Hadronic vacuum polarization correction to atomic energy levels

Abstract

The shift of atomic energy levels due to hadronic vacuum polarization is evaluated in a semiempirical way for hydrogenlike ions and for muonic hydrogen. A parametric hadronic polarization function obtained from experimental cross sections of $e^{-}{e}^{+}$ annihilation into hadrons is applied to derive an effective relativistic Uehling potential. The energy corrections originating from hadronic vacuum polarization are calculated for low-lying levels using analytical Dirac-Coulomb wave functions, as well as bound wave functions accounting for the finite nuclear size. Closed formulas for the hadronic Uehling potential of an extended nucleus as well as for the relativistic energy shift in case of a point-like nucleus are derived. These results are compared to existing analytic formulas from non-relativistic theory.

References in corpus (20)

• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• Theory of Light Hydrogenlike Atoms
• The hadronic light-by-light scattering contribution to the muon anomalous magnetic moment from lattice QCD
• High-precision measurement of the atomic mass of the electron
• New measurement of the $1S-3S$ transition frequency of hydrogen: contribution to the proton charge radius puzzle
• Hadronic vacuum polarization contribution to the anomalous magnetic moments of leptons from first principles
• Coherent laser spectroscopy of highly charged ions using quantum logic
• QED tests with highly-charged ions
• Hadronic Contributions to the Photon Vacuum Polarization and their Role in Precision Physics
• Theory of the Lamb shift in hydrogen and light hydrogen-like ions
• Lamb Shift in Muonic Hydrogen
• Hadronic Vacuum Polarization and the Lamb Shift
• QED shifts in multivalent heavy ions
• $g$-factor of Boronlike Argon ${}^{40}{\text{Ar}}^{13+}$
• Light-by-light scattering in the Lamb shift and the bound electron g factor
• High-precision measurements of $n=2\to n=1$ transition energies and level widths in He- and Be-like Argon Ions
• Stringent tests of QED using highly charged ions
• Two-loop self-energy in the Lamb shift of the ground and excited states of hydrogen-like ions
• QED corrections to the $g$ factor of Li- and B-like ions
• Skyrme-type nuclear interaction as a tool for calculating the finite nuclear size correction to atomic energy levels and the bound-electron $g$ factor

Cited by in corpus (2)

• Hadronic vacuum polarization correction to the bound-electron $g$ factor
• Influence of a Perfectly Conducting Plate on the Uehling Potential of QED