New Measurement of the Rydberg Constant Using Polarization Spectroscopy ofHα

Abstract

We have determined a new Rydberg value, $R_{\infty }=109\mathrm{}737.31476\left(32\right)\mathrm{}$ ${\mathrm{cm}}^{-1\mathrm{}}$, from an absolute wavelength measurement of the $2S_{\frac{1}{2}}-3\mathrm{}{P}_{\frac{1}{2}}$ component of the hydrogen Balmer-$\alpha$ line. Polarization spectroscopy of a mild helium-hydrogen discharge with a cw dye laser provided a threefold higher accuracy than the only previous Doppler-free measurement. Another twofold improvement can be obtained by a more precise wavelength measurement of a near-coincident ${}_{}{}^{127}{}_{}{}^{}\mathrm{I}_2^{}{}_{}{}^{}$ reference line.