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

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.

Figures (2)

• Figure 1: First-order self-energy diagram. The double line denotes the bound-electron propagator, the wavy line corresponds to the photon propagator, and the cross indicates the mass counterterm.
• Figure 2: Second-order self-energy diagram. The circle with a cross inside represents the local screening potential counterterm $\delta V=-V_{\rm scr}$. The other notations are the same as in Fig. \ref{['fig:se_1el']}. The mass counterterm diagrams are not shown.