Electron-impact single and double ionization of helium

Electron-impact ionization cross sections for helium are calculated using time-dependent close-coupling theory. The total wave function for the three electron system is expanded in nine dimensions, where three dimensions are represented on a radial lattice and a coupled channels expansion is used to represent the other six dimensions. Collision cross sections are obtained by t→∞ projection onto fully antisymmetric spatial and spin functions, with care as to orthogonality of different representations. Cross sections are also obtained using time-independent first- and second-order perturbative distorted-wave theory. Total cross sections are calculated at incident energies above the double ionization threshold for electron-impact single ionization leaving He⁺ in the $1s$, $2s$, and $2p$ states and for electron-impact double ionization. Both the single ionization cross section, leaving He⁺ in the $1s$ ground state, and the double ionization cross section are in excellent agreement with previous absolute experimental measurements.