On Inverse Scattering at a Fixed Energy for Potentials with a Regular   Behaviour at Infinity
  We study the inverse scattering problem for electric potentials and magnetic fields in $\ere^d, d\geq 3$, that are asymptotic sums of homogeneous terms at infinity. The main result is that all these terms can be uniquely reconstructed from the singularities in the forward direction of the scattering amplitude at some positive energy. 
Ricardo Weder and Dimitri Yafaev