Multidimensional Inverse Scattering in an Electric Field

We prove that the high velocity limit of the scattering operator of a two-body system in an external constant electric field determines uniquely the potential. In the case of anN-body system we prove that the high velocity limit of any one of the Dollard scattering operators determines uniquely the potential. Furthermore, we obtain a formula with error term for the reconstruction of the potential. We prove our results with a simple time-dependent method.