Regularized Lagrange-mesh calculations and electron correlation in the ground states of helium-like atoms

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Abstract
The Lagrange-mesh method proposed previously is used to discretize the two-electron Schrodinger equation. It is combined with recent and new regularization techniques which restore the validity of the underlying Gauss approximation. Excellent results are obtained for the correlation energies in the ground states of the isoelectronic atoms and ions H-, He, Li+ and Be2+ using a low-dimension mesh and ultra-fast matrix generation procedures. These demonstrate that the Lagrange-mesh method is able to combine accuracy and efficiency while retaining the distinctive simplicity of a grid approach. This opens new perspectives for Lagrange-mesh calculations in atomic physics.