A generalized hyper-netted chain approximation in the theory of classical fluids

A new approximation to the theory of a classical fluid of number density ρ in equilibrium at absolute temperature T is investigated. Although the model takes some account of the elementary diagrams, it is nevertheless such that all clusters retained in the number-density expansions of the total correlation function h(r) and the direct correlation function c(r) are of simple hyper-netted chain type. The approximation, which is defined by the integral equation h(r12) - c(r12) = ym(r12) ln y (r12) = ρ∫c(r13)h(r23)dr3 where y(r) = {1 + h(r)} exp{u(r)/kT} and u(r) is the interaction potential between two atoms at distance r apart, reduces to the hyper-netted chain approximation when m = 0.