Theory of vibrational energy exchange rates in chemical and molecular lasers

A quantum mechanical theory of near resonant transfer of vibrational energy is formulated and used to calculate energy transfer processes in chemical and molecular lasers. This theory is based on the existence of an exact solution to the pair of coupled differential equations describing the resonant transfer of excitation. The solution to this problem is used as the basis for a distorted wave solution to the nonresonant transfer problem.3 This approach has a number of advantages over the Born approximation in that it does not constrain the particles to travel along linear trajectories. These trajectories are distorted by the off-diagonal as well as the diagonal elements of the potential energy matrix. This effect can be very important in molecular collisions, involving the transfer of rotational and vibrational energy. As an illustration of this effect, this two-channel theory of transfer is applied to a number of energy transfer processes of interest in CO
2
, CO, HF, and DF chemical and molecular lasers. This theory is then generalized to the
N
channel scattering problem and applied to the problem of vibrational-rotational energy conversion in hydrogen halide (HF, DF, HCl, DCl) lasers.