Bulk Properties of a Fermi Gas in a Magnetic Field

TL;DR

This paper derives explicit formulas for the thermodynamic properties and pressure anisotropy of a Fermi gas in a magnetic field, considering charged and uncharged particles with anomalous magnetic moments at various temperatures.

Contribution

It provides new explicit formulae for the thermodynamic quantities of a Fermi gas in magnetic fields, including pressure anisotropy and effects of anomalous magnetic moments.

Findings

Pressure anisotropy increases with anomalous magnetic moments.

Explicit formulas valid at zero and finite temperature are derived.

Numerical results show increased anisotropy for protons and neutrons.

Abstract

We calculate the number density, energy density, transverse pressure, longitudinal pressure, and magnetization of an ensemble of spin one-half particles in the presence of a homogenous background magnetic field. The magnetic field direction breaks spherical symmetry causing the pressure transverse to the magnetic field direction to be different than the pressure parallel to it. We present explicit formulae appropriate at zero and finite temperature for both charged and uncharged particles including the effect of the anomalous magnetic moment. We demonstrate that the resulting expressions satisfy the canonical relations, Omega = - P_parallel and P_perp = P_parallel - M B, with M = - d Omega/d B being the magnetization of the system. We numerically calculate the resulting pressure anisotropy for a gas of protons and a gas of neutrons and demonstrate that the inclusion of the anomalous magnetic increases the level of pressure anisotropy in both cases.