Projection of accurate configuration-interaction wave functions forHe/emph>and the alkaline-earth-metal atoms onto simple rotor-vibrator wave functions

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Abstract
To quantify the extent of validity of the molecular model of atoms with correlated electrons, we project well-converged configuration-interaction wave functions for doubly excited states of He and for bound states of alkaline-earth-metal atoms onto simple rotor-vibrator wave functions for the ‘‘linear triatomic molecule’’ e-core-e. The three independent vibrational frequencies and the equilibrium electron-nucleus separation are treated as parameters which are varied to maximize the overlap with the well-converged functions. For intrashell states, the overlaps with harmonic normal-mode functions are generally quite large, about 85–95 % for the alkaline-earth-metals, and the corresponding optimized parameters are in rough agreement with the energy-level separations. The overlaps are improved by using an anharmonic local-mode representation, particularly for intershell states (corresponding to excited stretching vibrations), though the optimized parameters appear to lose some of the consistency shown by those in the harmonic normal-mode representation. A comparison is made of plots of the conditional probability densities based on rotor-vibrator functions and on independent-particle functions with those based on accurate functions. This shows clearly the superiority of the molecular picture over the independent-particle picture as a zero-order model for intrashell states of two-electron atoms.