TY  - RPRT
AU  - Kordt, Pascal
TI  - Single-site Green-function of the Dirac equation for full-potential electron scattering
VL  - 34
PB  - RWTH Aachen
VL  - Diplom (Univ.)
CY  - Jülich
M1  - PreJuSER-21592
SN  - 978-3-89336-760-3
T2  - Schriften des Forschungszentrums Jülich. Schlüsseltechnologien / Key Technologies
SP  - 138 S.
PY  - 2011
N1  - Record converted from JUWEL: 18.07.2013
N1  - RWTH Aachen, Diss., 2011
AB  - I 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.
LB  - PUB:(DE-HGF)15
UR  - https://juser.fz-juelich.de/record/21592
ER  -