Velocity correlation and collective modes in a rigid sphere fluid

A theory of the velocity autocorrelation function in terms of the longitudinal and transverse momentum current densities has recently been derived by Gaskell and Miller. It has been strikingly successful in some liquid metal-like systems, and we report its application here to a rigid sphere fluid, which perhaps provides a more searching test of its treatment of binary encounters. It has been necessary to derive expressions for the current correlation functions in an attempt to incorporate the observed collective effects in a dense fluid. For example, the existence of propagating shear wave modes has recently been demonstrated in molecular dynamics investigations, and we ensure that they are displayed by the transverse current model we use. When compared with data obtained from computer simulation studies our results for the velocity autocorrelation function in the dense fluid are quite impressive at short and intermediate times. However, they fail to reproduce the negative behaviour which persists over a period of many collision times, and which is a feature of the computer data. It is pointed out that this may be due to deficiences in the simple models we have derived for the currents.