Two-Loop Self-Energy Corrections to One-Photon Recombination Process in Hydrogen Atom
Kvasov P., Bobylev A., Lopez Javier J.R., Solovyev D., Solovyeva E., Zalialiutdinov T.

Received: October 12, 2025

DOI: 10.7868/S3034641X26010022

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In the framework of relativistic quantum electrodynamics, two-loop self-energy corrections to the cross section of one-photon recombination are investigated for bound states. Using the hydrogen atom as an example, it is demonstrated that the derived analytical expression is free from singular contributions, in contrast to the expression for the cross section of two-photon recombination, which inevitably contains inseparable resonant contributions corresponding to cascade one-photon transitions. Utilizing the obtained expression, numerical calculations of the two-photon part of the radiative correction to the spontaneous one-photon recombination coefficient are performed under the assumption of a Maxwellian distribution of free electrons. By employing a three-level recombination model for the primordial hydrogen plasma in the early Universe, it is demonstrated that the derived corrections to the ionization degree of primordial plasma approach the level of numerical precision typically required in theoretical recombination models, but remain below the current experimental sensitivity. Keywords}: quantum electrodynamics of bound states, two-loop corrections, electron self-energy, atomic recombination, Hydrogen atom.