HERMAN-WALLIS FACTORS FOR CARBON DIOXIDE CALCULATED BY DIRECT NUMERICAL DIAGONALIZATION (DND)

Calculations of Herman-Wallis factors for observed isotopic variants of carbon dioxide have been made by including the mixing of the perpendicular and parallel components of the dipole moment function which results from the Coriolis diagonalization. Comparisons with experiment and recent calculations using perturbation theory will be presented. Comparison of the observed and calculated Herman-Wallis parameters for the P- and R-branches will be shown for several bands in the 5- and $3-\\mu m$ regions. Good agreement has been obtained for most of the perpendicular bands in these regions. One particular band at $1881 cm^{-1}$ (20003 - 01101) has an experimental band intensity about one half that of the DND prediction. This prediction is effected strongly by the correlation with the ground state transition at $1932 cm^{-1}$ (11102 - 00001). When the effective transition intensities are plotted as functions of m for the P- and R-branches of the $1881 cm^{-1}$ band, one realizes much better agreement with the actual observed line intensities. The Q-branch Herman-Wallis parameters for the $15-\\mu m$ region also show excellent agreement with recent $observations.^{1}$ A phenomenon which has not been fully appreciated before is the presence of a separate term linear in J, derived from the Coriolls interaction of Q-branch lines. The effect in this region is that the J(J+1) dependence of the Q-branch Herman-Wallis factors, as derived for example by $Watson,^{2}$ is not strictly correct. This effect is even more striking in the 5- and $3-\\mu m$ regions.