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Numerical solution of the relativistic single-site scattering problem for the Coulomb and the Mathieu potential
Matthias Geilhufe1, Steven Achilles, Markus Arthur Köbis
1Max Planck Institute of Microstructure Physics, Weinberg 2, D-06120 Halle (Saale), Germany.
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).
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