$g$ Factor of Boron-like Tin

TL;DR

This paper reports the first high-precision measurement of the $g$ factor of boron-like tin, providing a crucial test of quantum electrodynamics and many-electron interactions at high atomic number, with implications for fundamental constants.

Contribution

It presents the first high-precision experimental measurement of the boron-like $g$ factor for $^{118} ext{Sn}^{45+}$ and compares it with advanced theoretical calculations, testing QED at high $Z$.

Findings

Measured $g$ factor: 0.6447038265(4)

Agreement with ab initio calculations within uncertainties

Demonstrates potential for determining the fine-structure constant

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 $0.644\,703\,826\,5(4)$ is consistent with the presented \textit{ab initio} state-of-the-art theory calculations, which predict a value of $0.644\,702\,9(8)$. 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 $\alpha$, 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.