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

Abstract
The scattering formula of Rutherford gives an expression for the number n1dΩ of electrons in a gas which are scattered from a beam of electrons over the solid angle dΩ by impacts with atoms, which are to be found along a certain length l of this beam. If + Ze is the charge of the nucleus of the atoms, — e and m 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 and n0 the total number of electrons which pass a certain cross-section of the beam, we have the well-known formula: n1 dΩ = n0Nl (Ze/4V)2 dΩ/sin4½Θ, (1) where Θ is the angle of scattering. When n0 = 1, N = 1, and l = 1 the scattering is usually expressed by Iθ dΩ, 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/sin4½Θ. (2) Taking into consideration the electrons around the nucleus Mott and Bethe find: Iθ = (e/4V)2 (Z -F)2/sin4½Θ, (3) where F is the atomic form factor, known from the scattering of X-rays, and also a function of (V sin2½Θ). The values calculated for helium by James have been used for F in this paper.

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