Collinear laser spectroscopy has been performed on He-like ${\mathrm{C}}^{4+}$ ions extracted from an electron-beam ion source (EBIS). In order to determine the transition frequency with the highest-possible accuracy, the line shape of the fluorescence response function was studied for pulsed and continuous ion extraction modes of the EBIS in order to optimize its symmetry and linewidth. We found that the best signal-to-noise ratio is obtained using the continuous beam mode for ion extraction. Applying frequency-comb-referenced collinear and anticollinear laser spectroscopy, we achieved a measurement accuracy of better than 2 MHz including statistical and systematic uncertainties. The origin and size of systematic uncertainties, as well as further applications for other isotopes and elements are discussed.

• Received 6 June 2023
• Accepted 9 October 2023

DOI:https://doi.org/10.1103/PhysRevA.108.062809