Microscopic Dielectric Constant in Insulators

A conventional expression for the microscopic dielectric constant as obtained by Adler and Wiser in the Hartree approximation lacks the self-polarization correction arising from the polarization of electrons by its own field and hence is invalid for tightly bound electrons. When the correction is introduced, the microscopic dielectric constant can still be expressed in terms of a simple formula. With the use of the "separable" approximation to the polarization, which holds well for tightly bound electrons, the result is shown to recapture the Lorentz-Lorenz formula for the macroscopic dielectric constant in the limit of completely localized electrons.