The Applicability of the Soft Core Model of Fluids to Dynamical Properties of Simple Liquids: The Velocity Autocorrelation Function

The velocity autocorrelation function, memory function and power spectrum for fluids interacting through the soft core potential φn = C/rn, where C(>0) and n(>3) are positive constants, are calculated both for n = 12 and n = 4, and are compared with the experiments both in Ar and Na near the corresponding freezing points. For n = 12 the memory function and spectrum are computed numerically from the result of molecular dynamics studies, and are used to test several approximate memory functions presented by many authors. There, the Gaussian II memory function is found to be the best approximation among them. By the use of this approximation the velocity autocorrelation function and the power spectrum as well as the memory function for n = 4 are calculated from the Monte Carlo result for the radial distribution function obtained by Schiff. Finally, it is shown that the significantly different behaviour of the power spectrum of Na from that of Ar can be accounted for by the difference of the value of n within our model, that is, n = 4 for the former, n = 12 for the latter.