Quantum mechanical perturbation expansion for thé second virial coefficient and the ursell-mayer function

Starting from a quantum mechanical diagrammatic expansion of the grand partition function 3, and of the coefficients Vbi in the activity expansion of 3, 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≥4a₀) 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.