A nonperturbative numerical evaluation of the one-photon electron self-energy for the K- and L-shell states of hydrogenlike ions with nuclear charge numbers Z =1 to 5 is described. Our calculation for the 1S1/2 state has a numerical uncertainty of 0.8 Hz in atomic hydrogen, and for the L-shell states (2S1/2 , 2P1/2 , and 2P3/2) the numerical uncertainty is 1.0 Hz. The method of evaluation for the ground state and for the excited states is described in detail. The numerical results are compared to results based on known terms in the expansion of the self-energy in powers of Zα.
U. D. Jentschura et al., "Electron Self-Energy for the K and L Shells at Low Nuclear Charge," Physical Review A. Atomic, Molecular, and Optical Physics, vol. 63, no. 4, pp. 425121-425129, American Physical Society (APS), Apr 2001.
The definitive version is available at https://doi.org/10.1103/PhysRevA.63.042512
Keywords and Phrases
Convergence Of Numerical Methods; Electron Transitions; Hydrogen; Ions; Nuclear Physics; Perturbation Techniques; Photons; Quantum Theory; Electron Self-energy; Nuclear Charges; Ground State
International Standard Serial Number (ISSN)
Article - Journal
© 2001 American Physical Society (APS), All rights reserved.