Scattering and (e,2e) reactions in classical s-wave helium

We study the classical collisions of electrons with one-electron atoms or ions in a model where both electrons are restricted to spherical states. At negative total energy, we calculate the probability for bound motion of both electrons occurring-as opposed to undelayed direct or exchange scattering. At positive total energy, we calculate the probability for (e,2e) reactions. There is a finite threshold for the onset of (e,2e) reactions. Its value depends on the nuclear charge and can be deduced from a simple transcendental equation. The general behavior of the probability for (e,2e) reactions as a function of energy is quite similar to the results of quantum-mechanical calculations and to experimental data.