  Scattering theory traditionally deals with the asymptotic behaviour of a
system far removed from the actual scattering event. Here we present an
experimental study of the one-dimensional scattering of a non-interacting
condensate of 87-Rb atoms from a potential barrier in the non-asymptotic
regime, for which the collision dynamics are still ongoing. We show that for
near-transparent barriers, there are two distinct transient scattering effects
that arise and dramatically change the momentum distribution during the
collision: a deceleration of wavepacket components in mid-collision, and an
interference between incident and transmitted portions of the wavepacket. Both
effects lead to the re-distribution of momenta giving rise to a rich
interference pattern that can be used to perform reconstruction of the
single-particle phase profile.
