On the derivation of the superposition-model formulae using the transformation relations for the Stevens operators

Abstract

The authors consider the relationship between Newman's superposition-model formulae and the recently derived transformation matrices Sk( phi , theta ) for the extended Stevens operators. The coordination factors Kkq( theta , phi ) are shown to be the matrix elements (Sk-1)0q. A general expression for Kkq in terms of the tabulated quantities cqk and (Sk)q0 is derived. Explicit expressions for Kkq, k=1 to 6, i.e. including odd-k coordination factors not listed hitherto, are given.