Self-energy of a charge near a surface

A new, general expression for the space-dependent self-energy of a projectile interacting with a many-particle target is derived. The exchange-correlation potential or image potential experienced by a charged particle exterior to, but near a surface, is calculated from this expression using a model in which the charge interacts with collective surface excitations. It is found that recoil is important near the surface and gives rise to interesting new quantum effects. Previously obtained classical and semiclassical results are shown to arise simply and readily from the formalism. The connection with surface bound states is discussed briefly.