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

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 $\delta \approx {\hslash }^{3}n(mT{)}^{-3/2}[g(1-bn){]}^{-1}$, 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.

Comments: 12 pages, 5 figures, 2 tables