Collective Motions in Classical Liquids. II

An improved version of the theory of Singwi et al. for the collective motions in classical liquids is described. The theory is based on a generalized mean-field approximation involving the polarization potential and the screened response function. The latter, instead of having a free-particle form or that corresponding to the true self-motion of the particle in a liquid, is assumed to be a sum of Gaussian functions weighted by the momentum distribution of the particles. The zero and fourth moments of the scattering law determine the polarization potential and the width of the Gaussians. Numerical calculations have been made for the spectral function of the longitudinal current correlations, quasielastic scattering, and absolute intensities for liquid argon in the range of momentum transfer 0.5-6.3 ${\mathrm{\AA }}^{-1\mathrm{}}$. The results are in excellent agreement with the molecular-dynamics calculations and recent experiments on a purely coherent sample of liquid argon.