Nonequilibrium Effects in Recombination-Dissociation Kinetics II

The selfconsistent theory of recombination-dissociation kinetics developed in an earlier article is derived in a more rigorous manner. A noniterative solution is obtained for the resulting equations describing the nonequilibrium distribution of the internal molecular energy levels. This method of solving these equations also leads to a number of interesting mathematical and physical insights about the importance of nonequilibrium effects in recombination-dissociation kinetics. Implicit in these equations is a method for calculating the vibrational relaxation times for both recombination and dissociation reactions. These same equations also arise in calculating the rate constant for a nontrivial model of a dissociating diatomic molecule. The mathematical techniques used to derive this information also allows us to show that the selfconsistent theory is really a generalization of the conventional steady-state approximation and a special case of a projection operator formalism for solving problems in nonequilibrium statistical mechanics.