epsilon \approx {\hslash }^{3}n(mT{)}^{-3/2}{g}^{-1}$, 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 $\epsilon$ 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.

arXiv comment10 pages, 3 figures. arXiv admin note: substantial text overlap with arXiv:2012.09695

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