Three-dimensional Collision Induced Vibrational Transitions in Homogeneous Diatomic Molecules

Download or read book Three-dimensional Collision Induced Vibrational Transitions in Homogeneous Diatomic Molecules written by C. Frederick Hansen and published by . This book was released on 1970 with total page 74 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.