On Inverse Scattering at a Fixed Energy for Potentials with a Regular Behaviour at Infinity

TL;DR

This paper proves that for certain electric and magnetic potentials in higher dimensions, the asymptotic behavior can be uniquely reconstructed from scattering data at a fixed positive energy, advancing inverse scattering theory.

Contribution

It establishes the unique reconstruction of asymptotic potential terms from fixed-energy scattering amplitude singularities for potentials with regular behavior at infinity.

Findings

Unique reconstruction of asymptotic potential terms

Scattering amplitude singularities determine potential behavior

Extension of inverse scattering results to broader classes of potentials

Abstract

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.