A simple formula for the vibrational structure of resonances in electron-molecule scattering

Starting from a simple model Hamiltonian an explicit expression for the resonant vibrational excitation cross section is obtained. The formula is applied to calculate the excitation functions for the symmetric-stretch vibrational channels of the 3.8 eV shape resonance of CO₂. The regular and non-trivial energy and channel-number dependence of the cross section is nicely reproduced. The results show a remarkable improvement over those obtained with existing theories which express the cross sections in terms of conventional vibrational overlap factors.