title: Numerical solution of the relativistic single-site scattering problem for the Coulomb and the Mathieu potential.
abstract: For a reliable fully-relativistic Korringa-Kohn-Rostoker Green function method, an accurate solution of the underlying single-site scattering problem is necessary. We present an extensive discussion on numerical solutions of the related differential equations by means of standard methods for a direct solution and by means of integral equations. Our implementation is tested and exemplarily demonstrated for a spherically symmetric treatment of a Coulomb potential and for a Mathieu potential to cover the full-potential implementation. For the Coulomb potential we include an analytic discussion of the asymptotic behaviour of irregular scattering solutions close to the origin (r << 1).
authors.affiliation: Max Planck Institute of Microstructure Physics, Weinberg 2, D-06120 Halle (Saale), Germany.
authors.forename: Matthias
authors.initials: M
authors.lastname: Geilhufe
authors.forename: Steven
authors.initials: S
authors.lastname: Achilles
authors.forename: Markus Arthur
authors.initials: MA
authors.lastname: Köbis
authors.forename: Martin
authors.initials: M
authors.lastname: Arnold
authors.forename: Ingrid
authors.initials: I
authors.lastname: Mertig
authors.forename: Wolfram
authors.initials: W
authors.lastname: Hergert
authors.forename: Arthur
authors.initials: A
authors.lastname: Ernst