New Measurement of the Rydberg Constant by Two-Photon Spectroscopy of Hydrogen Rydberg States

Abstract

We have made wavelength measurements of the three transitions 2S-8D, 2S-10D, and 2S-12D in atomic hydrogen and deuterium to determine a new value for the Rydberg constant, $R_{\infty }=109\mathrm{}737.315709\left(18\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, currently the most precise one. As reference we made use of an ${\mathrm{I}}_2$-stabilized He-Ne laser, compared to the standards of the Bureau International des Poids et Mesures. The H-D isotopic shifts have also been measured and a value for the proton-to-electron mass ratio deduced: $\frac{m_p}{m_e}=1836.152\mathrm{}59\left(24\right)\mathrm{}$.