Many-electron approach to atomic photoionization: Rydberg series of resonances and partial photoionization cross sections in helium, around then=2threshold

Transition probabilities involving the continuous spectrum of many-electron atoms exhibit a variety of resonance phenomena and deviations from independent-particle model predictions. We present a general theory of photoionization which (i) utilizes function spaces for initial and final states which are state specific and are based on numerical as well as on analytic basis sets. The valence, Rydberg, scattering, and virtual orbitals are optimized by different methods. (ii) In addition, our theory is formulated within a configuration-interaction, reaction-matrix, and multichannel quantum-defect approach suitable for the treatment of the continuous and of the discrete Rydberg spectrum via the use of numerical frozen-core Hartree-Fock channel orbitals. In this work we have calculated the cross sections for the simultaneous photoionization and photoexcitation to the n=2 shell of ${\mathrm{He}}^{+}$. Our results for the ratio of the cross section at the degenerate ${\mathrm{He}}^{+}$ thresholds 2s and 2p agree with those of published close-coupling calculations and disagree with those of a many-body perturbation theory. We also compute values for energies very close to and at the threshold, previously not available. The autoionization widths and quantum defects of the Rydberg series 2snp, 2pnd, and 2pns are also in agreement with previous close-coupling calculations.