Analysis of Relaxation Processes in a Multilevel System. A Many-Shot Expansion Technique

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Abstract
The relaxation of a gas of polyatomic molecules, excited to a particular energy, is analyzed in terms of a random walk through all relevant energy states to yield the various stable products. The quantum yield is taken as the probability of forming a given one of these products. This relaxation problem is solved by means of an asymptotic, natural expansion in terms of the events in the process which are physically the most significant. The first term in this many‐shot expansion is the strong collision result. For nearly strong collision processes and nonequilibrium systems this many‐shot expansion yields a rapidly converging series for an arbitrary ordered set of transition probabilities, and hence constitutes a computationally useful solution to the Pauli master equation for such a nonequilibrium system. The relaxation problem is analyzed in terms of some assumed sets of collisional transition probabilities, including a model that assumes statistical equilibration of vibrational energy in every collision complex. It is shown in an application to an actual laboratory system that such a highly efficient model predicts many‐shot behavior only slightly stronger than some recently observed experimental results.