THE GEOMETRICAL APPROACH TO MULTIDIMENSIONAL INVERSE SCATTERING

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.