Hitchhiker's guide to multiplet calculations

Abstract

Core level spectra from localized magnetic systems, such as 3d transition metal compounds or rare earths, obtained with high resolution synchrotron radiation can be simulated theoretically by calculating the transitions from the ground state to the allowed final states, e.g. 3dn → 2p53dn+1. Presented here is the angular momentum coupling theory, Racah-Wigner algebra, point group theory and multipole moment expansion behind such calculations for the dichroic spectra of x-ray absorption, photoemission and x-ray resonant magnetic scattering. The first part of this chapter reviews the standard results of multiplet theory and surveys the Cowan-Butler-Thole approach. The last part presents some more advanced topics, such as the x-ray optical activity, which is induced by interference between different electric and magnetic multipole fields, and the method of statistical moment analysis, which relates the moment distribution of the dichroic spectra to effective operators. © 2006 Springer.