Background: Near- and sub-barrier fusion reactions between doubly magic nuclei are important benchmarks for theoretical models to reproduce the experimental excitation functions. Here we consider the cases of ${}^{16}\mathrm{O}+{}^{16}\mathrm{O}, {}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$, and ${}^{16}\mathrm{O}+{}^{208}\mathrm{Pb}$, which have been measured previously, as well as ${}^{40}\mathrm{Ca}+{}^{90}\mathrm{Zr}$, even though $Z=40$ is not a major shell closure.

Purpose: We aim to perform a complete measurement of the excitation function of ${}^{16}\mathrm{O}+{}^{48}\mathrm{Ca}$, to investigate its behavior near and below the Coulomb barrier where no data are available. Qualitative considerations suggest that this case should follow a trend similar to the other doubly magic systems. However, this might be disproved by the experiment, due to the very large positive fusion Q value and/or to the possible existence of hindrance with a high energy threshold.

Methods: The experiment was performed at the XTU Tandem of Laboratori Nazionali di Legnaro INFN. 24–42 MeV ${}^{16}\mathrm{O}$ beams, with intensities up to 20 p nA, and ${}^{48}\mathrm{Ca}$ targets of $50\mu \mathrm{g}/{\mathrm{cm}}^2$ were used. The evaporation residues (ER) were detected by the electrostatic deflector setup PISOLO at forward angles, and identified by their energy and two independent times of flight, between the final Si detector and two microchannel plate (MCP) detectors.

Results: The clear separation of the evaporation residues in the $E$-ToF (time-of-flight) spectra allowed the excitation function to be measured down to ${\sigma }_{\mathrm{fus}}\sim 2\mu \mathrm{b}$. The results were compared with coupled-channels (CC) calculations using the Akyüz-Winther potential, and a small sub-barrier fusion enhancement was observed. We extracted the logarithmic derivative of the excitation function and the astrophysical $S$ factor, as well as the fusion barrier distribution where a single peak is observed, as predicted by the CC calculations. Comparing with other investigated doubly magic systems reveals an analogous behavior down to the lowest measured energies.

Conclusions: The $S$ factor develops a maximum vs energy, and the logarithmic derivative reaches the so-called $L_{\mathrm{CS}}$ value, at the rather high cross section $\simeq 0.8$ mb. This is evidence of the fusion hindrance phenomenon whose threshold follows the phenomenological systematics established for medium-light systems. A large positive $Q$ value for fusion does not play a role in the ${}^{16}\mathrm{O}+{}^{48}\mathrm{Ca}$ system. The CC model is able to reproduce the excitation function down to that point. At lower energies the fusion cross sections are consistent with the one-dimensional barrier tunneling limit. In the spirit of the adiabatic model, decreasing (and vanishing) coupling strengths reproduce the cross sections far below the barrier, while the hindrance model fails in that energy region.

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• Nuclear fusion
• Nuclear reactions