Electron scattering from diatomic polar molecules. II. Treatment by frame transformations

Abstract

The theory of Chang and Fano is applied to electron scattering by polar molecules. For collision energy $Eg{E}_{min}$ the problem can be treated accurately without numerical radial integration; the solution is presented in a form suited to an $R$-matrix treatment of the molecular core. The value of ${E}_{min}$ (in a.u.) is determined through $D\frac{\mathrm{Bj}}{{E}_{min}}l\ensuremath{\delta}\ensuremath{\ll}1$; when $\frac{E}{{E}_{min}}\ensuremath{\approx}\mathrm{a}\mathrm{few}$ eV, more extensive calculation is required beyond the bodyframe Born-Oppenheimer region. For this purpose a generalization of the Chang-Fano theory is developed. It consists of an adiabatic continuous transformation of frame, the frame used at each electron-molecule distance $r$ being determined directly by the dynamics of the problem. This procedure generates a coordination diagram for the known solutions to limiting cases, a diagram analogous to that used in quantum chemistry for connecting the united-atom and separated-atom limits of molecular-orbital theory. A new type of symmetry in the problem is made apparent. Preliminary discussion is made of the applicability of this method to more general problems of close coupling in the asymptotic region.