Do you have any reference for this statement? Does it mean that having two electrons, one with ##l=0,m_l=0,m_s=1/2## and the other ##l=2,m_l=2,m_s=1/2## (so ##L=2##, ##S=1##) is not allowed?UAn alternative expression of the rule (and one that relates directly to observables) is that L+S must be even in the CM frame (equal and opposite momentum) for any pair of identical particles, where L is the net orbital angular momentum and S is the net spin angular momentum.
Good question! The L+S rule comes from SU(2) couplings given the usual anti-symmetry. Off the top of my head I think the answer to your question is that you can't get those two specific orbital states in the CM frame because of the spatial symmetry relating the angular co-ordinates (their momenta point in opposite directions). So, for instance you could have l1 = l2 = 1 and then the L=1 state would require s1 = s2. From memory I think the original rule comes from the classic Jacob & Wick* paper on helicity states, but you can also find it in my spin-statistics papers (which I haven't linked because they are not accepted mainstream for other reasons). PM me if you want further information.Do you have any reference for this statement? Does it mean that having two electrons, one with ##l=0,m_l=0,m_s=1/2## and the other ##l=2,m_l=2,m_s=1/2## (so ##L=2##, ##S=1##) is not allowed?