Including Quadrupolar and Higher Order Interactions

Some modules such as so1ion allow also to calculate systems with higher order interactions such as quadrupolar interactions. Quadrupolar and higher order interactions can be calculated, which can be described by products of Stevens operators. The general two ion exchange coupling is

$${\mathcal H}_{JJ}= -\frac{1}{2} \sum_{nn'} \sum_ {ll'}... ...\alpha\alpha'}(nn') \hat I_{\alpha}^n \hat I_{\alpha'}^{n'}$$ (64)

For further information on the notation and symmetry restrictions to the parameters in the Hamiltonian refer to [1].