Total Cross Sections for the Excitation of the Triplet States in Molecular Nitrogen

Abstract

A consistent set of total cross sections for electron impact excitation of the $A^{3}\ensuremath{\Sigma}_{u}^{+}$, $B^{3}\ensuremath{\Pi}_{g}$, $W^{3}\ensuremath{\Delta}_{u}$, ${B}^{\ensuremath{'}}^{3}\ensuremath{\Sigma}_{u}^{\ensuremath{-}}$, $C^{3}\ensuremath{\Pi}_{u}$, $E^{3}\ensuremath{\Sigma}_{g}^{+}$, and $D^{3}\ensuremath{\Sigma}_{u}^{+}$ triplet states of molecular nitrogen from the $X^{1}\ensuremath{\Sigma}_{g}^{+}$ state has been calculated quantum mechanically for incident electron energies from threshold to 80 eV. The Ochkur-Rudge exchange scattering and Franck-Condon approximations were employed to obtain these cross sections. Minimum and double-minimum basis-set LCAO-MO wave functions centered on the nuclei were used, and the multicenter terms in the scattering amplitude were evaluated using a $\ensuremath{\zeta}$-function expansion. Rotationally averaged cross sections were calculated for excitation from ${v}^{\ensuremath{'}\ensuremath{'}}=0$ to individual ${v}^{\ensuremath{'}}$ levels of the excited electronic states. The calculated total cross section for excitation of the $B^{3}\ensuremath{\Pi}_{g}$ state is in good agreement with that deduced from recent experimental data for the process. The cross section for excitation of the $C^{3}\ensuremath{\Pi}_{u}$ state agrees well with one pair of experimental measurements and is a factor of 2 larger than another pair of measurements and about a factor of 4 larger than a fifth experimental determination and the previous calculations. The calculated cross section for excitation of the $A^{3}\ensuremath{\Sigma}_{u}^{+}$ state is a good deal larger than previous theoretical and experimental estimates. However, a comparison with recent experimental differential cross-section data indicates that the theoretical $A^{3}\ensuremath{\Sigma}_{u}^{+}$ total cross section is correct for incident energies greater than about 35 eV. The relative magnitude of these excitation cross sections leads to interesting predictions concerning ${\mathrm{N}}_{2}$ processes in the upper atmosphere.