When an atom is placed in a magnetic field region, we can have two possibilities: , when the external field is way greater than the internal field produced by the motion of electrons, and viceversa . These two cases give two different hamiltonians of perturbation. Hence we do distinguish the normal and anomalous Zeeman effects:
- Anomalous Zeeman effect:
In exercises, unless it is specified, you can not determin whether a given is greater than or not and so you have to evaluate both energy split terms and . In conclusion we want to remember the hamiltonian of the spin-orbit coupling:
And its energy spectrum, in the basis, is:
- ↑ Spin-orbit effect can be neglected. Hence is a perturbation for a normal hydrogen-like hamiltonian. Hence here we work in the basis.
- ↑ Spin-orbit can not be neglected, hence it has to be considered as part of the global hamiltonian to which is a perturbation.Hence here we work in the basis.