  There are very few systems of interacting particles (with continuous
variables) for which the entanglement of the concomitant eigenfunctions can be
computed in an exact, analytical way. Here we present analytical calculations
of the amount of entanglement exhibited by $s$-states of \emph{spherium}. This
is a system of two particles (electrons) interacting via a Coulomb potential
and confined to a $(d-1)$-sphere (that is, to the surface of a $d$-dimensional
ball). We investigate the dependence of entanglement on the radius $R$ of the
system, on the spatial dimensionality $d$, and on energy. We find that
entanglement increases monotonically with $R$, decreases with $d$, and also
tends to increase with the energy of the eigenstates. These trends are
discussed and compared with those observed in other two-electron atomic-like
models where entanglement has been investigated.
