Quantum Field Theory of Inelastic Diffraction. III. Dynamical Theory

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Abstract
Using our previously developed quantum field theory of electron-solid scattering, we construct a dynamical (i.e., multiple-scattering) theory of inelastic-low-energy-electron diffraction (ILEED) in which the incident electron scatters elastically from the lattice potential an arbitrary number of times both "before" and "after" an inelastic loss. We consider the two cases in which the electron's energy loss is caused by the excitation of a single surface or bulk plasmon. Three types of scattering processes occur: loss before (multiple elastic) diffraction, diffraction before loss, and diffraction before and after loss. The summation over all multiple-elastic-scattering events introduces renormalized elastic-diffraction vertices relative to those used in the kinematical "two-step" model described in Paper II of this series. In the cases of loss before diffraction and diffraction before loss, this renormalization is the only consequence of multiple elastic scattering. The processes of diffraction both before and after loss occur only in the dynamical theory and, consequently, are strictly multiple-scattering phenomena. Explicit expressions for the cross sections, suitable for numerical evaluation, are given for the case in which the elastic electron-ion-core scattering is described by the isotropic-scatterer model.