One-loop self-energy using a numerical Green function

Hugo D. Nogueira; Maen Salman; Jean-Philippe Karr

One-loop self-energy using a numerical Green function

Atomic Physics 2026-07-17 v1

Authors: Hugo D. Nogueira , Maen Salman , Jean-Philippe Karr

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.

Cite

@article{arxiv.2607.16026,
  title  = {One-loop self-energy using a numerical Green function},
  author = {Hugo D. Nogueira and Maen Salman and Jean-Philippe Karr},
  journal= {arXiv preprint arXiv:2607.16026},
  year   = {2026}
}