Photoionization cross-sections for atomic orbitals with random and fixed spatial orientation

Atomic photoionization subshell cross-sections and asymmetry parameters necessary for determining the differential cross-sections of randomly-oriented atoms have been calculated within the one-electron, central-potential model and the dipole approximation for all subshells of C, O, Al, Si, S, Ni, Cu, Ga, Ge, As, Se, In, Sb, Cs, Ba, Ce, Ta, W, Pt, Au, and Pb for a photon energy range from 20 to 1500 eV, and the relevant Cooper minima located to within 10 eV. These values are tabulated for general use, together with the associated radial matrix elements and phase shifts. Differential photoionization cross-sections for fixed-orientation s-, p- and d-orbitals have also been derived within the same model for a completely general experimental geometry, and closed-form expressions depending on radial matrix elements and phase shifts are given. For the special geometry of a polarized excitation source with polarization parallel to the electron emission direction, it is further shown that such oriented-atom cross-sections are exactly proportional to the probability distribution of the initial orbital, a result equivalent to that derived by using a plane-wave final-state approximation. However, detailed numerical calculations of cross-sections for oriented Cu 3d and O 2p orbitals in various general geometries and at various energies exhibit significant differences in comparison to plane-wave cross-sections. By contrast, certain prior angular-resolved X-ray photoemission studies of single-crystal valence bands are found to have been carried out in an experimental geometry that fortuitously gave cross-sections close to the plane-wave predictions.