Large-angle scattering of light ions in the weakly screened Rutherford region

Total differential cross-section ratios for scattering of ${\mathrm{H}}^{+}$, ${\mathrm{He}}^{+}$, and ${\mathrm{Li}}^{+}$ ions incident on bismuth-zinc and gold-carbon systems have been measured. The energy dependence of the cross sections was measured for each species at a fixed laboratory backscattering angle (${\varphi }_{\mathrm{lab}}=170\mathrm{}°$), using an amorphous carbon target implanted with 10-keV ${\mathrm{Zn}}^{+}$ and ${\mathrm{Bi}}^{+}$ at a depth of ∼2.7 μg/${\mathrm{cm}}^2$. Angular distributions (${\varphi }_{\mathrm{lab}}=15\mathrm{}°, \dots , 170°$) were measured for helium ions at four different energies, using selfsupporting vacuum-deposited polycrystalline carbon and gold foils. For the case of backscattering, the cross-section ratios $\frac{{\left(d\sigma \right)}_{\mathrm{Bi}}}{{\left(d\sigma \right)}_{\mathrm{Zn}}}$ deviate significantly from both the Rutherford-scattering law and the Lindhard, Nielsen, and Scharff differential-scattering cross section. The deviations of the absolute cross sections from the Rutherford cross sections amount to 3.5% for 1-MeV and 16% for 0.2-MeV helium on bismuth. The experimental results are in good agreement with exact classical differential-scattering cross sections based on the Lenz-Jensen and Dirac-Hartree-Fock-Slater atomic potentials. Simple analytical formulas describing the energy and angular dependence of the cross sections are presented.