Two‐Hilbert space formulations of the quantum statistical mechanics of reactive fluids: Dimer formation and decay

A two‐Hilbert space formalism is first used to develop a general class of representations for the quantum mechanics of N‐particle reactive systems. Here the N‐particle Hilbert space ℋ_N is supplemented by a larger arrangement channel space 𝒞_N of vectors with Hilbert space valued components for each N‐particle clustering, and an injection mapping of ℋ_N vectors into ‘‘physical’’ 𝒞_N vectors. Such representations, for which components of the latter vectors carry an appropriate physical clustering interpretation, provide a rigorous and flexible basis for describing the statistical mechanics of reactive fluids, where atoms and molecules are treated on an equal footing (the molecular picture). Corresponding equilibrium multispecies fugacity or virial expansions follow immediately. Here we focus on analysis of the (previously derived) arrangement channel BBGKY hierarchy for a system where recombination and dissociation, as well as exchange reactions, occur. This formulation (coupled with a corresponding scattering theory) automatically suggests a reactive Boltzmann ansatz which incorporates (standard) noninteracting asymptotic dynamics only for two‐molecule nonreactive and reactive exchange collisions. In contrast, e.g., with three molecule recombination, two‐molecule dynamics for all three pairs is included (as required for a description of recombination via gradual stabilization of metastables). Finally we compare the resulting reduced form of appropriate channel space hierarchy equations, for a process involving dimer formation and decay, with the corresponding kinetic equations of Lowry and Snider.