Single-site Green function of the Dirac equation for full-potential electron scattering
Kordt, Pascal
72 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
I 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.)
Forschungszentrum Juelich GmbH (Germany). Peter Gruenberg Institut (PGI), Quantum Theory of Materials (PGI-1/IAS-1)
Commercial reproduction prohibited; INIS; OSTI as DE21555650
Germany
2012-05-30
English
Miscellaneous
Related Information: Schriften des Forschungszentrums Juelich. Reihe Schluesseltechnologien/Key Technologies v. 34
Medium: ED; Size: 157 pages
ISBN 978-3-89336-760-3; ISSN 1866-1807
INIS-DE-1280
Other: ISBN 978-3-89336-760-3; ISSN 1866-1807; TRN: DE12F5358
DEN
2012-12-10
21555650
https://www.osti.gov/etdeweb/servlets/purl/21555650