Crossed-Beam Spectroscopy of Hydrogen: A New Value for the Rydberg Constant

In a crossed laser-atomic beam experiment the wavelengths of the $2s\ensuremath{-}3p$ transitions are measured in H and D to a precision of one part in ${10}^{9}$. Our value for the Rydberg constant is ${R}_{\ensuremath{\infty}}=109737.31521(11)$ ${\mathrm{cm}}^{\ensuremath{-}1}$. The fine-structure splittings of the $3p$ states in H and D are 3249.8(8) and 3251.7(7) MHz, respectively; the isotope shifts for the $2s\ensuremath{-}3{p}_{\frac{1}{2}}$ and $2s\ensuremath{-}3{p}_{\frac{3}{2}}$ transitions are 124 260.7(7) and 124 262.6(7) MHz, respectively. Our results largely agree with previous, less precise experiments and with theory.