Probing the nonlocal approximation to resonant collisions of electrons with diatomic molecules

A numerically solvable two-dimensional model introduced by the authors [Phys. Rev. A 73, 032721 (2006)] is used to investigate the validity of the nonlocal approximation to the dynamics of resonant collisions of electrons with diatomic molecules. The nonlocal approximation to this model is derived in detail, all underlying assumptions are specified and explicit expressions for the resonant and non-resonant (background) T matrix for the studied processes are given. Different choices of the so-called discrete state, which fully determines the nonlocal approximation, are discussed and it is shown that a physical choice of this state can in general give poorer results than other choices that minimize the non-adiabatic effects and/or the background terms of the T matrix. The background contributions to the cross sections, which are usually not considered in the resonant theory of electron-molecule collisions, can be significant not only for elastic scattering but also for the inelastic process of vibrational excitation