Perturbation theory for the radial distribution function in the presence of three-body forces

Abstract

Perturbation theory is used to consider the effect of the three-body potential on the radial distribution function g (r). We find that the effective pair potential, u^eff(1,2) =u (1,2)-kTρFg₀(1,3)g₀(2,3)f(1,2,3) d3, where g₀(i,j) is the true pair potential radial distribution function, is an appropriate model for the study of the effect of the triplet potential on the g (r). Dividing the effective pair potential into repulsive and attractive regions, the radial distribution function of the reference potential is evaluated. It is shown, by calculating the total g (r) for the effective pair potential that, to first order, the effect of the triplet potential on the g (r) is accounted for by its effect on the reference g (r). We find that the effect of the triple-dipole potential on the structure of liquids at low temperatures especially near the triple point is substantial.