Knowledge Bank

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 $(J,K\pm 3)$ state, through vibration-rotation interaction, $\Delta K=3$ transitions are weakly allowed in $C3v$ molecules. From considerations of molecular symmetry and of time reversal symmetry the mixing term should be of the form $(J+2-J-3)J2+J2(J+2-J-2)$ or $(J+3-J-3)\Pi 2o+\Pi go(J+2-J-3)$. Such a term is derived from the symmetric rotor Hamiltonian by a perturbation $procedure.1$ The theory is applied to $NH3$. 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 $NH3$ recently observed by Cheung, Rank. Townes, Thornton and $Welch.2$