I am not familiar with the notation used on wikipedia (http://en.wikipedia.org/wiki/Triplet_state). Is there a more physcial way to explain the cause of the triplet state (maybe without referencing the wave function)?
In my book it says the folllowing:
'For the overall spin of the electrons exist the possibilities S = 0 and S = 1, which is >why the term scheme of the Helium atom splits in a singulet and a triplet system.'
I also found that J (total angular momentum quantum number) = L+-S can be 0,1 and 2 but I can't see why.
On a related note: does the intercombination prohibition mean that one helium atom can only be singulet or triplet forever?
Edit1: Thanks for your quick answer. But aren't you implying in your solution that L=0 (due to L-S <= J <= L+S)?