Electron correlations in atomic valence shells: Magnesium and aluminum

We use a combination of R-matrix and hyperspherical coordinate techniques to study the effects of electron correlations in atomic valence shells. The 3snd-3p² mixing in Mg ¹Dᵉ is analyzed in detail and its relevance to the s²{p}ⁿ$d-${sp}ⁿ⁺²$ interactions throughout the row is indicated by a study of the 3${s}²$nd-3s3${p}²$ ${}²Dᵉ mixing in Al. Multichannel quantum-defect theory parameters for Mg ¹Dᵉ and Al ²Dᵉ are calculated ab initio. We obtain excellent agreement with experiment for the quantum defects of the 3snd series in Mg and a significant improvement over previous theoretical studies for the quantum defects of the 3s²nd series in Al. Two-electron correlations are illustrated by mapping their joint probability density for alternative eigenmodes.