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

TL;DR

This paper presents a method for highly accurate numerical calculations of slowly convergent atomic properties in two-electron ions and atoms, including negatively charged ions and helium-like ions across a range of nuclear charges.

Contribution

The paper introduces an approach to improve the accuracy of computations for slowly convergent properties in two-electron systems, covering a variety of ions and atoms in their ground states.

Findings

Achieved high-precision calculations of expectation values for electron-nucleus and electron-electron distances.

Extended the computational method to a range of ions from neutral helium to highly charged ions.

Demonstrated the effectiveness of the approach in handling slow convergence issues.

Abstract

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.