R-matrix calculation of differential cross sections for low-energy   electron collisions with ground and electronically excited state O2 molecules
  Differential cross sections for electron collisions with the O$_2$ molecule in its ground ${X}^{3}\Sigma_g^-$ state, as well as excited ${a}^{1}\Delta_g$ and ${b}^{1}\Sigma_g^+$ states are calculated. As previously, the fixed-bond R-matrix method based on state-averaged complete active space SCF orbitals is employed. In additions to elastic scattering of electron with the O$_2$ ${X}^{3}\Sigma_g^-$, ${a}^{1}\Delta_g$ and ${b}^{1}\Sigma_g^+$ states, electron impact excitation from the ${X}^{3}\Sigma_g^-$ state to the ${a}^{1}\Delta_g$ and ${b}^{1}\Sigma_g^+$ states as well as '6 eV states' of ${c}^{1}\Sigma_u^{-}$, ${A'}^{3}\Delta_u$ and ${A}^{3}\Sigma_u^{+}$ states is studied. Differential cross sections for excitation to the '6 eV states' have not been calculated previously. Electron impact excitation to the ${b}^{1}\Sigma_g^+$ state from the metastable ${a}^{1}\Delta_g$ state is also studied. For electron impact excitation from the O$_2$ ${X}^{3}\Sigma_g^-$ state to the ${b}^{1}\Sigma_g^+$ state, our results agree better with the experimental measurements than previous theoretical calculations. Our cross sections show angular behaviour similar to the experimental ones for transitions from the ${X}^{3}\Sigma_g^-$ state to the '6 eV states', although the calculated cross sections are up to a factor two larger at large scattering angles. For the excitation from the ${a}^{1}\Delta_g$ state to the ${b}^{1}\Sigma_g^+$ state, our results marginally agree with the experimental data except for the forward scattering direction. 
Motomichi Tashiro, Keiji Morokuma, Jonathan Tennyson