The $$^2{\mathrm{S}}_{1/2}{-}^2{\mathrm{P}}_{{1}/2}$$
2
S
1
/
2
-
2
P
1
/
2
and $$^2{\mathrm{S}}_{1/2}{-}^2{\mathrm{P}}_{{3}/2}$$
2
S
1
/
2
-
2
P
3
/
2
transitions in Li-like carbon ions stored and cooled at a velocity of $$\beta \approx 0.47$$
β
≈
0.47
in the experimental storage ring (ESR) at the GSI Helmholtz Centre in Darmstadt have been investigated in a laser spectroscopy experiment. Resonance wavelengths were obtained using a new continuous-wave UV laser system and a novel extreme UV (XUV) detection system to detect forward emitted fluorescence photons. The results obtained for the two transitions are compared to existing experimental and theoretical data. A discrepancy found in an earlier laser spectroscopy measurement at the ESR with results from plasma spectroscopy and interferometry has been resolved and agreement between experiment and theory is confirmed.