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 $\frac{{\phi }_p}{{\phi }_a}$. (The cross section is denoted by ${\phi }_p$ when the spins of the particles before scattering are parallel, by ${\phi }_a$ when antiparallel.) In the case of scattering of indistinguishable particles $\frac{{\phi }_p}{{\phi }_a}$ is different from unity at all energies and scattering angles and can be as small as zero. For particle-antiparticle scattering $\frac{{\phi }_p}{{\phi }_a}$ 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, $\frac{{\phi }_p}{{\phi }_a}$ is calculated for two particles of different masses $m$ and $\mu$. It is shown that also in this case, in principle, $\frac{{\phi }_p}{{\phi }_a}$ could be used for polarization measurements.