Electron correlation in the ground and low-lying excited states of alkaline earth atoms

Abstract

Variational wave functions are constructed for the ground and several low-lying excited states of the alkaline earth atoms Be, Mg, Ca, Sr, and Ba. Effective core potentials are employed to treat these atoms as pseudo-two-electron systems. Conditional probability distributions ρ(r2,θ12‖r1=ζ), representing the probability of finding one electron at a distance r2 from the nucleus with interelectronic angle θ12, given that the other electron is at a distance r1 from the nucleus, are plotted for several states of the alkaline earths at various values of ζ. We find that the molecular model which so successfully classifies and describes the collective rotational and vibrational states of doubly excited He carries over well to these ground and low-lying states of the lighter alkaline earths. For the heavier atoms, though the angular correlation remains strong, the application of the molecular model becomes less clear. Some states exhibit behavior intermediate between independent particle-like and collective, and ‘‘interloper states’’ appear which have no immediate interpretation in terms of a single vibrator-rotator model or relationship to the states of doubly-excited helium.