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On accurate computations of slowly convergent atomic properties in few-electron ions and electron-electron correlations

We discuss an approach to accurate numerical computations of slowly convergent properties in two-electron atoms/ions which include the negatively charged Ps$^{-}$ ($e^{-} e^{+} e^{-}$) and H$^{-}$ ions, He atom and positively charged, helium-like ions from Li$^{+}$ to Ni$^{26+}$. All these ions are considered in their ground $1^{1}S-$state(s). The slowly convergent properties selected in this study include the electron-nulceus $\langle r^{2 k}_{eN} \rangle$ and electron-electron $\langle r^{2 k}_{ee} \rangle$ expectation values for $k$ = 2, 3, 4 and 5.