Ab initio calculations of the $2p_{3/2}\to 2s$ transition in He-, Li-, and Be-like uranium

The bound-state QED approach is applied to calculations of the $2p_{3/2}\to 2s$ transition energies in He-, Li-, and Be-like uranium. For ${\mathrm{U}}^{90+}$ and ${\mathrm{U}}^{89+}$, standard perturbation theory for a single level is employed, while the calculations of ${\mathrm{U}}^{88+}$ have required its counterpart for quasidegenerate levels. The utilized approach merges the rigorous QED treatment up to the second order of perturbation theory with the higher-order electron-correlation contributions evaluated within the Breit approximation. The higher-order screened QED effects are estimated by means of the model-QED operator. The nuclear recoil, nuclear polarization, and nuclear deformation effects are taken into account as well. Along with the transition energies, their pairwise differences are calculated. The comprehensive analysis of the uncertainties due to uncalculated effects is carried out, and the most accurate theoretical predictions, which are in perfect agreement with available experimental data, are obtained.

Figure 1

First- and second-order Feynman diagrams, the contributions of which are rigorously evaluated in the present work (in each row from left to right): one-photon-exchange diagram, one-electron self-energy and vacuum-polarization diagrams (first line); two-photon-exchange diagrams (second line); two-electron self-energy and vacuum-polarization diagrams (third line). The counterterm diagrams are not shown. The double line denotes the electron propagator in the binding potential $V$. The wavy line corresponds to the photon propagator.