Abstract
In recent work on the rare-earth double nitrates, it has been found necessary to extend the theory of crystal fields to cases of C
3
v
symmetry. Operator equivalences are given for the potentials V
3
4
and V
3
6'
, defined by ∑
z
(
x
3
- 3
xy
2
) and Ʃ(11
z
3
- 3
zr
2
) (
x
3
- 3
xy
2
) respectively, and their matrix elements tabulated over a range of
J
(the total angular momentum) which includes the ground states of all the rare-earth ions. Operator-equivalent factors are given for certain excited levels in praseodymium and neodymium ions, and a method is described for finding these factors for levels which derive from terms that occur twice in a configuration of the form
f
n
. The dependence on
J
and
J
z
of the matrix elements of the crystal-field interaction between different
J
levels is given for the components of a crystal field with C
3
v
symmetry.
Reference7 articles.
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