Quantum Mechanical Perturbation Expansion for the Second Virial Coefficient and the Ursell‐Mayer Function

Starting from a quantum mechanical diagrammatic expansion of the grand partition function ξ, and of the coefficients Vb_l in the activity expansion of ξ, and making a term by term passage to the limit of classical nuclear motion, results in a corresponding diagrammatic expansion of the Ursell functions U_l(R₁, . . ., R_l). Presently only the expansion of the Ursell‐Mayer function f(R) has been explicitly examined and the terms up to second order perturbation theory, including exchange, have been evaluated. The truncated expansion gives a reasonably accurate expression of f(R) for long and medium range distances (R≥4_a0) and within this range can be transformed, to the same order of accuracy, into the classical standard form f(R)=exp[ −u(R)]− 1, although in principle an exact formulation in such a form is not necessarily possible.