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The one-dimensional, semiclassical theory of vibrational transitions in diatomic molecules is extended to three dimensions. Simple exponential interaction potentials are assumed and are spherically averaged to determine the collision trajectory that defines the perturbation. For use over the range of temperatures where small perturbation theory applies, fully analytic approximations are derived for the cross sections, the rate coefficients, and the relaxation rates. Vibrational transitions (predominantly changes of one vibrational level) are found to be accompanied by simultaneous rotational transitions (predominantly changes of zero and two rotational levels) with the result that vibrational transition rates are increased by 50 percent or more. The three-dimensional theory enables one to determine both the gradient and the magnitude of the potential, whereas only the gradient can be determined with one-dimensional theory. The theory can be fit to data reasonably well by appropriate choice of an "effective" interaction potential. This potential is considerably steeper and of shorter range than potentials appropriate for scattering. This is consistent with the concept that many interaction potentials exist for molecules, just as for atoms. We conclude that the steeper inner potentials are primarily responsible for vibrational transitions, whereas the outer potentials are primarily responsible for scattering.
Physical Chemistry, A Series of Monographs: Active Nitrogen presents the methods by which active nitrogen may be produced. This book is composed of five chapters that evaluate the energy content, molecular spectrum, and the emission of active nitrogen. Some of the topics covered in the book are the summary of light-emitting systems of active nitrogen; analysis of Long-Lived Lewis-Rayleigh Afterglow theory and Ionic theory of Mitra; reactions followed by induced light emission; and characteristics of homogeneous recombination. Other chapters deal with the analysis of metastable molecule theories and the mechanisms for reactions of active nitrogen involving direct N(4S) attack. The discussion then shifts to the rate constants for reactions induced by direct N(4S) attack. The evaluation of the Short-Lived Energetic Afterglow theory is presented. The final chapter is devoted to the examination of emission from molecular species with electronic energy levels below 9.76 eV. The book can provide useful information to physicists, students, and researchers.
A simplified mathematical model is derived that is useful for studying the effects of vibration-dissociation coupling in fluid flows. The derivation is based on energy-moment procedure for simplifying the master equations. To obtain the model equations it is assumed that the vibrational energy can be approximated by the introduction of two vibrational temperatures. The effects of molecular anharmonicity are also accounted for in an approximate manner. The parameters contained within the equations are evaluated by making comparisons with experimental data. It is shown that the model contains the minimum required structure allowing favorable agreement with existing experimental data. Numerical solutions are given for the quasi-steady zone behind a normal shock wave, for the complete structure of a shock wave, and for nozzle flow. The results provide the appropriate pre-exponential temperature dependence of the effective dissociation rate, yield and induction time before dissociation is observed, and, in the case of expanding flow, yield one-fourth less effective relaxation time than the Landau-Teller theory. The thermodynamic quantities for the vibrational mode (partition function, internal energy, and specific heat) agree accurately with like quantities evaluated from spectroscopic data. By the introduction of appropriate assumptions it is shown that the equations reduce to a form identical to the Marrone-Treanor model except for a "truncation factor". When the vibrational temperatures are not large, the model is identical to that of Landau and Teller. The numerical procedure used to integrate the system of rate and flow equations is also described.