Low-order perturbation theory for shake-up cross sections in atomic photoionization in a local-potential model

Cross sections for the process in which photoionization of an atom is accompanied by excitation of an electron from an occupied orbital to an unoccupied orbital are calculated in lowest order in perturbation theory. The calculation is carried out in a local-effective-potential model for the atom that permits the summation over the intermediate states by using the Green’s function for ordinary differential equations. It is assumed that the coupling scheme for the final ionic state is that the two holes couple to a state of definite $L_{12}$ and $S_{12}$ that then combines with the particle state to give a state of definite L and S. Expressions for the total cross section and asymmetry parameter are given for closed-shell atoms. Calculated results for Ne photoionization are compared with experimental results.