Coupling of angular momenta of many-electron atom

[boyu]

There are two cases introduced in the lecture notes, depending on strength of spin-orbital coupling in individual electrons, since $$V_{SL} \propto Z^{4}$$.

1) jj coupling, which is valid for large-Z atoms, where spin-orbital coupling > electrostatic replusion between electrons

2) L-S coupling or Russell-Saunders coupling, which is valid for low-Z atoms, where spin-orbital coupling < electrostatic replusion between electrons

My question is about the naming of these two cases: why is it called jj coupling for strong s-o coupling, and L-S coupling when it is weak?

 

[alxm]

It comes straight from how the individual orbital angular momenta (l) and spin angular momenta (s) combine to form the total angular momentum, J.

LS-coupling: J = L + S = sum(l) + sum(s)
jj-coupling: J = sum(j) = sum(l + s)