Abstract
A procedure is described for using orthogonal operators, nu k to reduce the residual discrepancies Delta i that result when a least-squares fit to the levels of an atomic configuration is carried out. Linear combinations nu 'j of the members of a given set of nu k for which the associated parameters p'j are strictly uncorrelated are constructed. The theory is applied to FE VI 3d24p. The mean error of 188 cm-1 obtained by Ekberg with 9 parameters is reduced in successive steps to 77, 15, 11 and 10 cm-1 with 12, 18, 19 and 21 parameters, respectively. The importance of a class of three-electron scalar operators is established. However, the nu k that are based on group theory are connected to the nu 'j by a unitary matrix that possesses significant off-diagonal components.