Partial wave Analysis of the First Order Born Amplitude of a Dirac Particle in an Aharonov-Bohm Potential

TL;DR

This paper performs a partial wave analysis of a Dirac particle in an Aharonov-Bohm potential, revealing unique contributions of the s-partial wave and uncovering an algebra involving the Dirac velocity operator.

Contribution

It introduces a partial wave analysis using total angular momentum basis for Dirac particles in AB potential, highlighting differences from scalar particles and discovering a new algebra.

Findings

The s-partial wave contributes to the scattering amplitude for Dirac particles.

The first order Born amplitude matches the exact amplitude for Dirac particles.

An algebra involving the Dirac velocity operator and angular observables is identified.

Abstract

A partial wave analysis using the basis of the total angular momentum operator J_3 is carried out for the first order Born amplitude of a Dirac particle in an Aharonov-Bohm (AB)potential. It is demonstrated that the s-partial wave contributes to the scattering amplitude in contrast to the case with scalar non-relativistic particles.We suggest that this explains the fact that the first order Born amplitude of a Dirac particle coincides with the exact amplitude expanded to the same order, where it does not for a scalar particle. An interesting algebra involving the Dirac velocity operator and the angular observables is discovered and its consequences are exploited.