Parametric fits in the atomic d shell

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Abstract
A study is made of the effective operator Xi that reproduces (to second order in perturbation theory) the displacements of the energy levels of dNs2 due to the interaction of this configuration with dN+1s. The matrix elements of Xi are broken up into separate n-electron parts of all the states of dN, and it is shown that Xi corresponds to quasi-spin ranks of 0 and 1 only. Contributions from the n=1 and n=2 parts of Xi to the classic electrostatic parameters Fk, alpha and beta are worked out, and it is shown that an orthogonalisation of the n=3 part to the electrostatic operators leads to corrections to the Fk but none to alpha and beta . This last result generalises to the f shell and also to all types of configuration interaction in which a single electron is excited. An orthogonalisation of the operators associated with alpha and beta is also carried out and a fit to the experimental levels of Cr IV 3d3 demonstrates that the parameters associated with the orthogonalised operators have smaller mean errors than the conventional ones.

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