A frequency-comb-referenced laser measurement of the 13C4+ hyperfine spectrum yields Rc(13C) = 2.4464(45) fm, six times more precise than electron scattering and in tension with the muonic-atom value.
Second-order hyperfine correction to H, D, and $^3$He energy levels
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abstract
The complete second-order hyperfine-interaction correction is calculated for centroid energy levels of H, D, and $^3$He atoms. For $^3$He, the corrections of $-2.075$~kHz and $-0.305$~kHz beyond the leading hyperfine-mixing contribution are obtained for the $2^1S$ and $2^3S$ states, respectively. These results shift the nuclear charge radii difference derived from the $^3$He -$^4$He isotope shift and largely resolve the previously reported disagreement between the muonic and electronic helium determinations [van der Werf et al., arXiv:2306.02333 (2023); Schuhmann et al., arXiv:2305.11679 (2023)].
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The nuclear charge radius of $^{13}\mathrm{C}$
A frequency-comb-referenced laser measurement of the 13C4+ hyperfine spectrum yields Rc(13C) = 2.4464(45) fm, six times more precise than electron scattering and in tension with the muonic-atom value.