  The entanglement properties of systems in which elastic and inelastic
reactions occur in projectile-target interactions is studied. A new measure of
entanglement, the scattering entropy, based on the unitarity of the $S-$matrix
(probability conservation), is suggested. Using simple models for both low- and
high-energy interactions, the amount of entanglement is found to track with the
strength of the inelastic interaction. The familiar example of the classical
``black disk", total absorption, model is found to correspond to maximum
entanglement. An analysis of high-energy $pp$ scattering data shows that
entanglement is near maximum for lab energies greater than about 1 GeV, showing
that the total absorption model is a reasonable starting point for
understanding the data.
