Abstract
We consider hyperfine-mediated effects for clock transitions in $^{176}\mathrm{Lu}^{+}$. Mixing of fine-structure levels due to the hyperfine interaction brings about modifications to the Land\'e $g$-factors and the quadrupole moment for a given state. Explicit expressions are derived for both the $g$-factor and quadrupole corrections, for which leading-order terms arise from the nuclear magnetic dipole coupling. High accuracy measurements of the $g$-factors for the ${}^{1}{S}_{0}$ and ${}^{3}{D}_{1}$ hyperfine levels are carried out, and they provide an experimental determination of the leading-order correction terms.
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