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000021592 1001_ $$0P:(DE-Juel1)VDB98376$$aKordt, Pascal$$b0$$eCorresponding author$$uFZJ
000021592 245__ $$aSingle-site Green-function of the Dirac equation for full-potential electron scattering
000021592 260__ $$aJülich$$bForschungszentrum Jülich GmbH Zentralbibliothek, Verlag$$c2011
000021592 300__ $$a138 S.
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000021592 4900_ $$0PERI:(DE-600)2445293-2$$aSchriften des Forschungszentrums Jülich. Schlüsseltechnologien / Key Technologies$$v34
000021592 502__ $$aRWTH Aachen, Diss., 2011$$bDiplom (Univ.)$$cRWTH Aachen$$d2011
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000021592 520__ $$aI present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schrödinger and the Dirac equation, followed by an efficient numerical solution, in both cases for potentials of arbitrary shape without an atomic sphere approximation. A numerically stable way to calculate the corresponding regular and irregular wave functions and the Green function is via the angular Lippmann-Schwinger integral equations. These are solved based on an expansion in Chebyshev polynomials and their recursion relations, allowing to rewrite the Lippmann-Schwinger equations into a system of algebraic linear equations. Gonzales et al. developed this method for the Schrödinger equation, where it gives a much higher accuracy compared to previous perturbation methods, with only modest increase in computational effort. In order to apply it to the Dirac equation, I developed relativistic Lippmann-Schwinger equations, based on a decomposition of the potential matrix into spin spherical harmonics, exploiting certain properties of this matrix. The resulting method was embedded into a Korringa-Kohn-Rostoker code for density functional calculations. As an example, the method is applied by calculating phase shifts and the Mott scattering of a tungsten impurity.
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