Irreducible tensor operator methods in intermediate-field coupling

The algebra of irreducible tensor operators is developed in the intermediate-field coupling case. The Wigner-Eckart theorem is formulated for a simple irreducible tensor operator as well as for the Kronecker and scalar products of these operators. The expressions required for the calculation of Coulomb repulsion, crystal field splitting, spin-orbit interaction, and Zeeman effect are given in detail. Recent applications to various problems in spectroscopy and magnetism of transition metal compounds are referred to.