Inverse Scattering at a Fixed Energy for Long-Range Potentials
  In this paper we consider the inverse scattering problem at a fixed energy for the Schr\"odinger equation with a long-range potential in $\ere^d, d\geq 3$. We prove that the long-range part can be uniquely reconstructed from the leading forward singularity of the scattering amplitude at some positive energy. 
Ricardo Weder and Dimitri Yafaev