A generalization of vineyard's convolution approximation

Abstract

The Fourier transform f ( k, t) of the density-desnity (van Hove) correlation function G ( r,t) is expressed as a function of the specific-particle distribution function f s ( k,v 1, t) describing diffusion and associated with the self-function I s( k,t) or G s ( r,t). the low-density (binary encounter) case is obtained also. The derivation is limited to classical statistics.