The inversion of the dielectric function in the presence of an interface

For a system containing a metal-vacuum interface an exact formal solution is presented for the inverse RPA dielectric function. The solution is valid for an arbitrary shape of the electron density profile at the surface. It contains(a) the inverse dielectric Lindhard function representing the bulk screening effects and (b) surface terms which describe the modification of the screening propertles near the interface. From the pole contribution of the surface term an exact equation for the surface plasmon dispersion is derived. In order to check the applicability of the general result for ?^?1, the surface plasmon dispersion and the screening length of a homogenous field applied perpendicular to the surface are briefly discussed by adopting the infinite barrier model.