Spin Selection Rule: Russell-Saunders vs. JJ Coupling

[djclub2005]

Does anyone have a good understanding of why the spin selection rule (delta S = 0) holds for Russell-Saunders coupling in smaller atoms, but not for jj-coupling in larger atoms? For example, a transition from a triplet 2P to singlet 1S in helium is "disallowed," but a transition from a triplet 6P to singlet 6P in Hg is allowed. Some explanations say that photons do not directly affect spin, but what about radio waves flipping spin in NMR/ESR?

Also, does anyone know why you can't go from, say, triplet 3S to singlet 2S? It seems that a spin flip 1/2 -> -1/2 should account for a photon's angular momentum, so this would be allowed?

I appreciate any input.

 

[alxm]

Does anyone have a good understanding of why the spin selection rule (delta S = 0) holds for Russell-Saunders coupling in smaller atoms, but not for jj-coupling in larger atoms?

Sure. First, let's clarify what the situation is: The angular momentum (L) and spin (S) are not independent quantities, so neither model is 'correct'. Rather, they're approximations based on the two extreme cases. In the Russell-Saunders approximation (LS-coupling), the assumption is that the spins combine to a total spin, S, and the angular momentum to a total L. This is only valid non-relativistically. That is to say that the relativistic fine structure levels have to be small in comparison to the splitting between LS levels.

In heavier atoms, relativistic effects lead to the fine structure being on the order of, or larger than the L and S coupling. You can no longer accurately describe the system in terms of its total L or S, and the total L and S are no longer conserved independently. So ΔS = 0 is not necessarily the case anymore.

Of course, since LS coupling is an approximation, a 'forbidden' transition just means a 'very unlikely' one. Which is all illustrated nicely by phosphorescence phenomena, which is usually due to excitation into a triplet state, followed by a radiative transition back to a singlet - the unlikelihood of which makes it a slow process.

For example, a transition from a triplet 2P to singlet 1S in helium is "disallowed," but a transition from a triplet 6P to singlet 6P in Hg is allowed. Some explanations say that photons do not directly affect spin, but what about radio waves flipping spin in NMR/ESR?

They're flipping the spin orientation, but not actually changing the overall spin state. You're going from, say, doublet(up) to doublet(down), not from singlet to doublet. Which is why ESR requires an open-shell molecule, and NMR a nucleus with non-zero spin. And you also need a big magnetic field to spit the spin levels between up and down (Zeeman effect).

Also, does anyone know why you can't go from, say, triplet 3S to singlet 2S? It seems that a spin flip 1/2 -> -1/2 should account for a photon's angular momentum, so this would be allowed?

It's not allowed, insofar LS-coupling is a valid approximation.

 

[djclub2005]

Thanks axlm, that was very helpful - I have one more raised question, if you don't mind?

For phosphorescence, you say there is a radiative transition back to a singlet. My understanding of a "forbidden" transition was that it could only be done through an intermediate generated through kinetic energy transfer, followed by an allowed radiative decay to the final state. When we see phosphorescence then, are we seeing the second allowed decay which comes by slowly due to the much lower probability of kinetic energy transfer/collisions, or are we actually seeing a "forbidden" transition in one step?

Thanks again for the great response.