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 (7)

• Measurement of the Positive Muon Anomalous Magnetic Moment to 0.46 ppm
• High-precision measurement of the atomic mass of the electron
• Coherent laser spectroscopy of highly charged ions using quantum logic
• 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
• QED corrections to the $g$ factor of Li- and B-like ions