A scaling theoretical analysis of vibrational relaxation experiments: rotational effects and long-range collisions

Expressions for the quantum number scaling of vibration-translation (VT) and vibration-vibration (VV) rates are derived. The derivation uses the recently developed scaling theory of non-reactive processes and invokes the assumption of rotational equilibrium. However, the VV and VT scaling relationships include rotational effects through the rotational energy gaps and the rotational distributions. The variables in this theory are a fundamental set of rates and the average collision range, l_c, for the particular inelastic process. The physically transparent meaning of these variables, combined with the a priori nature of the scaling coefficients, allows one to investigate actual dynamical effects and not just merely fit data. A detailed analysis of VV energy transfer in the COCO system is presented. Three conclusions are drawn: (1) rotational effects are crucially important in the scaling of the rates; (2) the process is predominantly long-range with l_c = 5.5 ± 0.5 au; and, (3) the available experimental data is consistent with single quanta vibrational changes in the VV rates.