Differential Angular Distribution of H and ${\mathrm{H}}^{+}$ Dissociation Fragments of Fast ${\mathrm{H}}_2^{+}$ Ions Incident on ${\mathrm{H}}_2$ Gas

Angular distributions of the fast H and ${\mathrm{H}}^{+}$ dissociation fragments produced in single collisions of ${\mathrm{H}}_2^{+}$ with ${\mathrm{H}}_2$ have been measured in the energy range 5-80 keV. The observed distributions are discussed in terms of three dissociation reactions, ${\mathrm{H}}_2^{+}$ → ${\mathrm{H}}^{+}$+H, $\mathrm{H}_2^{}{}_{}{}^{+}\to {\mathrm{H}}^{+}+{\mathrm{H}}^{+}+e$, and $\mathrm{H}_2^{}{}_{}{}^{+}+e\to \mathrm{H}+\mathrm{H}$, whose relative proportions vary strongly over the energy range of the investigation. Distributions of the component of velocity of the dissociation fragments transverse to the ${\mathrm{H}}_2^{+}$ beam direction are deduced from the measurements. The H-atom transverse velocity distributions are approximately independent of ${\mathrm{H}}_2^{+}$ projectile energy and are dominated by H atoms from the H+H dissociation reaction. The ${\mathrm{H}}^{+}$ transverse velocity distributions vary in width as the ${\mathrm{H}}_2^{+}$ ion energy is varied. At low energies, where the ${\mathrm{H}}^{+}$ production is dominated by the ${\mathrm{H}}^{+}$+H reaction, the transverse velocity spread is narrower than at high energies where the ${\mathrm{H}}^{+}+{\mathrm{H}}^{+}+e$ reaction dominates the ${\mathrm{H}}^{+}$ production. A theory of the dissociation mechanism which predicts the angular distribution of dissociation fragments is developed. The theory is based upon Born-approximation calculations of the dissociation cross section versus internuclear axis orientation and internuclear spacing of the ${\mathrm{H}}_2^{+}$ ions prior to the collision. These calculations, presently available only for the case of an H-atom target and for the $1s{\sigma }_g\to 2p{\sigma }_u$ dissociative transition of the incident ${\mathrm{H}}_2^{+}$ ion, were used to deduce the angular distribution of dissociation fragments in the laboratory coordinate system. Fairly comprehensive agreement is found between the calculated distribution and the observed ${\mathrm{H}}^{+}$ distribution for an ${\mathrm{H}}_2$ target at 10 keV where the H+${\mathrm{H}}^{+}$ dissociation mode dominates the ${\mathrm{H}}^{+}$ production. The theoretical model is used to discuss qualitatively the observed shapes and widths of the ${\mathrm{H}}^{+}$ and H transverse velocity distributions and to relate qualitatively the shapes of these distributions to the distribution of ${\mathrm{H}}_2^{+}$ ion internuclear spacings prior to the collision.