R -matrix calculation of differential cross sections for low-energy electron collisions with ground-state and electronically excited-state O 2 molecules

Differential cross sections for electron collisions with the ${\mathrm{O}}_{2}$ molecule in its ground $X\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{g}^{\ensuremath{-}}$ state, as well as excited $a\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Delta}_{g}$ and $b\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ states are calculated. As previously, the fixed-bond $R$-matrix method based on state-averaged complete active space self-consistent-field orbitals is employed. In addition to elastic scattering of electron with the ${\mathrm{O}}_{2}$ $X\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{g}^{\ensuremath{-}}$, $a\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Delta}_{g}$, and $b\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ states, electron impact excitation from the $X\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{g}^{\ensuremath{-}}$ state to the $a\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Delta}_{g}$ and $b\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ states as well as $6\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ states of $c\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{u}^{\ensuremath{-}}$, ${A}^{\ensuremath{'}}\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Delta}_{u}$, and $A\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{g}^{+}$ states is studied. Differential cross sections for excitation to the $6\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ states have not been calculated previously. Electron impact excitation to the $b\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ state from the metastable $a\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Delta}_{g}$ state is also studied. For electron impact excitation from the ${\mathrm{O}}_{2}$ $X\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{g}^{\ensuremath{-}}$ state to the $b\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ state, our results agree better with the experimental measurements than previous theoretical calculations. Our cross sections show angular behavior similar to the experimental ones for transitions from the $X\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{g}^{\ensuremath{-}}$ state to the $6\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ states, although the calculated cross sections are up to a factor of 2 larger at large scattering angles. For the excitation from the $a\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Delta}_{g}$ state to the $b\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ state, our results marginally agree with the experimental data except for the forward scattering direction.