We prove that the high velocity limit of the scattering operator of a
two-body system in an external constant electric field determines uniq
uely the potential. In the case of an N-body system we prove that the
high velocity limit of any one of the Dollard scattering operators det
ermines uniquely the potential. Furthermore, we obtain a formula with
error term for the reconstruction of the potential. We prove our resul
ts with a simple time-dependent method. (C) 1996 Academic Press, Inc.