$g$ Factor of Boron-like Tin

Abstract

In the ALPHATRAP experiment, the $g$ factor of boron-like ${}^{118}{\mathrm{Sn}}^{45+}$ has been measured with a $0.5$ parts-per-billion uncertainty. This is the first high-precision measurement of a heavy boron-like $g$ factor. The measured value of $0.6447038265(4)$ is consistent with the presented \textit{ab initio} state-of-the-art theory calculations, which predict a value of $0.6447029(8)$. So far, the only boron-like $g$ factor measured with high precision has been ${}^{40}{\mathrm{Ar}}^{13+}$. The measurement presented here therefore tests quantum electrodynamics as well as many-electron interactions at much higher $Z$. Furthermore, we discuss the potential for an independent determination of the fine-structure constant $\hat{I}\pm$, which can be achieved with a specific difference of $g$ factors, combining the presented results with the recent electron $g$-factor measurement of hydrogen-like tin.