Pseudo Jahn-Teller effect for a double: effect of a tetragonal field on the cubic E⊗ε system

The effect of tetragonal splitting of the electronic doublet on the properties of the cubic E(X) epsilon Jahn-Teller system is investigated taking account only of linear Jahn-Teller coupling. Ham reduction factors appropriate to the tetragonal symmetry are introduced, and their connection with the cubic reduction factors is established. A simple relation between the vibronic matrix elements of vibrational and electronic operators is derived. Numerical calculations are performed for weak to intermediate Jahn-Teller coupling where the electronic splitting competes with the Jahn-Teller interaction. The vibronic ground doublet is studied in detail. It is found that the reduction factor corresponding to q can drop below 1 / 2 considerably. Experimental consequences for electron paramagnetic resonance on a 2 E state in a tetragonal field and for Mossbauer spectroscopy on a 5 E state split by magnetic exchange are discussed. The theory predicts the spectra to be markedly different from what is expected either for a tetragonal purely electronic state or for a cubic Jahn-Teller coupled state.