One-loop self-energy using a numerical Green function

2026/07/17 by Hugo D. Nogueira, Maen Salman, Jean-Philippe Karr
#physics.atom-ph

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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.

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