Relaxation of Vibrational Nonequilibrium Distributions. I. Collisional Relaxation of a System of Harmonic Oscillators

Abstract

A theoretical study has been made of the collisional relaxation of a system of harmonic oscillators prepared initially in a vibrational nonequilibrium distribution. Using harmonic oscillator collisional transition probabilities we have obtained expressions which describe the relaxation of initial nonequilibrium δ‐function distributions and Boltzmann distributions to their final equilibrium state. Our results show that an initial Boltzmann distribution with ``temperature'' T<sub>0</sub> approaches the final equilibrium Boltzmann distribution at temperature T via a sequence of intermediate Boltzmann distributions with time‐dependent ``temperatures'' $T_0⩾\mathcal{T}\mathrm{(t)⩾T}$ for the case T₀>T. The initial δ‐function distribution relaxes to the final equilibrium Boltzmann distribution via a sequence of nonequilibrium distributions. The study of the relaxation of the mean energy shows that this relaxation depends only upon the mean energy of the initial distribution, and is independent of the form of the initial distribution. The relaxation time for the mean energy was found to be 1/k₁₀θ where k₁₀ is the collisional transition probability per second for transitions between levels one and zero $$Word$$ where θ=hv/kT. The results obtained in this paper pertain to a system at sufficiently high pressure so that radiative transitions can be neglected as compared with collisional ones.