Collective motion and effective potential in classical liquids

The concept of collective motion in classical liquids is discussed by using a general effective potential. In doing this a self-consistent memory function method is employed to analyse the density-density correlation function. The density response function is formulated rigorously in the form of a generalised random-phase approximation. The effective potential which appears therein is investigated by using successive approximations for a memory function. It is shown that the effective potential guaranteeing sum rules of the dynamical structure factor up to the fourth give a solid-like mean field in the high-frequency limit. From the lineshape of the dynamical structure factor corresponding to frequency-dependent potentials, effects of dynamical dampings are discussed.