Single-Site Green Function of the Dirac Equation for Full-Potential Electron Scattering
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Beschreibung
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.
Autor*in
Pascal Kordt
Themen in »Single-Site Green Function of the Dirac Equation for Full-Potential Electron Scattering«
Density Functional Theory Green Function Scattering