1331 The dynamical structure factor S(k, w) and the spectral function J(k, w) of the currentcurrent correlation function in classical simple liquids are studied by using the memory function formalism. A memory function appearing therein is expressed in terms of a second order memory function. By using the high-frequency expansion method the memory function is rigorously expressed in a closed form in terms of its free part and a polarization function. This formulation is shown to give a general

more »

... orm of the screened response function theory. On the assumption of a Gaussian time-dependence for the polarization function, numerical calculations of S (k, w) and J (k, w) are made at wave number k = 1.2"-4.0 A_, for liquid argon. The full width at half maximum of S(k, w), the frequency at a peak of J(k,w) and its peak height are also calculated. In comparing with the experimental results of neutron inelastic scattering measurements, excellent agreement is obtained in the line shape of S (k, w) and J(k, w). § I. Introduction The dynamical structure factor S(k, w) in classical simple liquids has been much studied during recent yearsY~1 21 Near the wave number at the first peak of the static structure factor S(k) many authors have made theoretical attempts to obtain the dispersion curve for the collective motion from the position at a peak of S (k, IJ)) or that of the spectral function J(k, IJ)) of the current-current correlation function. 131~161 The over-all behaviour of the dispersion curve obtained there is characterized roughly by the fourth-order frequency moment of S(k, w). However, since the experimental result of S(k, w) has not shown a side peak in that wave number region, the dispersion curve cannot be determined there. 31 " 71 Thus, the investigation of the line shape of S ( k, IJ)) itself becomes very important to clarify the correlated motion of atoms in liquids. In order to analyse the density-density correlation function for that purpose, the memory function formalism has been often employed as a convenient method.m~2 01 The conventional procedure of approximating a memory function is reviewed in Refs. 1) and 20). In a previous paper 211 which is referred to as I hereafter, we have made a different approach to the memory function by separating it into a kinetic part and the remaining part