  We investigate two-body collisions occurring during the time-of-flight
expansion of interacting three-dimensional lattice Bose superfluids. The number
of collisions is extracted from the observed s-wave scattering halos located
between the diffraction peaks of the superfluids. These faint halos can be
monitored thanks to the large dynamical range in densities associated with
detecting individual metastable Helium atoms. We monitor the number of
collisions as a function of the total atom number and of the amplitude of the
lattice, in a regime where the number of trapped atoms per lattice site is
large. In addition, we introduce a classical model of collisions that
quantitatively describes the experiment without adjustable parameters. Finally,
the present work validates quantitatively the assumption of a ballistic
expansion when investigating the Bose-Hubbard Hamiltonian with a unity
occupation of the lattice.
