The scattering of slow alpha particles by helium

Abstract

1. Gordon has proved that the scattering of particles by an inverse square field is the same on the wave mechanics as on the classical theory. Mott has however shown, from consideration of the symmetry of the wave functions, that the scattering is quite different from the classical when the scattering and scattered particles are identical. The scattering of alpha particles by helium is typical of the case of the collision of identical particles that have no pin and obey the Einstein-Bose statistics. For this case, the expression given by Mott for the number of alpha particles scattered between angles θ, and θ +dθ, in going a distance dr in a gas containing n atoms per unit volume, is N dθ dr = 4πnN₀e⁴/m²v⁴ {cosec⁴ θ + sec⁴ θ + 2 cosec² θ sec² θ cos u} dθ dr, (1) where u = 8/137 c/v log cot θ, (2) and N₀ is the total number of incident particles, v, m and e, their initial velocity, mass and charge and c the velocity of light.