Triplet correlation functions for hard spheres: Comparison of different approaches.

Abstract

We present numerical results of a comparison between several approximations for the determination of the triplet correlation functions of a simple liquid, which have been proposed during recent years; the system we have considered is a simple hard-sphere system. Two of the methods (one proposed by Barrat, Hansen, and Pastore [Phys. Rev. Lett. 58, 2075 (1987); Mol. Phys. 63, 747 (1988)], and the other one based on a formal density expansion of the triplet distribution function) are purely numerical; the other two methods are based on a density-functional theory (reproducing both thermodynamics and pair structure of the Wertheim-Thiele description of hard spheres) and provide for this special system analytic expressions of the triplet direct correlation function in q space. If the triplet configurations are not too close (i.e., at most one direct contact between the spheres), we find good agreement between the different methods; this is quite remarkable since these approximations have completely different conceptual origins. If, however, the three particles form configurations with rather short interparticle distances the differences in the results may become quite substantial.