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arXiv · 1506.07743

Numerical solution of the relativistic single-site scattering problem for the Coulomb and the Mathieu potential

Matthias Geilhufe·Steven Achilles·Markus Arthur Köbis·Martin Arnold·Ingrid Mertig·Wolfram Hergert·Arthur Ernst
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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 ($r\ll1$).

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Matthias Geilhufe, Steven Achilles, Markus Arthur Köbis, Martin Arnold, Ingrid Mertig, Wolfram Hergert, Arthur Ernst. 2015-06-26. Numerical solution of the relativistic single-site scattering problem for the Coulomb and the Mathieu potential. https://doi.org/10.1088/0953-8984%2F27%2F43%2F435202

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