SHORTCOMINGS OF SEPARABLE REPRESENTATIONS OF THE GREEN-FUNCTION IN MULTIPLE-SCATTERING THEORY FOR PHOTOELECTRON DIFFRACTION AND EXTENDED X-RAY ABSORPTION FINE-STRUCTURE

In most of the approximations for spherical-wave scattering, the angular momenta l and l' in the two-centre angular momentum representation of the free electron Green function are decoupled, in order to reduce the mathematical complexity. In the present paper, it is shown that the errors of these so-called separable approximations (e.g. the Taylor series magnetic quantum number expansion of Barton and Shirley, the reduced angular momentum expansion of Fritzsche and Rennert, and the scattering matrix formulation of Rehr and Albers) increase considerably with the kinetic energy of the electrons, if the distance between source and scatterer is small (i.e. if they are nearest neighbours). In particular, low accuracy in the forward scattering direction is a great problem. The origin of such errors is the oscillatory nature of the coupling between the two angular momenta in the Green function, which cannot be described adequately by separable approximations.