2
For a gas at thermal equilibrium, it is usually assumed that the velocity distribution follows an isotropic 3-dimensional Maxwell-Boltzmann (M-B) law.
This assumption classically implies the assumption of a "cos
~85°-88.5° from the normal to the surface and no deviation from the M-B law is found within the limits of our elementary set-up. Finally we suggest tracks to explore more parallel velocities, when surface details -roughness or structureand the atom-surface interaction should play a key role to restrict the applicability of a M-B-type distribution.3 I. The Maxwell-Boltzmann distribution of atomic velocities in a dilute gas and the signature of atoms moving close to a wall container.It is usually unquestioned, in the field of Atomic and Molecular Physics, that the atomic velocity distribution in a gas at thermal equilibrium is governed by a MaxwellBoltzmann (M-B) distribution for kinetic energy, with a 3-dimensional isotropy. This is even the basis for proposals aiming to measure the Boltzmann constant by the Doppler broadening of a thermal gas, in view of a redefinition of the temperature scale [1].However, in the vicinity of a wall, the isotropy is locally lost in a region, often called the Knudsen layer [2], where the atom-wall collisions modify the behavior of the gas. The microscopic description of an atom-surface collision or interaction is a rich field, which has been addressed experimentally for a long time. The possibility of a velocity distribution depending upon the vessel shape, has been sometimes considered, although the proofs for self-consistency seem delicate [3]. Despite the variety of behaviors found microscopically at the frontier of the gas, it remains usually assumed that the overall gas behavior obeys a M-B distribution (see e.g. [4]).As recalled in detail in the review by Comsa and David [5], which includes a significant historical approach, the distribution of atomic velocities established by Maxwell for an isotropic volume of a gas with molecules undergoing numerous collisions (the basis for the ideal gas kinetics) has been founded upon questionable hypotheses concerning the effect of the surface. The Maxwell model assumes that a fraction f of the molecules sticks onto the wall, for further scattering or "desorption" according to the expected "gas law", while the remaining fraction (1-f) just undergoes an ideal (specular) reflection on the wall.Retrospectively, it is clear that specular atomic reflection cannot be considered as a general 4 phenomenon for an unprepared surface and a high atomic density. Rather, quantum reflection on a wall potential is an effect well identified but difficult to observe, and applies to atoms cooled to extremely slow motion [6] (along the normal), while requiring perfectly polished surfaces [7]. For the desorption process, occurring on considerably longer time scale, arguments based upon conservation laws of the flux to and from the surface, combined with the assumed isotropic M-B distribution in the surrounding gas, lead to the cos law (Knudsen l...