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Single-site Green function of the Dirac equation for full-potential electron scattering

Abstract

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.)
Authors:
Publication Date:
May 30, 2012
Product Type:
Miscellaneous
Report Number:
INIS-DE-1280
Resource Relation:
Related Information: Schriften des Forschungszentrums Juelich. Reihe Schluesseltechnologien/Key Technologies v. 34
Subject:
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
OSTI ID:
21555650
Research Organizations:
Forschungszentrum Juelich GmbH (Germany). Peter Gruenberg Institut (PGI), Quantum Theory of Materials (PGI-1/IAS-1)
Country of Origin:
Germany
Language:
English
Other Identifying Numbers:
Other: ISBN 978-3-89336-760-3; ISSN 1866-1807; TRN: DE12F5358
Availability:
Commercial reproduction prohibited; INIS; OSTI as DE21555650
Submitting Site:
DEN
Size:
157 pages
Announcement Date:
May 31, 2012

Citation Formats

Kordt, Pascal. Single-site Green function of the Dirac equation for full-potential electron scattering. Germany: N. p., 2012. Web.
Kordt, Pascal. Single-site Green function of the Dirac equation for full-potential electron scattering. Germany.
Kordt, Pascal. 2012. "Single-site Green function of the Dirac equation for full-potential electron scattering." Germany.
@misc{etde_21555650,
title = {Single-site Green function of the Dirac equation for full-potential electron scattering}
author = {Kordt, Pascal}
abstractNote = {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.)}
place = {Germany}
year = {2012}
month = {May}
}