The two-loop self-energy: diagrams in the coordinate-momentum representation

Abstract

The paper reports a technique of evaluation of Feynman diagrams in the mixed coordinate-momentum representation. The technique is employed for a recalculation of the two-loop self-energy correction for the ground state of hydrogen-like ions with the nuclear charge numbers Z=10-30. The numerical accuracy is considerably improved as compared to the previous calculations. The higher-order (in Zα) remainder function is inferred from the numerical results and extrapolated towards Z=0 and 1. The extrapolated value for hydrogen is consistent (but still not in perfect agreement) with the analytical result obtained within the perturbative approach.

arXiv comment12 pages, 3 figures, 2 tables

References in corpus (13)

• New Limits to the Drift of Fundamental Constants from Laboratory Measurements
• Nonrelativistic QED approach to the Lamb shift
• CORRECTIONS OF ORDER ${\alpha }^2(Z\alpha {)}^5$ TO HYPERFINE SPLITTING AND LAMB SHIFT
• Two-loop self-energy correction in high-Z hydrogen-like ions
• Two-Loop Bethe Logarithms
• Logarithmic two-loop corrections to the Lamb shift in hydrogen
• Non-perturbative calculation of the two-loop Lamb shift in Li-like ions
• Two-loop self-energy correction in H-like ions
• Two-loop self-energy contribution to the Lamb shift in H-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 for the ground state of medium-Z hydrogen-like ions
• Leading logarithmic contribution to the second-order Lamb shift induced by the loop-after-loop diagram

Cited by in corpus (10)

• CODATA Recommended Values of the Fundamental Physical Constants: 2010
• 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
• Theory of the two-loop self-energy correction to the $\mathbf{g}$ factor in non-perturbative Coulomb fields
• Two-loop electron self-energy for low nuclear charges
• Improved bound-electron g-factor theory through complete two-loop QED calculations
• QED approach to valence-hole excitation in closed shell systems
• Two-loop electron self-energy in bound-electron $g$ factor: diagrams in momentum-coordinate representation