  Formulas and expectation values which are need to determine the lowest-order
QED corrections ($\sim \alpha^3$) and corresponding recoil (or finite mass)
corrections in the two-electron helium-like ions are presented. Other important
properties of the two-electron ions are also determined to high accuracy,
including the expectation values of the qausi-singular Vinti operator and
$\langle r^{-2}_{eN} \rangle$ and $\langle r^{-2}_{ee} \rangle$ expectation
values. Elastic scattering of fast electrons by the two-electron ions in the
Born approximation is considered. Interpolation formulas are derived for the
bound state properties of the two-electron ions as the function of the nuclear
electric charge $Q$.
