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

摘要

A purely group-theoretical approach (for which the symmetric group plays acentral r\^ole), based upon the use of properties of fractional-parentagecoefficients and isoscalar factors, is developed for the derivation of theCoulomb energy averaged over the states, with a definite spin, arising from anatomic configuration $n \ell^N$.