Year: 2026
Type: preprint
Abstract: We calculate the one-loop self-energy in hydrogenlike atoms using a numerical Green function obtained by solving the radial Dirac equation in an exponential basis set. The self-energy correction in the ground state of hydrogenlike uranium is obtained with about $10^{-5}$ relative uncertainty in the Feynman gauge. Using a convergence acceleration scheme, we extend our calculations to the region of low nuclear charges. Our results allow calculating the self-energy correction for the hydrogen atom with $10^{-4}$ relative uncertainty. Calculations in the Coulomb gauge are also presented, improving the precision to $10^{-5}$. Present limitations and possible improvements of our method are discussed.
Source: arXiv (Cornell University)
Institutions: Centre National de la Recherche Scientifique, Université Paris Sciences et Lettres, Laboratoire Kastler Brossel, École Normale Supérieure - PSL, Sorbonne Université, Laboratoire de Chimie Théorique, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Université Paris-Saclay, Université d'Évry Val-d'Essonne
Topic: Atomic and Molecular Physics
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
Award: G7677995805
OpenAlex ID: W7169777136
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