Self-diffusion model for memory functions in classical fluids

The Mori memory-function formalism is used to derive systematically a hierarchy of approximations relating the dynamic structure factor S(k,ω) of a dense classical fluid to its self-part Ss(k,ω). The formalism is applied to a column vector of dynamical variables whose components include the self and distinct parts, ρs and ρd, of the fluctuating density plus N time derivatives of these variables. Increasing N is analogous to a continued-fraction expansion of the memory functions, and builds in more short-time information about the correlation functions. In this manner approximations generated earlier by Vineyard, by Kerr, and by Ortoleva and Nelkin are concisely stated, and a new approximation which gives the first six frequency moments of S(k,ω) correctly is obtained. Since the sixth frequency moment of S(k,ω) is not known from molecular-dynamics calculations, it is used as a parameter to fit these calculations. Agreement for S(k,ω) to within a few percent is obtained for several k values and two thermo-dynamic states. The deduced value of the sixth frequency moment has a reasonable dependence on k, and may give useful information about the three-particle static correlation function.