  This paper explores the connections between particle scattering and quantum
information theory in the context of the non-relativistic, elastic scattering
of two spin-1/2 particles. An untangled, pure, two-particle in-state is evolved
by an S-matrix that respects certain symmetries and the entanglement of the
pure out-state is measured. The analysis is phrased in terms of unitary,
irreducible representations (UIRs) of the symmetry group in question, either
the rotation group for the spin degrees of freedom or the Galilean group for
non-relativistic particles. Entanglement may occurs when multiple UIRs appear
in the direct sum decomposition of the direct product in-state, but it also
depends of the scattering phase shifts. \keywords{dynamical entanglement,
scattering, Clebsch-Gordan methods}
