Classical theory of the dielectric function for an inhomogeneous electron gas

Abstract We develop a classical electrodynamical theory of the dielectric function for an inhomogeneous electron gas. The dielectric function in the high-frequency approximation (HFA) derived by Kitagawa is obtained in a simple manner. It is shown that, in an inhomogeneous electron gas, two different definitions of the dielectric function do not coincide with each other because of the breakdown of the translational invariance. Using our present method, we can calculate the dynamical potential for an arbitrary electron density that is very difficult to obtain by using other methods. We also describe analytic dielectric functions both for the HFA taking account of a higher-order correction and for the static limit.