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 matrix elements
Year: 2004
Type: review
Abstract: Spherical (S) and tesseral (T) tensor operators (TOs) have been extensively used in, for example, EMR and optical spectroscopy of transition ions. To enable a systematic review of the published tables of the operators and their matrix elements (MEs) we have generated the relevant tables by computer, using Mathematica programs. Our review reveals several misprints/errors in the major sources of TTOs—the conventional Stevens operators (CSOs—components ) and the extended ones (ESOs—all q ) for rank 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-related programs and interpretation of experimental data are discussed. Studies of high-spin complexes like Mn 12 ( S = 10) and Fe 19 ( S = 33/2) require operator and ME listings up to k = 2 S , which are not presently available. Using the algorithms developed recently by Ryabov, the generalized ESOs and their MEs for arbitrary rank k and spin S are generated by computer, using Mathematica . The extended tables enable simulation of the energy levels for arbitrary spin systems and symmetry cases. Tables are provided for the ESOs not available in the literature, with odd k = 3,5, and 7 for completeness; however, for the newly generalized ESOs with the most useful even rank k = 8,10, and 12 only, in view of the large listings sizes. General source codes for the generation of the ESO listings and their ME tables are available from the authors.
Authors: C Rudowicz, C Y Chung
Institution: City University of Hong Kong
Language: English
Field: Materials Science
Domain: Physical Sciences
Open Access status: bronze
Funder: City University of Hong Kong
OpenAlex ID: W2071897227