Independent nuclear charge radius determinations: bound-electron $g$ factor versus muonic atom spectroscopy

Abstract

We present an alternative method to determine absolute nuclear charge radii competitively via the bound electron $g$ factor of H-like ions. The method is demonstrated for $^{118}$Sn by extracting its radius with a precision of 0.1%. This is the second most precise radius ever determined from an electronic system. We benchmark our result against a state-of-the-art value derived from the spectrum of muonic $^{118}$Sn. This comparison reveals a 3.2$σ$ tension, prompting a careful reexamination of the calculations and calling for additional measurements. Crucially, after decades, we now have two independent methods to measure absolute charge radii with similar precision.