On the inversion of thermophysical properties

Abstract

A number of data-inversion techniques exist by which the intermolecular potential-energy function U(r) of a pair of spherical molecules may be determined from the thermophysical properties of the bulk system. The reasons for the success of such methods are investigated theoretically. Perturbations theory is used to show how the inversion functions G(T) that appear in these methods depend upon U(r). It is shown that the kind of slowly-varying perturbations that distinguish the potential-energy functions of realistic or pseudo-realistic systems have only a small influence on G(T). The poorly-understood inversion of the second virial coefficient is considered in detail. Emphasis is give to analytic approximations to the integral equations involved, rather than to their numerical investigation.