Note on the Theory of Elastic Low-Energy-Electron Diffraction from a Vibrating Lattice

Abstract
The multiple-scattering series for the elastic electron-solid differential cross section is reduced to a set of coupled equations for layer scattering amplitudes by first performing the partial-wave decomposition of this series and subsequently defining the layer amplitudes as subsums of the complete series. The resulting equations are identical to those derived by Laramore and Duke in a recent paper. However, Laramore and Duke's derivation, in which the subsums of the multiple-scattering series were performed prior to the partial-wave decomposition, contains an ambiguity in the latter step which is avoided by our analysis.