The impact-parameter calculations of Hansteen et al. [J. Phys. B 17, 3545 (1984)] for K-shell ionization are used to predict the cross sections for the double ionization of ${\mathrm{H}}_2$ and He by ${\mathrm{H}}^{+}$ and ${\mathrm{D}}^{+}$ projectiles as a function of projectile velocity. The calculated values in the case of the ${\mathrm{H}}_2$ target are typically a factor of 12 lower than the measured values, but the calculations and measurements show similar velocity dependencies. The results indicate that for projectile energies less than 1 MeV/amu, the double-ionization process of ${\mathrm{H}}_2$ occurs mainly by two independent interactions between the electrons and projectile. For the He target, the calculated and measured values for the double-ionization cross section are much closer in magnitude, but the calculations predict a more rapid falloff with projectile velocity than is observed.

• Received 6 May 1985

DOI:https://doi.org/10.1103/PhysRevA.32.1873