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Motivated by the doubly magic nature of the system $^{16}$O + $^{48}$Ca, we have measured [1] its fusion excitation function from above to far below the barrier at the Laboratori Nationali di Legnaro of INFN. We have used the $^{16}$O beams from the XTU Tandem accelerator. The fusion cross sections were measured down to a few μb by identifying the evaporation residues in a detector telescope, downstream of an electrostatic beam deflector.
Coupled-channel calculations with the Akyuz-Winther potential, including the lowest 2$^+$ and 3$^−$ states of $^{48}$Ca, well fit the data down to $\sigma_{fus}$≈ 0.8 mb. At lower energies, the hindrance effect shows up. The fusion barrier distribution has a single main peak.
At lower energies, the data are consistent with pure one-dimensional tunnelling, as observed for $^{12}$C + $^{24}$Mg,$^{30}$Si [2].
The logarithmic slope reaches the L$_{CS}$ value, and the S factor develops a maximum vs energy. The low-energy data are well fit by an empirical approach simulating the coupling strength damping (adiabatic model), while the hindrance model fits the S factor maximum but not its increase at the lowest energies.
Doubly-magic systems were previously investigated, and the present case $^{16}$O + $^{48}$Ca confirms their common trend when the various Coulomb barriers are considered.
The phenomenological systematics proposed for heavier, stiff systems several years ago [3] have required adjusting the fit parameters, leading to updated hindrance predictions for the light systems of astrophysical interest.
[1] A.M. Stefanini et al., to be published
[2] G. Montagnoli et al., J. Phys. G 49, 195101 (2022); Phys. Rev. C 97, 024610 (2018)
[3] C.L. Jiang et al., Phys. Rev. C 79, 044601 (2009)
