Electron and proton scattering by hydrogen atoms in a coupled state approximation

The excitation of atomic hydrogen by electron and proton impact is examined. Some of the available theoretical methods are discussed, in particular the methods of the first and second born approximation., the close coupling approximation and the Glauter approximation are outlined. The close coupling approximation is presented in both the wave and impact parameter formulations. The neglect of the continuum states in the eigenfunction expansion of the close coupling method is shown to be unsatisfactory and the methods of including the effects of these states described. The relationship between the two forms of close coupling approximation is explored via the eikonal approximation, and the Glauber approximation is shown to be a solution of a set of close coupled equations where all states are approximately included. A close coupling approximation that includes some eigenstates explicitly and the rest, including the continuum states, approximately is present. The method is applied in the impact parameter approximation to electron and proton collisions with hydrogen. Results are presented for the 1s - 2s and the 1s - 2p excitation cross sections and are compared with the available experimental cross sections. The comparison is inconclusive and suggestions are made for further work. Comparison with other theoretical predictions suggest that the effects of charge transfer on the direct excitation process are not allowed for despite the inclusion of the continuum states.