Double folding model calculation applied to fusion reactions

The interaction potential between a spherical and a deformed nucleus is calculated within the double-folding model for deformed nuclei.We solve the double folding potential numerically by using the truncated multipole expansion method.The shape,separation and orientation dependence of the interaction potential,fusion cross section and barrier distribution of the system 16O+154Sm are investigated by considering the quadrupole and hexadecapole deformations of 154Sm.It is shown that the height and the position of the barrier depend strongly on the deformation and the orientation angles of the deformed nucleus.These are quite important quantities for heavy-ion fusion reactions,and hence produce great effects on the fusion cross section and barrier distribution.     

Nucleon--nucleon interactions in the double folding model for fusion reactions

Nucleus--nucleus potentials are determined in the framework of double folding model for M3Y--Reid and M3Y--Paris effective nucleon--nucleon (NN) interactions. Both zero-range and finite-range exchange parts of NN interactions are considered in the folding procedure. In this paper the spherical projectile--spherical target system ¹⁶O+²⁰⁸Pb is selected for calculating the barrier energies, fusion cross sections and barrier distributions with the density-independent and density-dependent NN interactions on the basis of M3Y--Reid and M3Y--Paris NN interactions. The barrier energies become lower for Paris NN interactions in comparison with Reid NN interactions, and also for finite-range exchange part in comparison with zero-range exchange part. The density-dependent NN interactions give similar fusion cross sections and barrier distributions, and the density-independent NN interaction causes the barrier distribution moving to a higher position. However, the density-independent Reid NN interaction with zero-range exchange part gives the lowest fusion cross sections. We find that the calculated fusion cross sections and the barrier distributions are in agreement with the experimental data after renormalization of the nuclear potential due to coupled-channel effect.     

Pauli blocking potential applied to heavy-ion fusion reactions

In this study, the Pauli blocking potential between two colliding nuclei in the density overlapping region is applied to describe the heavy nuclei fusion process. Inspired by the Pauli blocking effect in the \begin{document}$ \alpha $\end{document}-decay of heavy nuclei, the Pauli blocking potential of single nucleon from the surrounding matter is obtained. In fusion reactions with strong density overlap, the Pauli blocking potential between the projectile and target can be constructed using a single folding model. By considering this potential, the double folding model with a new parameter set is employed to analyze the fusion processes of 95 systems. A wider Coulomb barrier and shallower potential pocket are formed in the inner part of the potential between the two colliding nuclei, compared to that calculated using the Akyüz-Winther potential. The fusion hindrance phenomena at deep sub-barrier energies are described well for fusion systems \begin{document}$ ^{16} $\end{document}O + \begin{document}$ ^{208} $\end{document}Pb and \begin{document}$ ^{58} $\end{document}Ni + \begin{document}$ ^{58} $\end{document}Ni.     

Systematic analysis of fusion barrier heights and positions for proton projectiles using the single folding model

The nuclear potentials between protons and different target nuclei are calculated by using the single folding model with the density-dependent nucleon-nucleon interaction.The fusion barrier heights and positions for proton projectiles fusing with different target nuclei with masses from 51 amu to 139 amu are systematically shown,with charge numbers and root-mean-square radii of the interacting nuclei.The parameterized formulas for the fusion barrier height and position are obtained for proton projectile fusing with the different nuclei.The calculated results of parameterized formulas are compared to empirical values,as well as those of the proximity potential and AkyüzWinther(AW) potential.It is shown that the calculated results agree perfectly with theirs.The parameterized formulas can reproduce the exact barrier heights and positions for proton fusion systems.     

利用双折叠模型对弹核为α的熔合垒高度和位置的系统学分析

本文系统分析了α粒子与不同的靶核熔合时, 势垒高度和位置与相互作用核的电荷数和均方根半径的关系. 通过基于密度依赖的核子-核子相互作用(CDM3Y6)的双折叠模型来计算核势. 得到了当弹核为α时垒高度和位置的参数化公式. 通过分析质量数从16到238的原子核表明, 参数化公式可以精确地再现弹核为α的熔合反应的垒高度和位置, 其精确度在±1%以内. 此外, 其结果还能很好地和实验值, 经验值, Royer, KNS, AW和亲近势的结果相符合.     

Calculation of decay half-lives for superheavy elements using the double folding model

α decay half-lives of some new synthesized superheavy elements, possibly synthesized superheavy elements and decay products are calculated theoretically within the WKB approximation by using microscopic m-nucleus interaction potentials. These nuclear potentials between the α particle and daughter nuclei are obtained by using the double folding integral of the matter density distribution of the α particle and daughter nuclei with a density-dependent effective nucleon-nucleon interaction, in which the zero-range exchange term is supplemented. The calculated α decay half-lives are compared with those of the different models and experimental data. It is shown that the present calculation successfully provides the half-lives of the observed αdecays for some new superheavy elements and therefore gives reliable predictions for α decay of possibly synthesized superheavy elements in future experiments.     

双折叠模型对相互作用势实部的计算

用双折叠模型计算了核核碰撞的相互作用势, 其中核子-核子相互作用势采用M3Y-Reid和M3Y-Paris形式, 交换部分考虑了有限力程的密度依赖的核子-核子相互作用, 程序用于重离子散射光学势实部的计算. 回顾了折叠模型的普遍特征和讨论了理论计算过程, 对各种类型的核子-核子相互作用下计算的相互作用势进行比较, 发现双折叠模型对大部分系统相互作用势的实部取得了满意的结果. 因此这个工作为重离子相互作用势的折叠计算提供了很好的方法.     

Nuclear dynamical octupole deformation in heavy-ion reactions

Within the quantum molecular dynamics (QMD) model, the dynamical octupole deformation is studied as a function of the central distance between the projectile and target in the approaching process of heavy-ion fusion reactions. The dependence of the maximum dynamical octupole deformations on the incident energies is also investigated. The dynamical octupole deformations can be observed during the approaching process, and the maximum dynamical octupole deformations become more significant with decreasing incident energies. The distributions of the proton and neutron centers in the projectile and target are also investigated, respectively. In the approaching process of heavy-ion fusion reactions, the separation between proton centers for two nuclei is larger than that between neutron centers because of the strong Coulomb potential.     

Effects of the entrance channel mass asymmetry in fusion reactions

The symmetric and asymmetric fusion reaction systems forming the same compound nuclei 26Al,30Si,38Ar and 170Hf are investigated with the frame of improved isospin dependent quantum molecular dynamics model.The entrance channel mass asymmetry dependence of compound nucleus formation is found by analyzing the shell correction energies,the Coulomb barriers and the fusion cross sections.The calculated fusion cross sections agree quantitatively with the experimental data.The results indicate that compound nucleus formation is favorable for the systems with larger mass asymmetry because of the smaller Coulomb contribution to the fusion barrier.     

熔合反应中入射道质量不对成度效应

The symmetric and asymmetric fusion reaction systems forming the same compound nuclei ^26Al, ^30Si, ^38Ar and ^170Hf are investigated with the frame of improved isospin dependent quantum molecular dynamics model. The entrance channel mass asymmetry dependence of compound nucleus formation is found by analyzing the shell correction energies, the Coulomb barriers and the fusion cross sections. The calculated fusion cross sections agree quantitatively with the experimental data. The results indicate that compound nucleus formation is favorable for the systems with larger mass asymmetry because of the smaller Coulomb contribution to the fusion barrier.     

Asymmetric barrier model for heavy ion fusion and its relation to channel coupling

A new asymmetric parabolic effective fusion barrier model for heavy ion fusion is developed.     

Exploiting barrier distributions to investigate breakup effects in the fusion of 9Be+208Pb

The availability of precisely measured fusion excitation functions have allowed the determination of experimental fusion barrier distributions. This concept is utilised in ⁹Be+²⁰⁸Pb reaction, to reliably predict the expected complete fusion cross-sections. However, the measured cross-sections are found to be only 68% of those predicted. The large cross-sections observed for incomplete fusion products support the interpretation that this suppression of fusion is caused by ⁹Be breaking up into charged fragments before reaching the fusion barrier.     

Shielding effects in fusion reactions with a proton-halo nucleus

To explain the experimental observation that the fusion cross-section of a proton-halo nucleus with a heavy target nucleus is not enhanced as expected,the shielding hypothesis was proposed,where the proton-halo nucleus is polarized and the valence proton shielded by the core.In the frame of the improved quantum molecular dynamics model,the fusion reaction 17F on 208Pb around the Coulomb barrier is simulated.The existence of the shielding effect is verified by the microscopic dynamics simulations.Its influence on the effective interaction potential is also investigated.     

Structure information from fusion barriers

It is shown that the analysis of fusion barrier distributions is not always an unambiguous test or a ‘fingerprint’ of the structure information of the colliding nuclei. Examples are presented with same fusion barrier distributions for nuclei having different structures. The fusion excitation functions for ¹⁶O+²⁰⁸Pb, using the coupled reaction channel (CRC) method and correct structure information, have been analysed. The barrier distributions derived from these excitation functions including many of the significant channels are featureless, although these channels have considerable effects on the fusion excitation function. However, a simultaneous analysis of the fusion, elastic and quasi-elastic channels would fix the structure and the reaction unambiguously.     

Simplification of Double Folding Model Calculations in Study of Interaction Between Two Deformed Nuclei

The Double Folding （DF） model calculation of the internuclear potential in heavy-ion interactions when the participant nuclei are deformed in their ground states involves a six-dimensional integral. Using the multipole expansion in these calculations, the DF six-dimensional integral reduce to the sum of the products of three single-dimensional integrals. In this paper we have presented a procedure for the calculation of the radius dependent functions in the multipole expansion of the nuclear density and their Fourier transforms. We have also reduced the DF model integrals to the sum of the single dimensional integrals using the obtained relations for the radius dependent functions in the multipole expansion and their Fourier transforms.     

Light ion fusion in deformation model

Experiments with heavy ions at moderate energies show the importance of deformation in heavy ion collisions. A deformation model which takes deformation dynamically into account is developed. Having described fusion and deep inelastic collision for a very heavy system (Xe + Bi) and a medium heavy system (Ar + Th) at various energies successfully, we turn to some comparatively lighter heavy ions where fusion is the most dominant feature. Fusion cross-sections for six pairs of lighter systems (³⁵Cl +¹¹⁶Sn,⁵⁸Ni+⁶²Ni,³⁵Cl+⁶²Ni,³²S+²⁴Mg,²⁴Mg+²⁴Mg and¹²C+²⁷Al) have been obtained using our deformation model which agree well with experiment. The two-slope-behaviour of fusion excitation function which is an important feature of light ion fusion systematics is also obtained, in our model calculations for all the systems studied.     

Determination of the nucleon-nucleon interaction in the ImQMD model by nuclear reactions at the Fermi energy region

The nucleon-nucleon interaction is investigated by using the improved quantum molecular dynamic （ImQMD） model with three sets of parameters IQ1, IQ2 and IQ3, in which the corresponding incompressibility coefficients of nuclear matter are different. The charge distributions of fragments are calculated for various reaction systems at different incident energies. The parameters strongly affect the charge distributions and the fragment multiplicity spectrum below the threshold energy of nuclear multifragmentation. The fragment multiplicity spectrum for 238U＋197Au at 15 A MeV and the charge distributions for 129Xe＋12~Sn at 32 and 45 A MeV, and 197Au＋197Au at 35 A MeV are reproduced by the ImQMD model with the set of parameter IQ3. It is found that： 1） The charge distribution of the fragments and the fragment multiplicity spectrum are good observables for testing the model and the parameters. 2） The Fermi energy region is a sensitive energy region for studying nucleon-nucleon interaction.     

L-dependent heavy ion fusion potentials

The energyE and angular momentuml dependence of optical potential for fusion of¹⁶O+²⁰⁸Pb system, observed by Christleyet al [5], is expressed as a function of radial kinetic energy (ɛ) instead of explicitE andl dependence. It is shown that the effects of different channel couplings, which result in different effective potentials, can also be parametrized as a function ofɛ. A correlation is obtained between the energy dependent part of this effective potential and the maximum of the spin enhancement around the Coulomb barrier and both these quantities depend on the details of the channel couplings.     

Effects of the tensor force on low-energy heavy-ion fusion reactions: a mini review

In recent several years, the tensor force, one of the most important components of the nucleon–nucleon force, has been implemented in time-dependent density functional theories and it has been found to influence many aspects of low-energy heavy-ion reactions, such as dissipation dynamics, sub-barrier fusions, and low-lying vibration states of colliding partners. Especially, the effects of tensor force on fusion reactions have been investigated from the internuclear potential to fusion crosssections systematically. In this work, we present a mini review on the recent progress on this topic. Considering the recent progress of low-energy reaction theories, we will also mention more possible effects of the tensor force on reaction dynamics.     

近垒能量下重核熔合几率的量子路径积分计算

针对近垒能量下经典涨落耗散模型预期的重核熔合几率比实验结果偏小的问题, 发展了一种实时间路径积分方法并用于研究重核熔合激发函数, 给出了包含量子涨落效应的解析表达式。 计算了几个对称和近似对称反应系统的熔合几率, 结果表明理论结果与实验值符合较好。 还讨论了颈部增长对熔合障碍的影响。 A real time path integral approach is developed in order to work out a correct solution to a problem for the smaller result of the fusion probability of heavy nuclei based on the classical diffusion model at sub barrier energies. An analytical expression for the quantum fusion probability is proposed,which contains the quantum fluctuation effect. The fusion probabilities of several symmetrical and approximate symmetrical systems are calculated, the heoretical results are in agreement with the experimental data. The influence of the neck length and its fluctuation upon the fusion hindrance is discussed.