QED calculations of the $2p$-$2s$ transition energies in Li-like ions

TL;DR

This work delivers systematic, ab initio QED calculations for Li-like ions with $Z=10$--$100$, focusing on the $2s$, $2p_{1/2}$, and $2p_{3/2}$ states and the $2p_{1/2}$--$2s$ and $2p_{3/2}$--$2s$ transitions. It employs an extended Furry picture with a local screening potential, combining Dirac-Coulomb-Breit energies (via MBPT and CI) with one- and two-photon electron-structure QED corrections and QED screening, plus a model for higher-order screening, to achieve high-precision results. The study demonstrates strong agreement with experimental data across a broad $Z$ range, and identifies the dominant sources of theoretical uncertainty that shift with $Z$ (DCB at low $Z$, screening and two-photon QED at mid-range, and one-electron two-loop QED at high $Z$), while enabling precise determinations of nuclear charge radii from transition energies. It also critically assesses the accuracy of approximate QED treatments based on the model QED operator, showing good performance for most transitions but highlighting limitations for fine-structure differences and very high-precision radius extractions. The results provide stringent tests of bound-state QED in strong fields and substantial input for future radius determinations and theory improvements (notably complete one-electron two-loop QED corrections).

Abstract

Systematic QED calculations of ionization energies of the $2s$, $2p_{1/2}$, and $2p_{3/2}$ states, as well as the $2p_{1/2}$--$2s$ and $2p_{3/2}$--$2p_{1/2}$ transition energies are performed for Li-like ions with the nuclear charge numbers $Z = 10$--$100$. The convergence of QED perturbative expansion is improved by using the extended Furry picture, which starts from the Dirac equation with a local screening potential. An ab initio treatment is accomplished for one- and two-photon electron-structure QED effects and the one-photon screening of the self-energy and vacuum-polarization corrections. This is complemented with an approximate treatment of the two-photon QED screening and higher-order (three or more photon) electron-structure effects. As a result, the obtained theoretical predictions improve upon the accuracy achieved in previous calculations. Comparison with available experimental data shows a good agreement between theory and experiment. In most cases, the theoretical values surpass the experimental results in precision, with only a few exceptions. In the case of uranium and bismuth, the comparison provides one of the most stringent tests of bound-state QED in the strong-field regime. Alternatively, the obtained results can be employed for high-precision determinations of nuclear charge radii.