Microscopic theory of some surface effects in a dense electron gas

We consider interacting electrons confined to a slab of finite thickness or a half space in the random phase approximation. The electronic charge is assumed to be neutralized by a homogeneous positive background. A linear response function is introduced from which it is possible to calculate the induced density variation of the electron gas, caused by an external field. The linear response function also determines the Helm-holtz free energy and, by a sum rule, the density of the undisturbed system. The interaction of a classical point charge with the electrons of a half-space is discussed. In addition, a formula for the surface energy is given.