Determination of the energy level structure for dsup(N) and fsup(N) ions in cubic environment within the intermediate crystal field method

A method of determination of the crystal field energy levels and the fine structure of a paramagnetic ion in a crystal based on the Hamiltonian of anisotropic spin-orbit coupling in the cubic crystalline field is reviewed for the intermediate field case. Methods of irreducible tensor operators are used. General formulas for the matrix elements of the field states, including the reduction coefficients, are proposed. Some properties of these coefficients and extensive tables of their numerical values for the most important cases are given. (author)