Energy dependence of the fusion and elastic scattering ofO16+Ca40

In a study of the system ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$, the total evaporation-residue cross section has been measured at nine energies, and elastic-scattering angular distributions at five energies, within the range $40 \mathrm{MeV}\le E_{\mathrm{lab}}\le 214 \mathrm{MeV}$. The fusion cross section is observed to saturate above $E_{\mathrm{lab}}=63\mathrm{}$ MeV. Several possible mechanisms to explain this effect are considered, and the shortcomings of each are pointed out. The model based on a critical distance in the entrance channel is judged the most nearly acceptable. At the highest bombording energies the fusion residues exhibit (1) angular distributions which suggest significant emission of energetic $\alpha$ particles (or larger clusters), and (2) total cross sections in conflict with expectations based on the vanishing of the rotating-liquid-drop model fission barrier. An optical model analysis of the elastic-scattering data is used to extract total reaction cross sections (${\sigma }_{\mathrm{reac}}$). The nonlinear dependence of ${\sigma }_{\mathrm{reac}}$ on $\frac{1}{E_{\mathrm{c}.\mathrm{m}.\mathrm{}}}$ is noted and the implications for the extraction of "interaction barrier" and "fusion barrier" parameters are discussed. A method for unified analysis of low-energy elastic-scattering and fusion data, based on the assumption that a single potential is relevant to both, is suggested. Simultaneous fits to 56-MeV elastic-scattering and lowenergy fusion measurements for ${}_{}{}^{16}{}_{}{}^{}\mathrm{O}$+${}_{}{}^{40}{}_{}{}^{}\mathrm{Ca}$ are attained with Woods-Saxon potentials only if the real well diffuseness is constrained to the range (0.50±0.05) fm, a value not compatible with several proposed potentials based on liquid-drop model concepts. The real potentials preferred in this low-energy analysis are not capable of providing good optical model fits to the highest-energy elastic data.