Excited-state equilibration and the fluorescence-absorption ratio

In any complex system at temperature T the absorption cross-section and flu orescent power at a given photon energy are connected by a simple relation if the system is in thermal equilibrium while occupying one particular elec tronic excited state. Although this situation is impossible in principle be cause of finite excited-state lifetimes, it is often approximated to the ex tent that the simple relation, which is expressed as a linear function of e nergy with slope -1/k(B)T, holds in a variety of cases. (The usual symbols for Boltzmann's constant and absolute temperature are used.) Observed devia tions are of two principal kinds: a slope characteristic of some temperatur e T* other than ambient, and departures from a single pure straight line. T he latter may include seemingly random variations and in some cases multipl e regions of straight-line behavior. We have recently introduced an effecti ve temperature T*(E), derived from the actual local slope of the putative s traight line at energy E, which turns out to be a very sensitive detector o f deviations from the ideal and, we believe, from equilibrium in the excite d state. Plots of T*(E) display a variety of features. An anomaly in the T* (E) spectrum of chlorophyll a can be analyzed on this model, indicating a s econd weakly fluorescent state about 70 meV below the well-known Q(y) band. The cases of chlorophyll and many others are included in a selective revie w of applications of the universal relation to fluorescent systems.