  We investigate the entanglement-related features of the eigenstates of two
exactly soluble atomic models: a one-dimensional three-electron Moshinsky
model, and a three-dimensional two-electron Moshinsky system in an external
uniform magnetic field. We analytically compute the amount of entanglement
exhibited by the wavefunctions corresponding to the ground, first and second
excited states of the three-electron model. We found that the amount of
entanglement of the system tends to increase with energy, and in the case of
excited states we found a finite amount of entanglement in the limit of
vanishing interaction. We also analyze the entanglement properties of the
ground and first few excited states of the two-electron Moshinsky model in the
presence of a magnetic field. The dependence of the eigenstates' entanglement
on the energy, as well as its behaviour in the regime of vanishing interaction,
are similar to those observed in the three-electron system. On the other hand,
the entanglement exhibits a monotonically decreasing behavior with the strength
of the external magnetic field. For strong magnetic fields the entanglement
approaches a finite asymptotic value that depends on the interaction strength.
For both systems studied here we consider a perturbative approach in order to
shed some light on the entanglement's dependence on energy and also to clarify
the finite entanglement exhibited by excited states in the limit of weak
interactions. As far as we know, this is the first work that provides
analytical and exact results for the entanglement properties of a
three-electron model.
