Theory of the Elastic Scattering of Electrons in Molecular Hydrogen
Proceedings of the Royal Society A
Since tbe introduction of quantum mechanical methods, the theory of scattering of electrons by atoms and ions has been developed very considerably. In the case of elastic collisions it is possible to determine the effective cross sections presented by atoms to a beam of electrons, from a knowledge of the potential in the atom.* This has been done for helium by Mottf and the calculated cross sections agree well with the experimental. Unfortunately, the simplest theoretical case, that of the
... e, that of the elastic scattering of electrons by atomic hydrogen, the theory of which has been given by Elsasser, $ is extremely difficult to attain experimentally, 50 to 60 per cent, atomic hydrogen being the maximum at present attainable. It thus would seem of interest to consider what effects would be expected by using molecular instead of atomic hydrogem This case is also novel in that we are considering an axially symmetrical field and the number of electrons scattered through a given angle depends on the orientation of the axis relative to the initial and final beams. In an actual case the axes of the molecules may be taken as in random directions, the hydrogen molecule having no permanent dipole moment and so being only slightly oriented by the electric field of the incident beam. This permits us to average the scattering over all orientation to obtain experimental conditions. § 1. General Description of Method.-It is necessary to restrict the calculation to electron velocities of such magnitude that resonance effects are not of importance and consider elastic collisions. Let tjq be the wave-function repre senting the state of the scattering system, n 0, nx unit vectors in the direction of the initial and final electron motions, m the electron mass, h Planck's con stant, v the electron velocity, and k = 27t mvjh. Then we find, from Born's collision formula,! that the scattering cross * * * § * Providing the electron beam is not too slow, when the theory fails, t ' Proc.