Effects of quantum statistics near the critical point of nuclear matter

Abstract

Effects of quantum statistics for nuclear matter equation of state are analyzed in terms of the recently proposed quantum van der Waals model. The system pressure is expanded over a small parameter $\delta \propto n(mT)^{-3/2}[g(1-bn)]^{-1}$, where $n$ and $T$ are, respectively, the particle number density and temperature, $m$ and $g$ the particle mass and degeneracy factor. The parameter $b$ corresponds to the van der Waals excluded volume. The corrections due to quantum statistics for the critical point values of $T_c$, $n_c$, and the critical pressure $P_c$ are found within the linear and quadratic orders over $\delta $. These approximate analytical results appear to be in a good agreement with exact numerical calculations in the quantum van der Waals model for interacting Fermi particles: the symmetric nuclear matter ($g=4$) and the pure neutron matter ($g=2$). They can be also applied to the system of interacting Bose particles like the matter composed of $\alpha$ nuclei.