The ground state of atomic two‐electron systems in the independent particle model

Scaled variational functions of the form \documentclass{article}\pagestyle{empty}\begin{document}$ \phi _{\alpha k} = e^{ - (Z - 1 + e^{ - \alpha kr})kr} $\end{document} , where Z is the nuclear charge and α is a parameter, and \documentclass{article}\pagestyle{empty}\begin{document}$ \phi _{\beta \alpha k} = e^{ - (\beta + e^{ - \alpha kr})kr} $\end{document} , where both α and β are parameters, are used for the description of the ground state of atomic two‐electron systems in the independent particle model. The scale factor k has been introduced in order to satisfy the virial theorem. Apart from the energy, a number of one‐electron expectation values have been calculated and the results are compared with those obtained from other variational functions. The function ϕ α k yields already a good approximation to the Hartree–Fock solution whereas with the function ϕ βα k the Hartree–Fock results are practically reproduced.