First direct determination of the Boltzmann constant by an optical method C. Daussy, M. Guinet, A. Amy-Klein, K. Djerroud, Y. Hermier 1 , S. Briaudeau 1 Ch.J. Bordé, and C. Chardonnet Laboratoire de Physique des Lasers, UMR CNRS 7538, Institut Galilée, Université Paris 13, 99, ave J.-B. Clément – 93430 Villetaneuse – France (1) Permanent address : Institut national de Métrologie LNE-INM – CNAM – La Plaine Saint- Denis Abstract We have recorded the Doppler profile of a well-isolated rovibrational line in the ν 2 band of 14 NH 3 . Ammonia gas was placed in an absorption cell thermalized by a water-ice bath. By extrapolating to zero pressure, we have deduced the Doppler width which gives a first measurement of the Boltzmann constant, k B , by laser spectroscopy. A relative uncertainty of 2×10 -4 has been obtained. The present determination should be significantly improved in the near future and contribute to a new definition of the kelvin. PACS: 06.20.Jr, 33.20.Ea, 42.62.Fi The tremendous progress in high precision measurements during recent decades will lead unavoidably to a complete renewal of fundamental metrology. There is a strong tendency to relate the base units to fundamental constants [1]. As an example, this has been done in 1983 by fixing the velocity of light, c and thus defining the length unit from the time unit, because the second is the fundamental unit which is realized, by far, with the best accuracy. The unit of temperature could follow the same line. Up to now, the kelvin is defined by the temperature (273.16 K) of the triple point of water (TPW) which implies a particular property of macroscopic matter. Instead, the temperature of a sample has a microscopic interpretation and can be related through the Boltzmann constant to the mean energy, E, per particle and per degree of freedom according to the well-known expression: T k E B 2 1 = . This energy may itself be related to a frequency via Planck constant. This paper presents a first accurate experiment which gives a direct measurement of such a frequency, in a gas at a well-defined temperature. Fixing the value of k B would connect temperature and time units. But, before fixing the value of the Boltzmann constant it is necessary to verify precisely the consistency of the value of k B in the present context. The accepted value in the CODATA [2], k B B =1,380 6505 (24) x 10 J K , is derived from the value of the ideal gas constant, R, and the Avogadro constant N -23 -1 A , by the relation: k B =R/N A . The relative uncertainty of k B is 1.8×10 and should come mostly from that for R because the uncertainty of N -6 A is 1.7×10 [2]. But, there is presently an inconsistency at the level of 10 between the values of N -7 -6 A derived from the Si sphere and from the watt balance experiment [3]. Very few experiments lead to an accurate determination of k B or R [4]. Up to now, the accepted value of R comes from a single experiment by Moldover et al. [5] performed before 1988 by acoustic gas thermometry. An alternative and indirect measurement of the Boltzmann constant was proposed along an approach based on the virial expansion of the Clausius-Mossotti equation [6]. This relates the permittivity of helium, ε, to its molar polarisability, A ε . which implies a QED calculation. Here, we propose a direct determination of the Boltzmann constant by laser spectroscopy [1]. The principle consists in recording the linear absorption in vapour phase and measuring the Doppler width of an atomic or molecular line in a cell at the thermodynamic equilibrium. In the Doppler limit, the line shape is a Gaussian (for an optically thin medium) and k B T is given by: