Self-energy corrections to the ionization energies in sodium-like ions: comparison of the \textit{ab initio} QED and model-QED-operator approaches

TL;DR

This paper compares two methods, ab initio QED and model-QED-operator, for calculating self-energy corrections to ionization energies in sodium-like ions across a range of nuclear charges, validating the model approach.

Contribution

The study provides a detailed comparison between rigorous QED calculations and the model-QED-operator method for many-electron ions, demonstrating their agreement and validating the model's accuracy.

Findings

Good agreement between the two methods across all tested ions.

Validation of the model-QED-operator approach for complex many-electron systems.

Enhanced convergence of perturbation series with screening potentials.

Abstract

Calculations of the self-energy corrections to ionization energies of the $3s$, $3p_{1/2}$, and $3p_{3/2}$ states in sodium-like ions with nuclear-charge numbers $Z=30$, $50$, $70$, and $92$ are presented. The calculations are performed using two approaches: the rigorous bound-state QED formalism and the model-QED-operator method. Within the first method, the first and second orders of the QED perturbation theory formulated in the Furry picture are evaluated. Various screening potentials are included into the initial approximation to partially take into account the electron-electron interaction effects already at the lowest order, thereby accelerating the convergence of perturbation series. Within the second approach, different implementations of the model-QED operator, including its incorporation into the relativistic configuration-interaction calculations, are considered. A detailed comparison of the results obtained by these two independent methods is presented, demonstrating good agreement and thus validating the accuracy and efficiency of the model-QED-operator approach for many-electron systems.