The interaction between the spin of the nucleus and the angular momentum of the electron causes a further (hyperfine) splitting of atomic states. It is called hyperfine because it is also order like the fine structure corrections, but it is smaller by a factor of about because of the mass dependence of the spin magnetic moment for particles.
The magnetic moment of the nucleus is
We computed the hyperfine contribution to the Hamiltonian for
For the hydrogen ground state we are just adding two spin particles so the possible values are . The transition between the two states gives rise to EM waves with cm.
We will work out the effect of an external B field on the Hydrogen hyperfine statesboth in the strong field and in the weak field approximation. We also work the problem without a field strength approximation. The always applicable intermediate field strength result is that the four states have energies which depend on the strength of the B field. Two of the energy eigenstates mix in a way that also depends on B. The four energies are
Jim Branson 2013-04-22