Low-energy electron scattering by atomic hydrogen: IV. The effect of resonances on excitation in e^--H scattering

Abstract

The 1S, 3S, 1P, 3P and 1D partial cross sections for e--H scattering given in two of the preceding papers are analysed using many-channel resonance theory. Partial widths, resonance positions and the background scattering matrix are obtained. The peak at 11.5 ev in the 1s-2s excitation cross section is shown to follow from interference of resonant and non-resonant processes. This interference is examined in detail and is shown to imply that the scattering matrix can be simplified by transforming it to a representation which diagonalizes the long-range 1/r2 potentials coupling the degenerate n = 2 states. The scattering matrix in this representation is obtained, and it is found that the resonance states decay into the same linear combination of states at the n = 2 threshold that are excited from the ground state. Some general results in multi-channel resonance theory, applicable to such situations, are then proved. Finally the origin of the 1P H- autoionizing state at 10.24 ev is discussed, and its position and width are obtained.