The 12C+12C sub-barrier fusion cross section is calculated within the framework of a Time Dependent Hartree-Fock (TDHF) based classical model using the Feynman Path Integral Method. The modified astrophysical S*-factor is compared to direct and indirect experimental results. A good agreement with the direct data is found. In the lower energy region, where recent analyses of experimental data obtained with the Trojan Horse Method (THM) lead to contrasting results, the model predicts an S* factor half way between those results. Low energy resonances revealed in the THM data are added to the calculation and the relative reaction rate in the Gamow region is calculated. The role of different resonances is discussed in detail and their influence on the reaction rate at temperatures relevant to stellar evolution is investigated.
Using different Skyrme interactions, we have carried out a comparative analysis of fusion barriers for a wide range of interacting nuclei in the framework of semiclassical Skyrme energy density formalism. The results of our calculations reveal that SVI, SII, and SIII Skyrme forces are able to reproduce the empirical values of barrier heights with higher accuracy than the other considered forces in this formalism. It is also shown that the calculated nucleus-nucleus potentials derived from such Skyrme interactions are able to explain the fusion cross sections at energies near and above the barr…
Multi-neutron transfer coupling in sub-barrier 32S+90,96Zr fusion reactions
以32S+90Zr和32S+96Zr为基准反应，研究了库仑势垒以下聚变过程中中子转移的作用.一个完整的耦合通道计算的聚变激发函数已进行了两个系统，通过使用多中子转移耦合的中子更丰富的反应。通过NTFus程序计算，包括Zagrebaev半经典模型下的中子转移通道的耦合，在亚势垒能量下很好地再现了32 S +96 Zr的熔合截面的增强。我们发现40Ca+90Zr和40Ca+96Zr熔合激发函数的效应相似。
Role of break-up processes in fusion enhancement of drip-line nuclei at energies below the Coulomb barrier
本文对$^{11}$ Be + $^{208}$ Pb反应进行了真实的耦合道计算，讨论了入射核破碎对亚势垒熔合的影响。我们离散的粒子连续态，这是与破碎过程中，并构造耦合形状因子，这些国家的微观基础上的能量。引入边界条件求解耦合通道方程，从而定义了库仑势垒内完全聚变的通量。结果表明，完全熔合截面显着增强，由于连续态的耦合相比，没有耦合的情况下，在能量低于库仑势垒，而他们被阻碍在势垒以上的能量。
The fusion dynamic mechanism of heavy-ions at energies near the Coulomb barrier is complicated and still not very clear up to now. Accordingly, a self-consistent method based on the CCFULL calculations has been developed and applied for an ingoing study of the effect of the positive Q-value neutron transfer (PQNT) channels in this work. The typical experimental fusion data of Ca + Ca and Ni + Ni is analyzed within the unified calculation scheme. The PQNT effect in near-barrier fusion is further confirmed based on the self-consistent analysis and extracted quantitatively.
Energy dependence of potential barriers and its effect on fusion cross-sections
已知相对运动和内部结构之间的耦合通过动态地改变碰撞核的密度来影响聚变屏障。这种效应预计在势垒顶部附近的能量更强，其中密度的变化比在更高的能量下有更长的时间来发展。定量地，现代TDHF计算能够预测现实的融合阈值。然而，势垒随轰击能量的演化还有待于实验数据的证实。其目的是通过比较聚变截面计算得到的潜力在不同的轰击能量与实验数据的势垒的能量依赖性的签名。对$^{40}$ Ca + $^{40}$ Ca和$^{16}$ O + $^{208}$ Pb系统进行比较。熔合截面由密度约束TDHF方法计算的电势计算。在这两种情况下，耦合降低了低能量的势垒。偏离伍兹-撒克逊核势也观察到在最低的能量。一般来说，给定能量附近的聚变截面可以通过在该能量下计算的势更好地再现。坐标相关的质量起着至关重要的作用，为再现的势垒下融合截面。只有当势垒的变化在分布所跨越的能量范围内是显著的时，才能在实验势垒分布中发现势能的能量依赖性的影响。$^{16}$ O + $^{208}$ Pb的情况似乎如此，但$^{40}$ Ca + $^{40}$ Ca的情况并非如此。这些结果表明，在TDHF计算预测的势垒的能量依赖性是现实的。这证实了TDHF方法可以用来研究重离子碰撞中相对运动和内部自由度之间的耦合。
Simultaneous Optical Model Analyses of Elastic Scattering, Breakup, and Fusion Cross Section Data for the $^{6}$He + $^{209}$Bi System at Near-Coulomb-Barrier Energies
Breakup of $^{9}$Be on $^{209}$Bi above and near the Coulomb barrier as a molecular single-particle effect: its influence on complete fusion and scattering
用绝热双中心壳模型方法研究了轰击能量在库仑势垒之上和附近时，$^{9}$ Be弹丸在$^{209}$ Bi靶上的破碎。研究了$^{9}$ Be $% \to $ n $+2α$破碎通道对完全熔合、弹性和非弹性截面的影响。结果表明，在碰撞核到达库仑势垒之前不久，抛射体$^{9}$ Be的分裂可能是由于分子单粒子效应。
The sub-barrier capture (fusion) reactions $^{32}$S+$^{90,94,96}$Zr, $^{36}$S+$^{90,96}$Zr, $^{40}$Ca+$^{90,94,96}$Zr, and $^{48}$Ca+$^{90,96}$Zr with positive and negative $Q$-values for neutron transfer are studied within the quantum diffusion approach and the universal fusion function representation. For these systems, the s-wave capture probabilities are extracted from the experimental excitation functions and are also analyzed. Different effects of the positive $Q_{xn}$-value neutron transfer in the fusion enhancement are revealed in the relatively close reactions $^{32}$S+$^{94,96}$Zr an…
The vast knowledge of strong influence of quadrupole deformation $β_2$ of colliding nuclei on heavy-ion subbarrier fusion reactions inspires a desire to quest the sensitivity of fusion dynamics to higher order deformations, such as $β_4$ and $β_6$ deformations. However, such studies have rarely been carried out, especially for deformation of projectile nuclei. In this article, we investigated the role of $β_4$ of the projectile nucleus in fusion of the $^{28}$Si + $^{92}$Zr system. We demonstrated that the fusion barrier distribution is sensitive to the sign and the value of the $β_4$ paramete…
Background: The nuclear interaction potential and hence the fusion barrier formed between the interacting nuclei are the keys to understanding the complex fusion process dynamics. Purpose: This work intends to explore the fusion barrier characteristics of different target-projectile combinations within the relativistic mean-field (RMF) formalism. Methods: The density distributions of interacting nuclei and the microscopic R3Y NN interaction are obtained from relativistic mean-field (RMF) formalism for non-linear NL1, NL3, TM1, and relativistic-Hartree-Bogoliubov (RHB) approach for DDME2 parame…
Fusion at deep subbarrier energies: potential inversion revisited
对于单个势垒，可以基于WKB近似来反转势垒穿透性以产生势垒厚度。我们将这种方法应用于能量远低于库仑势垒的重离子聚变反应，并直接确定碰撞核之间的核间势。为此，我们假设，在深亚势垒能量的融合截面的势垒分布中的最低势垒。$^{16}$ O + $^{144}$ Sm和$^{16}$ O + $^{208}$ Pb反应的反转核间势比唯象势厚得多。我们讨论了这样的厚势的一个后果，通过拟合的倒位与Bass函数。
Non-local effects on the heavy-ion fusion at sub-barrier energies
研究了重离子光学势中的泡利非定域性对亚势垒熔合反应的影响。圣保罗势考虑了泡利非定域性，被广泛用于分析弹性散射，最近也被应用于重离子聚变。然而，在推导圣保罗势时所采用的近似，基于中子诱导反应的Perey-Buck半经典处理，必须对带电粒子隧穿势垒进行评估。本说明的目的就是探讨这一问题。我们认为广泛研究的系统$^{16}$ O + $^{208}$铅的能量跨越势垒区从10兆电子伏以下的10兆电子伏以上。似乎非定域性起着次要的作用。我们认为圣保罗的潜力在整个地区都是相当充分的。
The cross sections for the deep sub-barrier fusion reaction of light nuclei are calculated within the theoretical framework of the selective resonant tunneling model. In this model, assumption of a complex square-well nuclear potential is invoked to describe the absorption inside the nuclear well. The theoretical estimates for these cross sections agree well with the experimentally measured values. The features of the astrophysical S-factor are derived in terms of this model. Present formalism appears to be particularly useful for the low energy resonant reactions between two charged nuclei.
Damping of Quantum Vibrations Revealed in Deep Sub-barrier Fusion
我们证明了当两个碰撞的原子核相互靠近时，它们的量子振动在接触点附近被阻尼。我们表明，这种阻尼是负责在深亚势垒融合反应中测量的融合阻碍现象。为了证明这一点，我们首次将随机相位近似（RPA）方法应用于二体$^{16}$ O + $^{16}$ O和$^{40}$ Ca + $^{40}$ Ca系统.我们计算了两个相互接近的原子核的八极跃迁强度。计算得到的跃迁强度在接触点附近急剧下降，强烈地暗示了各核的相对运动与振动内禀自由度之间的量子耦合消失。在此基础上，我们还用耦合道方法计算了$^{40}$ Ca + $^{40}$ Ca体系的熔合截面，其中阻尼因子模拟了耦合的消失.计算结果与实验数据吻合较好，表明在深亚势垒聚变反应中确实发生了从突变到绝热的平稳过渡。
We introduce a new microscopic approach to calculate the dependence of fusion barriers and cross-sections on isospin dynamics. The method is based on the time-dependent Hartree-Fock theory and the isoscalar and isovector properties of the energy density functional (EDF). The contribution to the fusion barriers originating from the isoscalar and isovector parts of the EDF is calculated. It is shown that for non-symmetric systems the isovector dynamics influence the sub-barrier fusion cross-sections. For most systems this results in an enhancement of the sub-barrier cross-sections, while for oth…
Extended Optical Model Analyses of Elastic Scattering and Fusion Cross Sections for 6Li + 208Pb System at Near-Coulomb-Barrier Energies by using Folding Potential
基于扩展的光学模型方法，将极化势分解为直接反应（DR）和熔合两部分，对近库仑能区$^{6}$ Li + $^{208}$ Pb体系的弹性散射和熔合截面数据进行了$χ^{2}$分析.折叠电位用作裸电位。结果表明，极化势的DR部分的实部是排斥性的，这与连续介质离散耦合通道（CDCC）计算的结果和折叠势所需的归一化因子是一致的.此外，还发现极化势的DR部分和熔合部分分别满足色散关系。
We have constructed an empirical formulae for the fusion and interaction barriers using experimental values available till date. The fusion barriers so obtained have been compared with different model predictions based on the proximity, Woods-Saxon and double folding potentials along with several empirical formulas, time dependent Hartree-Fock theories, and the experimental results. The comparison allows us to find the best model, which is nothing but the present empirical formula only. Most remarkably, the fusion barrier and radius show excellent consonance with the experimental findings for …
Signature of Shallow Potentials in Deep Sub-barrier Fusion Reactions
我们扩展了最近的研究，解释了陡峭的下降在聚变截面在能量远低于库仑势垒的对称双核系统64 Ni +64 Ni到另一个对称系统，58 Ni +58 Ni，和不对称系统64 Ni +100 Mo。在这个方案中，核势的内部部分对核物质状态方程的非常敏感的依赖性决定了重叠组态的经典允许区域的减小，从而在远低于势垒的轰击能量下熔合截面的减小。在耦合通道方法中，考虑了靶和射弹中2+和3-态的耦合以及相互激发和双声子激发，计算了上述体系的熔合截面、S因子和对数导数，并与实验结果进行了比较，发现即使在最低能量下，计算结果也与实验数据符合得很好。我们预测，特别是，一个明显的双峰的S-因子的远亚势垒融合的58 Ni +58 Ni，应进行实验测试。
Systematic calculations of the Coulomb barrier parameters for collisions of spherical nuclei are performed within the framework of the double folding approach. The value of the parameter $B_Z=Z_PZ_T/(A^{1/3}_P+(A^{1/3}_P)$ (which estimates the Coulomb barrier height) varies in these calculations from 10 MeV up to 150 MeV. The nuclear densities came from the Hartree-Fock calculations which reproduce the experimental charge densities with good accuracy. For the nucleon-nucleon effective interaction two analytical approximations known in the literature are used: the M3Y and Migdal forces. The cal…
