Photon and Electron Polarization in High-Energy Bremsstrahlung and Pair Production with Screening

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The matrix element for bremsstrahlung and pair production is written in a particularly simple form which reduces to the wellknown matrix element for nonrelativistic energies, in terms of a vector which is closely related to the nonrelativistic current density vector.The cross section for high-energy bremsstrahlung and pair production involving arbitrarily polarized photons and electrons has been calculated. The Coulomb and screening effects are taken into account exactly. It is found that the screening and Coulomb corrections to the polarization-dependent part of the cross section are analytically of the same form and numerically of the same magnitude as the corrections to the polarization-independent part of the cross section found earlier. We also give the cross section for bremsstrahlung summed over spin and polarization directions and integrated over the direction of motion of the final particle, i.e., the angular distribution of the radiation, which has a very simple form.Formulas are given for the linear and circular polarization of bremsstrahlung from arbitrarily polarized electrons and for the spin polarization of pairs from arbitrarily polarized photons. The circular polarization of bremsstrahlung from longitudinally polarized electrons is complete at the upper end of the spectrum and is much larger than from transversely polarized electrons throughout the spectrum. In the same way, circularly polarized photons produce longitudinally polarized electron-positron pairs, the probability of producing transversely polarized pair particles being, in general, much smaller. The faster one of the pair particles is always polarized in the same sense as the photon. On the other hand, the linear polarization of bremsstrahlung is smallest at the upper end of the spectrum and increases with decreasing photon energy. It is independent of the spin of the initial electron if one sums over the spin of the final particle. The circular polarization of the emitted photons is to a high degree independent of screening and Coulomb corrections, at the high energies considered here. The linear polarization is, however, significantly dependent on these corrections. Similar conclusions hold for pair production from circularly and linearly polarized photons, respectively.Finally, the electron spin-photon polarization correlation for bremsstrahlung and pair production is discussed. The depolarization, because of bremsstrahlung, of polarized electrons passing through matter is calculated and is appreciable over a radiation length. It is greater for a transversely polarized electron than for a longitudinally polarized electron.