Scaled variance, skewness, and kurtosis near the critical point of nuclear matter

TL;DR

This paper investigates nucleon number fluctuations near the critical point of nuclear matter using the van der Waals equation with Fermi statistics, revealing divergence and complex behavior of statistical measures.

Contribution

It applies the VDW equation with Fermi statistics to study fluctuations near the nuclear matter critical point, highlighting the behavior of higher-order moments.

Findings

Scaled variance diverges at the critical point

Skewness remains nearly zero in the crossover region

Kurtosis becomes significantly negative near the critical point

Abstract

The van der Waals (VDW) equation of state predicts the existence of a first-order liquid-gas phase transition and contains a critical point. The VDW equation with Fermi statistics is applied to a description of the nuclear matter. The nucleon number fluctuations near the critical point of nuclear matter are studied. The scaled variance, skewness, and kurtosis diverge at the critical point. It is found that the crossover region of the phase diagram is characterized by the large values of the scaled variance, the almost zero skewness, and the significantly negative kurtosis. The rich structures of the skewness and kurtosis are observed in the phase diagram in the wide region around the critical point, namely, they both may attain large positive or negative values.