Quantum electrodynamics (QED) is a powerful tool for describing the electronic structure of atomic and molecular systems. After its final formulation in the late 1940s, it was primarily applied to light systems. However, since the mid-1980s, when the experimental possibility to study heavy few-electron ions appeared, highly charged ions have become an object of intense research. Calculations of the Lamb shift in H-like and 2p_{1/2}-2s transition in Li-like uranium are now regarded as benchmarks for stringent tests of bound-state QED. Meanwhile, the QED treatment of Be-like ions can also be challenging. The conventional QED perturbation theory for single levels, which has demonstrated high accuracy for H-like and Li-like ions, may yield unreliable results for Be-like ions due to strong mixing between closely spaced energy levels of identical symmetry.

In this report, a brief overview of the application of the QED perturbation theory for quasidegenerate levels to the study of the electronic structure of Be-like ions is given. The method merges all relevant first- and second-order QED contributions as well as third- and higher-order electron–electron correlation contributions evaluated in the Breit approximation. Recently obtained theoretical predictions [1,2] are compared with the results of high-precision measurements and previous relativistic calculations.

[1] A. V. Malyshev et al., PRA 110, 062824 (2024).
[2] A. V. Malyshev et al., PRA 112, 062811 (2025).