We can think of the nucleus as a single particle with spin
.
This particle is actually made up of protons and neutrons which are
both spin
particles.
The protons and neutrons in turn are made of spin
quarks.
The magnetic dipole moment due to the nuclear spin is much smaller than
that of the electron because the mass appears in the denominator.
The magnetic moment of the nucleus is

where is the

In any case, the nuclear dipole moment is about 1000 times smaller than that for e-spin or . We will calculate for states (see Condon and Shortley for more details). This is particularly important because it will break the degeneracy of the Hydrogen ground state.

To get the perturbation, we should find from (see Gasiorowicz page 287) then calculate the energy change in first order perturbation theory . Calculating the energy shift for states.

Now, just as in the case of the
, spin-orbit interaction,
we will define the total angular momentum

It is in the states of definite and that the hyperfine perturbation will be diagonal. In essence, we are doing degenerate state perturbation theory. We could diagonalize the 4 by 4 matrix for the perturbation to solve the problem or we can use what we know to pick the right states to start with. Again like the spin orbit interaction, the

For the hydrogen ground state we are just adding two spin particles so the possible values are .

* Example:
The Hyperfine Splitting of the Hydrogen Ground State.*

The transition between the two states gives rise to EM waves with cm.

Jim Branson 2013-04-22