The exact solution for a simplified model of electron scattering by hydrogen atoms

Abstract

A simplified electron-hydrogen excitation problem is solved for low and medium energies by neglecting all angular momentum. The integrals arising can be expressed in terms of hypergeometric functions, so that accurate solutions can be computed rapidly. This model situation still includes an effect that complicates more realistic problems, that of strong coupling between an infinite number of open channels, and the associated need for an adequate continuum representation. These results are therefore of importance in testing other methods which have been used, or are under development, for solving the full physical problem.