Survey of deep sub-barrier heavy-ion fusion hindrance phenomenon for positive 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 has been carried out by using the coupled-channels (CC) theory that is based on the proximity formalism. The present work theoretically explores the role of surface energy coefficient and energy-dependent nucleus-nucleus proximity potential in 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 5 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 are able to 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 about the performance of the present theoretical approach in reproducing the experimental fusion barrier distributions for different colliding systems.