  The quantum entanglement for the two electrons in three-body atomic systems
such as the helium atom, the hydrogen negative ion and the positronium negative
ion are investigated by employing highly correlated Hylleraas functions to
represent the ground states of such systems. As a measure of the spatial
entanglement, the linear entropy of the reduced density matrix is calculated
for the ground states. The required four-electron (12-dimensional) integrals
are solved analytically such that they are suitable for machine computations.
Results are compared with other calculations when available.
