Radiation trapping of the3P1−1S0resonant transitions of xenon and krypton in Xe-Kr, Xe-Ar, and Kr-Ar mixtures: Kinetic analysis and determination of the van der Waals broadening coefficients

This work concerns radiation trapping of the 123-nm krypton and 147-nm xenon lines, in the presence of a lighter rare gas, as well as the study of the decay processes of the relevant resonant states due to inelastic collisions. It deals with Kr-Ar, Xe-Kr, and Xe-Ar mixtures. Pulsed, brief selective excitation of the $\mathrm{Xe}{(}^3{P}_1)$ or $\mathrm{Kr}{(}^3{P}_1)$ resonant states by three-photon absorption was achieved by means of a tunable dye laser. Spectral and temporal analysis was then performed. The time resolved luminescence, filtered in the vacuum ultraviolet region, obeys a decay law described by the sum of two exponential terms which are attributed to the deexcitation of the ${}^3{P}_1$ and ${}^3{P}_2$ states. The decay constants are estimated by the maximum likelihood method applied to a Poisson statistical law. In order to correctly determine the collision rate constants, it is important to account for variations of the apparent lifetime according to the gas concentration. Analysis of both systematic experimental errors and statistical errors leads to a good estimation of the accuracy of the results obtained. For each mixture, the variation of the time constants as a function of partial pressures allows a determination of the resonance broadening coefficient and van der Waals broadening coefficient of the transition studied, as well as the two- and three-body inelastic collision rates relative to the ${}^3{P}_1$ and ${}^3{P}_2$ states. There exists no energy transfer between the two gases. For binary rare-gas mixtures, where only the heavier gas is excited, homonuclear and heteronuclear three-body reactions account for the decay of the ${}^3{P}_1$ state. Nevertheless, for the ${}^3{P}_2$ state we observe both two- and three-body collisions. In order to simulate resonance radiation trapping, a numerical method based upon Monte Carlo techniques was used. Calculations were first performed and validated for an infinite cylinder. The difference between calculation and experiment was less than 1%. Then the program was adapted to our real experimental conditions and applied to the binary mixtures studied. A good agreement was found between experiments and calculations. Furthermore, our program allows us to obtain information not easily obtained experimentally.