The nuclear charge radius of $^{13}\mathrm{C}$

Abstract

The size is a key property of a nucleus. Accurate nuclear radii are extracted from elastic electron scattering, laser spectroscopy, and muonic atom spectroscopy. The results are not always compatible, as the proton-radius puzzle has shown most dramatically. Beyond helium, precision data from muonic and electronic sources are scarce in the light-mass region. The stable isotopes of carbon are an exception. We present a laser spectroscopic measurement of the root-mean-square (rms) charge radius of $^{13}\mathrm{C}$ and compare this with ab initio nuclear structure calculations. Measuring all hyperfine components of the $2\,^3\mathrm{S} \rightarrow 2\,^3\mathrm{P}$ fine-structure triplet in $^{13}\mathrm{C}^{4+}$ ions referenced to a frequency comb allows us to determine its center-of-gravity with accuracy better than $2\,\mathrm{MHz}$ although second-order hyperfine-structure effects shift individual lines by several $\mathrm{GHz}$. We improved the uncertainty of $R_\mathrm{c}(^{13}\mathrm{C})$ determined with electrons by a factor of $6$ and found a $3\sigma$ discrepancy with the muonic atom result of similar accuracy.