COULOMB AND SPIN-ORBIT INTERACTION MATRIX-ELEMENTS IN THE D(2)D' CONFIGURATION

The d(2)d' configuration is analysed in group-theoretical terms. Start ing from the table given by Condon and Odabasi for the configuration d 2d', we determine a set of convenient group-theoretical basis states, and rewrite the Coulomb matrix elements in terms of this new basis. Li near combinations from the different parts of the Coulomb operators ar e formed such that they have simple group transformation properties in our scheme. The sequence of groups that we use is U(20) superset of S OT(3) x U(10) superset of SOT(3) x SOS(3) x U(5) superset of SOT(3) x SOS(3) x SO(5) superset of SOT(3) x SOS(3) x SOL (3), where T denotes the isospin of Simonis et al, in which electrons with the same angular momentum I but different principal quantum numbers n are accommodated by introducing the eigenvalue M-T of T-0. Using the Wigner-Eckart the orem and selection rules on the higher symmetry groups, the tables of the Coulomb and spin-orbit matrix elements for the reconstituted opera tors (with simple group transformation properties) are much simplified in terms of these basis states.