  We demonstrate an interference method to determine the low-energy elastic
scattering amplitudes of a quantum gas. We linearly accelerate two ultracold
atomic clouds up to energies of 1.2 mK and observe the collision halo by direct
imaging in free space. From the interference between $s$- and $d$- partial
waves in the differential scattering pattern we extract the corresponding phase
shifts. The method does not require knowledge of the atomic density. This
allows us to infer accurate values for the $s$- and d-wave scattering
amplitudes from the zero-energy limit up to the first Ramsauer minimum using
only the Van der Waals $C_{6}$ coefficient as theoretical input. For the
$^{87}$Rb triplet potential, the method reproduces the scattering length with
an accuracy of 6%.
