Survey of deep sub-barrier heavy-ion fusion hindrance phenomenon forpositive and negative Q-value systems using the proximity-type potential

A systematic survey of the accurate measurements of heavy-ion fusion cross sections at extreme sub-barrier energies is performed using the coupled-channels (CC) theory that is based on the proximity formalism. This work theoretically explores the role of the surface energy coefficient and energy-dependent nucleus-nucleus proximity potential in the mechanism of the fusion hindrance of 14 typical colliding systems with negative \begin{document}$Q$\end{document}-values, including ¹¹B+¹⁹⁷Au, ¹²C+¹⁹⁸Pt, ¹⁶O+²⁰⁸Pb, ²⁸Si+⁹⁴Mo, ⁴⁸Ca+⁹⁶Zr, ²⁸Si+⁶⁴Ni, ⁵⁸Ni+⁵⁸Ni, ⁶⁰Ni+⁸⁹Y, ¹²C+²⁰⁴Pb, ³⁶S+⁶⁴Ni, ³⁶S+⁹⁰Zr, ⁴⁰Ca+⁹⁰Zr, ⁴⁰Ca+⁴⁰Ca, and ⁴⁸Ca+⁴⁸Ca, as well as five typical colliding systems with positive \begin{document}$Q$\end{document}-values, including ¹²C+³⁰Si, ²⁴Mg+³⁰Si, ²⁸Si+³⁰Si, ³⁶S+⁴⁸Ca, and ⁴⁰Ca+⁴⁸Ca. It is shown that the outcomes based on the proximity potential along with the above-mentioned physical effects achieve reasonable agreement with the experimentally observed data of the fusion cross sections \begin{document}$\sigma_{\rm{fus}}(E)$\end{document}, astrophysical \begin{document}$S(E)$\end{document} factors, and logarithmic derivatives \begin{document}$L(E)$\end{document} in the energy region far below the Coulomb barrier. A discussion is also presented on the performance of the present theoretical approach in reproducing the experimental fusion barrier distributions for different colliding systems.