  We study the quantum entanglement produced by a head-on collision between two
gaussian wave packets in three-dimensional space. By deriving the two-particle
wave function modified by s-wave scattering amplitudes, we obtain an
approximate analytic expression of the purity of an individual particle. The
loss of purity provides an indicator of the degree of entanglement. In the case
the wave packets are narrow in momentum space, we show that the loss of purity
is solely controlled by the ratio of the scattering cross section to the
transverse area of the wave packets.
