Fully differential single-photon double ionization of magnesium

The valence-shell double ionization of atomic magnesium is calculated using a grid-based representation of the $3s^2$ electron configuration in the presence of a fully-occupied frozen-core configuration. Atomic orbitals are constructed from an underlying finite element discrete variable representation (FEM-DVR) that facilitate accurate representation of the interaction between the inner shell electrons with those entering the continuum. Comparison between the similar processes of double ionization of the $ns^2$ atoms helium, beryllium and magnesium are presented to further illuminate the role of valence-shell electron correlation in atomic targets with analogous configurations and symmetries. Both a time-independent and time-dependent formalism for evaluating double ionization amplitudes is applied to these many-electron targets. Results are compared with recent theoretical calculations and experimental measurements.