I've never liked the definition of forbidden transitions as "transitions not predicted under the broader approximation", because its rare that anybody actually lays out why a given approximation is used, and therefore why that approximation is inappropriate for the "forbidden" situation.

The reality is that with e.g. 21 cm Hydrogen, or 500.7 nm Oxygen (which I knew by heart, back in the day), its hard to keep a given atom in the appropriate state long enough for it to relax by emitting the appropriate photon. Indeed, we can't create a pure enough vacuum in a large enough chamber that such things happen frequently enough to be measurable.

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Calwestjobs 8 months ago | parent [-]

laser, maser, like, other excitation / energy saturation does not work here ?

	▲	petsfed 8 months ago \| parent [-]
		No, because you need ultra-cold or ultra-low density (or both, as with 21 cm hydrogen) gas. If your mean free path divided by your mean molecular velocity is significantly less than the relaxation time, then the the atom/molecule gets knocked out of the necessary high-energy state well before the transition occurs with sufficient frequency. With [O III] in particular, it only gets into the necessary state via collisions (that's the easy part) occurring in extremely low density plasma, but then it relaxes via photon emission (that's the hard part). So if it gets knocked around by another collision, then the photon never gets emitted in the first place.