Structure of the Triplet Distribution Function

Abstract

In the Born, Green, and Yvon (BGY) theory of fluids it is necessary to postulate a relation connecting the pair distribution function g12 and the triplet distribution function g123. The most famous relation is the superposition approximation which asserts that the triplet distribution function is equal to the product of the pair distribution functions of the three constituent pairs of molecules. If the resulting expression for g123 is expanded in powers of the density it is found that the lowest-order term is exact and that the higher-order terms are approximated with fair success. In addition, the superposition approximation gives good values for g123 at high densities. However, the BGY theory is very sensitive to errors in g123 and, as a result, poor values for the equation of state are obtained when the BGY theory is used in conjunction with the superposition approximation. In this investigation two improvements to the superposition approximation are examined. These approximations are a considerable improvement over the superposition approximation. Both yield an expression for g123 which is exact in the lowest- and first-order terms in the density and yield good approximations to the second-order term in the density. Numerical results are given for Gaussian molecules and for hard spheres.