The interaction of fast electrons with light atoms

A model is presented that describes the non-relativistic scattering of electrons from light atoms at energies above the single ionization threshold of the target. The simplest form of this approximation is considered, and application made to elastic collisions with hydrogen and helium atoms. This requires the numerical solution of a second order integrodifferential equation, and a technique that achieves this is discussed. Supplementing this model with a distorted wave approximation gives a description of the excitation of any target state. This is illustrated for the l (^1) S → 2 (^1) s, 2 (^3) s and 2 (^1) f transitions in helium and the 1s → 2s transition in hydrogen. Differential, integrated and total cross-sections are presented in the energy range 50-200 eV for hydrogen and50-500 eV for helium. In addition, the relative populations and phases of the magnetic sub-levels of the 2 (^1) p state of helium, following excitation from the ground state, have been computed. Finally, the use of dispersion relations as a consistency check on experimental data is demonstrated for electron neon and positron-helium scattering.