A convolution approximation for Van Hove correlation function in liquids

The relative motions of particles in a simple liquid may be described as one-dimensional radial diffusion in an effective potential of the mean force. This effective potential may be obtained by an iteration procedure with the Vineyard approximation as the initial step. Using a harmonic approximation for the potential, the “distinct” part of the Van Hove time-dependent correlation function is then the convolution of a modified radial distribution function with a modified self-correlation function. The former describes the average positions of particles whereas the latter describes the density profile around the average position. For liquid argon, this modified convolution procedure appears to give results in satisfactory agreement with molecular dynamics.