QED calculations of intra- <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>L</mml:mi> </mml:math> -shell doubly excited states in Be-like ions

The rigorous quantum-electrodynamic (QED) approach is employed to calculate the energies of the $2p2p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1,2}$, $2p2p{\phantom{\rule{0.16em}{0ex}}}^{1}{D}_{2}$, and $2p2p{\phantom{\rule{0.16em}{0ex}}}^{1}{S}_{0}$ states of selected Be-like highly charged ions over a wide range of nuclear-charge numbers, $18\ensuremath{\leqslant}Z\ensuremath{\leqslant}92$. Combined with the previously reported energies of the $2s2p{\phantom{\rule{0.16em}{0ex}}}^{3}{P}_{0,1,2}$ and $2s2p{\phantom{\rule{0.16em}{0ex}}}^{1}{P}_{1}$ 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 quasidegenerate 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.