R -matrix calculation of electron collisions with electronically excited O 2 molecules

Low-energy electron collisions with ${\mathrm{O}}_{2}$ molecules are studied using the fixed-bond $R$-matrix method. In addition to the ${\mathrm{O}}_{2}$ $X\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{g}^{\ensuremath{-}}$ ground state, integrated cross sections are calculated for electron collisions with the $a\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Delta}_{g}$ and $b\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ excited states of ${\mathrm{O}}_{2}$ molecules. Thirteen target electronic states of ${\mathrm{O}}_{2}$ are included in the model within a valence configuration interaction representations of the target states. Elastic cross sections for the $a\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Delta}_{g}$ and $b\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ excited states are similar to the cross sections for the $X\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{g}^{\ensuremath{-}}$ ground state. As in case of excitation from the $X\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{g}^{\ensuremath{-}}$ state, the ${\mathrm{O}}_{2}^{\ensuremath{-}}$ ${\ensuremath{\Pi}}_{u}$ resonance makes the dominant contribution to excitation cross sections from the $a\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Delta}_{g}$ and $b\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ states. The magnitude of excitation cross sections 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 is about ten times larger than the corresponding cross sections from the $X\phantom{\rule{0.2em}{0ex}}^{3}\ensuremath{\Sigma}_{g}^{\ensuremath{-}}$ to the $b\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ state. For this $a\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Delta}_{g}\ensuremath{\rightarrow}b\phantom{\rule{0.2em}{0ex}}^{1}\ensuremath{\Sigma}_{g}^{+}$ transition, our cross section at $4.5\phantom{\rule{0.3em}{0ex}}\mathrm{eV}$ agrees well with the available experimental value. These results should be important for models of plasma discharge chemistry which often requires cross sections between the excited electronic states of ${\mathrm{O}}_{2}$.