Vibrational relaxation in fluids: Calculations based on a many-body scattering formalism

We evaluate the density dependence of the rate constant for vibrational to translational energy relaxation of a dilute diatom in a fluid based on an expression we recently obtained. The results are compared with experimental data on H2 relaxation by H2 over a wide range of density. The rate constant is expressed as a time correlation function of the inelastic potential responsible for the vibrational transition, with time evolution occurring on the two potential surfaces corresponding to the initial and final oscillator states. A cumulant expansion method is used to relate this two-state evolution to correlation functions on one surface, and leads to correlation functions of the fluid density relative to the diatom’s location. The relative density correlation function is evaluated approximately by further development of a kinetic theory for the motion of a specific pair of particles in a dense gas. The rate constant is related to the solution of a generalized Smoluchowski equation for the distribution function of the specific pair, under the influence of the potential of mean force and a space and time dependent diffusion coefficient. The dilute gas rate constant is calculated using the cumulant expansion method and compared with the results of conventional atom–diatom scattering. The calculated dense fluid rates without cumulant corrections are compared with the experimental rates. The effect of the cumulant corrections on the dense fluid rates are evaluated and found to be small, which we attribute to the approximate method of their calculation. A detailed discussion of the discrepancy between calculated and experimental rates is given. A comparison of our theory with the independent binary collision model is made.