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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” F λ, 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, G L, 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 …