Rotation–Vibration Coupling in Diatomic Molecules and the Factorization Method. I. Closed Form Formulas for the Vibration Intensities

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Abstract
It is shown that the factorization method followed by an “accelerated" operatorial formalism or an equivalent matrix procedure leads to explicit formulas for calculating transition matrix elements. The calculation has been completely carried out for the pure vibration case of diatomic molecules, for any degree k of the dipole moment Taylor's expansion. The intuitive approximate proportionality between the radial dipole matrix element and an overlap integral is demonstrated.

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