Gauss-Seidel-Aitken perturbation expansions for interlayer multiple scattering in LEED: bootstrap acceleration method

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Abstract
Two commonly used perturbation schemes for calculation of interlayer multiple scattering in low-energy electron diffraction are alternatively derived as applications of the Gauss-Seidel-Aitken (GSA) double-sweep iterative method for solution of systems of linear equations. In a reciprocal-space representation, the GSA procedure leads directly to Pendry's 'renormalised forward scattering' method. In an angular-momentum-space representation, the GSA procedure leads to a method related to, but faster than, the original formulation of Zimmer and Holland's 'reverse-scattering perturbation' method. It is further shown that the rates of convergence of the iterative procedures can be increased by altering the normal starting conditions. The bootstrap acceleration procedure consists of using as starting values for the iterative schemes, self-consistent, converged, layer-scattering amplitudes rather than single-scattering amplitudes. The self-consistent amplitudes are obtained from a previous calculation carried out, for example, for a slightly different value of the incident electron energy.