The spin-spin and spin-other-orbit interactions for thef 2 electron configuration

Abstract

(ricevuto il 23 Aprile 1993; approvato il 9 Luglio 1993)Summary. --The spin-spin and the spin-other-orbit interaction matrices for the f2 electronic configuration have been calculated using irreducible tensor operators and are given in terms of the Marvin radial integrals M k (k = 0, 2, 4). -Introduction.By far the biggest contribution to the energy of the multiplets of the fn configuration comes from the mutual electron-electron electrostatic repulsion and the spin-orbit interaction (between two magnetic dipoles). However, additional interactions need to be included in the effective Hamiltonian for a more accurate analysis of energy level structures of rare earths [1][2][3][4][5][6][7][8][9]. They are, among others, the higher-order electrostatically correlated perturbations, the dominant being the two-particle[10] and the three-particle (for systems with n t> 3) configuration interactions [ll]. In addition to the usual spin-orbit interaction there are magnetic interactions of relativistic origin (Breit Hamiltonian) which arise from the couplings of orbital and spin angular moments of different electrons. These interactions include the orbit-orbit interaction, the spin-spin interaction (Hss) and the interaction between the spin of one electron and the orbital motion of another, called the spin-other-orbit interaction (Hsoo). The orbit-orbit interaction is usually not considered explicitly since its effect can be absorbed into the configuration interaction [3,10]. It has been found [2,7,11] that for a better fit between experiment and theory the smaller but essential contributions of Hss and H~oo need to be considered. Araki in a classic paper [12] suggested that these interactions may have an appreciable effect on the intervals of multiplets in spectra of heavy elements, thus explaining, in part, the deviations from the Land~ interval rule.1273

Chebyshev-series representation for the energy levels of U4+

“…The matrices of the SS and SO0 interactions were taken from ref. [19]. The combined matrices containing complete electrostatic, spin-orbit and the above three interactions were diagonalised for various values of the parameters involved to find the best fit to the experimental data, taken from ref.…”