The nuclear charge radius of 13C

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 ¹³C and compare this with ab initio nuclear structure calculations. Measuring all hyperfine components of the 2 ³S \({\to}\) 2 ³P fine-structure triplet in ¹³C⁴⁺ ions referenced to a frequency comb allows us to determine its center-of-gravity with accuracy better than 2 MHz although second-order hyperfine-structure effects shift individual lines by several GHz. We improved the uncertainty of R_c(¹³C) determined with electrons by a factor of 6 and found a 3σ discrepancy with the muonic atom result of similar accuracy.