Quantum diffraction and threshold law for the Temkin-Poet model of electron-hydrogen ionization

Relying on an entirely ab initio quantum-mechanical scheme, we investigate the threshold behavior of a model electron-impact ionization problem in which the target hydrogen atom interacts with the incident electron only by monopole. The total ionization cross section for a singlet is shown to follow the threshold law of an exponential form as proposed by Macek and Ihra , thus supporting the argument based on the local instability of the "ridge'' motion despite the reported absence of classical ridge trajectories. Below the classical threshold, quantum diffraction allows the two electrons to have a large probability amplitude in the region inaccessible to the classical trajectories. The energy distribution for singlet in final continuum channels is shown to have a hitherto unexpected V-shaped structure at energies between 0 and 1 a.u. above the ionization threshold. The V structure becomes sharper toward the threshold while it approaches the quadratic form surmised by Bray at higher energies. [S1050-2947(99)02206-4].