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

In a crossed laser-atomic beam experiment the wavelengths of the $2s-3p$ transitions are measured in H and D to a precision of one part in ${10}^9$. Our value for the Rydberg constant is $R_{\infty }=109\mathrm{}737.31521\left(11\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$. 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 $2s-3p_{\frac{1}{2}}$ and $2s-3p_{\frac{3}{2}}$ 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.