130_notes.dvi

• See Example 24.3.2:The Hyperfine Splitting in a Weak B Field.*

The result of this is example is quite simpleE=En 00 +A 2

(

f(f+ 1)−^32

)

+μBBmf. It has the
hyperfine term we computed before and adds a term proportionaltoBwhich depends onmf.

In the strong field limit we use states|msmi〉and treat the hyperfine interaction as a perturbation.
The unperturbed energies of these states areE=En 00 + 2μBBms+gμNBmI. We kept the small
term due to the nuclear moment in the B field without extra effort.

• See Example 24.3.3:The Hyperfine Splitting in a Strong B Field.*

The result in this case is

E=En 00 + 2μBBms+gμnBmI+AmsmI.

Finally, we do the full calculation.

• See Example 24.3.4:The Hyperfine Splitting in an Intermediate B Field.*
  The general result consists of four 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

E=En 00 +

A

4

±μBB

and

E=En 00 −

A

4

±

√(

A

2

) 2

+ (μBB)^2.

These should agree with the previous calculations in the two limits: B small, or B large. The figure
shows how the eigenenergies depend on B.