The Influence of Close Coupling on the Threshold Behaviour of Cross Sections of Electron-Hydrogen Scattering

Abstract

The behaviour of cross sections in the neighbourhood of thresholds depends on the character of the interaction of particles at large distances. For the short-range forces Wigner showed that the inelastic cross sections depend on energy as k_f^2l_f+1 where k_f, l_f are the momentum and angular momentum in the final state. The present article investigates the threshold behaviour for electron-hydrogen scattering where an essential influence is being exerted by close coupling, which leads to long-range forces. It is found that for electron-hydrogen scattering the k_f^2l_f+1 dependence no longer holds because of the strong polarization interaction produced by the colliding electron when the hydrogen atom is in the excited state. Cross sections in the neighbourhood of the threshold oscillate. Inelastic cross sections approach zero only at an energy above the threshold of the order of the relativistic splitting between levels.