Path-integral calculation of the third virial coefficient of quantum gases at low temperatures

TL;DR

This paper develops a path-integral method to calculate the third virial coefficient of quantum gases, incorporating exchange effects, and applies it to helium isotopes with high accuracy at low temperatures.

Contribution

It introduces a path-integral approach that includes exchange effects for calculating virial coefficients, improving accuracy over previous models at low temperatures.

Findings

Accurate third virial coefficients for 3He and 4He from 2.6 to 24.56 K.

Exchange effects are crucial below about 7 K for precise results.

Uncertainties are smaller than existing experimental data.

Abstract

We derive path-integral expressions for the second and third virial coefficients of monatomic quantum gases. Unlike previous work that considered only Boltzmann statistics, we include exchange effects (Bose-Einstein or Fermi-Dirac statistics). We use state-of-the-art pair and three-body potentials to calculate the third virial coefficient of 3He and 4He in the temperature range 2.6-24.5561 K. We obtain uncertainties smaller than those of the limited experimental data. Inclusion of exchange effects is necessary to obtain accurate results below about 7 K.