Absolute frequency and isotope shift of the magnesium (3s2) 1S0 → (3s3d) 1D2 two-photon transition by direct frequency-comb spectroscopy

We use a picosecond frequency-doubled mode-locked titanium sapphire laser to generate a frequency comb at 431 nm in order to probe the (3s(2)) S-1(0) -> (3s3d) D-1(2) transition in atomic magnesium. Using a second, self-referenced femtosecond frequency comb, the absolute transition frequency and the Mg-24 and Mg-26 isotope shift is determined relative to a global-positioning-system-referenced hydrogen maser. Our result for the transition frequency of the main isotope Mg-24 of 1 391 128 606.14(12) MHz agrees with previous measurements and reduces its uncertainty by four orders of magnitude. For the isotope shift we find delta nu(26,24) = 3915.13(39) MHz. Accurate values for transition frequencies in Mg are relevant in astrophysics and to test atomic structure calculations.