A quantum field theoretic approach to the calculation of reduction factors in Jahn-Teller systems. I. General theory

Abstract

Ham reduction factors are defined in the context of a field theoretic formalism and are thus generalised to cover arbitrary choices of electronic states, linear and nonlinear ion-lattice couplings, anharmonic lattice interactions, the mixing of electronic levels, second- and higher-order reduction factors and notably the effect of temperature in populating a distribution of vibronic states. Symmetry considerations are integrated with the field theoretic formalism in diagram form. Calculational techniques are described in some detail. Comparison is made with a similar generalisation of the standard definition of the reduction factor, which however implies the choice of particular vibronic states and does not include the effects of finite temperature. Symmetry considerations allow the first-order reduction factor to be written as a sum of products of 6j symbols (of the relevant symmetry group) and physical parameters. This in turn prescribes the form of sum rules linking the reduction factors in some approximation. The most important sum rules are exact at second order if the ion-lattice interaction contains only time-even operators. As a concrete illustration of the results, a simple tetragonal example is analysed in some detail.