Nuclear Charge Radii of Carbon Isotopes Determined by Laser Spectrosocpy of C⁴⁺ Ions

Laser spectroscopy is a powerful tool to study the size and shape of nuclei by measuring the isotope shift and hyperfine splitting of atomic or ionic transitions. The technique of collinear laser spectroscopy has been used for almost 50 years to study short-lived isotopes. At the Collinear Apparatus for Laser spectroscopy and Applied physics (COALA), we have applied it recently to He-like (C⁴⁺) carbon isotopes. The results are important benchmarks for atomic theory as well as for ab initio calculations of light nuclei.

In ¹²C⁴⁺ we measured the transition frequencies of all 1s2s ³S₁ → 1s2p ³P_J fine-structure transitions with more than 3 orders of magnitude improved accuracy and extracted an “all-optical” nuclear charge radius from the transition frequencies center-of-gravity. The isotope ¹³C has nuclear spin, which causes hyperfine-induced fine-structure mixing that shifts individual hyperfine lines by more than 2 GHz. By measuring the complete hyperfine structure of all fine-structure transitions, we were able to determine the isotope shift of the triplets center-of-gravity with 2-MHz accuracy and to extract the nuclear charge radius with three times improved precision compared to all previous elastic-electron and muonic-atom measurements [3]. A systematic deviation between charge radii determined by electron-nucleus and muon-nucleus interactions is observed and awaits solution by more accurate measurements using these techniques. The radii are compared with latest ab initio nuclear charge structure calculations using valence-space in-medium SRG and in-medium no core shell model calculations.