The intensities of transitions within the 4fN configurations of lanthanide ions are strongly dependent on the environment of the ion. The electric dipole transitions that dominate the solid state and solution spectra are forbidden for an isolated ion. They only become allowed when the symmetry is reduced from the full rotational symmetry of a free ion to the point group symmetry at an ion in a condensed matter environment.

The phenomenological and ab initio descriptions of lanthanide intensities are much less developed than the description of crystal field split energy levels. This is due to various technical problems, both experimental and theoretical, that will be alluded to in this chapter. As a result, the detailed fitting of transitions between crystal field split levels is still relatively uncommon, over 35 years since it became possible.

The methods described here are relevant to the sharp line spectra of lanthanide and actinide ions in crystals, though the examples refer mostly to lanthanides. A detailed analysis of the broadband spectra typical of transition metal systems generally requires the addition of extra theoretical machinery to take account of vibronic progressions, Franck–Condon factors, etc. Analyses of the intense 4fN ↔ 4fN−15d transitions of lanthanide ions also require extensions.

The history of the field, particularly that of fitting total transition intensities between J multiplets, has been covered in a number of reviews [Pea75, Hüf78, GWB98].