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” ${\mathrm{F}}_{\lambda ,\lambda \prime }$(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, ${\mathrm{G}}_{\mathrm{L},\mathrm{L}\prime }$(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., (6×6) matrices. The lowest-order (1×1) matrix ${\mathrm{F}}_{00,00}$ 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.