Kinetic theory of dimer formation and decay

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Abstract
Guided by the equilibrium statistical mechanics of ideal gas mixtures, we postulate a form for the density operator ρ(N) for an N‐atom gas consisting of M monomers and D dimers (M +2D = N). The reduced density operators ρ(n) derived from ρ(N) are investigated and it is shown how ρ(1) and ρ(2) are related to the monomer density operator ρf and the dimer density operator ρb. Kinetic equations for ρf and ρb are obtained which include the effects of bimolecular collisions and those termolecular collisions which lead to either dimer formation or dissociation. These equations are ``derived'' from the N‐atom von Neumann equation within the philosophy of the Boltzmann equation; that is, assuming molecular chaos before the collision event. This coupled pair of kinetic equations for ρf and ρb is a natural generalization of the Boltzmann equation to include atomic recombination and diatomic breakup in gaseous systems.