Charge-state dependence of binary-encounter-electron cross sections and peak energies

The charge-state dependence of the binary-encounter-electron (BEE) double-differential cross section (DDCS) at 0° with respect to the beam direction resulting from collisions of 1 MeV/amu ${\mathrm{H}}^{+}$, ${\mathrm{C}}^{\mathit{q}+}$, ${\mathrm{N}}^{\mathit{q}+}$, ${\mathrm{O}}^{\mathit{q}+}$, ${\mathrm{F}}^{\mathit{q}+}$, ${\mathrm{Si}}^{\mathit{q}+}$, and ${\mathrm{Cl}}^{\mathit{q}+}$, and 0.5 MeV/amu ${\mathrm{Cu}}^{\mathit{q}+}$ with ${\mathrm{H}}_2$ is reported. The data show an enhancement in the BEE DDCS as the charge state of the projectile is decreased, in agreement with the data reported by Richard et al. [J. Phys. B 23, L213 (1990)]. The DDCS enhancement ratios observed for the three-electron isoelectronic sequence ${\mathrm{C}}^{3+}$:${\mathrm{C}}^{6+}$, ${\mathrm{N}}^{4+}$:${\mathrm{N}}^{7+}$, ${\mathrm{O}}^{5+}$:${\mathrm{O}}^{8+}$, and ${\mathrm{F}}^{6+}$:${\mathrm{F}}^{9+}$ are about 1.35, whereas a DDCS enhancement of 3.5 was observed for ${\mathrm{Cu}}^{4+}$. The BEE enhancement with increasing electrons on the projectile has been shown by several authors to be due to the non-Coulomb static potential of the projectile and additionally to the e-e exchange interaction. An impulse-approximation (IA) model fits the shape of the BEE DDCS and predicts a ${\mathit{Z}}_{\mathit{p}}^2$ dependence for the bare-ion cross sections. The IA also predicts a binary peak energy that is independent of q and ${\mathit{Z}}_{\mathit{p}}$ and below the classical value of 4t, where t is the energy of electrons traveling with the projectile velocity. We observed a BEE energy shift ΔE (ΔE=4t-${\mathit{E}}_{\mathrm{peak}}$, where ${\mathit{E}}_{\mathrm{peak}}$ is the measured energy at the peak of the binary encounter electrons) that is approximately independent of q for the low-${\mathit{Z}}_{\mathit{p}}$ ions, whereas the measured ΔE values for Si, Cl, and Cu were found to be q dependent.