Detailed Balance in Optical Transitions in Molecules and Solids

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Abstract
Recent theoretical and experimental work has shown that the simplest form of the Einstein equation relating induced absorption and spontaneous emission probabilities (characterized by Σ and τ−1) is not generally valid for impurities or color centers in solids, liquids, or molecules. Separate computations of these probabilities in systems exhibiting sizeable Stokes's shifts resolve some of the problems; they also disclose the difficulties involved in obtaining any connection between Σ and τ. Here we consider how the transition probabilities between a pair of electronic-vibrational states are related. Observable quantities, i.e., integrated absorption cross section and the radiative decay time, involve sums and averages over the vibrational states, and no definite theoretical information relates these quantities. However, there is a simple connection between induced and spontaneous emission probabilities. New experiments which could yield information about the rate of lattice relaxation are suggested from this point of view.