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 ee+ 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 the case of a pointlike nucleus are derived. These results are compared to existing analytic formulas from nonrelativistic theory.

S. Breidenbach, E. Dizer, H. Cakir, and Z. Harman., “Hadronic vacuum polarization correction to atomic energy levels”, Phys. Rev. A 106, 042805 (2022).


Related to Project B02