The two-loop self-energy for the ground state of medium-Z hydrogen-like ions

Abstract

The two-loop self-energy correction to the ground state Lamb shift is calculated for hydrogen-like ions with the nuclear charge Z=10-30 without any expansion in the binding field of the nucleus. A calculational technique is reported for treatment of Feynman diagrams in the mixed coordinate-momentum representation, which yields significant improvement in numerical accuracy as compared to previous results. An extrapolation of the all-order numerical data towards Z=1 yields a result for the higher-order remainder function for hydrogen. The previously reported disagreement between the all-order and the perturbative approaches is reduced to the marginal agreement.

4 pages, 1 table, 3 figures

References in corpus (4)

• Nonrelativistic QED approach to the Lamb shift
• Two-Loop Bethe Logarithms
• Non-perturbative calculation of the two-loop Lamb shift in Li-like ions
• Two-loop QED corrections with closed fermion loops

Cited by in corpus (19)

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• QED tests with highly-charged ions
• Relativistic recoil, electron-correlation, and QED effects on the 2p_j-2s transition energies in Li-like ions
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• Progress in quantum electrodynamics theory of highly charged ions
• Theory of bound-electron g factor in highly charged ions
• QED calculation of the ground-state energy of berylliumlike ions
• Two-loop QED corrections with closed fermion loops for the bound-electron g factor
• Two-loop self-energy in the Lamb shift of the ground and excited states of hydrogen-like ions
• Ground-state ionization energies of boronlike ions
• The Lamb shift of the $1s$ state in hydrogen: two-loop and three-loop contributions
• The two-loop self-energy: diagrams in the coordinate-momentum representation
• Nuclear recoil corrections to the Lamb shift of hydrogen and light hydrogen-like ions
• Virtual Delbrück scattering and the Lamb shift in light hydrogen-like atoms
• Two-loop electron self-energy for low nuclear charges
• Ab initio calculations of the $2p_{3/2}\to 2s$ transition in He-, Li-, and Be-like uranium
• Two-loop electron self-energy with accelerated partial-wave expansion
• Ro-vibrational spin-averaged transitions in the hydrogen molecular ions
• Two-loop electron self-energy in bound-electron $g$ factor: diagrams in momentum-coordinate representation