Crystal Field Effects on Multiplets Observed in Open d- and f- shells

The subject of the thesis is to study a crystal field and spin-orbit coupling effects on multiplets observed in open d- and f-shells. The Coulomb interaction is considered by building the electrostatic matrix, where the required Gaunt coefficient are calculated recursively. Continuous fractions are used to produce Gaunt coefficients in the form of square roots of rational numbers to verify them. L-S coupling between orbital and spin angular momenta is assumed. Due to the spherical symmetry of the Coulomb potential, orbital and spin angular momenta are conserved separately. The corresponding quantum numbers are used to classify the eigenstates of the electrostatic matrix. These are compared with the eigenstates of simplified approximations to the electrostatic matrix. Then a cubic or tetragonal crystal field is introduced to electrostatic Hamiltonian and the interplay of Hund's rule and crystal-field splitting is studied. Finally spin-orbit coupling is added