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

TL;DR

This paper investigates the inverse scattering problem at fixed high energy for multidimensional Newton equations with short-range electromagnetic fields, establishing uniqueness results under specific symmetry and decay conditions.

Contribution

It provides a new uniqueness theorem for inverse scattering at fixed energy in multidimensional Newton equations with electromagnetic fields, assuming spherical symmetry and localized magnetic fields.

Findings

Proves uniqueness of potential and field reconstruction under given conditions.

Extends classical inverse scattering results to multidimensional Newton equations.

Utilizes and builds upon foundational results by Firsov and Keller-Kay-Shmoys.

Abstract

We consider the inverse scattering problem at fixed and sufficiently large energy for the nonrelativistic and relativistic Newton equation in $\R^n$, $n \ge 2$, 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.