The generalization of the extended Stevens operators to higher ranks and spins,and a systematic review of the tables of the tensor operators and their matrixelements

Abstract

Spherical (S) and tesseral (T) tensor operators (TOs) have been extensively used in, forexample, EMR and optical spectroscopy of transition ions. To enable a systematic review ofthe published tables of the operators and their matrix elements (MEs) we have generatedthe relevant tables by computer, using Mathematica programs. Our review reveals severalmisprints/errors in the major sources of TTOs—the conventional Stevens operators(CSOs—components ) and the extended ones (ESOs—allq) forrank k = 2,4, and 6—as well as of some STOs with . The implications of using incorrect operators and/or MEs for the reliability of EMR-relatedprograms and interpretation of experimental data are discussed. Studies of high-spin complexes likeMn12 (S = 10)and Fe19 (S = 33/2) require operatorand ME listings up to k = 2S, which are not presently available. Using the algorithms developed recentlyby Ryabov, the generalized ESOs and their MEs for arbitrary rankk andspin S are generated by computer, using Mathematica. The extended tables enablesimulation of the energy levels for arbitrary spin systems and symmetry cases.Tables are provided for the ESOs not available in the literature, with oddk = 3,5, and 7 for completeness; however, for the newly generalized ESOs with the most useful even rankk = 8,10, and 12 only, in view of the large listings sizes. General source codes for the generation ofthe ESO listings and their ME tables are available from the authors.