Analysis of the ambiguities in the definition of the local complex potential in resonant electron-molecule scattering

The alternative definitions of the local complex potential for nuclear motion in short-lived electronic states are discussed. It is shown that different definitions may yield very different potentials in the case of broad resonances. Within an exactly solvable model the electron scattering cross sections calculated in the various local approximations are compared with one another and with the exact results. It is found that there is no generally preferable local potential. The local potential obtained by a Breit-Wigner analysis of the phaseshift gives superior results in the elastic channel, whereas the local potential determined from the pole of the S matrix yields better results in the vibrationally inelastic channels. As a by-product of the analysis, it is found that wildly differing local complex potentials may yield very similar electron scattering cross sections. This casts serious doubts on the uniqueness and reliability of empirical local complex potentials obtained by fitting experimental scattering cross sections.