Ambiguities in the parametrization of4fN−4fNelectric-dipole transition intensities

For most symmetries the standard parametrization of one-photon electric-dipole transitions between crystal-field levels of the ${4f}^N$ configuration of lanthanide ions produces identical intensities for several quite different parameter sets. An alternative scheme makes this multiplicity transparent as independent sign choices for each subset of parameters corresponding to distinct polarizations. In addition, the alternative parametrization allows separate fits to data for different polarizations.