On the isothermal density derivative ofG(r) and a new theory of the pair correlation function of hard spheres

Abstract

A new representation is obtained for the isothermal density derivative ofg(r). It explicitly exhibits the contributions of potential energy terms that are not pairwise additive. Consideration of a previously known result shows that one has to be rather cautious when using it to obtain information on the triplet correlation function from the well-known relation between this function andδg/δρ, due to large cancellations which take place at high density. By integrating with respect to density the new representation forδg/δρ, after a suitable closure has been introduced, we obtain an augmented Percus-Yevick equation for hard spheres which has full thermodynamic consistency. The equation of state and the cavity functiony(r) are very accurate at low density and considerably improve PY at medium density, so that this appears to be a useful new approach to the theory of fluids, but it is necessary to improve the closure in order to treat a dense fluid.