Van der Waals equation of state for asymmetric nuclear matter

TL;DR

This paper extends the van der Waals equation of state to asymmetric nuclear matter by incorporating Fermi statistics corrections, analyzing critical behavior, and comparing with Skyrme functional predictions.

Contribution

It introduces a modified van der Waals model with Fermi statistics corrections for asymmetric nuclear matter, linking critical properties with experimental data and Skyrme theory.

Findings

Derived pressure and free energy corrections due to Fermi statistics.

Analyzed the critical line in pressure-temperature-composition space.

Determined incompressibility coefficient along the critical line.

Abstract

The application of van der Waals equation of state to the asymmetric nuclear matter is considered in a critical state region. The corrections to the van der Waals pressure and free energy due to the Fermi statistics are obtained starting from the Thomas--Fermi entropy expression which ensures the fulfilment of Nernst theorem. The derived corrections account for the effective nucleon mass and neutron-proton isotopic asymmetry. The parameters of van der Waals equation of state are deduced taking the experimental value of critical temperature for symmetric nuclear matter and testing the model of van der Waals with statistics corrections included against the theory of Skyrme energy density functional. Critical line in pressure-temperature-composition space is considered. Incompressibility coefficient is determined along the critical line as a function of nuclear matter composition. Jump in the value of specific heat upon crossing critical line is discussed.