We prove that in multidimensional short-range potential scattering the
high velocity limit of the scattering operator of an N-body system de
termines uniquely the potential. For a given long-range potential the
short-range potential of the N-body system is uniquely determined by t
he high velocity limit of the modified Dollard scattering operator. Mo
reover, we prove that any one of the Dollard scattering operators dete
rmines uniquely the total potential, We obtain as well a reconstructio
n formula with an error term. Our simple proof uses a geometrical time
-dependent method. (C) 1995 American Institute of Physics.