Exchange and Direct Second Virial Coefficients for Hard Spheres

Abstract

We have separated the quantum‐mechanical second virial coefficient for hard spheres B into two terms. The first represents the contribution of a Boltzmann gas, and the second is an exchange term embodying the effects of quantum statistics. Numerical computation of B to high precision then allows us to analyze the temperature dependence of the exchange term, which is found to decrease exponentially with temperature, and to determine the asymptotic expansion of the Boltzmann term at high temperatures.