One-loop electron self-energy with accelerated partial-wave expansion in Coulomb gauge

Abstract

Numerical calculations of the electron self-energy without any expansion in the binding nuclear field are required in order to match the rapidly advancing precision of experimental spectroscopy. For the lightest elements, particularly hydrogen, these computations are complicated by large numerical cancellations and the slow convergence of the partial-wave expansion. Methods with accelerated convergence of the partial-wave expansion have been recently put forward [V. A. Yerokhin, K. Pachucki, V. M. Shabaev, Phys. Rev. A 72, 042502 (2005); J. Sapirstein and K. T. Cheng, Phys. Rev. A 108, 042804 (2023)]. In our work we extend the accelerated-convergence methods to the previously hardly accessible region of nuclear charges $Z<5$ and higher excited states.

References in corpus (7)

• Electron Self Energy for Higher Excited S Levels
• Precise determination of the 1s Lamb Shift in hydrogen-like lead and gold ions using microcalorimeters
• Perturbation Approach to the Self Energy of non-S Hydrogenic States
• Calculations of QED effects with the Dirac Green function
• Self-energy screening effects in the $g$ factor of Li-like ions
• Two-loop electron self-energy for low nuclear charges
• Two-photon exchange corrections to the $g$ factor of Li-like ions