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) expu (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.