Series perturbations in atomic spectra: Superposition-of-configurations calculations on Al I and Al II

Configuration-interaction calculations, using only Hartree-Fock discrete-state configurations, are reported for the two perturbed series, $3sn{f}^{3}F$ of Al II and $3s^{2}n{d}^{2}D$ of Al I. While good results are obtained for term values and oscillator strengths in Al II, this is not the case for Al I, where the calculations predict the $3s3p^2$ perturber to be expelled into the continuum. To study this case more closely, superposition of configurations (SOC) calculations, which include all correlation effects, were carried out on the five lowest ${}_{}{}^2{}_{}{}^{}D$ states of Al I. These results indicate that the perturber actually remains in the discrete spectrum, but loses its identity and is smeared out over the entire series. New Rydberg orbitals are extracted from the SOC wave functions which are quite different from the Hartree-Fock but very similar to those of the Coulomb approximation. Various truncations of the SOC functions are also analyzed and the implications for the correlation problem discussed.