High Temperature Limit of the Exchange Third Virial Coefficient for Hard Spheres

Abstract

The exchange terms in the three-particle cluster integral for a hard sphere gas are analysed in the limit that the thermal wavelength is much shorter than the hard sphere diameter. Asymptotic evaluations are achieved by the construction of upper and lower bounds with the same leading functional dependence. In this limit the term arising from a cyclic permutation of three particles dominates over the term arising from the transposition of a pair of particles. These calculations use path integral methods; the results agree with classical path estimates.