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.
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- J. Sapirstein and K. T. Cheng, Phys. Rev. A. 108, 042804 (2023).
