The scattering of fast β-particles by electrons

Abstract

In a recent paper, it has been shown, using the expansion method, that the simple relativistic expressions govern the transfer of momentum and energy during the close collisions of fast β-particles with electrons. The present paper gives an account of an investigation of the scattering of fast β-particles by electrons, using the expansion method. Among the many formulæ which have been proposed to express the interaction of two electrons, the relativistically invariant expression due to Möller appears to be the most satisfactory theoretically. Möller has referred the scattering for all velocities to a Lorentz frame of co-ordinates in which the momenta of the two electrons are equal and opposite. The observed angle of scattering θ is connected with θ*, the angle of scattering in the Lorentz frame, by the relation x=cos θ*=2-(γ+3) sin² θ/2+(γ-1) sin² θ (1) where γ=1/(l-β²)^½ and β=v/c, v being the relative velocity of the two particles before collision and c the velocity of light.