# Spin orbit interaction and LS coupling

1. Apr 25, 2010

### ian2012

I hope someone can help me out here.

I am having difficulty understanding what the difference is between the spin orbit interaction and LS coupling scheme in atoms. I know the spin orbit interaction (or spin orbit coupling) is due to the interaction of say an electron's spin with it's orbital motion. But i am confused about the LS coupling, apparently the neglect of the spin-orbit interaction means the LS coupling approximation holds?

(My confusion starts with understanding the residual electrostatic interaction. Apparently when you have a two valence electron atom, the central field approximation cannot completely account for the repulsion between them. So for example, in silicon the ground configuration is: (1s2)(2s2)(2p6)(3s2)(3p2), however in an excited configuration: 3p4p, and due to LS coupling, you get 36 states, 6 terms... I can't picture what is going on?)

Last edited: Apr 25, 2010
2. Apr 27, 2010

### DrDu

If spin-orbit coupling is negligible, spin and orbital momentum won't talk to each other and are both conserved quantities and you can classify states by total orbital momentum L and total spin momentum S (besides the occupation of the orbitals).
The energy of states with different L or S will in general also be different once you go beyond the central potential approximation and take electronic correlation effects into account. (Spin is an important quantity because it also modifies the orbital part of the electronic wavefunction as the total electronic wavefunction has to be anti-symmetric. Compare the case of a dihydrogen molecule, where the bound state corresponds to an electronic singlett (paired electrons)).
In light atoms, spin-orbit interaction is small and you can then take it into account using perturbation theory for degenerate states. It will then lead to a splitting of the terms (specified by L and S) into term components differing in the value of total electronic angular momentum J.