Interaction of charges with surface polaritons

A quantum-mechanical Hamiltonian of a nonrelativistic charge interacting with long-wavelength nonradiative surface polaritons in a semi-infinite solid is constructed. The theory is applied to determine the velocity and retardation corrections to the image potential, and the problem is solved exactly in the no-recoil (semiclassical) approximation, which is justified for particles of large momenta. The influence of retardation in inelastic energy spectra of electrons in low-energy-electron diffraction and reflected-high-energy-electron diffraction is considered in detail, and it is shown to be negligible for grazing-incidence electrons, though it generally changes the spectrum of outgoing electrons.