Application of Faddeev Techniques to the Quantum Theory of the Third Virial Coefficient

Cluster coefficients for a quantum gas can be related by means of a Laplace transform to the resolvent of an interacting system. Techniques developed by Faddeev are applied in order to express resolvents in terms of quantities which satisfy coupled integral equations. The resulting theory for the cluster coefficients is free of convergence difficulties encountered in series expansions of those coefficients in terms of a binary-collision kernel or two-body scattering matrix. Present computational difficulties necessitate an approximate solution of the Faddeev equations. The assumption of a separable two-body scattering matrix makes possible such a solution and a subsequent calculation of cluster coefficients.