APPLICATION OF UNITARY-GROUP METHODS TO COMPOSITE SYSTEMS

The unitary-group approach is extended to the treatment of composite s ystems such as ionic states in molecules (ligands, etc.). Those are re presented hierarchically in terms of SU(n)-based Weyl-Young tableaux w hich reflect the permutational symmetry of the ionic sites themselves labeled by SU(2) based tableaux which, in turn, reflect the internal e lectronic structure. Matrix elements of quantum-mechanical tensor oper ators, including both spin-independent and spin-dependent multipole-mu ltipole interactions, are presented using corresponding spin-graphical representations. The hierarchy of the state definitions is shown to r eveal the ''fine structure'' of the ionic interactions.