Precision Measurement of the Rydberg Constant by Laser Saturation Spectroscopy of the BalmerαLine in Hydrogen and Deuterium

We have determined a new Rydberg value, $R_{\infty }=109737.3143\mathrm{}\left(10\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, with an order of magnitude improvement in precision, by measuring the absolute wavelengths of resolved fine-structure components of the Balmer $\alpha$ line in hydrogen and deuterium, excited in a dc gas discharge. Doppler broadening was eliminated by saturation spectroscopy with a pulsed dye laser. An iodine-stabilized He-Ne laser was the wavelength standard. Possible sources of systematic errors have been carefully investigated.