A semiclassical approximation for sudden S-matrix elements in rotational excitation and simple methods for electron scattering by strongly polar molecules

Abstract

The authors use a new expression to find fixed-rotor S-matrix elements from the first-order change in classical action and then employ frame transformation theory to obtain Arthurs and Dalgarno SMatrix elements (1960). They relate this result to the sudden approximation of Kramer and Berstein (1964) and apply it to scattering by the important electron-dipole potential, finding analytic expressions for S-matrix elements. These are shown to be in good agreement with close-coupling results for orbital angular momentum quantum number, L>or=5, for D=2.59 ea_O. For electron-dipole collisions, differential cross sections from the ground state have been calculated directly using this action for the angular region where the Born approximation is invalid. Interference effects are found to be responsible for the sharp minima obtained in the close-coupling calculations for the 0 to 0 and 0 to 1 cross sections. Employing the same action, integral cross sections from the ground state to any other level are obtained and empirical formulae presented for the cross section between any two levels and for the total cross section out of any level. Good agreement with a variety of close-coupling calculations has been obtained.