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

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 ) = ℏ k /2 Mc for sufficiently small k is shown to yield g ( r ) ~ 1 - (ℏ/2π 2 n 0 Mc ) r -4 where n 0 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 ϕ( r ) ~ - Ar -6 , g ( r ) ~ 1 - (1/ kT ){ S (0)} 2 ϕ r in regions well away from the critical point. For simple liquid metals, such as sodium, neglecting Fermi surface blurring, ϕ( r ) ~ Br -3 cos 2 k f r and this gives g ( r ) ~ 1 - (1/ kT ){ S (2 k f )} 2 ϕ r where k f is the magnitude of the Fermi wave vector.