Electron-impact cross sections for exciting the oxygen molecule from the ground electronic level to the ns${\mathrm{\sigma }}_{\mathit{g}}$, np${\mathrm{\sigma }}_{\mathit{u}}$, nd${\mathrm{\sigma }}_{\mathit{g}}$, nf${\mathrm{\sigma }}_{\mathit{u}}$, np${\mathrm{\pi }}_{\mathit{u}}$, nd${\mathrm{\pi }}_{\mathit{g}}$, and nf${\mathrm{\pi }}_{\mathit{u}}$ Rydberg levels associated with the ${\mathrm{O}}_2^{+}$(B ${}_{}{}^2{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{\mathrm{-}}{}_{}{}^{}$) and ${\mathrm{O}}_2^{+}$(b ${}_{}{}^4{}_{}{}^{}\mathrm{\Sigma }_{\mathit{g}}^{\mathrm{-}}{}_{}{}^{}$) cores are presented. For each Rydberg series of a given l, m, and ${\mathrm{O}}_2^{+}$ core state, the cross sections exhibit n dependence of the form ${\mathit{n}}^{\mathrm{-}\mathrm{\alpha }}$ with α varying from one series to another in the range of 1.47 to 4.60 in contrast to the more universal ${\mathit{n}}^{\mathrm{-}3}$ dependence for the hydrogen atom. The potential cusps at the two nuclear sites of the molecule make the Rydberg orbital density near the origin quite different from that of the hydrogen atom, thereby spoiling the simple ${\mathit{n}}^{\mathrm{-}3}$ dependence.

• Received 17 May 1990

DOI:https://doi.org/10.1103/PhysRevA.42.4391