Analytical Theory of Multiquantum Vibrational Excitation in Molecular Collisions

Multiquantum vibration–translation energy transfer is considered within the framework of the distorted‐wave approximation. The restriction to harmonic‐oscillator selection rules is removed by treating any transition as a sequence of virtual one‐quantum transitions, permitting retention of all the vibrational states, but only the initial and final translational states, in the eigenfunction expansion. Vibrational matrix elements are the same as those of Rapp and Sharp, but translational wavefunctions include the effect of energy transfer; consequently, excitation probabilities display more complicated dependence on final vibrational quantum number than do the classical results. Cross sections for CO compare favorably with Marriott's numerical studies. Relaxation times compiled from the cross sections exhibit a three‐part temperature dependence: (1) at very low temperature, the relaxation time is exponential in $\text{1\hspace{0.17em}/\hspace{0.17em}T}$ , (2) in a large range of intermediate temperatures, relaxation is described by a multiquantum generalization of the Landau–Teller theory, exact within the restriction of weakly coupled states, (3) at very high temperature, the relaxation time is given by an impulsive formula.