Resonances in two-electron atoms below the critical charge

Abstract

The critical nuclear charge Zc required for a heliumlike atom to have at least one bound state was recently determined with high accuracy from variational calculations. Analysis of the wave functions further suggested that the bound state changes smoothly into a shape resonance as Z crosses the critical value. Using variational calculations combined with the complex coordinate rotation method, we study the energy and width of the resonance for Z \textless{} Zc, thus providing direct evidence of the validity of this hypothesis. The variation of the resonance width with Z is found to be in good agreement with a model derived from analysis of the 1/Z perturbation series.