Scattering and Polarization of Electrons

The possibility of accounting for the small polarization of electrons, as observed in the double scattering experiments and the anomalously small scattering of fast electrons ($E\gtrsim 500$ kev) in heavy scattering materials, by the assumption of non-Coulombian forces near the nucleus is investigated. It is assumed that the range of the anomalous forces is of the order of the nuclear (or electron) radius so that for all energies of interest ($E<\mathrm{}2\mathrm{}$ Mev), the range is much smaller than the wave-length of the electrons. Consequently, the scattering of only $s_{\frac{1}{2}}$ and $p_{\frac{1}{2}}$ electrons need be considered. Without any further assumptions as to the nature of the forces it is found that the phase shifts due to the deviation from the pure Coulomb field are too small to account for the observed scattering and asymmetry (relative difference between scattering at azimuth 0 and $\pi$ in double scattering) unless the inside wave functions at the boundary are nearly equal to the irregular part of the outside wave functions. In general this can be the case for either the $s_{\frac{1}{2}}$ or the $p_{\frac{1}{2}}$ wave function so that either the $s_{\frac{1}{2}}$ or the $p_{\frac{1}{2}}$ waves are scattered anomalously with appreciable phase shifts, but not both. The results for the scattering and asymmetry, at 90° in Au, when only one wave is scattered are: For the scattering of $s_{\frac{1}{2}}$ waves the asymmetry has a minimum value which for low energies, 100 to 300 kev, is 5 to 6 times greater than the observations allow; at higher energies, 500 to 1500 kev the scattering intensity has a minimum value of 25 to 40 percent of the Coulomb scattering which is somewhat larger than the observed ratio but is perhaps not beyond the limits of experimental error. The asymmetry corresonding to this minimum scattering is about the same as the asymmetry for the Coulomb field, viz. about 5 percent at these energies. Without any measurements at high energies it is difficult to exclude the possibility that the asymmetry may be as large as this. When only $p_{\frac{1}{2}}$ waves are scattered anomalously the correct asymmetry and scattering may be obtained at low energies. At high energies the minimum scattering is 70 to 80 percent of the Coulomb scattering which seems much too large. Therefore in order to obtain an asymmetry and scattering which are not in obvious disagreement with the observations it is necessary to assume either a large range or a specialized form for the non-Coulombian forces. The specialized form must be such that either of the following may take place: (1) At low energies only the $p_{\frac{1}{2}}$ wave is scattered and at high energies only the $s_{\frac{1}{2}}$ wave is scattered. (2) Both waves are scattered at all energies despite the small range of the forces. In the first case it seems necessary to postulate an interaction which has a rather strong energy dependence in the energy region where the scattering begins to depart from the Coulombian value. In the second case it is seen that the interaction must be very large, several times $137m{c}^2$, and in addition a rather special energy dependence would seem necessary. Insofar as these possibilities do not seem plausible it would appear that the anomalous scattering and asymmetry must be explained on grounds other than the existence of non-Coulombian forces.