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-3$p^2$ mixing in Mg ${}_{}{}^1{}_{}{}^{}\mathrm{D}_{}^{\mathrm{e}}{}_{}{}^{}$ is analyzed in detail and its relevance to the $s^2$ $p^n$d-${\mathrm{sp}}^{n+2\mathrm{}}$ interactions throughout the row is indicated by a study of the 3$s^2$nd-3s3$p^2$ ${}^2$ $D^e$ mixing in Al. Multichannel quantum-defect theory parameters for Mg ${}_{}{}^1{}_{}{}^{}\mathrm{D}_{}^{\mathrm{e}}{}_{}{}^{}$ and Al ${}_{}{}^2{}_{}{}^{}\mathrm{D}_{}^{\mathrm{e}}{}_{}{}^{}$ 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 3$s^2$nd series in Al. Two-electron correlations are illustrated by mapping their joint probability density for alternative eigenmodes.