Statistical and quantum photoionization cross sections in plasmas: Analytical approaches for any configurations including inner shells

Statistical models combined with the local plasma frequency approach applied to the atomic electron density are employed to study the photoionization cross-section for complex atoms. It is demonstrated that the Thomas-Fermi atom provides surprisingly good overall agreement even for complex outer-shell configurations, where quantum mechanical approaches that include electron correlations are exceedingly difficult. Quantum mechanical photoionization calculations are studied with respect to energy and nl quantum number for hydrogen-like and non-hydrogen-like atoms and ions. A generalized scaled photoionization model (GSPM) based on the simultaneous introduction of effective charges for non-H-like energies and scaling charges for the reduced energy scale allows the development of analytical formulas for all states nl. Explicit expressions for nl = 1s, 2s, 2p, 3s, 3p, 3d, 4s, 4p, 4d, 4f, and 5s are obtained. Application to H-like and non-H-like atoms and ions and to neutral atoms demonstrates the universality of the scaled analytical approach including inner-shell photoionization. Likewise, GSPM describes the near-threshold behavior and high-energy asymptotes well. Finally, we discuss the various models and the correspondence principle along with experimental data and with respect to a good compromise between generality and precision. The results are also relevant to large-scale integrated light-matter interaction simulations, e.g., X-ray free-electron laser interactions with matter or photoionization driven by a broadband radiation field such as Planckian radiation.