# QUADRATIC HERMAN-WALLIS CORRECTION FACTORS FOR SYMMETRIC-TOP MOLECULES. APPLICATION TO THE $H_{3}^{+}$ ION.

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 Title: QUADRATIC HERMAN-WALLIS CORRECTION FACTORS FOR SYMMETRIC-TOP MOLECULES. APPLICATION TO THE $H_{3}^{+}$ ION. Creators: Watson, J. K. G. Issue Date: 1990 Publisher: Ohio State University Abstract: The Herman-Wallis correction factors to the intensities of allowed rovibronic transitions of symmetric-top molecules can be written in the form $F = \{1 + A_{1}^{j} mj + A_{1}^{k} m_{K} + A_{2}^{JJ(Q)}\sqrt{[J(J + 1)} - m_{s}^{2} + A_{2}^{JJ(PR)}m_{J}^{2} + A_{2}^{KK}\overline{K^{2}} + A_{2}^{JK} m_{J}M_{K}\}^{2}$ where $m_{J} = \frac{1}{2} [J^{\prime}(J^{\prime} + 1) - J^{\prime\prime}(J^{\prime\prime} + 1), m_{K} = \frac{1}{2} [K^{2} - K^{\prime 2}]\overline{J(J + 1)} = \frac{1}{2} J^{\prime}(J^{\prime} + 1) + J^{\prime\prime}(J^{\prime\prime} + 1)]$, and $\overline{K^{2}} = \frac{1}{2}[K^{2}+ (K^{\prime 2} + K^{\prime 2}]$. 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 $A_{2}$ coefficients are related to the parameters $\Theta_{K}^{7}$ and $\Theta_{k}^{\beta 7}$ in the effective dipole moment $operator^{1}$. Values of the $A_{1}$ and $A_{2}$, coefficients obtained by fitting the ab initio line strengths of $H_{3}^{+}$ calculated by Miller and $Tennyson^{2,3}$ 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 $laboratory^{3,4}$ and from $Jupiter^{5}$. Description: $^{1.}$ M. R. Aliev and J. K. G. Watson, in Molecular Spectroscopy: Modern Research, Vol. III (ed. K. Narahari Rao), pp. 1-67 (1985). $^{2.}$ S. Miller and J. Tennyson, Astrophys. J. 335, 486-490 (1988). $^{3.}$ W. A. Majewski, P. A. Feldman, J. K. G. Watson, S. Miller, and J. Tennyson, Astrophys. J. 347, L51-L54 (1989). $^{4.}$ W. A. Majewski, M. D. Marshall, A. R. W. McKellar, J. W. C. Johns, and J. K. G. Watson, J. Mol. Spectrosc, 122, 341-355 (1987). $^{5.}$ P. Drossart, J.-P. Maillard, J. Caldwell, S. J. Kim, J. K. G. Watson, W. A. Majewski, J. Tennyson, S. Miller, S. K. Atreya, J. T. Clarke, J. H. Waite, Jr., and R. Wagener, Nature 340, 539-541 (1989). Author Institution: Herzberg Institute of Astrophysics, National Research Council of Canada, Ottawa URI: http://hdl.handle.net/1811/18209 Other Identifiers: 1990-RF-8