High resolution spectroscopy of the hydrogen atom - III. Wavelength comparison and Rydberg constant determination

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Abstract
This paper is the last of a series giving a detailed description of our recent determination of the Rydberg constant. Here we carefully describe the wavelength comparison procedure. The wavelengths of the three two-photon transitions 2S-8D, 2S-10D, and 2S-12D in hydrogen and deuterium are compared to that of an I2-stabilized He-Ne laser which is the present best reference in the optical domain. The key of this comparison is a high stability Fabry-Perot cavity etalon. The reflective phase shifts are taken into account by changing the length of this cavity ("virtual mirrors method"). In order to measure the Fresnel phase shift we study the frequency difference between the first transverse mode and the fundamental mode of the cavity. From the six measured wavelengths we deduce a new value for the Rydberg constant, R∞ = 109737.315709(18) cm-1, currently the most precise one. The H-D isotopic shifts have been also measured and a value for the proton-to-electron mass ratio is deduced: mp/me = 1836.15259(24)