l-Type Doubling in Energy Levels of Carbon Dioxide Coupled by Fermi Resonance

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Abstract
In this paper we discuss the l-type doubling in levels of linear molecules which are coupled by Fermi resonance; in particular we consider here a triad of such levels in carbon dioxide. In principle, it becomes necessary to consider simultaneously the perturbations related to both anharmonic resonance interaction and l-type doubling. A further analysis reveals, however, that we are justified in carrying out an approximate solution, in which we first consider the resonance interaction as if l-type doubling did not occur and subsequently find the energy levels associated with +l and —l as a result of small perturbations on the two-fold degenerate levels involved. It appears that the applicability of the well-known formula Δν=qJ(J+1), in which q is the l-type doubling constant, is inherent to this approximation. The agreement between q values computed by our method and those obtained experimentally is very satisfactory indeed.