Oscillatory energy dependence of resonant electron-molecule scattering

The cross sections for the vibrational excitation of N2 molecules bombarded by electrons show a strong peak between 2 and 3 eV, split up into a regular sequence of minor peaks reminiscent of distinct resonances. However, the minor peaks appear in the different final channels at different energies and with slightly different spacings, a behaviour which could be understood on the resonance picture only as the result of some interference effect. An explanation of the phenomenon is offered, based on the assumption (for which reasons are given) that the nuclear wave function in the intermediate N2- ion is a standing wave whose amplitude varies slowly, and whose nodes move slowly as the energy changes. As the nodes drift over the nodes of the final states of the residual molecule, the overlap integrals of the intermediate and final states oscillate, and hence the cross sections oscillate too. The spacing of the minor peaks in energy and their relative displacement for the different final states can be understood in terms of the drifting nodes in an energy representation, and in the corresponding time representation in terms of the motion of the nuclear wave packet.

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