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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 Îµ5, uniformly for three bounded vibrational quantum numbers n1, n2, and n3; and nuclear angular momentum quantum numbers â â ¤ kÎµ-3/4 for k > 0. Here the small parameter Îµ is the fourth root of the ratio of the electron mass to an average nuclear mass.