Scattering problem with nonlocal separable potential of rank-two: Application to statistical mechanics

In this paper, we present a formulation of statistical mechanics of a thermodynamic system consisting of free particles and independent correlated pairs interacting via nonlocal potential in terms of the scattering properties. Some quantum statistical properties such as energy, heat capacity, second virial coefficient, virial pressure and quantum correction of kinetic energy are described analytically. The difference between the resolvents of the interacting and free Hamiltonians, represented as R^(z), that is associated with particle correlations is used for the evaluation of the properties. The statistical properties are related to correlated states, when making a pole expansion of the analytically continued momentum matrix element of R^(z). The present work illustrates these relations for a three-dimensional nonlocal separable potential of rank-two.