# Conservation of Angular Momentum: atomic transitions vs exciton decay

I have a question about the role of photon angular momentum in two different sets of selection rules:

• In atomic transitions within the dipole approximation, I've seen the selection rule as: $\Delta l = \pm 1, \quad \Delta m= 0, \pm 1, \quad \Delta s=0$ (eg here).

• Overall, this makes sense to me in terms of angular momentum conservation with the photon being spin-1.
• But when dealing with excitons in organic materials, I've heard that triplet (ie spin-1) excitons decay much more slowly because they require a spin-flip...and singlet (ie spin-0) excitons don't (see for example page 13 here).

• The requirement of a spin-flip means that a phonon must be involved (?) to supply angular momentum, which makes the radiative decay of triplets much less likely. And consequently, this limits the efficiency of organic opto-electronics because for every useful singlet produced, three less-useful triplets are produced.

But my question is why does the photon angular momentum play a role in atomic transitions, such that there must be a change in the orbital angular momentum of the electron, while it does not play a role in the selection rules of excitons, such that the decay of an exciton should itself conserve angular momentum (without the photon) in order to be likely?

Furthermore, if triplet exciton decay is forbidden by angular momentum conversation issues, why does the triplet creation probability seem not suffer that same suppression?

I feel that this must be related to one aspect of the atomic transition rule that I don't quite see as obvious, the $\Delta s=0$ requirement.

Anyhow, if anyone could supply some insight on this topic, I'd really appreciate it. Thanks!

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