Two-loop self-energy in the Lamb shift of the ground and excited states of hydrogen-like ions

Abstract

The two-loop self-energy correction to the Lamb shift of hydrogen-like ions is calculated for the $1s$, $2s$, and $2p_{1/2}$ states and nuclear charge numbers $Z=30$-$100$. The calculation is performed to all orders in the nuclear binding strength parameter $Z\alpha$. As compared to previous calculations of this correction, numerical accuracy is improved by an order of magnitude and the region of the nuclear charges is extended. An analysis of the $Z$-dependence of the obtained results demonstrates their consistency with the known $Z\alpha$-expansion coefficients.

18 pages, 6 figures

References in corpus (6)

• Nonrelativistic QED approach to the Lamb shift
• Two-Loop Bethe Logarithms
• Non-perturbative calculation of the two-loop Lamb shift in Li-like ions
• Calculation of the One- and Two-Loop Lamb Shift for Arbitrary Excited Hydrogenic States
• Two-loop QED corrections with closed fermion loops
• The two-loop self-energy: diagrams in the coordinate-momentum representation

Cited by in corpus (14)

• QED tests with highly-charged ions
• Theory of the Lamb shift in hydrogen and light hydrogen-like ions
• QED calculations of the $n=2$ to $n=1$ x-ray transition energies in middle-$Z$ heliumlike ions
• Probing new physics using Rydberg states of atomic hydrogen
• Theory of the two-loop self-energy correction to the $\mathbf{g}$ factor in non-perturbative Coulomb fields
• Calculations of QED effects with the Dirac Green function
• 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
• Improved bound-electron g-factor theory through complete two-loop QED calculations
• Hadronic vacuum polarization correction to atomic energy levels
• Bound state equations in Riemannian geometry
• 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