Influence of Vibration-Rotation Interaction on Line Intensities in Vibration-Rotation Bands of Diatomic Molecules

Abstract

The influence of vibration-rotation interaction on line intensities in vibration-rotation bands of diatomic molecules had been recognized and treated approximately many years ago. In the present paper matrix elements have been calculated for the P and R branches of the 0—1, 0—2 and 1—2 transitions taking into account the interaction of rotation and vibration as well as the mechanical and electrical anharmonicity. For the 0—1 and 1—2 transitions the intensities of corresponding absorption lines in the P and R branches are proportional, in first order approximation, to [1+4γθJ]J and [1—4γθ(J+1)](J+1), respectively, where J is the rotational quantum number of the initial state, γ=2Be/ωe, θ=M0/M1re and M0 and M1 are the first two coefficients in the electric dipole moment expansion about the equilibrium internuclear distance re. Corrections to the above expressions that are proportional to γ2 have also been obtained. Formulas are given for the total integrated band intensity and for the line intensities summed over each branch taken individually. In the case of certain molecules, such as HCl for which θ≅1, it is possible to determine the magnitude of sign of θ by applying the above analyses to experimental data. For molecules such as CO, where θ≪1, the effect is negligible for the fundamental transition. A semiclassical interpretation of the influence of vibration-rotation interaction on line intensity has also been given.