Optical Frequency Measurement of the $2\mathit{S}-12\mathit{D}$ Transitions in Hydrogen and Deuterium: Rydberg Constant and Lamb Shift Determinations

We have performed a pure optical frequency measurement of the $2S-12D$ 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, $R_{\infty }=109\mathrm{}737.31568516\left(84\right){\mathrm{cm}}^{-1\mathrm{}}$ (relative uncertainty of $7.7\times {10}^{-12\mathrm{}}$) and for the $1S$ and $2S$ Lamb shifts $L_{1S}=8172.837\mathrm{}\left(22\right)\mathrm{MHz}$ and $L_{2S-2P}=1057.8446\mathrm{}\left(29\right)\mathrm{MHz}$ [respectively, $L_{1S}=8183.966\mathrm{}\left(22\right)\mathrm{MHz}$, and $L_{2S-2P}=1059.2337\mathrm{}\left(29\right)\mathrm{MHz}$ for deuterium]. These are now the most accurate values available.