ANALYTICAL TREATMENT OF THE QUADRATIC AND NONRELATIVISTIC RENNER-TELLER EFFECT FOR A TRIATOMIC MOLECULE IN A PI-ELECTRONIC STATE .2. HIGH-ENERGY AND HIGH ANGULAR-MOMENTUM LIMIT

This work presents an analytical approach to the Renner-Teller effect in the high energy and high angular momentum limit from a quantal viewpoint, and deals with a linear triatomic molecule in a PI electronic state within the harmonic oscillator approach, ignoring the spin-orbit coupling. The second order ordinary differential equation in the complex plane that results from a recently reported matrix-integral transformation is of singular perturbation type like that of the high energy limit, but it cannot be solved fully employing the matched asymptotic expansions method. Nevertheless, with the help of physical arguments, exponentially small energy splittings at the Fermi resonance points have been obtained and, taking into account earlier semiclassical results, a reasonably good quantization condition for the vibronic energy levels has been determined. On the other hand, the nonadiabatic region corresponds to deep under barrier positions of the system.