Abstract
In this paper, we present the significant progress made by an experiment dedicated to the determination of the Boltzmann constant, kB, by accurately measuring the Doppler absorption profile of a line in ammonia gas at thermal equilibrium. This optical method based on the first principles of statistical mechanics is an alternative to the acoustical method, which has led to the unique determination of kB published by the Committee on Data for Science and Technology with a relative accuracy of 1.7×10−6. We report on the first measurement of the Boltzmann constant carried out by using laser spectroscopy with a statistical uncertainty below 10 p.p.m., more specifically 6.4 p.p.m. This progress results from the improvement in the detection method and in the statistical treatment of the data. In addition, we have recorded the hyperfine structure of the probed ν2 saQ(6,3) rovibrational line of ammonia by saturation spectroscopy and thus determine very precisely the induced 4.36 (2) p.p.m. broadening of the absorption linewidth. We also show that in our well-chosen experimental conditions, saturation effects have negligible impact on the linewidth. Finally, we suggest directions for future work to achieve an absolute determination of kB with an accuracy of a few p.p.m.
Highlights
A renewed interest in the Boltzmann constant is related to the possible redefinition of the International System of Units (SI) [1,2,3,4,5,6,7,8,9,10,11,12]
We report on the first measurement of the Boltzmann constant by laser spectroscopy with a statistical uncertainty below 10 ppm and give a first evaluation of the uncertainty budget, which shows that the effect of the hyperfine structure of the probed line needs to be taken into account
Recent experimental developments to reduce the statistical uncertainty on the Boltzmann constant determined by linear absorption of ammonia around 10 μm have been reported
Summary
A renewed interest in the Boltzmann constant is related to the possible redefinition of the International System of Units (SI) [1,2,3,4,5,6,7,8,9,10,11,12]. The principle [26, 27] consists in recording the Doppler profile of a wellisolated absorption line of an atomic or molecular gas in thermal equilibrium in a cell This profile reflects the Maxwell-Boltzmann distribution of velocities along the laser beam axis. 2. The experimental setup The principle of the experiment consists in recording the linear absorption of a rovibrational ammonia line in the 10 μm spectral region, the ammonia gas being at thermal equilibrium in a cell. The experimental setup The principle of the experiment consists in recording the linear absorption of a rovibrational ammonia line in the 10 μm spectral region, the ammonia gas being at thermal equilibrium in a cell The width of such a line is dominated by the Doppler width due to the molecular velocity distribution along the probe laser beam. It is necessary to have a good knowledge of that structure in order to take it into account in the line shape analysis
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