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Transition frequencies and fine-structure splittings of the $2\,{}^3\!S_1\rightarrow 2\,{}^3\!P_{\!J}$ transitions in helium-like $^{12}\mathrm{C}^{4+}$were measured by collinear laser spectroscopy on a 1-ppb level. Accuracy isincreased by more than three orders of magnitude with respect to previousmeasurements, enabling tests of recent non-relativistic QED calculationsincluding terms up to $m\alpha^7$. Deviations between the theoretical andexperimental values are within theoretical uncertainties and are ascribed to$m\alpha^8$ and higher-order contributions in the series expansion of theNR-QED calculations. Finally, prospects for an all-optical charge radiusdetermination of light isotopes are evaluated.

Collinear Laser Spectroscopy of $2\,{}^3\!S_1 \rightarrow 2\,{}^3\!P_{\!J}$ transitions in helium-like $^{12}\mathrm{C}^{4+}$