  We study the scattering of a matter-wave from an interacting system of bosons
in an optical lattice, focusing on the strong-interaction regime. Analytical
expressions for the many-body scattering cross section are derived from a
strong-coupling expansion and a site-decoupling mean-field approximation, and
compared to numerically obtained exact results. In the thermodynamic limit, we
find a non-vanishing inelastic cross section throughout the Mott insulating
regime, which decays quadratically as a function of the boson-boson
interaction.
