SECTION 5.2. QUANTUM-MECHANICAL TREATMENT 49
the larger the atomic weight. Hence, it is larger for the rare earths than for the 3d transition
elements.
In view of the energy consideration given above, one has to adopt the following
procedure for dealing with these interactions. The spin–orbit interaction is the strongest
interaction for rare-earth-based materials. Therefore, the spin–orbit coupling has to be
dealt with first. Subsequently, the crystal–field interaction can be treated as perturbation to
the spin–orbit interaction. This is how we have proceeded thus far, indeed. First, we have
angular momentum
dealt with the spin–orbit interaction in the form of the Russell–Saunders coupling. The total
and its component are constants of the motion after application of
the Russell–Saunders coupling, and J and are good quantum numbers. Consequently,
we have calculated the perturbing influence of the crystal field with the representation
as basis (see Table 5.2.1).