Incoherent scattering functionSs(q,ω)for classical liquids

Within the Mori theory, a kinetic equation for the phase-space density of a tagged particle in a classical liquid is derived which describes the particle motion in a self-consistent wave number and frequency-dependent effective potential. It is shown that for small wave numbers $q$ the particle is almost bound in a trapping potential, that at some critical wave number $q_0$ the trapping potential breaks down, and that for large $q$ the particle propagates almost freely. The theory is applied to the calculation of the self-correlation function $S_s(q,\omega )$ for liquid argon and rubidium, and the breakdown of the trapping potential is shown to explain the observed oscillatory $q$ dependence of the half-width of $S_s(q,\omega )$.