Table 4: Selection rules for the ro-vibration transitions in addition to $\Delta J = 0,\ \pm 1$. The transitions in brackets are weaker than the main transitions. For ro-vibrational transitions, the parity of Ka+Kc+v3 has to be conserved. Transitions of type a only occur for oblate molecules, whereas transitions of type c are only found for prolate molecules. Both oblate and prolate molecules can have b-type transitions.
Transition Criterion $\Delta K_{{a}}$ $\Delta K_{{c}}$
a-type $\mu_a \neq 0$ $0, \pm 2\ (\pm 4,\ ...)$ $\pm 1\ (\pm 3,\pm 5,\ ...)$
b-type $\mu_b \neq 0$ $\pm 1, \pm 3\ ( \pm 5,\ ...)$ $\pm 1, \pm 3\ ( \pm 5,\ ...)$
c-type $\mu_c \neq 0$ $\pm 1\ (\pm 3,\pm 5,\ ...)$ $0, \pm 2\ (\pm 4,\ ...)$


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