  We investigate the relativistic kinematics of the spin-polarized collision of
deuterium incident on tritium, producing ${}^4$He and a neutron. Within the
context of special relativity, we apply the conservation of four momentum and
the conservation of intrinsic spin, which leads to a system of ten equations.
We impose initial conditions such that the deuterium is moving along the
x-axis, the tritium is stationary at the origin of coordinates, and the
classical spin vector of the deuterium (spin magnitude = 1) is along the
+z-axis, while the classical spin vector for tritium (spin magnitude = 1/2) is
along the $-$z-axis. We expand the ten conservation equations to second order
in velocities and we solve them for the velocity components of the neutron, its
unit-spin-orientation vector, and the velocity components of the ${}^4$He
nucleus, as a function of the incident deuterium energy. We find that this
analytic solution agrees closely with the numerical solution of the ten
(unexpanded) equations. For a given energy of deuterium, we find that there are
two solutions, each solution having a unique velocity for the emitted neutron
and helium nucleus. The two solutions are related to each other by reflection
in the plane perpendicular to the deuterium spin and containing the initial
deuterium velocity vector.
