Knowledge Bank

Angular momentum and irreducible tensor $methods1$ are used to elucidate the selection rules for a four-photon transition in symmetric-top molecules. The form of the eighty-one $(34)$ radiative transition operators between electronic states of different irreducible representations in the molecular point groups will be derived. The concomitant line strength over N and K states as well as special selection rules such as those for $K=0.\Delta K=0$, etc. will also be obtained, using the symmetry and angular momenta of the transition operators. For four-photon scattering between degenerate states, the special spin-selection rule for the permutational symmetry of the degenerate-state self products will be explained from the view point of time-reversal invariance.