Abstract
The unitary-group approach is extended to the treatment of composite systems such as ionic states in molecules (ligands, etc.). Those are represented hierarchically in terms of SU(n)-based Weyl-Young tableaux which reflect the permutational symmetry of the ionic sites themselves labeled by SU(2) based tableaux which, in turn, reflect the internal electronic structure. Matrix elements of quantum-mechanical tensor operators, including both spin-independent and spin-dependent multipole-multipole interactions, are presented using corresponding spin-graphical representations. The hierarchy of the state definitions is shown to reveal the ``fine structure'' of the ionic interactions.
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