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Nuclear dynamics in resonant electron-molecule scattering beyond the local approximation: model calculations on dissociative attachment and vibrational excitation

Within the framework of Feshbach's projection operator formalism, the calculation of cross sections for resonant electron-molecule scattering and dissociative attachment can be reduced to the treatment of nuclear dynamics in an energy-dependent, complex and non-local potential. In this work, a new method to solve the difficult problem of nuclear motion in the non-local potential is developed. The method is based on the parametrisation of the potential energy curves of the target molecule and the projected resonance state by Morse functions. The non-local part of the potential is represented in a separable form, using the Lanczos, (1950) basis of the Morse Hamiltonian as the basis set for the expansion. Numerically exact non-local calculations are performed, and the accuracy of the local approximation is critically assessed for a model representing dissociative attachment via a d-wave shape resonance. For the examples considered it is found that the most important corrections to the local approximation result from the energy dependence of the entry and exit amplitudes.