Coulomb Energy Averaged over the $n{\ell }^N$-Atomic States with a Definite Spin

Abstract

A purely group-theoretical approach (for which the symmetric group plays a central rôle), based upon the use of properties of fractional-parentage coefficients and isoscalar factors, is developed for the derivation of the Coulomb energy averaged over the states, with a definite spin, arising from an atomic configuration $n{\ell }^N$.

arXiv comment12 pages, Tex File