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

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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.