Polarization effect in scattering of Dirac particles by a central potential in the zero-energy limit

Abstract

The scattering of Dirac particles by a central potential is revisited. An analytic analysis is carried out for the behavior of the phase shifts and the cross sections for unpolarized and polarized particles in the zero-energy limit. Special attention is paid to the polarization effect in the zero-energy limit. For incident particles with longitudinal polarization, it turns out that their polarization is in general kept unchanged after scattering, consistent with naive physical judgement. However, when the central potential takes some special form such that it supports a critical-energy solution in some specific angular momentum channel, the situation is dramatically changed, and a considerable part of the scattered particles have their original polarization reversed. For a spherical square well potential with appropriate depth, up to 53.8% of the scattered particles may have their polarization reversed.