ANOMALOUS INTENSITIES IN WEAK PERPENDICULAR BANDS OF $CO_{2}$
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Date
1955
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Publisher
Ohio State University
Abstract
Based on Nielsen’s general theory of rotational intensity anomalies induced by Coriolis interactions in polyatomic molecules, a quantitative explanation can be given for the intensities of individual lines and integrated branches in the weak perpendicular bands of $CO_{2}$. In addition to the well-known band at $2077 cm^{-1}$, we have observed a number of other perpendicular bands in the $5-\mu$ region, as well as the $1 3^{1} 0$ band at $3339 cm^{-1}$. In all these bands the intensity of lines in one branch increases continuously above the normal, while in the opposite branch (usually the R-branch) the intensity decreases to zero and then returns at higher J. Theory and experiment both require that the rigid-rotation intensity expressions be multiplied by ${F}_{v} = (1 + \zeta_{v}{m})^{2}$, where m is the ordinal number of the line, and\[ {\zeta_v}={B(\omega_{2}+\omega_{3})\over R_v(\omega_{2}\omega_{3})^{1/2}}{\sum\limits_{v^{\prime}}}{R_{v^{\prime}}}{C_{vv^{\prime}}}/(E_v-E_{v^{\prime}}) .\] Here, $R_{v^{\prime}}$ is the dipolar transition moment to the observed perpendicular band; $R_v^{\prime}$ the transition moments to all parallel bands $v^{\prime}$; and the $C_{vv^{\prime}}$ coefficients that may be calculated by perturbation theory from the vibrational wavefunctions and the energy spacings of the levels. The large values of $\zeta_{v}$ in the present instance result from the smallness of $R_{v}$ and the existence of the much stronger nearby parallel band at $2349 cm^{-1}$. We obtain for the $\pi-\Sigma$ bands[FIGURE]
Description
Author Institution: Laboratory of Astrophysics and Physical Meteorology^{*}, The Johns Hopkins University; Applied Physics Laboratory^{**}, The Johns Hopkin's University