In an introduction I read the following sentences:

"In excited singlet states, the electron in the excited orbital is paired (by opposite spin) to the second electron in the ground-state orbital. Consequently, return to the ground state is spin allowed and occurs rapidly by emission of a photon."

I'm not really sure if I understand this correctly. What does "spin allowed" mean?.

Normally, the selection rules are $\Delta m=\pm 1$. If the electron just decays to the ground state, this shouldn't depend on the state of the second electron in the ground state, does it? Do the selection rules change if the whole Atom is in a singlet state?Btw when the Atom is excited, the Atom isn't in a singlet state anymore?

  • $\begingroup$ I'm guessing "spin allowed" means that spin of the excited electron doesn't need to flip in order to transition to the ground state. $\endgroup$ – QuantumDot Jun 8 '16 at 12:22
  • $\begingroup$ The electric dipole selection rules are $\Delta m=±1$ on the orbital angular momentum, with no change in the spin, because electric fields don't affect magnetic dipoles. To flip a spin you need a magnetic dipole transition (a.k.a. M1 transition), and those can happen (as can electric quadrupole E2 transitions for which $\Delta \ell=±2$) but they're so much less likely than electric dipole transitions that they're usually considered forbidden. $\endgroup$ – Emilio Pisanty Jun 8 '16 at 12:37

The "spin allowed" refers to the fact that the exited electron can decay to the ground-state orbital without changing it spin.

The proces is $|\uparrow_{es},\downarrow_{gs}> \to |\uparrow_{gs},\downarrow_{gs}>$ wich is ok.

The opposite $|\downarrow_{es},\downarrow_{gs}> \to |\downarrow_{gs},\downarrow_{gs}>$ is prohibited since $|\downarrow_{gs},\downarrow_{gs}>$ violates the Pauli exclusion principle. For this to decay, a spin-flip has to occur, an I assume that spin-flipping processes are more rare than simple emissions of photons.

  • $\begingroup$ D'oh, you answered 2 second after my comment! $\endgroup$ – QuantumDot Jun 8 '16 at 12:22
  • $\begingroup$ Does this mean that you can guess the selectrion rules somehow just by considering the pauli principle? $\endgroup$ – anonymous Jun 8 '16 at 12:52
  • $\begingroup$ @user9996 Not really, the section rules depend on which types of external processes affect you system. For instance, the section rules for the hydrogen atom (and harmoinc ocilator) come about by assuming a spatially constant electric field. The Pauli principle is more like a roadblock, it can prevent a selection rule that would otherwise be allowed. $\endgroup$ – Mikael Fremling Jun 8 '16 at 14:08

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