  Entanglement of the two scattered particles is expected to occur in elastic
collisions, even at high energy where they are in competition with inelastic
ones. We study how to evaluate quantitatively the corresponding entanglement
entropy $S_{\rm EE}.$ For this sake, we regularize the divergences occurring in
the formal derivation of $S_{\rm EE}$ using a regularization procedure acting
on the two-particle Hilbert space of final states. A quantitative application
is performed in proton-proton collisions at collider energies, comparing the
results of $S_{\rm EE}$ with two different cut-offs and with a
volume-regularization obtained by a prescription fixing the finite two-body
Hilbert space volume. A significant entanglement is found which persists even
at the highest available energies.
