Theoretical Study Of The Fusion Hindrance In Heavy-ion Fusion Reactions At Deep Sub-barrier Energies

Nuclear reaction is one of the important methods to understand and investigate the properties of nuclei.The heavy-ion fusion reaction is not only an important way to understand the properties of heavy nuclei and the nucleus-nucleus strong interactions,but also the main method to synthesize the new elements and superheavy nuclei at present.In heavy-ion fusion reactions,the formation of compound nucleus by merging projectile and target is a basic process of quantum tunneling.In the early model of fusion reactions,both projectile and target are assumed to be structureless particles and an one-dimensional potential between them is employed to calculate the fusion cross sections.This approach can reproduce the experimental data of fusion cross sections well at the colliding energies near and above the Coulomb barrier.With the decrease of the colliding energies down to the sub-barrier energies,there is a strong coupling effect between the relative motion and the intrinsic degrees of freedom of nuclei,such as vibrational excitation,rotational excitation,and nucleon transfer,so the multidimensional coupled-channels model is proposed to describe the coupling effects.As compared with the fusion cross sections calculated by one-dimensional barrier penetration model,the enhancement of experimental fusion cross sections at sub-barrier energies can be described well by the coupled-channels model with a weighted sum of the tunneling probabilities of multiple barriers,which are resulted from the splitting of the potential between two colliding nuclei owing to the coupled-channels effects.In recent years,due to the advancements of experimental techniques,it is possible to measure the fusion cross sections precisely down to extremely low incident energies.It is noted that the experimental fusion cross sections at deep sub-barrier energies are overestimated by the coupled-channels model.This unexpected feature is referred to as“fusion hindrance at deep sub-barrier energies”.This phenomenon has attracted a lot of interests in heavy-ion fusion reactions and the research on this topic help understand the interactions of two colliding nuclei and the mechanisms of fusion reactions.Two different theoretical models have been proposed to account for the fusion hindrance at deep sub-barrier energies according to the relationship between the time scales of density variation and fusion process.?1?Adiabatic model,which assumes that the fusion occurs slowly and the densities of two colliding nuclei after contact have a redistribution.This density variation feature results in the damping of coupled-channels effects and the fusion process is dominated by an one-body adiabatic potential after contact.?2?Sudden model,which hypothesizes the fusion occurs faster than density variation,i.e.,the compound nuclei is formed by two colliding nuclei with frozen density.A strong repulsive interaction appears in the overlapping region owing to the Pauli blocking effects.Although based on the opposite mechanisms,by introducing the different potentials and reasonable parameters,the fusion cross sections calculated by these two models at deep sub-barrier energies are in agreement with the experimental data.In this thesis,the above two models are used to study the fusion hindrance at deep sub-barrier energies.Firstly,based on the adiabatic model,13 phenomenological nuclear effective potentials are employed to make a detailed comparison of the experimental and calculated fusion cross sections.After two colliding nuclei contact,the adiabatic process is introduced to calculate the fusion cross sections at the above-and sub-barrier energies for 16 fusion reactions and the?²values of fusion cross sections versus the barrier height and barrier width are given.At deep sub-barrier energies,a systematic investigation is made to study the fusion hindrance by taking Krappe-Nix-Sierk,Bass?1980?,and Akyüz-Winther nuclear potentials as examples.For newly observed fusion systems¹¹B+¹⁹⁷Au,¹²C+¹⁹⁸Pt,and⁴⁰Ca+⁹⁰Zr,the calculated fusion cross sections are in good agreement with experimental data by considering the damping of coupled-channels effects.The results of astrophysical S factor and logarithmic derivative at deep sub-barrier energies show a close dependence on the behavior of potentials inside the Coulomb barrier.For newly observed light mass system¹²C+³⁰Si,the fusion cross sections by considering the damping factor show the coupling effect in relatively light mass system is weak.In addition,inspired by recent studies of?-cluster decay in radioactivity nuclei?as the reverse process of fusion reactions?,such as²¹²Po?²⁰⁸Pb+?,a Pauli blocking term depending on the density overlap of projectile and target nuclei is introduced into the nuclear interaction between them,and a microscopic calculation of fusion reactions for?+¹⁹⁷Au,?+²⁰⁸Pb,?+²⁰⁹Bi,and?+²³⁸U systems is proposed.As compared to the?-core potential obtained from the double-folding potential with standard Michigan-3-Yukawa effective nucleon-nucleon interaction,the one including the Pauli blocking interaction results in a shallow“pocket”in the inner part.In order to analyze the density dependence of Pauli blocking potential,we make a comparison of fusion cross sections between two extreme neutron density distributions of target nuclei,namely,?1?“skin type”with same diffuseness but different half-density radii in density dis-tributions of proton and neutron,and?2?“halo type”with same half-density radii but different diffuseness.The fusion cross sections resulting from the potential considering Pauli blocking effects are also compared with the experimental data in detail.In order to further study the influence of Pauli blocking effects on the fusion hindrance at deep sub-barrier energies,the Pauli blocking potential in n?-nucleus-induced fusion reactions,in which the projectiles,such as the nuclei¹²C,¹⁶O,²⁴Mg,and²⁸Si,are assumed to be consisted by n?particles,is constructed by a single folding procedure based on the microscopic Pauli blocking effect of?-cluster decay in radioactive nuclei.Analogous to the?-induced fusion reactions,a shallow“pocket”is also formed in the inner part of the Coulomb barrier of n?-nucleus-induced fusion reactions by considering the Pauli blocking effect.At deep sub-barrier energies,this shallow pocket potential reduces the partial fusion cross sections and shields the contributions of high angular momentum partial waves on fusion.The experimental fusion cross sections at deep sub-barrier energies can be described well for fusion systems¹²C+¹⁹⁸Pt,¹⁶O+²⁰⁸Pb,¹²C+³⁰Si,²⁴Mg+³⁰Si,and²⁸Si+³⁰Si.In addition,the Pauli blocking potentials in various projectiles¹²C,²⁴Mg,and²⁸Si with the same target³⁰Si are made a detailed comparison.It is found there is an exponential increasing of the Pauli blocking potentials versus the density of target in relatively heavy mass fusion systems²⁴Mg+³⁰Si and²⁸Si+³⁰Si as well as a linear increasing in light mass fusion system¹²C+³⁰Si,which indicates the Pauli blocking effect in relatively light mass system is weak and the corresponding fusion hindrance is hard to observe.This work is not only helpful to studying the hindrance of the heavy-ion fusion reaction at deep sub-barrier energies in the laboratory on earth,but also to understanding the fusion process in the astrophysical environments for light mass systems,such as¹²C+¹²C and¹⁶O+¹⁶O fusion reactions.