Optical Frequency Measurement of the2S−12DTransitions in Hydrogen and Deuterium: Rydberg Constant and Lamb Shift Determinations

We have performed a pure optical frequency measurement of the $2S\ensuremath{-}12D$ two-photon transitions in atomic hydrogen and deuterium. From a complete analysis taking into account this result and all other precise measurements (by ourselves and other authors), we deduce optimized values for the Rydberg constant, ${R}_{\ensuremath{\infty}}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}109737.31568516(84){\mathrm{cm}}^{\ensuremath{-}1}$ (relative uncertainty of $7.7\ifmmode\times\else\texttimes\fi{}{10}^{\ensuremath{-}12}$) and for the $1S$ and $2S$ Lamb shifts ${L}_{1S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8172.837(22)\mathrm{MHz}$ and ${L}_{2S\ensuremath{-}2P}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1057.8446(29)\mathrm{MHz}$ [respectively, ${L}_{1S}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}8183.966(22)\mathrm{MHz}$, and ${L}_{2S\ensuremath{-}2P}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1059.2337(29)\mathrm{MHz}$ for deuterium]. These are now the most accurate values available.