TY - RPRT
TI - Single-site Green function of the Dirac equation for full-potential electron scattering
AB - 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.)
AU - Kordt, Pascal
KW - 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
KW - 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS
KW - ALGEBRA
KW - ALGORITHMS
KW - ANALYTICAL SOLUTION
KW - COMPUTER CODES
KW - DIRAC EQUATION
KW - ELECTRON-ION COLLISIONS
KW - FUNCTIONALS
KW - GREEN FUNCTION
KW - IMPURITIES
KW - LIPPMANN-SCHWINGER EQUATION
KW - MATRICES
KW - NUMERICAL SOLUTION
KW - PHASE SHIFT
KW - POLYNOMIALS
KW - POTENTIAL SCATTERING
KW - RECURSION RELATIONS
KW - RELATIVISTIC RANGE
KW - RUBIDIUM
KW - SCHROEDINGER EQUATION
KW - SERIES EXPANSION
KW - SPHERICAL HARMONICS
KW - TUNGSTEN
KW - WAVE FUNCTIONS
DO -
UR - https://www.osti.gov/etdeweb/servlets/purl/21555650
PB -
CY - Germany
PY - 2012
DA - 2012-05-30
LA - English
J2 -
C1 - Forschungszentrum Juelich GmbH (Germany). Peter Gruenberg Institut (PGI), Quantum Theory of Materials (PGI-1/IAS-1)
C2 -
ER -