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I was looking at the example of a helium neon laser where the helium atoms can have excited atoms that arent allowed to decay back into the ground state because they violate selection rules of $\Delta l = ^+_-1$ and $\Delta J,m_j=^+_-1 , 0$. Why do the selection rules apply only 1 way? I wouldve thought any excited states that are forbidden to decay back to the ground state ought not to be allowed to be excited into? How can an electron go up one way but be forbidden to fall back to the same energy level from where it was originally excited?

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Metastable states can get populated by relaxation from more highly excited states. And those more highly excited can by populated by various mechanisms, for example electrical discharge, electron transfer, etc.

That is why there are two gases in this laser.

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Well the selection rules for a transition depend upon the interaction being used and any approximations applied. The rules you refer to come form the dipole approximation applied to the interaction of charged particles with single photons.

As you guessed, if modelling both absorbtion and emission of photons in this scheme then the selection rules apply to both types of transition so indeed if single photons excite electrons in this approximation the same selection rules apply. Incidentally these rules are strongly related to the fact that the photon has spin 1 and is massless (so only the $\pm 1$ helicity states are present).

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  • $\begingroup$ "As you guessed, if modelling both absorbtion and emission of photons in this scheme then the selection rules apply to both types of transition" I am a bit confused about this. In the context of a HE NE laser, I though the idea was that an electron was excited into states which it could not decay back from is this a misunderstanding? I feel that in the context of both the answers here, it is much more likely that the electron was excited into a higher energy state which then relaxed into the meta stable state, rather than directly being excited into it via the ground state. $\endgroup$ Jan 10, 2020 at 20:52
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    $\begingroup$ As I said, if you have a more complicated situation that is not well described by the dipole approximation (likely for laser physics) then the selection rules can very easily change. $\endgroup$
    – nox
    Jan 10, 2020 at 21:03

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