Experimental test of the distribution of atomic trajectories at grazing incidence in a micrometric thin vapour cell

For a gas at thermal equilibrium, the velocity distribution is usually assumed to follow an isotropic 3-dimensional Maxwell-Boltzmann (MB) law. Several sub-Doppler laser spectroscopy techniques for confined gases (including selective reflection spectroscopy at an interface under normal incidence, micro and nano-cell of vapors, …) rely on the specific contribution of atoms moving nearly parallel to the boundary of a vapour container. For these techniques, a dilute gas regime is considered, with atomic trajectories essentially governed by wall collisions, rather than by atom-atom collisions. In spite of speculations of a metrological sub-Doppler resolution with microcells for experiments on extremely narrow lines (see e.g. [1]), based upon the expected response of atoms following truly grazing trajectories (i.e. very slow “normal” velocities), experimental demonstrations have been restricted to sub-Doppler lines as narrow as 1/50 th of the Doppler width [2, 3], owing to the relatively strong transitions used until now. The presence of such very slow atoms is highly questionable, for technological reasons (such as the local roughness of the surface itself), but also because of more fundamental issues[4], such as the atom-surface interaction (notably van der Waals type [3]), and mostly to the law itself of desorption from the surface. Indeed, the assumption of a MB velocity distribution implies a “cos θ” law for the flux of atoms leaving the surface, an hypothesis which cannot be justified by surface physics [5]. Moreover, the very few experimental investigations on this topic [6] were not suitable to test grazing incidences.