On the Quantum Theory of Electronic Impacts

It is shown that the previous treatment of electronic collisions has been incomplete; the error consists in the neglect of terms in the solution which correspond to an interchange of the colliding electron with one of those in the atom. The corrected first order cross section for elastic collisions is evaluated by Dirac's method for atomic hydrogen and helium. The complete solution for hydrogen is set up by Born's method for hydrogen; it is shown that the elastic cross section becomes infinite, for low velocities, with the reciprocal of the velocity; it is further shown that the first order cross section reduces to that already obtained. For hydrogen this is a monotonically increasing function; for atoms with completely paired electrons the monotonic increase is broken by a minimum at velocities corresponding to about a volt; the higher the azimuthal quantum number of the paired valence electrons, the more marked the minimum, and the lower the voltage at which it occurs.