Coulomb Scattering of Electrons at Very Small Angles

Electrostatic scattering of highly relativistic electrons at very small angles is discussed. The Hartree wave function is used to calculate the screening effects for the smallest angles. The calculations are facilitated by a theorem which states that, in the Born approximation for elastic scattering by any physical central potential, the total cross section in the relativistic limit is independent of energy.Both the "elastic" (nuclear) and "inelastic" (electronic) contributions to the scattering are investigated. It is found that at very small angles the inelastic differential cross section exceeds by many times the elastic differential cross section. Numerical calculations were carried out for scattering by nitrogen atoms, where the total cross section of the scattering by atomic electrons is 3.6 times the total cross section due to screened nuclear scattering.