Judd–Ofelt theory in a new light on its (almost) 40th anniversary

Abstract

The standard Judd–Ofelt theory of one photon electric dipole transitions in f N systems is discussed in the language of the one particle parametrization scheme. An overview of various physical mechanisms that contribute to the Judd–Ofelt intensity parameters is performed. The analysis of the morphology of these parameters is based on the static model of their original derivation, dynamic model, electron correlation third order approach, spin–orbit interaction influence, and an exotic perturbation caused by a specific mass shift. As a new aspect of the investigations on the physical nature of f↔f transitions, a transformation of the Judd–Ofelt effective operators to their relativistic version is presented. In this approach the transition amplitude is expressed by the effective double tensor operators, acting within the 4f N shell, and effectively representing relativistic contributions. In particular, the relativistic form of the crystal field potential is employed, and in addition, the interactions through the crystal field potential within the spin–orbital space are included.