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I am trying to find a resource that can explain how σ and ∏ lines obtain their polarizations.

I have not found resource that actually show the calculation or solid explanation that show this.The references are usually state that σ and ∏ have circular polarization and linear polarization respectively. But they did not explain why, assume that it is a given fact.

Some resources in the internet seems to explain this by conservation of angular momentum J. Since in Normal Zeeman Effect S=0 for both states involved in the transition, L is conserved. So, the resources reasoned that for Δml=1,-1 , a photon with spin 1 or -1 will be produced. They correspond to left and right circularly polarized light. For Δml=o, they state that there will be equal amount of photon with spin 1 and -1. This corresponds to a linearly polarized light. It seems a lot of hand waving argument.

I have checked some textbooks like Fowles' Modern Optics. It has 2 pages explanation with pictures. It interpret the transition as an oscillating dipole. The example discussed 1s and 2p transitions of Hydrogen atoms. The book do not give any calculation. I also prefer to have an explanation how to apply the explanation for different orbitals, not only 1s and 2p transitions.

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# Trying to find references for polarization effect of Normal Zeeman Effect

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