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

Abstract

The scattering formula of Rutherford gives an expression for the number n 1 d Ω of electrons in a gas which are scattered from a beam of electrons over the solid angle d Ω by impacts with atoms, which are to be found along a certain length l of this beam. If + Z e 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 n 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 N l (Z e /4V) 2 d Ω/sin 4 ½Θ, (1) where Θ is the angle of scattering. When n 0 = 1, N = 1, and l = 1 the scattering is usually expressed by I θ d Ω, where I θ is the so-called “scattered intensity.’’ According to Rutherford’s formula we get for the classical scattering due to the nucleus: I θ = ( e /4V) 2 Z 2 /sin 4 ½Θ. (2) Taking into consideration the electrons around the nucleus Mott and Bethe find: I θ = ( e /4V) 2 (Z -F) 2 /sin 4 ½Θ, (3) where F is the atomic form factor, known from the scattering of X-rays, and also a function of (V sin 2 ½Θ). The values calculated for helium by James have been used for F in this paper.