Rotational Excitation of Diatomic Molecules by Slow Electrons: Application toH2

The theory of electron scattering from a rigid rotator is applied to the case of low-energy scattering of electrons from hydrogen molecules in ground electronic and vibrational states. The coupled equations are solved numerically and the resulting $S$ matrix is used to calculate elastic, rotational excitation, and rotational de-excitation cross sections. The electron-molecule interaction potential is based on the approximate charge distribution of ${\mathrm{H}}_2$ and includes the effects of polarization, which are shown to be important. Cross sections are given for several rotational states, and it is pointed out that while the elastic and inelastic cross sections are found to depend on the initial rotational angular momentum $j$ of the molecule, their variation in $j$ is such that the total cross section remains independent of $j$. The effects of "back coupling" and coupling with higher rotational states are illustrated by comparing the results of the close-coupling calculation with those of the Born and distorted-wave methods; the distorted-wave and close-coupling results for rotational excitation are found to agree within 20 percent for all energies.