When resonance between vibration frequencies of polyatomic molecules sets in, the contacthyphen;transformation method proposed by Shaffer, Nielsen, and Thomas is not directly applicable. It has been shown by Nielsen that a contact transformation method may still be used to advantage when computing rotationhyphen;vibration energies to a second order of approximation, the transformation function being, however, a modified one. This problem is treated here when the question of the computation of the rotationhyphen;vibration energies is extended to a fourth order of approximation.
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