Electron-phonon coupling in image-potential bound states

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Abstract
We study the real and imaginary part of the electron proper self-energy when an electron is trapped in an image-potential bound state at a metal surface. This is done within the framework of a simple model which treats the metal as a semi-infinite sheet of dielectric. The two separate mechanisms explored for the coupling of the electron to substrate phonons are the modulation of the image potential and that of the dipole layer by the sinusoidal rippling of the surface by a phonon. We find that the former process dominates the latter by an order of magnitude, when their respective contributions to the proper self-energy are examined. We argue that for electron energies that lie in the fine-structure resonances which appear in low-energy electron diffraction (LEED) data, there should be anomalies in the thermal diffuse scattering produced by the couplings described here.