Partial wave analysis of the first order Born amplitude of a Dirac particle in an Aharonov-Bohm potential

A partial wave analysis using the basis of the total angular momentum operator J₃ is carried out for the first order Born amplitude of a Dirac particle in an Aharonov-Bohm potential. It is demonstrated that the s partial wave contributes to the scattering amplitude in contrast with the case with scalar nonrelativistic 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.