The ground state inversion potential method: Application to the calculation of photoionization cross sections

Abstract

We present a simple one-electron central potential method which allows atomic photoionization cross sections to be calculated to an accuracy comparable to that of the best Hartree–Fock calculations available. The method relies upon the frozen core assumption and the fact that a good approximation to the Hartree–Fock potential seen by the photoelectron can be obtained by inversion of the corresponding ground state orbital as tabulated in the literature. The potential is assumed to be local and independent of final state energy in distinction to the true Hartree–Fock potential which is generally nonlocal due to exchange. Subshell photoionization cross sections for photon energies between 0 and 1500 eV have been calculated for helium, neon, argon, and krypton and compared with the Hartree–Fock results of Kennedy and Manson and available experimental values. The agreement is good except for near-threshold cross sections for deep lying orbitals. The method is compared with the Herman–Skillman approximation. The simplicity and computational efficiency of the present method suggest that it will be of use in practical calculations, particularly for heavy atoms. It offers a promising alternative to the widely used Hartree–Slater and Herman–Skillman calculations.

Depurated inversion method for orbital‐specific exchange potentials

“…In some cases, the reconstructed potential may be distorted beyond recognition . The same type of procedure was suggested many years ago by Hilton et al, in applications circumscribed to the calculation of photoionization processes of atoms, water, and other molecules . These papers, in turn, refer to the earlier work in atomic polarizability carried out by Sternheimer and Dalgarno and Parkinson .…”

Perturbation theory in a strong-interaction regime with application to 4d-subshell spectra of Ba and La

“…However, in many cases one has knowledge only of a wavefunction in numerical form. In this case, one can obtain the local potential from (Cadioli et al 1972, Hilton et al 1977 giving the effective local potential…”

Local Effective Hartree–Fock Potentials Obtained by the Depurated Inversion Method

“…The inversion scheme has been applied in different frameworks, from the density functional theory [7][8][9] to exact soluble models. 10 The procedure has been also applied in the calculation of atomic polarizability 11,12 and photoionization processes of atoms 13,14 and molecules. [15][16][17] In our methodology, 1 we assume that the HF is turned into a set of KS-type equations, whose solutions are the HF orbitals and energies:…”