Low-energy electron scattering from CO. II.Ab initiostudy using the frame-transformation theory

Abstract

The frame-transformation theory has been employed to extend first-principles studies of electron-molecule collisions to heteronuclear diatomic systems. The Wigner-Eisenbud $R$ matrix has been introduced at the boundary point of the molecular-core radius---which defines the inner region---in a molecule-fixed frame of reference in the fixed-nuclei approximation. The solutions of the scattering equations in the outer region, where rotational motion of the nuclei is taken into account, are continued by transforming the $R$ matrix to the space frame of reference. This procedure has been applied to a model calculation of thermal-energy electron scattering from CO. The dependence of the rotational transition cross sections on the core radius has been studied. A general methodology has been developed for adapting the single-center pseudopotential method to the proposed amalgamation of the $R$-matrix and frame-transformation theories in order to perform a fundamental calculation of the interior problem. A comprehensive study of ${e}^{\ensuremath{-}}$-CO scattering is carried out on the basis of this methodology. In the present application the dipole term in the multipole expansion of the static potential, computed from the ground-electronic state wave functions of the CO molecule, has been renormalized so that it reproduces, asymptotically, the experimentally measured magnitude of the dipole moment of carbon monoxide. The calculated momentum-transfer cross section is in good agreement with the experimental measurements for thermal-energy ${e}^{\ensuremath{-}}$ scattering from CO. The rotational excitation and deexcitation, and total scattering and momentum-transfer cross sections computed from this method also reproduce the 1.75 eV $^{2}\ensuremath{\Pi}$ resonance; while those obtained from an extension of the model calculation mentioned above fail to do so. In particular, it is found that for rotationally inelastic scattering in the resonance region the cross sections for 0\ensuremath{\rightarrow}4 and 1\ensuremath{\rightarrow}3 transitions are the largest among those which start from the ground and first rotational states of CO molecule, respectively. The angular distributions for various electron impact transitions in CO have also been computed.