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In general, J = L + S

For small atoms, LS coupling dominates the angular momentum related component of the Hamiltonian. That means we calculate:

L

_{total}= l

_{1}+ l

_{2}+ ....

S

_{total}= s

_{1}+ s

_{2}+ ....

and then,

J

_{total}= L

_{total}+ S

_{total}.

For larger atoms we calculate j = l + s for each electron before summing:

J

_{total}= j

_{1}+ j

_{2}+ ....

So for smaller it atoms it seems like we can think of all the electrons as one single particle with the combined properties of all the electrons. This suggests that the electrons do not interact with each other at all. I mean that the spin and the angular momentum do not effect one another.

For the larger atoms, we think in terms of total angular momentum. This suggests that the spin and angular momentum of electrons may effect other electrons but that if we know the total angular momentum of each single electron then we know everything we need to know.

Am I drawing reasonable conclusions here?