Van der Waals Equation of State with Fermi Statistics for Nuclear Matter

The van der Waals (VDW) equation of state is a simple and popular model to describe the pressure function in equilibrium systems of particles with both repulsive and attractive interactions. This equation predicts an existence of a first-order liquid-gas phase transition and contains a critical point. Two steps to extend the VDW equation and make it appropriate for new physical applications are carried out in this paper: 1) the grand canonical ensemble formulation; 2) an inclusion of the quantum statistics. The VDW equation with Fermi statistics is then applied to a description of the system of interacting nucleons. The VDW parameters $a$ and $b$ are fixed to reproduce the properties of nuclear matter at saturation density $n_0=0.16$ fm$^{-3}$ and zero temperature. The model predicts a location of the critical point for the symmetric nuclear matter at temperature $T_c\cong 19.7$ MeV and nucleon number density $n_c \cong 0.07$ fm$^{-3}$.