Asymptotic form of correlation functions in classical fluids and in liquid helium 4

Abstract

A solution is proposed to e old problem of the asymptotic form of the radial distribution function g(r) for both quantal and classical liquids. For the quantal fluid helium 4 at absolute zero, Feynman's result that the structure factor S(k) = k/2Mc for sufficiently small k is shown to yield g(r) ~ 1 - (/2π2n0Mc)r-4 where n0 is the mean density and c is the sound velocity. For classical liquid insulators, such as argon, where the long-range van der Waals interaction may be written as (r) ~ -Ar-6, g(r) ~ 1 - (1/kT){S(0)}2r in regions well away from the critical point. For simple liquid metals, such as sodium, neglecting Fermi surface blurring, (r) ~ Br-3 cos 2kfr and this gives g(r) ~ 1 - (1/kT){S(2kf)}2r where kf is the magnitude of the Fermi wave vector.