Judd-Ofelt theory: past, present and future

The original Judd-Ofelt theory is briefly presented in the terms of effective operators defined in the traditional form that has been used for many years for the interpretation of the f spectra of rare earths. The semi-empirical approach of the Judd-Ofelt theory that defines the one-particle parametrization scheme is modified here. The unit tensor operators that act within the orbital space are replaced by double tensor operators acting within the spin-orbital space. This extension enables one to include the impact of the relativistic effects upon the transition amplitude. At the same time it leads to a generalization of the theoretical approach to f --> f transitions, especially in the case of those that are not described by the standard scheme.