Scattering of Longitudinally Polarized Fermions

Cross sections for scattering of longitudinally polarized Dirac particles are calculated. The results are presented in terms of the ratio of cross sections φₚφₐ. (The cross section is denoted by φₚ when the spins of the particles before scattering are parallel, by φₐ when antiparallel.) In the case of scattering of indistinguishable particles φₚφₐ is different from unity at all energies and scattering angles and can be as small as zero. For particle-antiparticle scattering φₚφₐ is close to unity at nonrelativistic energies, but at relativistic energies approaches the value of the corresponding ratio for indistinguishable-particle scattering. Thus, in both these cases, the scattering process provides a method for measuring longitudinal polarization. Thirdly, φₚφₐ is calculated for two particles of different masses m and μ. It is shown that also in this case, in principle, φₚφₐ could be used for polarization measurements.