Nuclear Shape Effect on the $g$ Factor of Hydrogenlike Ions

The nuclear shape correction to the $g$ factor of a bound electron in the $1S$ state is calculated for a number of nuclei in the range of charge numbers from $Z=6$ up to $Z=92$. The leading relativistic deformation correction has been derived analytically, and also its influence on one-loop quantum electrodynamic terms has been evaluated. We show the leading corrections to become significant for mid-$Z$ ions and for very heavy elements to even reach the ${10}^{-6}$ level.

Figure 1

Various contributions to the $g$ factor: $\delta g_{1\mathrm{L}}$ stands for one-loop all-order QED corrections, $\delta g_{\mathrm{FS}}$ for the finite-size effect, $\delta g_{\mathrm{rec}}$ for the recoil correction, and $\delta g_{\mathrm{ND}}$ for the nuclear deformation correction, and $\delta g_{2\mathrm{L}}[(Z\alpha {)}^n]$ represents two-loop QED corrections at order $(Z\alpha {)}^n$ (see 30).