The theory of electron-ion collisions

The results of recent large scale R-matrix calculations are used to study the convergence of the close coupling approximation for the calculation of electron excitation cross sections for atoms and ions. For the electron excitation of atoms these studies suggest that to obtain reliable cross sections below the ionization threshold it is necessary to include in the calculations a number of bound states which lie above the state under consideration. If the incident electron energy is just above the ionization threshold it is found that, even if we include a large number of bound states in the calculation, the cross section results do not converge to the true result and it is necessary to take account of continuum states in the close coupling expansion. However for the electron excitation of ions the convergence of the close coupling expansion is more rapid than that for atoms and the rate of convergence appears to increase as the nuclear charge of the ion increases