Born cross sections for ion-atom collisions

Selected total cross sections are calculated in the closure-Born approximation for the ions ${\mathrm{Li}}^{+}$, ${\mathrm{Cs}}^{+}$, and ${\mathrm{Au}}^{+}$ incident on several gas constituents. Targets included are H, ${\mathrm{H}}_2$, He, C, N, and O. Four general types of cross sections are considered depending on whether the incident ion or target atom is scattered elastically or inelastically. Expressions are given for the Born cross sections to the first two orders in an expansion in ${\beta }^{-2\mathrm{}}$, where $\beta =\frac{v}{c}$ and $v$ is the relative velocity. The atomic form factors and incoherent-scattering functions for the ions ${\mathrm{Cs}}^{+}$ and ${\mathrm{Au}}^{+}$, which are required in order to evaluate the leading-order cross-section parameters, are calculated from the relativistic and nonrelativistic Hartree-Fock wave functions. Results are also given for some of the energy moments of the dipole-oscillator-strength distributions for ${\mathrm{Cs}}^{+}$ and ${\mathrm{Au}}^{+}$, as determined from the ground-state wave functions. These parameters, together with atomic properties taken from the literature for ${\mathrm{Li}}^{+}$ and the various targets considered are then used to evaluate the cross sections to the first two orders in the expansion.