Transition Probabilities in Multilevel Systems: Calculation from Impulsive and Steady-State Experiments

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Abstract
The study of collision‐induced transitions of molecules in a system of many energy levels is discussed in an analysis of time‐dependent and steady‐state experiments. These results are used in a discussion, with numerical examples, of the difficulties in calculating the transition probabilities from observed population distributions. An intimate conceptual and mathematical relationship is established between two types of experiments which are possible at present. One is an impulse, or time‐dependent experiment such as excitation with a fast flash lamp and snapshot observation after a known delay time. The other is a steady‐state experiment in which molecules are fed into the system (a gas or a surface) at a single energy level, for example, and undergo transitions among the available levels in competition with a first‐order removal process such as spontaneous radiation or desorption from a surface. The ideas summarized above are used to develop procedures for calculating transition probabilities from observed population distributions. Numerical examples and qualitative considerations indicate that when transitions involving more than single quantum jumps are involved, the experimental data must be known to much higher accuracy than that desired in the transition probabilities. The difficulties increase rapidly as the number of levels in the system increases.