Fusion of 40 Ca + 40 Ca and other Ca + Ca systems near and below the barrier

The fusion excitation function of ${}^{40}\mathrm{Ca}+{}^{40}\mathrm{Ca}$ has been measured from well above the Coulomb barrier, down to low energies where the cross section is as small as $\ensuremath{\simeq}$20 $\ensuremath{\mu}$b, and the astrophysical $S$ factor possibly reaches a maximum vs energy. The results of coupled-channels calculations using the $\mathrm{M}3\mathrm{Y}+\mathrm{repulsion}$ potential are presented. A detailed comparison is made with recently published data on the fusion of ${}^{40}\mathrm{Ca}+{}^{48}\mathrm{Ca}$ and of ${}^{48}\mathrm{Ca}+{}^{48}\mathrm{Ca}$, including the excitation functions, their low-energy slopes and the barrier distributions. The presence of the fusion hindrance phenomenon in all cases is pointed out, as well as the influence of the strong octupole excitation in ${}^{40}$Ca and of nucleon transfer channels with positive $Q$ values in ${}^{40}\mathrm{Ca}+{}^{48}\mathrm{Ca}$