B. Bildstein et G. Kahl, TRIPLET CORRELATION-FUNCTIONS FOR HARD-SPHERES - COMPARISON OF DIFFERENT APPROACHES, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics, 47(3), 1993, pp. 1712-1726
We present numerical results of a comparison between several approxima
tions for the determination of the triplet correlation functions of a
simple liquid, which have been proposed during recent years; the syste
m we have considered is a simple hard-sphere system. Two of the method
s (one proposed by Barrat, Hansen, and Pastore [Phys. Rev. Lett. 58, 2
075 (1987); Mol. Phys, 63, 747 (1988)], and the other one based on a f
ormal density expansion of the triplet distribution function) are pure
ly numerical; the other two methods are based on a density-functional
theory (reproducing both thermodynamics and pair structure of the Wert
heim-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 ap
proximations have completely different conceptual origins. If, however
, the three particles form configurations with rather short interparti
cle distances the differences in the results may become quite substant
ial.