Expansion for the Quantum Second Virial Coefficient Using Hard-Sphere Basis Functions

Abstract

Following the general approach to the calculation of the quantum second virial coefficient first developed by Wigner and Kirkwood, an expansion in powers of h² is derived for B(T) using hard‐sphere basis functions rather than the free particle functions used in the Wigner—Kirkwood calculation. A variational method is utilized to determine the hard sphere diameter that gives the best second virial coefficient. Computed values of B(T) which are presented here indicate that a considerable improvement over the Wigner—Kirkwood calculation is obtained, both in the direct (Boltzmann statistics) and in the exchange virial coefficient.