Collective Motions in Classical Liquids

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Abstract
A theory of collective motions in classical liquids, which is valid at short wavelengths and high frequencies, is presented. This theory is based on a self-consistent-field method, which can be viewed as a generalization of the random-phase approximation. The existence of collective effects is considered at the outset by introducing a self-consistent "polarization" potential that provides the restoring force and a "screened" response function. The density response function is expressed in terms of these two functions. The local field corrections enter the polarization potential via the static structure factor of the liquid. Various approximations for the polarization potential and the screened response function, and their relation to the first few moments of the spectral function of the density response, are examined. These approximations are tested by explicit numerical calculations of the spectral function of the longitudinal current correlations for liquid argon. It is found that an over-all good agreement with the data is obtained for the case in which the screened response function is equal to the response function for the self-motion of atoms and the polarization potential is determined through the zeroth-moment sum rule. There are no adjustable parameters in the theory.