Fusion of ¹²C + ²⁴Mg at extreme sub-barrier energies

<jats:title>Abstract</jats:title> <jats:p>A recent experiment on <jats:sup>12</jats:sup>C + <jats:sup>24</jats:sup>Mg sub-barrier fusion was performed. Standard coupled-channels calculations clearly over-estimated the low energy cross sections and there was indication of a maximum of the astrophysical <jats:italic>S</jats:italic> factor vs energy. In the present work further measurements have been performed on the same system, and we extended the excitation function to lower energies down to <jats:italic>σ</jats:italic> ≃ 4 <jats:italic>μ</jats:italic>b, confirming the existence of the hindrance phenomenon. Additional energy points near the barrier were added as well. In agreement with the result of previous experiment, the hindrance energy threshold is observed to correspond to a remarkably large cross section. The present new data allow to better define the <jats:italic>S</jats:italic>-factor maximum, that is well fitted using two parametrizations of either the hindrance or the adiabatic model. We also performed coupled-channels calculations using a Woods–Saxon potential. Far below the barrier we observe that the coupling strengths decrease and tend to vanish, indeed one-dimensional tunnelling calculations well reproduce the excitation function. Further precise cross section measurements at slightly lower energies are needed to discriminate between the adiabatic and hindrance models. This would give a reliable guidance for the extrapolation to the systems of astrophysical interest, like <jats:sup>12</jats:sup>C + <jats:sup>12</jats:sup>C and <jats:sup>16</jats:sup>O + <jats:sup>16</jats:sup>O.</jats:p>