Vibrational and Rotational Excitation of Molecular Hydrogen by Electron Impact

Abstract

The close-coupling approximation is used to calculate integral and differential cross sections for pure vibrational excitation $\sigma (v=0\mathrm{}\to 1, \Delta j=0)$ and $\sigma (v=0\mathrm{}\to 2, \Delta j=0)$, and for simultaneous rotational-vibrational excitation $\sigma (v=0\mathrm{}\to 1, \Delta j=2)$ of ${\mathrm{H}}_2$ by slow-electron impact. Static-field and electron-exchange effects, long-range quadrupole, and an effective polarization potential are included in the $e-{\mathrm{H}}_2$ interaction. Pure vibrational cross sections are found to depend on the initial rotational state $j$ of the molecule, but the total vibrational cross section is almost independent of $j$. Cross sections are compared with experiments for energies $E\le 10$ eV. For $2<E<\mathrm{}5\mathrm{}$ eV, $\sigma (v=0\mathrm{}\to 1,\Delta j=0)$ and $\sigma (v=0\mathrm{}\to 1,j=1\to 3)$ are 50% larger than experimental values while agreement is better in the remaining energy regions. For $1<E<\mathrm{}3\mathrm{}$ eV, $\sigma (v=0\mathrm{}\to 2,\Delta j=0)$ is in good agreement with experiment but is understimated for $E>\mathrm{}3\mathrm{}$ eV. Differential scattering cross sections for vibrational excitation are found to be dominated by the polarization potential at low angles, and by the short-range potential at large angles.