Luigi Moretti

The Boltzmann constant from the H2 18O vibration–rotation spectrum: complementary tests and revised uncertainty budget

We report on complementary tests and measurements regarding our recent determination of the Boltzmann constant, kB, by means of Doppler broadening thermometry, also providing additional information as compared to previous articles. A revised uncertainty budget is illustrated, including some new components that were ignored in previous spectroscopic experiments, and better quantifying other components that were estimated to be negligible. In particular, we consider the relativistic Doppler effect, the perturbation caused by the finite bandwidth of the detection system and the influence of the spontaneous emission content of the probe laser. These new components do not increase the global uncertainty which still amounts to 24 ppm. Our value for the Boltzmann constant is 1.380 631 (33) × 10−23 J K−1, which is the best determination reported so far by using an optical method.

The lineshape problem in Doppler-width thermometry

Typically eliminated in any experiment of time and frequency metrology, the Doppler broadening effect can be regarded as a gift of nature for the purpose of measuring the thermodynamic temperature of a gaseous sample. Nevertheless, Doppler-width retrieval from highly-accurate absorption spectra is surely not an easy task as it requires an adequate knowledge of the lineshape function, accounting for the different mechanisms that contribute to the overall linewidth. Semiclassical theories provide several possibilities, more or less accurate in reproducing the observed profiles. Here, the influence of the choice of the lineshape model in Doppler-width thermometry is investigated in the physical situation of self-colliding O molecules. A large number of absorption profiles were simulated, using the uncorrelated version of the speed-dependent Galatry profile and setting different values for the gas pressure, the signal-to-noise ratio and the Dicke-narrowing parameter. Spectral analysis was performed by means of different models, in order to retrieve the zero-pressure value of the Doppler width. It turned out that precision and accuracy can be pushed to extreme levels provided that the signal-to-noise ratio is sufficiently high (namely, larger than 50,000) and that a speed-dependent lineshape model is used.