Absolute frequency measurement of the 2S-8S/D transitions 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(infinity) = 109 737.315 685 9(10) cm(-1) with an uncertainty of 9 x 10(-12). From the isotope shift, we derive a precise value of the 2S Lamb shift in deuterium [L(2S-2P) = 1059.230(9) MHz] and the difference of the quadratic charge radii of deuteron and proton.