QED calculations of intra-$L$-shell doubly excited states in Be-like ions

TL;DR

The paper addresses precise QED predictions for intra-$L$-shell excitations in Be-like HCIs, where strong level mixing challenges standard perturbation theory. It employs an ab initio approach combining QED perturbation theory up to second order in the Furry picture with Breit-approximation CI for higher-order interelectronic effects, supplemented by a model-QED operator and nuclear-recoil/polarization corrections. Results cover energies of the intra-$L$-shell states $2p2p\,^3P_{0,1,2}$, $2p2p\,^1D_2$, and $2p2p\,^1S_0$ for $Z=18$–$92$, relative to the ground state $2s2s\,^1S_0$, and show excellent agreement with experimental data while updating the one-electron two-loop contributions. The work provides the most accurate description to date and establishes a benchmark for future experimental and theoretical studies of Be-like HCIs, enabling stringent tests of bound-state QED in regimes of strong relativistic and correlation effects.

Abstract

The rigorous QED approach is employed to calculate the energies of the $2p2p\,^3P_{0,1,2}$, $2p2p\,^1D_2$, and $2p2p\,^1S_0$ states of selected Be-like highly charged ions over a wide range of nuclear-charge numbers, $18 \leqslant Z \leqslant 92$. Combined with the previously reported energies of the $2s2p \, ^3P_{0,1,2}$ and $2s2p \, ^1P_1$ states [A. V. Malyshev et al., Phys. Rev. A 110, 062824 (2024)], the obtained results are used to study various intra-$L$-shell transition energies. Strong level mixing, caused by the proximity of states with the same symmetry, is overcome by means of the QED perturbation theory for quasi-degenerate levels. The applied approach merges a rigorous perturbative QED treatment up to the second order with the consideration of electron-electron correlation contributions of the third and higher orders evaluated within the Breit approximation. The higher-order screened QED effects are estimated using the model-QED-operator approach. The nuclear-recoil and nuclear-polarization effects are also taken into account. The obtained predictions represent the most accurate theoretical description of the electronic structure of Be-like ions to date and demonstrate good agreement with available experimental data.