Algebraic-eikonal approach to electron-molecule scattering: Diatomic molecules

We propose an algebraic-eikonal approach to electron-molecule scattering. In this approach the coupling to both rotational and vibrational molecular states is taken into account simultaneously and to all orders in the coupling strength. We present closed analytic expressions for the transition matrix elements for the two dynamical symmetries of the vibron model for diatomic molecules, the U(3) and O(4) limits. It is shown that the large-N limit of the O(4) result corresponds to the rigid-rotor case. The extension to triatomic and polyatomic molecules is straightforward.