Jahn-Teller effect in EPR spectra: Three-state theory forE2orbital states in cubic symmetry

An effective Hamiltonian for an excited $A_1$ or $A_2$ vibronic singlet and a ground $E$ vibronic doublet is used to describe electron-paramagnetic-resonance spectra from ${}_{}{}^2{}_{}{}^{}E$ orbital states in cubic symmetry. The zero-field splitting between the ground vibronic doublet and the excited vibronic singlet, the strain interaction, and the Zeeman interaction are included. From perturbation theory an analytical solution is obtained as a function of (i) the ratio of the zero-field splitting $3\Gamma$ to the random-strain splitting $\delta$, (ii) the vibronic reduction parameters $q$ and $r$, (iii) the crystallographic orientation of the applied magnetic field, and (iv) the parameters needed to describe the Zeeman interaction for cubic symmetry. The random character of the internal strains is included in the numerical calculations of the line shapes and angular variations. From these calculations those features which characterize the static, "intermediate," and dynamic Jahn-Teller effects are presented for the {100}, {110}, {111}, and {112} planes and for the ground and excited states.