  We present a modified version of the Judd-Ofelt theory, which describes the
intensities of f-f transitions by trivalent lanthanide ions (Ln$^{3+}$) in
solids. In our model, the properties of the dopant are calculated with
well-established atomic-structure techniques, while the influence of the
crystal-field potential is described by three adjustable parameters. By
applying our model to europium (Eu$^{3+}$), well-known to challenge the
standard Judd-Ofelt theory, we are able to give a physical insight into all the
transitions within the ground electronic configuration, and also to reproduce
quantitatively experimental absorption oscillator strengths. Our model opens
the possibility to interpret polarized-light transitions between individual
levels of the ion-crystal system.
