The Born-Oppenheimer Approximation for Triatomic Molecules with Large Angular Momentum in Two Dimensions

We study the Born-Oppenheimer approximation for a symmetric linear triatomic molecule in two space dimensions. We compute energy levels up to errors of order ε⁵, uniformly for three bounded vibrational quantum numbers n₁, n₂, and n₃; and nuclear angular momentum quantum numbers â ≤ kε^-3/4 for k > 0. Here the small parameter ε is the fourth root of the ratio of the electron mass to an average nuclear mass.