Scattering of spin-polarized electron in an Aharonov--Bohm potential

TL;DR

This paper investigates how spin-polarized electrons scatter in an Aharonov-Bohm potential, deriving scattering amplitudes and cross sections while considering spin interactions, and concludes that bound states are not possible in this system.

Contribution

It provides explicit solutions for scattering amplitudes and cross sections for spin-polarized electrons in an Aharonov-Bohm potential, including spin interactions, and discusses bound state absence.

Findings

Derived expressions for scattering amplitude and cross section.

Showed that bound electron states cannot form in this system.

Analyzed the zero-radius flux tube model in the Born approximation.

Abstract

The scattering of spin-polarized electrons in an Aharonov--Bohm vector potential is considered. We solve the Pauli equation in 3+1 dimensions taking into account explicitly the interaction between the three-dimensional spin magnetic moment of electron and magnetic field. Expressions for the scattering amplitude and the cross section are obtained for spin-polarized electron scattered off a flux tube of small radius. It is also shown that bound electron states cannot occur in this quantum system. The scattering problem for the model of a flux tube of zero radius in the Born approximation is briefly discussed.