Hard-Core Insertion in the Many-Body Problem

Abstract

Under many conditions, short-range interparticle forces may be simulated by hard cores. The excluded-volume condition which this implies is equivalent to a single restriction upon the microscopic pair distribution. A short-range nonsingular equivalent potential plays a dominant role in this formulation, and its precise value depends upon the approximation used for the remaining long-range forces. A few of these approximations are examined; they yield simplifications of well-known integral equations in the theory of fluids. Possible perturbation solutions are investigated. For example, the corrections to plasma distributions due to short-range cores can be found in this fashion. The method is generalized by using a single condition on the mean radial distribution, permitting application to quantum mechanics, to mixtures, and to external forces. The special case of the Bose hard-sphere fluid is considered.