Inverse scattering at fixed energy for the multidimensional Newton equation in short range radial potentials

Abstract

We consider the inverse scattering problem at fixed and sufficiently large energy for the nonrelativistic and relativistic Newton equation in ${\mathbb{R}}^n$, $n\ge 2$, with a smooth and short range electromagnetic field $(V,B)$. Using results of [Firsov, 1953] or [Keller-Kay-Shmoys, 1956] we obtain a uniqueness result when $B$ is assumed to be zero in a neighborhood of infinity and $V$ is assumed to be spherically symmetric in a neighborhood of infinity.