Abstract
A state-of-the-art approach for calculating the finite nuclear size correction to atomic energy levels and the bound-electron $g$ factor is introduced and demonstrated for a series of highly charged hydrogen-like ions. Firstly, self-consistent mean-field calculations based on the Skyrme-type nuclear interaction are employed in order to produce a realistic nuclear proton distribution. In the second step, the obtained nuclear charge density is used to construct the potential of an extended nucleus, and the Dirac equation is solved numerically. The ambiguity in the choice of a Skyrme parametrization is supressed by fine-tuning of only one parameter of the Skyrme force in order to accurately reproduce the experimental values of nuclear radii in each particular case. The homogeneously charged sphere approximation, the two-parameter Fermi distribution and experimental nuclear charge distributions are used for comparison with our approach, and the uncertainties of the presented calculations are estimated. In addition, suppression of the finite nuclear size effect for the specific differences of $g$ factors is demonstrated.
Highlights
Charged ions represent one of the simplest and most well-understood physical systems, and yet they still continue to provide an extremely rich scope of opportunities for fundamental research
It can be seen that, once the value of rms radius is fixed, the calculated magnitudes of the FNS corrections become stable, despite the significant differences between the parameter sets. We tested this observation on a wide range of ions and parametrizations, and we found that the ambiguity in the choice of a Skyrme parameter set was largely suppressed in all cases by adjusting the rms nuclear radius
We have demonstrated the use of the Skyrme-Hartree-Fock nuclear-structure method as a tool for calculating the finitenuclear-size effect in highly charged ions
Summary
Charged ions represent one of the simplest and most well-understood physical systems, and yet they still continue to provide an extremely rich scope of opportunities for fundamental research They have been extensively used in past years for various high-precision tests of quantum electrodynamics, making it one of the most well-tested theories in physics [1,2,3,4,5]. The FNS correction can be calculated with a higher accuracy numerically by using the Fermi distribution as a model for nuclear charge density [29]. In this paper we present calculations of the FNS correction to atomic energy levels and the bound-electron g factor based on a more detailed description of nuclear charge distributions. The theoretically calculated nuclear charge densities are in a good agreement with the experimental ones These results pave the way for a more accurate description of nuclear-structure effects in atomic systems.
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