Electron scattering in helium. Absolute measurements at 90° and 45°

The scattering formula of Rutherford gives an expression for the numbern 1 d Ω of electrons in a gas which are scattered from a beam of electrons over the solid angled Ω by impacts with atoms, which are to be found along a certain lengthl of this beam. If + Ze is the charge of the nucleus of the atoms, —e andm the charge and the mass of the electron, V the potential difference through which the electrons are accelerated, N the number of atoms in unit volume andn 0 the total number of electrons which pass a certain cross-section of the beam, we have the well-known formula:n 1 d Ω =n 0 Nl (Ze /4V)2 d Ω/sin4 ½Θ, (1) where Θ is the angle of scattering. Whenn 0 = 1, N = 1, andl = 1 the scattering is usually expressed by Iθ d Ω, where Iθ is the so-called “scattered intensity.’’ According to Rutherford’s formula we get for the classical scattering due to the nucleus: Iθ = (e /4V)2 Z2 /sin4 ½Θ. (2) Taking into consideration the electrons around the nucleus Mott and Bethe find: Iθ = (e /4V)2 (Z -F)2 /sin4 ½Θ, (3) where F is the atomic form factor, known from the scattering of X-rays, and also a function of (V sin2 ½Θ). The values calculated for helium by James have been used for F in this paper.