SCATTERING-MATRIX FORMULATION OF CURVED-WAVE MULTIPLE-SCATTERING THEORY - APPLICATION TO X-RAY-ABSORPTION FINE-STRUCTURE

Curved-wave multiple-scattering contributions to XAFS (x-ray-absorption fine structure) are calculated with use of an efficient formalism similar to that based on the plane-wave approximation, but with scattering amplitudes f replaced by distance-dependent scattering matricesF Here =kR, k being the photoelectron wave number and R is a bond vector, while the matrix indices =represent terms in a convergent expansion that generalizes the small-atom approximation. This approach is based on an exact, separable representation of the free propagator (or translation operator) matrix elements, GL,L(kR), in an angular momentum L=(l,m) and site basis. The method yields accurate curved-wave contributions for arbitrarily high-order multiple-scattering paths at all positive energies, including the near-edge region. Results are nearly converged when the intermediate summations are truncated at just six terms, i.e., (6×6) matrices. The lowest-order (1×1) matrix F00,00 is the effective, curved-wave scattering amplitude, f, and yields a multiple-scattering expansion equivalent to the point-scattering approximation. Formulas for multiple-scattering contributions to XAFS and photoelectron diffraction are presented, and the method is illustrated with results for selected multiple-scattering paths in fcc Cu. © 1990 The American Physical Society.