Optical-Model Description of Low-Energy Collisions Between Heavy Ions

An optical model has been used to describe the elastic scattering of ${\mathrm{O}}^{16}$+${\mathrm{C}}^{12}$, ${\mathrm{N}}^{14}$+${\mathrm{C}}^{12}$, and ${\mathrm{N}}^{14}$+${\mathrm{Be}}^9$ for energies near and above the Coulomb barrier. Using a Woods-Saxon form for both the real and imaginary potentials, good agreement with the experimental data is obtained. Quantitative differences between ${\mathrm{O}}^{16}$+${\mathrm{C}}^{12}$, which exhibits well-developed diffraction structure, and the other two systems, which exhibit less pronounced diffraction structure, are well accounted for by the model and mainly reflect differences in the size of the imaginary potential, a small imaginary potential being associated with the large amplitude diffraction oscillation. The parameters determined by fitting the elastic scattering data yield reaction cross sections in agreement with measured data. Although the model gives a good description of the data there are difficulties in the physical interpretation which arise from the deep interpenetration of the colliding ions implied by the model; for ${\mathrm{O}}^{16}$+${\mathrm{C}}^{12}$, which requires a small absorption in order to fit the large diffraction oscillations, the mean free path inside the potential is ∼6 F. Such a deep interpenetration does not seem physically realistic, yet, within the framework of the model it appears to be a necessary condition for producing the observed amplitude of diffraction oscillations.