[en] An imaginary part of the dielectric matrix is derived based on a first order perturbation expansion of the valence electron states in a local potential model of the crystal. The results are used to estimate the electronic contributions to the phonon damping in aluminum and lead. The corrections which have been obtained are of the same order of magnitude at small phonon momenta as the damping earlier calculated for the free electrons. However, the discrepancies between the theoretical and experimental results still remain. The major contribution to damping seems to originate in anharmonic effects, even at 80 deg K