On the interaction of a radiation field with a nl sup(N) type configuration

A comparison is made between electric-dipole matrix elements within a nl sup(N) type configuration, as given by the length and velocity formulae. Within the approximation of considering each excited configuration as a degenerate one, it is shown that up to second order the matrix elements of the momentum operator are vanishing in contrast with the Judd-Ofelt theory. This conclusions shows that it is a serious error to use the Judd-Ofelt wave functions and the velocity formula. However, up to third order, in addition to even and odd rank tensors which enter on the same footing in the matrix elements, the velocity formula predicts the contribution of two and three- particle operators which depend on the energy difference between configurations in the same way as the one-particle operators. A brief discussion of the results is made. (Author)