Transition-Matrix Theory of Low-Energy Electron Diffraction

Abstract

A transition-matrix formulation is presented for calculating the scattering amplitude of an elastically scattered beam from a crystal with perfect two-dimensional periodicity in the surface plane. The scattering amplitude is expressed in the transition-matrix expansion for a general potential. When applied to the muffin-tin potential model, Beeby's multiple-scattering low-energy electron diffraction (LEED) theory, Kambe's modified Korringa-Kohn-Rostoker theory, Shen's application of the Shen-Krieger variational LEED theory, and the transition-matrix LEED theory can be transformed to give the identical exact solution of this problem. In analogy to the pseudopotential formalism in the energy-band theory, the scattering amplitude can be written in Born expansions for an effective potential which is, in general, weaker than the crystal potential for the nearly-free-electron model. It is shown that the infinity of the tangent of a phase shift can result in a resonance peak in the reflectance.