Knowledge Bank

The Herman-Wallis correction factors to the intensities of allowed rovibronic transitions of symmetric-top molecules can be written in the form $F=\{1+A1jmj+A1kmK+A2JJ(Q)[J(J+1)-ms2+A2JJ(PR)mJ2+A2KKK2―+A2JKmJMK\}2$ where $mJ=12[J\prime (J\prime +1)-J\prime \prime (J\prime \prime +1),mK=12[K2-K\prime 2]J(J+1)―=12J\prime (J\prime +1)+J\prime \prime (J\prime \prime +1)]$, and $K2―=12[K2+(K\prime 2+K\prime 2]$. When different $(J\prime ,K\prime )-(J\prime \prime ,K\prime \prime )$ transitions mix together, the square root of the above factor can be applied to each transition moment. For parallel bands the terms in mK are absent. In fundamental bands the $A+2$ and $A2$ coefficients are related to the parameters $\Theta K7$ and $\Theta k\beta 7$ in the effective dipole moment $operator1$. Values of the $A1$ and $A2$, coefficients obtained by fitting the ab initio line strengths of $H3+$ calculated by Miller and $Tennyson2,3$ will be compared with the results of perturbation calculations. The correction factors are important at the high rotational temperatures observed in emission speetra in the $laboratory3,4$ and from $Jupiter5$.