Diagram methods for reduction factor calculations in Jahn-Teller systems (1981)
AuthorsPayne, S. H.show all
A novel method is developed for the description and calculation of Ham reduction factors in 'Jahn-Teller active' systems which are weakly coupled to many lattice modes. Diagrammatic many-body perturbation theory for finite temperatures is combined with diagrammatic group theory into a coherent formalism, whose essential features are readily visualized. The method lends itself to economical calculation of reduction factors (given the recent availability of 6j symbols for crystal point group) and also to generalization of the traditional single multiplet 'Jahn-Teller problem'. Multimode effects may be distinguished experimentally by searching for particular combinations of reduction factors, associated with particular Feynman diagrams, that vanish to all orders in systems with a continuous symmetry group and to fourth order in all systems, within a single-mode coupling model. General expressions for reduction factors are derived for octahedral systems up to at least fourth order, and including lattice anharmonicity and non-linear electron-phonon coupling. The effects of symmetric vibrations and intermultiplet coupling on reduction factors, and generalization to second order reduction factors, are investigated.