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Perturbation theories in low energy electron diffraction: t-matrix and τ-matrix approaches

Elsevier B.V.
Publication Date
DOI: 10.1016/0039-6028(73)90176-3


Abstract Two perturbation approaches to low energy electron diffraction (LEED) are discussed within the inelastic collision model: t-matrix approach recently proposed by Tong, Rhodin and Tait (all scatterings treated to third order), and τ-matrix approach (layer scattering is treated exactly while all interlayer scatterings are treated to third order). Both approaches are applied to the calculation of rotation diagrams for the (001) surface of Al. In the case of a single layer third-order perturbation results for the magnitude and phase of the scattering amplitude are compared to the exact results and found to be in fairly good agreement over a large range of elastic scattering cross-sections. When all scatterings (up to third order) are considered for an infinite crystal, the differences between the exact and third-order t-matrix perturbation resutls become quite substantial ; marked improvement is achieved if the layer scattering is treated exactly, but the remaining difference may be significant enough (depending on the application) to suggest that interlayer scattering may not always be treated by perturbation, and thus renormalization of the type proposed by Pendry may be necessary.

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