Orthogonal operators: extension to hyperfine structure and equivalent p- and f-electrons

Orthogonal operators are a next step in the semi-empirical description of complex spectra. Orthogonality yields optimal independence and thus least correlation between the operators. The increased stability of the fitting process is used to include higher-order many-body as well as fully relativistic effects. The calculated eigenvalues are frequently an order of magnitude more accurate with respect to a conventional semi-empirical approach. The resulting eigenvectors may not only be put to use to calculate transition probabilities and g-factors, but also to calculate hyperfine structure A and B constants. We illustrate our first steps in this field with two examples of first spectra of the iron group elements. The results are compared to current experimental hyperfine structure A-values while strong and weak points of the method are discussed. In particular to be able to deal with lanthanides and actinides, the orthogonal operator method is completed with the definition of operators for equivalent p- and f-electrons.