Small-atom approximations for photoelectron scattering in the intermediate-energy range

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Abstract
Five approximate models for describing the scattering of spherical waves by central potentials are explored. The point-scattering model introduced by Lee and Pendry [Phys. Rev. B 11, 2795 (1975)] allows a short-range potential to be close to the source; a new homogeneous-wave model lifts the restriction on the potential diameter, but requires asymptotic incident waves. The popular plane-wave model requires both an infinitesimal-diameter potential and incident waves at their asymptotic limit. For realistic potentials at near-neighbor separations, none of these models is adequate: Even a hybrid model combining features of the point-scattering and homogeneous-wave methods does not allow for amplitude variation across the potential. The fifth small-atom model is based on a Taylor-series, magnetic-quantum-number expansion of the addition theorem for screened spherical waves. This Taylor-series approximation has the homogeneous-wave model as its zeroth-order term and the exact spherical-wave scattering process as its limit. Multiple-scattering equations for angle-resolved photoemission extended fine structure (ARPEFS) are derived and the effectiveness of these approximations is compared. We demonstrate that while the plane-wave model is reasonably accurate for near-180° backscattering, small-angle scattering requires the curved-wave-front corrections available in the Taylor-series-expansion method.