A Class of Null Spectroscopic Coefficients

Abstract

The irreducible representations occurring in the decomposition of the Kronecker products U × U and W × W for irreducible representations U and W of the groups G₂ and R₇ are separated into symmetrical and antisymmetrical parts. Application of the Wigner‐Eckart theorem yields new selection rules and explains many of the apparently accidental zeros in the tabulation by Nielson and Koster of the reduced matrix elements of various single‐particle tensor operators for the electronic configurations fⁿ. The method is applied in detail to the magnetic spin‐spin interaction between electrons in the f shell, and the new selection rules are presented in tables.