On the Absence of Polarization in Electron Scattering

In an attempt to explain the discrepancy between Mott's theory and the observational results on the polarization of electrons in the double scattering experiment, we have investigated the depolarizing effect of (1) multiple elastic scattering, (2) inelastic scattering with spin change of the incident electron and (3) exchange scattering in which the exchanged electrons have opposite spins. Although multiple scattering actually takes place in the Au foils used in the experiments, the depolarization caused by such scattering is negligible. For a screened Coulomb field and electrons of 100 kv the depolarization in a 2.5 ×{} 10^-5 cm Au foil is only 2.2 percent whereas a 90-100 percent depolarization is needed to reconcile theory and experiment. The depolarization caused by inelastic scattering is about 100 times smaller than that caused by elastic scattering. The small depolarization in these two cases is due to the fact that while there are many elastic and inelastic collisions, most of these collisions take place with small scattering angle ϑ and for small angles the depolarization per collision is small (of order ϑ²). The main contribution to the depolarization by inelastic collisions comes then from large scattering angles at which inelastic scattering is relatively infrequent. The exchange scattering contributes practically no depolarization ({~}10^-12). While the depolarization per collision in each exchange process is relatively complete, the number of exchange processes is extremely small due to interference ({~}10^-14 times the number of elastic collisions). Therefore the absence of polarization in electron scattering cannot be explained on the basis of the processes considered here.A discussion of the validity of the first Born approximation is given (Appendix {}2). It is shown that in the case that the Born expansion parameter e²Zv is of order unity, the first Born approximation gives a result for the scattered intensity which is accurate to within 20 percent or better. The depolarization is given with an accuracy of 18 percent or better.