Non-uniqueness of phase shift in central scattering due to monodromy

TL;DR

This paper reveals that in 2D scattering with a repulsive central potential, the phase shift cannot be uniquely defined because of a topological obstruction akin to monodromy, challenging traditional scattering theory assumptions.

Contribution

It demonstrates the non-uniqueness of phase shifts in 2D scattering caused by a monodromy-like topological obstruction, a novel insight in scattering theory.

Findings

Phase shift non-uniqueness in 2D scattering

Topological obstruction similar to monodromy identified

Challenges traditional assumptions in scattering characterization

Abstract

Scattering at a central potential is completely characterized by the phase shifts which are the differences in phase between outgoing scattered and unscattered partial waves. In this letter it is shown that, for 2D scattering at a repulsive central potential, the phase shift cannot be uniquely defined due to a topological obstruction which is similar to monodromy in bound systems.