We derive new, simplified formulas for the scattering of l=1 spherical waves from central potentials, as a basis for discussing curved-wave-front corrections to single-scattering plane-wave models for angle-resolved photoemission extended fine structure and extended x-ray-absorption fine structure. A differential form for the expansion of the screened spherical wave replaces the usual Gaunt-integral form to facilitate the summation over equivalent magnetic sublevels in the scattered wave. Spherical-wave scattering factors are defined and interpreted as corrections to the plane-wave scattering factor. We argue and demonstrate by example that the remarkable success of plane-wave models does not result from reaching the spherical-wave asymptotic limit; instead, successive partial-wave corrections cancel for backscattering at high energy. The new scattering formulas allow curved-wave-front numerical calculations to be performed with little more effort than with plane-wave formulas.

• Received 1 April 1985

DOI:https://doi.org/10.1103/PhysRevB.32.1892