Memory-function approach to the excitation spectra of an electron liquid

An expression for the density-response function has been obtained using Mori's memory-function formalism. This is consistent with the high-frequency behavior of the response function, but involves an unknown memory function. The memory function is calculated in the free-particle approximation. The results for the dynamical structure factor $S(q,\omega )$ are analogous to those obtained using the generalized random-phase approximation. The free-particle memory function is then renormalized to include the finite lifetime of the electrons and holes. Using the renormalized memory function, the results obtained for the dynamical structure factor for aluminum explain broadly all the interesting features recently observed by Platzman and Eisenberger using x-ray inelastic scattering experiments.