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 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 proxim-ity potential in the mechanism of the fusion hindrance of 14 typical colliding systems with negative Q-values,in-eluding ^(11a)B+^(197)AU,^(12)C+^(198)Pt,^(16)O+^(208)Pb,^(28)Si+^(94Mo),^(48)Ca+^(96)Zr,^(28Si+)^(64)Ni,^(58)Ni+^(58)Ni+,^(60)Ni+^(89)Y,^(12)C+^(204)Pb,^(36)S+^(64)Ni,^(36)S+^(90)Zr,^(40)Ca+^(90)Zr,^(40)Ca+^(40Ca)and ^(48)Ca+^(48)Ca,,as well as five typical colliding systems with positive Q-values,ineluding ^(12)C+^(30)Si,^24Mg+^(30)Si,^(36)Si+^(48)Ca, and ^(40)Ca+^(48)Ca.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(Tfus(£),astrophysical S(E)factors,and logarithmic derivatives L(E)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.

Non-frozen process of heavy-ion fusion reactions at deep sub-barrier energies

The hindrance in heavy-ion fusion reactions a deep sub-barrier energies is investigated using the double folding model with a hybrid method between the frozen and adiabatic density approximations.In this method,the density distributions of the projectile and the target depend closely on the distance between them.As the distance decreased,the half-density radii of the colliding nucle gradually increased to the half-density radius of the compound nucleus.The total potential based on this non-frozen approximation generates a slightly shallower pocket and becomes more attractive inside the pocket compared to that obtained from the frozen approximation.A damping factor was used to simulate the decline of the coupled channel effects owing to the density rearrangement of the two colliding nuclei.The calculated fusion cross-sections and astrophysical S factors at the deep sub-barrier energies are both in good agreement with the experimental data for the medium-heavyNi+Ni and medium-lightMg+Si mass systems.In addition,it was concluded that the apparent maximum of the S factors most likely appears in fusion systems with strong coupling effects.

Pauli blocking potential applied to heavy-ion fusion reactions

In this study,the Pauli blocking potential between two colliding nuclei in the density overlapping regionis applied to describe the heavy nuclei fusion process.Inspired by the Pauli blocking effect in theα-decay of heavynuclei,the Pauli blocking potential of single nucleon from the surrounding matter is obtained.In fusion reactionswith strong density overlap,the Pauli blocking potential between the projectile and target can be constructed using asingle folding model.By considering this potential,the double folding model with a new parameter set is employedto analyze the fusion processes of 95 systems.A wider Coulomb barrier and shallower potential pocket are formed inthe inner part of the potential between the two colliding nuclei,compared to that calculated using the Akyüz-Win-ther potential.The fusion hindrance phenomena at deep sub-barrier energies are described well for fusion systems^(16)O+^(208)Pb and^(58)Ni+^(58)Ni.