Absolute Frequency Measurement of the2S−8S/DTransitions in Hydrogen and Deuterium: New Determination of the Rydberg Constant

We have performed a pure optical frequency measurement of the $2S-8S/D$ two-photon transitions in atomic hydrogen and deuterium. These frequencies are directly compared to a new frequency standard, a diode laser stabilized to a two-photon transition at 778 nm in rubidium. We deduce a new value for the Rydberg constant, $R_{\infty }=109\mathrm{}737.3156859\left(10\right){\mathrm{cm}}^{-1\mathrm{}}$ with an uncertainty of $9\times {10}^{-12\mathrm{}}$. From the isotope shift, we derive a precise value of the $2S$ Lamb shift in deuterium $[L_{2S-2P}=1059.230\mathrm{}(9\left)\mathrm{MHz}\right]$ and the difference of the quadratic charge radii of deuteron and proton.