I LS coupling and spin orbit interaction

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Why do you need a weak spin orbit interactions in individual electrons in order to use the LS coupling?
From what I know, we are free to combined angular momentum whenever [L1, L2]=0 and this should be true on the orbital angular momentum (and spin) of the electrons because they are differential operators of different electrons (different coordinates).
Moreover, even the above reason is enough for me, under spin orbit interaction, the orbital angular momentum and spin angular are good quantum numbers to indicate the state of an electron when using perturbation theory (they are n l s j mj).
So why?
 
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Thanks for the thread! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post? The more details the better.
 

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