A quantum field theoretic approach to the calculation of reduction factors in Jahn-Teller systems. III. Γ5, Γ8⊗(Σ( α1+ε + τ2)) in octahedral symmetry

Abstract

For pt.II see ibid., vol.16, no.14, p.2705 (1983). The method and results of the two previous papers are extended to triplet and quartet electronic states in octahedral symmetry. Explicit expressions are given for all reduction factors to fourth order, including nonlinear, anharmonic and symmetric interactions. Sum rules for reduction factors, and the conditions under which they are broken, are discussed in detail for each system, in the general coupling case, in the case where one coupling symmetry only is assumed, and in the case of equal coupling. A general proof is given for all Jahn-Teller systems, including tetrahedral and icosahedral systems, that sum rules associated with time-reversal considerations at second order are also valid at fourth order to the case of coupling to isoenergetic modes. For triplet systems weak tau 2 coupling together with nonlinear and anharmonic effects may be expected to have disproportionately large effects by inducing violations of sum rules and by introducing resonant terms. For quartet systems many novel sum rules are discussed. By testing such rules or by measuring the temperature dependence of a reduction factor it is possible in principle to determine whether either coupling symmetry is dominant and whether any of nonlinear, anharmonic and symmetric coupling effects are significant in practice.