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The velocity distribution of molecules contained in a vessel with walls of different temperatures is shifted from the equilibrium distribution. To elucidate the kinetic behavior of the molecules in the vessel, the measurement of the velocity distribution is essential and will be a fertile source to get information on the interaction of the molecules with the surfaces. In our previous study on the photo-desorption of hydrogen molecules from cryogenic surfaces, we developed a sensitive detection method of molecular hydrogen by using a resonant-enhanced multiphoton ionization (REMPI) and we observed a Doppler broadening of the resonant line width at elevated temperatures. To estimate the amount of the Doppler width of the REMPI line profile of the hydrogen molecules, we made an analysis on the velocity distribution in a spherical cryogenic chamber with inlet openings. In the analysis, we considered a spherical vessel with a pair of openings along the line intersecting the center of the vessel. The opening is not only for the molecules evacuated but also for the laser beam of the REMPI. The molecular flux into the opening was thought to be in thermal equilibrium with a vacuum chamber which contained the cryogenic vessel. Based on the calculation of the kinetic theory of free molecular flow, we estimated the velocity distribution of hydrogen molecules along the direction of the laser beam under several geometries of the openings and the temperature distributions of the vessel wall. The measurement of the Doppler width of the REMPI line profile is meaningful and useful for the analysis of molecular behavior in a cryogenic vacuum system and other vacuum systems where non-uniform molecular velocity distribution is essential. |