CALCULATED INTENSITIES AND VIBRATION-ROTATION INTERACTION IN $^{12}C^{16}O_{2}$ MOLECULE

Abstract

The moments of transition of a vibration-rotation line, in a parallel infrared band without resonance, can be expressed as $R_{0}+$$R_{1}m+R_{2}m^{2} + \ldots$. The $R_{\ell}’ s$ are related to the constants $M_{ijk}$.. of the expansion of the dipole moment, along the normal coordinates, by the linear equations: $\Sigma\beta_{\ell}^{ijk}..$ M${ijk}..$. = R${\ell}$. These equations are used in two ways: (1) the M${ijk}..$ $’$s are determined from the experimental R${0}$$^{\prime}$s of several bands; (2) the values thus obtained for the M${ijk}..$ are used to calculate the R${\ell}$ with l $\neq$ 0. The coefficients $\beta_{\ell}^{ijk}..$ are calculated by using perturbed wave functions computed up to the fifth order, and the problem of their convergence is studied since the perturbating operators of the potential expansion are rather large in $CO_2$. The potential constants used are those determined recently by I. Jobard and A. Chedin (to be published). In case of resonance there is another contribution to the R${\ell}$$^{\prime}$s ($\ell \neq$ 0) which can be computed from R${0}$ and from the resonance phenomenon only (without the knowledge of the M$_{ijk}$$^{\prime}$.(s). In some cases, this contribution alone gives good agreement with experiment.