Spin–orbit coupling
Time:05/24/2011
As we sawin the examples of Chapter 2, an electron with orbital angular momentumbehaves like a circulating electric current, and so has a magnetic moment with anassociated magnetic field. In addition, an electron possesses a magnetic momentas a result of its spin. The magnetic moment from the electron’s spin interacts withthe magnetic field from its orbital motion. The resulting interaction is called thespin–orbit coupling.
The magnitude of the spin–orbit coupling is determined by the charge on theatomic nucleus, which in turn depends on the atomic number, Z. This can beunderstood by pretending that the electron is fixed in space, with the nucleusorbiting around it, rather than the other way around. The current generated bythe circulating nucleus is stronger for a larger nuclear charge. In fact the spin–orbit interaction is proportional to Z4 . As a result the spin–orbit interactionis almost negligible in the hydrogen atom, but increases rapidly with atomic number.
The way in which we calculate the total angular momentum of all the electrons in an atom, given the l and s quantum numbers of the individual electrons, depends on the relative magnitudes of the orbit–orbit, spin–orbit, and spin–spin couplings.http://www.everbeenmagnet.com
In the remainder of this section we will discuss two different schemes for estimating the total angular momentum of a many-electron atom. This is not straightforward,but it is very important, since it’s the total angular momentum of the electrons which determines the magnetic moment of an atom. And that, after all, is what we are interested in!
