Resonance energy transfer and spontaneous photon emission

The Perrin-Forster theory of sensitized fluorescence is extended by replacing the Coulomb interaction wth its relativistic counterpart, the Breit interaction. The transition matrix element is evaluated in a multipole expansion. The matrix element i s found to be modulated by the retardation factor eikR and to contain terms whch fall off only as l/R. The relation of these terms to spontaneous photon emission and their application to exciton theory are discussed. The phenomenon of resonance energy transfer or 'sensitized fluorescence' was discovered experimentally by Cario and Franck (1923). They exposed a mixture of mercury and thallium vapour to a frequency of light which could only be absorbed by the mercury. The fluorescence spectrum of the mixture contained frequencies which could only be emitted by the thallium, demonstrating a transfer of excitation energy between the two species. An explanation of the phenomenon was proposed by J. Perrin (1926, 1927) on the basis of classical coupled oscillator theory. Later Kallman and Lon-don (1928) and F. Perrin (1932) put forward a quantum theory of resonance energy transfer which has since been improved by other authors, notably by Forster (1946, 1948, 1949, 1960). Many of the predictions of this theory have been verified by experiments on the sensitized fluorescence of organic dye solutions, together with experiments on the related phenomena of concentration depolarization and self-quenching of fluores-The basic idea of the Perrin-Forster theory can be seen from the following example. Let #n(l)#n,(2) represent the total wave function of two molecules with the first in an excited state and the second in the ground state. Let #n.(l)#fl,&?) represent the two-molecule system in the opposite situation, i.e. with the second molecule excited and the first in the ground state. If there is no interaction or overlap between the two molecules, and if the possibility of radiation is neglected, then both #n(l)#n.(2) and #f141)#n42) will be stationary states. However, if the two molecules are close to one another, their interaction will produce a certain probability per unit time 1 / ~ ~-~ for a transition in which the excitation energy is passed from the first molecule to the second. In the Perrin-Forster theory, the interaction energy which is responsible for the transition is given by I