General Theory of Decay Processes in Molecules

In this paper a unified treatment of the decay theory is presented to reformulate the existing one in a more explicit form by treating radiative and vibronic interactions simulta neously. This treatment is based upon the Green function formulation in terms of the second quantization. Here the· molecular eigenstate is treated as a Fermion. The retarded Green function related to any physical processes is obtained by use of the method of equation of motion. From the analysis of the self-energy part, one and two-photon processes are discussed in detail. First, in order to compare the pr~sent treatment with perturbation theory or the configuration interaction method, it is applied to a simple system. Next, an application to a three-level system shows a good agreement with the results of Mower's theory. Finally, for the system consisting of a discrete state and a continuum, the radiative decay in the case of internal conversion is properly discussed under the approximation that only the diagonal part· of the self-energy part is taken into account. § I. Introduciion Many processes concerning ex.cited states of molecules are of great interest. The transition from one state to the other by absorption or emission of a photon is elucidated in detail by Heitler 1l on the basis of time-dependent perturbation theory. Recently, from studies of :fluorescence and phosphorescence in considerab ly large molecules, it has been noticed that intramolecular radiationless transi tions also play important roles. Thus the radiationless electronic relaxation process in molecules is of considerable interest as well as the radiative one in molecular spectroscopy. The radiationless transition between the electronic states of the same multiplicity is referred to an internal conversion, while the transi tion between states of different multiplicity is called intersystem crossing. In discussing the above processes, perturbation theory is not applicable in general, because the transitic,m occurs between nearly degenerate levels and the interaction energy is much large than the energy separation. Therefore a number of non perturbative treatments have been presented. In particular, Mower2l treated the 'stimulated transition between closely coupled unstable states. His treatment is based upon a Green function formulation for the transition amplitude in which the states of interest are selected by suitable projection operators. This method is originally the s~me as Feshbach's treatment in the nuciear reaction theory,