Self-energy of a fast-moving charge near a surface

Abstract

The self-energy of an external moving charged particle near a surface is studied within the fast-charge approximation. For a reflecting trajectory, a formula for the complex self-energy, valid for an arbitrary dielectric function of the medium and angle of incidence, is first derived by means of a semiclassical analysis in which the imaginary part is obtained from a classical evaluation of the work done by the moving charge. This work is discussed in terms of conservative and dissipative contributions. The formula for the complex self-energy is then recovered from a quantum mechanical formulation in which the passage to the semiclassical limit is readily made. The quantum approach is used later to obtain a semiclassical formula for the complex self-energy when the charged particle penetrates the medium.