On the interpretation of vibrational relaxation times

Abstract

Rate laws for the evolution of vibrational energy level populations are derived when the Bethe–Teller law is obeyed. It is assumed that a Boltzmann distribution is maintained via rapid V–V processes. A variety of different rate laws result depending on the size and direction of the perturbation, the extent from equilibrium, and how classical the oscillator is at the initial and final conditions. An earlier analysis by Breshears is shown to be a special case. A prescription is given for procedures to compare relaxation times obtained from shock tube experiments and from laser-induced fluorescence experiments, when T–V energy transfer processes are rate-determining. Corrections for thermal effects are included. Shock tube, fluorescence, and chemical activation experiments are proposed which provide meaningful conditions for testing the Bethe–Teller law and for testing the existence of a Boltzmann distribution.