The Jahn-Teller effect in a p state equally coupled to E_g and T_2g vibrations

The Jahn-Teller Hamiltonian for an electronic p state equally coupled to E_g and T_2g vibrations in cubic symmetry, is diagonalized numerically. The invariance of the phonon Hamiltonian under the five dimensional rotation group, R₅, is used to get the matrix elements, and for this some fractional parentage coefficients for the reduction of R₅ to R₃ are calculated. The reduction factors K(E) and K(T₁) are calculated, lineshapes and zero phonon line intensities are given for s to p and p to s transitions. The wavefunction in strong coupling is worked out in a new coordinate system, and its properties match those derived from the numerical diagonalization. The s to p lineshapes are markedly different from those calculated by semiclassical methods, even in strong coupling.