# Effects of quantum statistics near the critical point of nuclear matter

## TL;DR

This paper investigates how quantum statistics influence the nuclear matter equation of state near the critical point using a quantum van der Waals model, providing analytical corrections validated by numerical calculations for Fermi and Bose systems.

## Contribution

It introduces analytical corrections for the critical point parameters in the quantum van der Waals model, applicable to both Fermi and Bose interacting particles.

## Key findings

- Quantum statistical corrections align well with numerical results.
- Analytical formulas for critical parameters are derived up to quadratic order in small parameter δ.
- Results are applicable to nuclear matter and Bose systems like alpha nuclei.

## 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.