On the Quantum Theory of the Capture of Electrons

Abstract

In Section 1 the method of a previous ${\mathrm{paper}}^{1}$ is applied to find the rate at which $\ensuremath{\alpha}$ particles capture electrons from atoms. The mean free path for capture varies roughly with the sixth power of the velocity of the $\ensuremath{\alpha}$ particle, and in good agreement with Rutherford's ${\mathrm{experiments}.}^{3}$ The value of the mean free path is computed for capture in air, and agrees with the experimental value.In Section 2 the probability of radiative recombination of electrons and protons is computed. The cross section for recombination becomes infinite for small relative velocities with the inverse square of the velocity; for high velocities it is given by ${10}^{\ensuremath{-}18}{W}^{\ensuremath{-}\frac{5}{2}}$, where $W$ is the energy in volts of the incident electrons.