$\Delta K=3$ TRANSITIONS IN SYMMETRIC TOP MOLECULES.
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Date
1969
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Ohio State University
Abstract
Normally the electric dipole selection rules for rotational transitions in symmetric top molecules are $\Delta J = 0, \pm 1$ and $\Delta K = 0$. However, because of mixing of the (J.K) state with the $(J, K\pm3)$ state, through vibration-rotation interaction, $\Delta K = 3$ transitions are weakly allowed in $C_{3v}$ molecules. From considerations of molecular symmetry and of time reversal symmetry the mixing term should be of the form $(J_{+}^{2} - J_{-}^{3}) J_{2} + J_{2} (J_{+}^{2} - J_{-}^{2})$ or $(J_{+}^{3} - J_{-}^{3}) \Pi^{o}_{2} + \Pi^{o}_{g} (J_{+}^{2} - J_{-}^{3})$. Such a term is derived from the symmetric rotor Hamiltonian by a perturbation $procedure.^{1}$ The theory is applied to $NH_{3}$. In particular the probability of spontaneous emission from the (J = 2, K = 2) level to the (J = 1, K = 1) level is calculated to be $8.1 \times 10^{-10}$ of the allowed (J = 2, K = 1) to (J = 1, K = 1) transition. This electric dipole transition may play a role in equilibrating these two states of interstellar $NH_{3}$ recently observed by Cheung, Rank. Townes, Thornton and $Welch.^{2}$
Description
$^{1}$T. Oka. J.Chem. Phys, 47, 5410 (1967). $^{2}$A.C. Cheung, D.M. Rank, C.H. Townes, D.D. Thornton and W.J. Welch, Phys. Rev. Letters 21, 1701 (1968).
Author Institution: Division of Pure Physics, National Research Council of Canada
Author Institution: Division of Pure Physics, National Research Council of Canada