part 1 a

Hamiltonian (multipolar charge moment)

The representations of CEF potentials (V) in the spherical coordination:

Were:

Pnm - Legendre functions,
Ynm - spherical harmonic functions,
Znm - tesseral harmonic.

The most elementary expressions of the elements of the multipolar series (in Cartesian co-ordination): 

The examples of the visual presentation (in cartesian co-ordinate system) of the elements of the multipolar series Vnm.