Total and ionization cross sections in a simplified model of electron-hydrogen scattering

The total cross section (inclusive of all scattering) is calculated as a function of energy for a simplified model of electron-hydrogen scattering in which all terms involving nonzero angular momenta are neglected. Only the ${}_{}{}^1{}_{}{}^{}S$ state is considered. The two-body Schrödinger equation is integrated numerically, and the optical theorem is used to determine the total cross section. The results agree rather well with those obtained from a pseudostate expansion. High and low bounds are given for the ionization cross section, and these are compared with estimates of ionization obtained from a pseudostate expansion.