Elastic Collisions of Electrons with Helium

Abstract

IN view of the recent experiments of Dymond and Watson on the scattering of electrons in helium (Proc. Roy. Soc., vol. 122, p. 571), it has been of interest to work out the scattering predicted by the wave mechanics. The method used is that of Born (Göttinger Nachrichten, p. 146, 1926), and involves two separate approximations. In the first place, we neglect the polarisation of the atom by the incident electron, the atom being treated as an electrostatic centre of force. We have used the field calculated for helium by Hartree (Proc. Camb. Phil. Soc., vol. 24, p. 111). Secondly, we have calculated only the first approximation of Born, which is sufficient only if the de Broglie wave-length of the incident electrons is large compared to the classical distance of closest approach. Neither approximation will introduce a serious error if the energy of the incident electrons is large compared to the ionisation energy of the atom. For 200-volt electrons the error should not be greater than about 20 per cent.