%AKordt, Pascal
%D2012
%I; Forschungszentrum Juelich GmbH (Germany). Peter Gruenberg Institut (PGI), Quantum Theory of Materials (PGI-1/IAS-1)
%J
%K72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS, 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS, ALGEBRA, ALGORITHMS, ANALYTICAL SOLUTION, COMPUTER CODES, DIRAC EQUATION, ELECTRON-ION COLLISIONS, FUNCTIONALS, GREEN FUNCTION, IMPURITIES, LIPPMANN-SCHWINGER EQUATION, MATRICES, NUMERICAL SOLUTION, PHASE SHIFT, POLYNOMIALS, POTENTIAL SCATTERING, RECURSION RELATIONS, RELATIVISTIC RANGE, RUBIDIUM, SCHROEDINGER EQUATION, SERIES EXPANSION, SPHERICAL HARMONICS, TUNGSTEN, WAVE FUNCTIONS
%PMedium: ED; Size: 157 pages
%TSingle-site Green function of the Dirac equation for full-potential electron scattering
%XI present an elaborated analytical examination of the Green function of an electron scattered at a single-site potential, for both the Schroedinger 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 Schroedinger 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. (orig.)
%0Miscellaneous
Germany Other: ISBN 978-3-89336-760-3; ISSN 1866-1807; TRN: DE12F5358 DEN English