Quantum scattering in helically twisted geometries: Coulomb-like interaction and Aharonov-Bohm effect

TL;DR

This paper analyzes quantum scattering of charged particles in a helically twisted space, revealing how geometry and magnetic flux influence Coulomb-like interactions and scattering properties.

Contribution

It derives exact solutions for scattering in a twisted geometry with AB flux, linking geometry-induced Coulomb effects to known Coulomb-AB problems.

Findings

Exact scattering solutions and phase shifts obtained

Scattering amplitude and cross sections derived

Pole structure consistent with bound states

Abstract

We investigate the scattering of a charged quantum particle in a helically twisted background that induces an effective Coulomb-like interaction, in the presence of an Aharonov-Bohm (AB) flux. Starting from the nonrelativistic Schr\"odinger equation in the twisted metric, we derive the radial equation and show that, after including the AB potential, it can be mapped onto the same Kummer-type differential equation that governs the planar $2D$ Coulomb $+$ AB problem, with a geometry-induced Coulomb strength and the azimuthal quantum number shifted as $m\to m-\lambda$. We construct the exact scattering solutions, obtain closed expressions for the partial-wave $S$ matrix and phase shifts, and derive the corresponding scattering amplitude, differential cross section, and total cross section. We also show that the pole structure of the $S$ matrix is consistent with the bound-state quantization previously obtained for the helically twisted Coulomb-like problem.