New approach on calculating Green's functions in Full-Potential Multiple Scattering Methods.*

The most common methods of computing Green's functions in modern full-potential multiple scattering applications rely on solving Schr\"{o}dinger (Dirac) equations for regular and irregular solutions of a single-site scatterer over an energy contour in the complex plane. While, for spherical potentials, the standard formulae for calculating the Green's function are numerically stable they often result in unphysical behavior for non spherical potentials, particularly close to the nucleus and for large angular momentum quantum numbers. Here we use a new analytical and numerical method that does not require calculation of the irregular solution, to which the numerical instability can be traced. The new approach results in the correct analytic behavior and numerical stability.