# selection rules and singlet state

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?

• 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. – QuantumDot Jun 8 '16 at 12:22
• 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. – Emilio Pisanty Jun 8 '16 at 12:37

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.