Microscopic Dielectric Susceptibility of Germanium

Abstract

The microscopic dielectric susceptibility $\epsilon \mathrm{}\left(q\right)\mathrm{}$ is calculated for germanium using the shell model. It is found that except at $q=0\mathrm{}$ the longitudinal and transverse susceptibilities differ and are anisotropic. The results agree qualitatively with Penn's isotropic quantum model based on the random-phase approximation. It is suggested that the quantitative differences may in part represent shortcomings of the RPA in treating the stiffness of covalent bonds.