An alternative formulation of the Judd-Ofelt theory of f ↔ f transitions

Abstract

A contribution is made to the discussion about the choice between length and velocity formulae which describe the interaction between matter and a radiation field. The analysis is illustrated by the Judd-Ofelt theory of one-photon electric dipole transitions between the levels of 4f N configuration of rare earth ions in crystals. The standard effective operators which contribute to the transition amplitude are one-particle tensor operators of even rank and are defined within the electric gauge of an electromagnetic field. When the radiation gauge is applied, the transition amplitude is determined by new effective operators which are of odd rank. The latter are one-, two- and three-particle objects and are caused by the non-local character of the Hartree-Fock potential of the zeroth-order hamiltonian defined within the central field approximation. The new effective operators are expressed in terms of the so-called perturbed functions; it is demonstrated that their angular factors and radial terms are of the same general structure as in the case of effective operators of the standard Judd-Ofelt theory.