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_{F}and m

_{J}are the respective magnetic quantum numbers.

The relevant F selection rules are delta_m

_{F}= 0, 1 and -1, delta_F = 0, 1 and -1.

And similarly, the J selection rules are delta_m

_{J}= 0, 1 and -1, delta_J = 0, 1 and -1.

My question is, when considering a transition involving nuclear spin, in addition to satisfying the delta_F and delta_m

_{F}selection rules, do we have to also satisfy the delta_J and delta_m

_{J}selection rules at the same time?

A specific example involving two successive transitions is attached. The transitions satisfy the delta_F and delta_m

_{F}selection rules but violate the delta_m

_{J}selection rules. Would such a two step process be allowed or forbidden? I'd appreciate any insight. Thank you!