The Born closure approximation for the scattering amplitude of an electron-molecule collision

Abstract

When the fixed-nuclei (FN) approximation is applied to the calculation of electron scattering from a polar molecule, the resulting cross section diverges in the forward direction of scattering. This is due to the long-range nature of the interaction between the electron and the molecular dipole. To avoid this difficulty, a hybrid method is proposed for the calculation of the scattering amplitude. This method is based on the FN approximation for a close collision and the Born approximation for a distant collision. The present paper describes the detailed formulation of the method for practical applications. Furthermore the present approach is extended to other long-range interactions (due to quadrupole moment and/or polarization effect) and to a dipole-allowed vibrational excitation. In these cases, while no divergence occurs, it is often difficult to confirm the convergence of the partial-wave expansion. With the employment of the present approach, it is much easier to confirm the convergence and hence to obtain reliable cross sections. The formulas are given for diatomic molecules as well as for polyatomic ones.