  We investigate the time evolution of entanglement in a process where a mobile
particle is scattered by static spins. We show that entanglement increases
monotonically during a transient and then saturates to a steady-state value.
For a quasi-monochromatic mobile particle, the transient time depends only on
the group-velocity and width of the incoming wavepacket and is insensitive to
the interaction strength and spin-number of the scattering particles. These
features do not depend on the interaction model and can be seen in various
physical settings.
