Self-energy diagram for axially symmetric systems

The study and description of atomic spectra requires the systematic
consideration of quantum electrodynamic (QED) corrections.
In one-electron systems, the leading QED corrections for a bound electron correspond
to the self-energy (SE) and vacuum polarization (VP) diagrams.
To date, methods for calculating them are well developed
for spherically symmetric systems—atoms and ions [1–4].
Molecules, on the other hand, do not possess such symmetry and
only approximate methods for estimation of the corresponding corrections are available [5-6].

In this work, we propose a method that allows for a rigorous
calculation of the SE diagram contribution to the
bound-state energy of two-center systems.
The auxiliary–symmetric dual kinetic balance method (A-DKB) [7] is used to solve
the Dirac equation with a two-center potential;
a number of well-known techniques [1] are generalized to the case of axially symmetric systems.

The SE diagram contribution to the ground-state energy of the one-electron uranium diatomic quasimolecule U_2^183+ is calculated. The results obtained
are in reasonable agreement with the results of Refs. [8-9],
where the same contributions were
calculated within the partial expansion of the two-center potential.

[1] V. A. Yerokhin and V. M. Shabaev, Phys. Rev. A 60, 800 (1999).
[2] V. A. Yerokhin et al., Phys. Rev. A 111, 012802 (2025).
[3] O. V. Andreev et al., Phys. Rev. A 85, 022510 (2012).
[4] D. A. Glazov et al., Phys. Rev. Lett. 123, 173001 (2015).
[5] V. M. Shabaev et al., Phys. Rev. A 88, 012513 (2013).
[6] A. A. Kotov et al., Atoms 9(3), 44 (2021).
[7] E. B. Rozenbaum et al., Phys. Rev. A 89, 012514 (2014).
[8] A. N. Artemyev and A. Surzhykov, Phys. Rev. Lett. 114, 243004 (2015).
[9] A. N. Artemyev et al., Phys. Rev. A 106, 012813 (2022).
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