Configuration Interaction Effects inlNConfigurations

The effects of configuration interactions on the energy-level structure of $l^N$ type configurations have been studied. In previous work the linear theory has sought to augment the usual Hamiltonian for an $N$-electron system with additional two-body scalar interactions. In the present study it is shown that by choosing suitable scalar interactions it is possible to include, to second order, all the electrostatic interactions with configurations having two electrons excited from the $l^N$ configuration. The form of the scalar interactions, together with expressions for the interaction constants in terms of the radial integrals, has been derived explicitly using perturbation theory. Effective three-body interactions are introduced to account for the perturbations due to one-electron excitations. The physical significance of the interaction constants associated with the linear theory is clarified. Formulas are given for the matrix elements of the electrostatic interaction between the $l^N$ configuration and the different species of perturbing configurations. An identity which greatly simplifies the summations arising from the second-order perturbation is established.