For heavier elements with larger nuclear charge, the spin-orbit interactions become as strong as the interactions between individual spins or orbital angular momenta. In those cases the spin and orbital angular momenta of individual electrons tend to couple to form individual electron angular momenta.
In j-j coupling, the orbital angular momentum 'l', and spin angula momentum 's' of each electron are first coupled to form a total angular momentum 'j' for that electron. These single-electron total angular momenta are then combined into a total angular momentum 'J', for the group of electrons. This is in contrast to LS coupling, where the total orbital angular momentum L, and total spin S, of the system are calculated first and then combined to the total angular momentum 'J', of the whole system.
ji=li + si
J=∑ ji
Russel-Saunders coupling is more important for transition metals than j-j coupling.
In general, the results from both coupling schemes (L-S and J-J) are different.