Quasiclassical theory of the dynamical E × E Jahn-Teller effect including spin-orbit interaction

The dynamical Jahn-Teller effect including spin-orbit coupling is considered in the coordinate and momentum representations of the nuclear motion. The momentum representation is used for the asymptotical solution of the dynamical equations in the quasiclassical Landau-Zener parametric limiting case. Vibronic energy levels of the E E Jahn-Teller effect with spin-orbit coupling are calculated from the quasiclassical secular equation. They are compared with numerically exact energy levels obtained by the diagonalization of the Hamiltonian matrix in a harmonic oscillator basis. The comparison reveals reasonable accuracy of the quasiclassical approximation for a wide range of quantum numbers and system parameters. The quasiclassical analysis provides insight into the nature of the non-adiabatic dynamics of E E Jahn-Teller systems with spin-orbit coupling.