Some unexpected proportionalities between components of the spin—other-orbit interaction in the f shell

Abstract

The reduced matrix elements of the component z i of the inter-electronic spin-other-orbit interaction have been calculated for all the states of the atomic f shell. Three of the z i , each of which belongs to the irreducible representation (30) of Racah's group G2, are found to exhibit matrix elements that are often related to one another in ways that go beyond what the Wigner-Eckart theorem, generalized to G2, would predict. Examples are presented for matrix elements whose bras belong to the IR (20) of G2 and whose kets belong to (31). The challenges to current theory are discussed.