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- TL;DR Summary
- Disregarding some of spin-orbital states by exclusion principle

If we combine the two spin-orbital states with ##l=1, s=1/2##, we obtain the combined states with ##J=3/2## and ## J=1/2##. Also, we know that the exclusion principle forbids the two electrons with identical spin-orbital states ##|l,s,m_l,m_s>##. If we combine the two combined states with ##J=3/2##, we would have the resultant states with ##J=3,2,1,0##. Among these resultant states all the states with ##J=3## and ##J=1## are forbidden according to the exclusion principle. I am justified how the states with ##J=3## and ##m_J=3,2,1,-1,-2,-3## are constructed from the two identical spin-orbitals with ##|l=1,s=1/2,m_l,m_s>## and why they are forbidden. However, I can not understand why the state with ##J=3, m_J=0## is forbidden by exclusion principle. I appreciate any help.