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@TECHREPORT{Kordt:21592,
      author       = {Kordt, Pascal},
      title        = {{S}ingle-site {G}reen-function of the {D}irac equation for
                      full-potential electron scattering},
      volume       = {34},
      school       = {RWTH Aachen},
      type         = {Diplom (Univ.)},
      address      = {Jülich},
      publisher    = {Forschungszentrum Jülich GmbH Zentralbibliothek, Verlag},
      reportid     = {PreJuSER-21592},
      isbn         = {978-3-89336-760-3},
      series       = {Schriften des Forschungszentrums Jülich.
                      Schlüsseltechnologien / Key Technologies},
      pages        = {138 S.},
      year         = {2011},
      note         = {Record converted from JUWEL: 18.07.2013; RWTH Aachen,
                      Diss., 2011},
      abstract     = {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.},
      cin          = {PGI-1 / IAS-1},
      ddc          = {500},
      cid          = {I:(DE-Juel1)PGI-1-20110106 / I:(DE-Juel1)IAS-1-20090406},
      pnm          = {Grundlagen für zukünftige Informationstechnologien},
      pid          = {G:(DE-Juel1)FUEK412},
      typ          = {PUB:(DE-HGF)15},
      url          = {https://juser.fz-juelich.de/record/21592},
}