  The quantum entanglement for the two electrons in the excited states of the
helium-like atom/ions is investigated using the two-electron wave functions
constructed by the B-spline basis. As a measure of the spatial
(electron-electron orbital) entanglement, the von Neumann entropy and linear
entropy of the reduced density matrix are calculated for the 1s2s 1,3S excited
states for systems with some selected Z values from Z=2 to Z=100. Results for
the helium atom are compared with other available calculations. We have also
investigated the entropies for these excited states when the nucleus charge is
reduced from Z=2 to Z=1. At such a critical charge, all the singly-excited
states of this system become unbound, and the linear entropies and the von
Neumann entropies for the excited states are approaching 1/2 and 1,
respectively, the limits for the entropies when one electron is bound to the
nucleus, and the other being free.
