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(θ) replaced by distance-dependent ''scattering matrices'' Fλ,λ'(ρ,ρ'). Here ρ=kR, k being the photoelectron wave number and R is a bond vector, while the matrix indices λ=(μ,ν) 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 λ summations are truncated at just six terms, i.e., (6x6) matrices. The lowest-order (1x1) matrix F00,00 is the effective, curved-wave scattering amplitude, f(ρ,ρ',θ), 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