New general results on the self-energy of fast electrons interacting with metal surfaces are presented with emphasis on the energy-loss problem in electron microscopy. Some applications to both spherical and planar targets are considered. Our results are relevant to the understanding of inelastic electron scattering near small structures, at the nanometer scale.

• Received 16 September 1986

DOI:https://doi.org/10.1103/PhysRevB.35.1521