The Convergence of the Close Coupling Expansion

The convergence of the expansion of the total wave function, for electron-hydrogen scattering, in hydrogen-atom eigenstates is investigated. Calculations of the cross sections Q (1s-1s), Q (1s-2s) and Q (1s-2p), both including and excluding the 3s and 3p states of hydrogen, are carried out. It is found that the inclusion of the 3s and 3p states reduces considerably the calculated values of Q (1s-2s) and Q (1s-2p) and brings these cross sections into better agreement with experiment. It is concluded that the close-coupling expansion is poorly convergent for excitation cross sections in electron-hydrogen scattering.