LS coupling

The central field approximation, in which all the electrons are reckoned to move in a common spherically-symmetric field. The rest of their repulsion, the part which is not spherically symmetric, is called the residual electrostatic interaction. It is easy to write down the mathematical form of this residual electrostatic interaction. The upshot is that the quantum numbers on which the energy of the whole atom depends are now ni; li; L; S, and this whole method of approximation is called LS coupling or Russell-Saunders coupling. The things which are coupled in this coupling are:
1. All the individual orbital angular momenta couple together to make ^L.
2. All the individual spin angular momenta couple together to make ^S.
The central field approximation is the correct starting point for all atoms, and after that it have both the residual electrostatic interaction and the spin-orbit interaction.
Zeeman Effect
The Zeeman effect is the name given to the splitting observed in spectral lines when the source of those lines is placed in an external magnetic field. Splitting of a single spectral line into three components in the presence of an external magnetic field is called the normal Zeeman effect. Any time the g-values of the upper and lower states are the same, this pattern results. When the g-values are different, much more complicated patterns are possible. These, for historical reasons, are called the anomalous Zeeman effect.