The scattering and polarization of fast electrons by heavy elements

Abstract

Using the methods of a previous joint paper, the calculation of the scattering and polarizetion of electrons with energies between 5·4 and 1060 keV is extended to the whole angular range for the atomic field of gold. It is found that even at the highest energies the angular distribution of the scattering does not exhibit a monotonic fall with increasing angle, and that the asymmetry in double scattering reaches a maximum value which is quite large at angles greater than 90°. The variation of the total elastic cross-section with energy is also mvestigated. A simple closed formula for the scattering is obtained by transforming Dirac’s equations into a single differential equation of the same form as Schrodinger’s equation but with a modified ‘scattering potential’, and then using this potential in Born’s approximation. The resulting formula gives angular distributions to which the exact values of the scattering appear to approach more and more closely as the energy of the electrons increases. In connexion with the discrepancies between the results of various observers for the scattering and the polarization at 90°, it is shown that if a long-range repulsive field is added to the field of the atom so as appreciably to reduce the scattering, the asymmetry in double scattering is reduced by a larger factor.