Exact solution for the dynamical Jahn-Teller effect in E ⊗ ϵ and Γ8 ⊗ τ2 systems

The analytical formulation of the dynamical J-T problem leads to a system of two ordinary linear first order differential equations, whose solutions are required to belong to the space of entire functions. This condition determines the energy eigenvalues. It can be formulated in terms of a convergent continued fraction which defines a transcendental equation between the interaction constant and the energy (with the angular momentum quantum number as parameter). For an estimate the continued fraction is approximated with high accuracy by a periodic continued fraction in which the first m partial numerators are treated exactly. In this way we derive the eigenvalue condition that had been conjectured in [14].