Precision spectroscopy of the 3s-3p fine structure doublet in Mg+

We apply a recently demonstrated method for precision spectroscopy on strong transitions in trapped ions to measure both fine structure components of the 3s-3p transition in 24-Mg+ and 26-Mg+. We deduce absolute frequency reference data for transition frequencies, isotope shifts and fine structure splittings that are in particular useful for comparison with quasar absorption spectra, which test possible space-time variations of the fine structure constant. The measurement accuracy improves previous literature values, when existing, by more than two orders of magnitude.