Crystal-Field Interactions--Phenomenological Theory of Crystal Fields

Abstract

In the presence of a crystal field we take the interaction of an ion whose electronic configuration is nℓ^N as

$${H_3} = \sum\limits_{kq} {B_{kq}^ * } \sum\limits_{i + 1}^N {{C_{kq}}} \left( {\mathop {{r_i}}\limits^ \wedge } \right)$$

((8.1))

where the C_kq are unnormalized spherical harmonics given by

$${C_{kq}}\left( {\hat r} \right) = {\left[ {4\pi /\left( {2k + 1} \right)} \right]^{1/2}}{Y_{kq}}\left( {\hat r} \right).$$