A note on low energy scattering for homogeneous long range potentials

TL;DR

This paper explicitly computes the zero-energy scattering matrix for attractive, radial, long-range potentials, confirming a prior conjecture and advancing understanding of quantum scattering in such systems.

Contribution

It provides the first explicit calculation of the zero-energy scattering matrix for a class of long-range potentials, confirming a previous conjecture.

Findings

Explicit zero-energy scattering matrix derived

Confirmation of Derezinski and Skibsted's conjecture

Advances in understanding long-range potential scattering

Abstract

We explicitly calculate the scattering matrix at energy zero for attractive, radial and homogeneous long-range potentials. This proves a conjecture by Derezinski and Skibsted.