Dynamical current correlation functions of simple classical liquids for intermediate wave numbers

The longitudinal and transversal current-current correlation functions of simple classical liquids are expressed in terms of restoring forces and frequency-dependent relaxation kernels within the frame-work of Mori's theory. The spectra of the relaxation kernels are approximated by the decay of one-mode excitation into pairs of two longitudinal modes and into pairs of one longitudinal and one transversal mode. The decay vertex is given by an irreducible three-particle distribution function which is approximately expressed in terms of two-particle distribution functions taking three-particle hard-core correlations into account. The resulting nonlinear integral equations are solved by iteration for liquid argon parameters and the obtained current excitation spectra are compared with the curves found by computer simulations and by neutron scattering experiments.