Self-energy correction to the bound-electron g factor: approximate treatment of the one-potential contribution in momentum space

High-precision measurements of the bound-electron g factor in hydrogen and other few-electron ions provide stringent tests of quantum electrodynamics in the presence of a magnetic field and enable independent determination of fundamental constants. Interpreting these experiments requires equally accurate theoretical calculations, particularly for the electron self-energy correction representing a dominant QED contribution.

In this work, we focus on the vertex self-energy diagram for the bound-electron g factor. The contribution of this diagram suffers from ultraviolet (UV) divergences. In order to separate them out, an expansion of electron propagators in terms of binding potential is applied. The UV-divergent term is calculated in momentum space after a renormalization. In principle, the remainder of the vertex contribution can be evaluated in coordinate space, but the slow convergence of partial-wave expansions in coordinate space significantly limits the accuracy of calculations. In [1], it was proposed to additionally separate the next-to-divergent term of the potential expansion, the so-called one-potential contribution, and to treat it in momentum space. This considerably improved the convergence. However, the obtained closed-form expression for the one-potential contribution in momentum space was rather complicated. Based on a fruitful idea first proposed in [2], we have derived several approximations for the one-potential contribution. Separation of these approximations from the UV-finite term keeps the same effect on the convergence of the partial-wave expansions, but they can be calculated more easily.

1. V.A. Yerokhin, et al., Phys. Rev. A.69, 052503 (2004).
2. J. Sapirstein and K. T. Cheng, Phys. Rev. A. 108, 042804 (2023).