Dissociation of the Hydrogen Molecule Ion by Electron Impact

The dissociation cross section of ${\mathrm{H}}_2^{+}$ for bombardment by electrons is investigated taking into account the effect of exchange collisions by use of the Born-Oppenheimer approximation. Both the post and prior interactions are considered. Theoretical results are presented for the transition in which the molecule ion is raised from the ground state $1s\sigma {{}_{}{}^2{}_{}{}^{}\Sigma _g^{}{}_{}{}^{}}^{+}$ to the lowest-lying repulsive state $2p\sigma {{}_{}{}^2{}_{}{}^{}\Sigma _u^{}{}_{}{}^{}}^{+}$ and then dissociates. The Franck-Condon principle is assumed throughout, and a classical average is taken over the molecular orientations. Numerical results are given for the dissociation cross sections as a function of energy both with and without the inclusion of exchange effect. The agreement between the post- and prior-interaction cross sections near the threshold energy is poor.