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Single-particle and electron-pair densities at the origin in the ground state of helium-like ions

Here we study the single-particle and the electron-pair densities for the ground state of two-electron atomic systems using the wavefunctions which provide the best values for the energy known up to now. Special attention is paid to the convergence of some properties of the densities when we increase the dimension of the basis used. With these functions we have increased significantly the precision in the determination of the single-particle and the electron-pair densities at the origin and, therefore, of Kato's cusp conditions.