PHONON ANALYSIS IN MULTIPHONON TRANSITIONS

In the investigation of multiphonon transitions, single-mode or single-frequency models are widely used. In view of the fact that such oversimplified models can be seriously inadequate, the present work bridges the gap between the complexity of the general formal theory and the simplicity required for concrete applications by introducing the concept of multi-frequency models. That is, the theory is so formulated that a general system can be approximated by multi-frequency models of any degree of elaboration. A statistical thermodynamic formalism is developed for treating such multi-frequency models, which, on the one hand, greatly reduces the labour of calculation with such models and, on the other hand, leads directly to a simple statistical distribution law for numbers of phonons of each frequency participating in a multiphonon transition. Applications of the theory to concrete models lead to certain general conclusions on frequency dispersion effects in multiphonon transitions. The use of the theory is further demonstrated by fully accounting for the paradoxical experimental results reported by Jia and Yen that the isotopic substitution of H by D in CsMn Cl₃· 2H₂O reduces the multiphonon nonradiative transition probability of excited Mn²⁺ ion by more than ten-fold, and yet leaves the corresponding luminescence phonon sideband little changed. In the last section of the paper, the relation between the statistical thermodynamic formalism and existing multiphonon transition theory is elucidated, thereby the theoretical basis of the statistical formalism becomes clearly defined.