Energy dependence of the fusion and elastic scattering ofO16+Ca40

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Abstract

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 $40 \mathrm{MeV}\ensuremath{\le}{E}_{\mathrm{lab}}\ensuremath{\le}214 \mathrm{MeV}$. The fusion cross section is observed to saturate above ${E}_{\mathrm{lab}}=63$ 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 $\ensuremath{\alpha}$ 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 (${\ensuremath{\sigma}}_{\mathrm{reac}}$). The nonlinear dependence of ${\ensuremath{\sigma}}_{\mathrm{reac}}$ on $\frac{1}{{E}_{\mathrm{c}.\mathrm{m}.}}$ 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\ifmmode\pm\else\textpm\fi{}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.NUCLEAR REACTIONS Fusion and elastic scattering of $^{16}\mathrm{O}$+$^{40}\mathrm{Ca}$, $40<~{E}_{\mathrm{lab}}<~214$ MeV; measured ${\ensuremath{\sigma}}_{\mathrm{fusion}}(E)$, ${\ensuremath{\sigma}}_{\mathrm{elastic}} (\ensuremath{\theta},E)$; evaluation of various mechanisms for saturation of ${\ensuremath{\sigma}}_{\mathrm{fusion}}$ at high energies; optical model analysis of ${\ensuremath{\sigma}}_{\mathrm{elastic}}$; simultaneous analyis of low-energy elastic and fusion data; deduced $s$-wave barrier parameters, real well diffuseness of nucleus-nucleus potential.

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