Tackling the uncertainty of the nuclear-polarization correction to the bound-electron $g$ factor by means of the nuclear Skyrme interaction

Abstract

The Coulomb part of the leading-order nuclear-polarization correction to the bound-electron $g$ factor of hydrogenlike ions is investigated in a microscopic approach from the nuclear point of view. To this end, the effective Skyrme force is employed to model nucleon-nucleon interactions, with the energies and the reduced transition probabilities of collective nuclear excitations being obtained in the Hartree-Fock-based random-phase approximation. These nuclear parameters serve as input for the nuclear-polarization correction, evaluated via effective self-energy diagrams where the photon propagator is modified by a nuclear-polarization insertion. A diverse set of Skyrme parameterizations is probed for $^{40}\text{Ca}^{19+}$, $^{60}\text{Ni}^{27+}$, $^{90}\text{Zr}^{39+}$, and $^{120}\text{Sn}^{49+}$, and the results are compared to the common approach involving experimental nuclear data and estimates based on energy-weighted sum rules. As a result, tighter constraints on the theoretical uncertainties of the nuclear-polarization corrections are obtained, providing key input for high-precision measurements of the bound-electron $g$ factors of heavy hydrogenlike ions.