Spherical-wave corrections in photoelectron diffraction

We present a formulation of photoelectron diffraction which generalizes that based on the plane-wave approximation. Explicit expressions for K- and L-shell photoemission are given. Single-scattering terms are treated exactly in terms of effective distance-dependent scattering amplitudes $f^{\left(i\right)}$(θ,R). Spherical-wave corrections in the theory can be approximated with use of asymptotic expansions for the one-particle propagators. This spherical-wave approximation (SWA) explains observed corrections to the plane-wave approximation and is found to be in good agreement with the full, single-scattering, spherical-wave treatment. The relation between photoelectron diffraction and x-ray-absorption fine structure (XAFS) is discussed with use of a generalized optical theorem.