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.     

重离子碰撞中熔合位垒的研究

熔合位垒的研究对熔合反应以及超重核合成有重要的意义。在改进的同位旋相关的量子分子动力学(ImIQMD)模型框架下,提取了熔合反应体系40Ca+40Ca,48Ca+208Pb,48Ca+204Pb和16O+154Sm的熔合位垒。研究了壳修正能对熔合位垒的影响、动力学位垒的能量依赖性、同位旋效应以及形变核的方向效应。计算发现壳修正能降低了熔合反应的位垒。在研究动力学位垒的能量依赖性时,发现位垒高度和位垒半径表现出相反的能量依赖行为。在动力学反应中,当两个核距离接近时,缺中子体系的库仑势同样表现出一定的能量依赖性。对于丰中子体系,由于中子屏蔽作用,库仑势基本没有能量依赖性。     

Influence of entrance channel properties on heavy-ion reaction dynamics

In the fusion of heavy nuclei, there is a distribution of fusion barrier energies resulting from coupling between intrinsic motion and internal degrees of freedom. Precise experimental measurements of excitation functions have allowed the extraction of the distributions by taking the second derivative using a point-difference method. In the case of statically deformed nuclei, experimental data shows that the different fusion barrier energies correspond to different physical configurations of the colliding nuclei, the latter affecting the subsequent dynamical trajectories over the potential energy surface, influencing the ultimate reaction products, as for example in quasi-fission. The fusion barrier distribution is also valuable in understanding the fusion of weakly bound nuclei, enabling a reliable prediction of the expected fusion cross-sections, and thus the determination of fusion suppression factors at above-barrier energies. Received: 1 May 2001 / Accepted: 4 December 2001     

7Li quasi-free scattering off the α-cluster in 9Be nucleus

Spectra of coincident charged particles from the reactions induced by a 52 MeV ⁷Li beam incident on a beryllium target were measured. Strong contributions of the ⁷Li quasi-free scattering off the α-cluster in ⁹Be nucleus were observed. This observation supports the conclusions from the study of complete fusion of weakly bound light nuclei at low energies that the “fragility” of the nuclei makes their fusion less probable. Received: 1 June 1998     

QMD模型的改进及其在低能重离子反应中的应用

丰中子核以及重核熔合机制的研究以及中能重离子碰撞中多重碎裂的研究都迫切需要一个统一的、自洽的微观动力学模型.经过对量子分子动力学模型进行根本的改进,发展了一个新的、适用于低能以及中能重离子反应的统一描述的微观动力学模型.改进的量子分子动力学(ImQMD)模型能够将整个熔合反应过程中的动力学效应、同位旋效应以及弹靶质量不对称效应等比较全面地、自洽地考虑进来,从而给熔合反应的研究提供了一个新的途径.ImQMD模型能够很好地再现一系列核的基态性质以及10多个熔合反应的激发函数(包括丰中子核熔合体系以及实验最新测量的132Sn+64Ni熔合体系).此外还运用该模型初步探索了重核熔合过程中复合体系的寿命与体系的入射能量、体系大小以及体系的中子质子比的依赖关系. We have developed a new microscopic dynamical model called improved quantum molecular dynamical model (ImQMD). This model can describe the fusion process at energies near the Coulomb barrier as well as the multifragmentation process at intermediate energies in heavy-ion collision (HIC) uniformly. By using this model, fusion cross sections (including some of neutron-rich nuclei reactions and that of newly measured~(132)Sn+~(64)Ni fusion reaction) of tens reactions can be reproduced remarkably well. In fusi...     

Isotopic dependence of fusion cross-sections – linear relationships

A systematic study of isotopic dependence of fusion cross-section is carried out by adding neutrons gradually to N=Z colliding nuclei. We find that fusion barrier position increases and height decreases, both linearly with the increase of N/Z ratio of the compound system. The increase in barrier position is larger compared to decrease in barrier height. In terms of these linear relationships, a parameterized form of fusion cross-sections is given for the neutron-rich colliding nuclei. The fusion cross-sections are also enhanced linearly with the N/Z ratio, and this enhancement is larger for lower incident centre-of-mass energies and independent of the choice of reaction partners. Experimental data and other theoretical studies are called for to verify these results. Received: 27 February 1998 / Revised version: 22 May 1998     

基于双核模型对超重元素合成机制的研究

在双核模型基础上，考虑了熔合与准裂变的竞争，通过数值法求解主方程，计算了⁵⁰Ti，⁵⁸Fe+²⁰⁸Pb，²⁰⁹Bi这4个反应系统通过冷熔合反应合成超重元素的激发函数，得到了与实验比较符合的结果.计算了不同入射能量时各角动量分波对熔合概率和超重核存活概率的影响以及对蒸发剩余截面的贡献.这些结果对进一步理解超重核的合成机制有重要意义. 关键词： 超重元素 双核模型 熔合反应 蒸发剩余截面     

Production cross sections for the heaviest nuclei in complete fusion reactions induced by heavy ions

Production of the heaviest nuclei in complete fusion reactions induced by heavy ions has been considered in a systematic way in the framework of the conventional barrier passing model coupled with the statistical model. Available data on excitation functions for fission and production of evaporation residues (ER) in very asymmetric combinations induced by ions lighter than Ne on actinide target nuclei are described rather well in the framework of these models. The data allow one to adjust model parameters and to reveal the quasi-fission effect caused by the interaction with deformed target nuclei, which is manifested in the suppression of the ER production at sub-barrier energies. For reactions induced by Mg and heavier projectiles, quasi-fission is starting to suppress fusion (ER production) at energies above the Coulomb barrier. One has to introduce empirically the quantity of the fusion probability P_fus to reproduce the ER excitation functions in the framework of the conventional approach. The exponential dependence of P_fus on the combined fissility parameter (a similar parameter that was introduced for the extra-push energy scaling) was found in search for scaling for the P_fus values resulting from the data analysis.     

Nuclear Potential and Fusion Cross Sections for Synthesizing Super-Heavy Elements in Di-nuclear Systems

A double foMing method with simplified Skyrme-type nucleon nucleon interaction is used to calculate the nuclear interaction potential between two nuclei. The calculation is performed in tip-to-tip orientation of the two nuclei if they are deformed. Based on this method, the potential energy surfaces~ the fusion probabilities and the evaporation residue cross sections for some cold fusion reactions leading to super-heavy elements within di-nuclear system model are evaluated. It is indicated that after the improvement, the exponential decreasing systematics of the fusion probability with increasing charge number of projectile on the Pb based target become better and the evaporation residue cross sections are in better agreement with the experimental data.     

Dynamic potential barrier in the entrance phase of heavy-ion fusion reactions

Based on the improved quantum molecular-dynamics (ImQMD) model, the incident energy dependence of dynamic potential barriers is investigated in the entrance channel of fusion reactions. The height of the dynamic barrier increases with the incident energy at energies around the Coulomb barrier. The calculated lowest dynamic barrier approaches to the adiabatic barrier, while the highest one goes up to the sudden potential barrier. To understand the energy dependence of the dynamical barrier we study the neck formation and shape evolution of the system which causes the dynamic lowering of the barrier.     

Fusion and transfer reactions in beams of light loosely bound nuclei at energies in the vicinity of the Coulomb barrier

Experiments devoted to studying cross sections for fusion and transfer reactions induced by the interaction of beams of halo-like (⁶He), cluster (⁶Li and ⁷Li), and loosely bound (³He) nuclei with nuclei of light and heavy elements are described. The cross sections obtained experimentally for such reactions are analyzed. Special features in the behavior of the cross sections for the formation of evaporation residues and products of transfer reactions at energies in the vicinity of the Coulomb barrier are revealed. In particular, an increase in the cross sections for fusion and transfer reactions involving halo-like nuclei and proceeding at energies in the subbarrier region is observed. The cross sections for neutron-transfer and light-cluster-transfer reactions reachmaximum values at an energy in the vicinity of the Coulomb barrier for the reaction being considered.     

弱束缚原子核引起的熔合反应机制研究

弱束缚原子核引起的熔合反应机制研究是近几十年中实验核物理研究的重要课题之一。相比于放射性核束,加速器提供的稳定弱束缚原子核束流的强度要高几个数量级,利用稳定弱束缚原子核作为弹核进行反应机制的研究,可以在保证统计性和准确性的基础上,深入研究原子核的破裂、转移等反应道对熔合过程的耦合作用。已有很多实验数据表明,在库仑位垒附近,弱束缚原子核引发的熔合反应有很多有趣的现象,例如完全熔合截面的“垒下增强”和“垒上压低”。本文主要回顾近年来弱束缚原子核“垒上压低”的研究结果,并探讨造成“垒上压低”的可能原因。完全熔合截面“垒上压低”的主要原因是弱束缚原子核在进入熔合位垒之前发生破裂,从而降低了完全熔合反应道的入射通量。同时,实验研究表明完全熔合截面压低的程度可能与靶核质量数以及靶核结构相关。目前,在实验上对弱束缚原子核引起的熔合反应研究主要有3种测量方法,分别为$\gamma$射线测量方法、带电粒子测量方法以及带电粒子-$\gamma$射线符合测量的方法。其中,带电粒子-$\gamma$射线符合测量的方法在反应道鉴别方面具有明显的优势。本文对这3种测量方法进行了概要介绍,并就国内外对运用这3种方法开展的研究进行了介绍,包括本研究组在此方面的研究工作。此外,对弱束缚原子核引起的熔合反应近期在理论方面的研究工作也做了些介绍。     

Analytical calculation of fusion cross-sections

We analyse the fusion cross-sections, calculated by using two different analytical parameterisations and compare them with the experimental data. Both the parameterisations are based on ion-ion potentials calculated within the framework of Skyrme energy density formalism. In the first case, the ion-ion potential (including the spin-density term) was parameterised and then, by adding the Coulomb potential, one could compute the fusion barrier analytically. In the second case, the calculated fusion barrier heights and positions were parameterised directly. Both of these (previously) reported parameterisations are used here to calculate the fusion barriers and fusion excitation functions for more than 50 reactions belonging to the s-d and f-shell nuclei. A detailed comparison of these parametrisations with the experimental and several other theoretical results shows that both of these parameterisations are able to reproduce the experimental data equally well. As the (second) direct parameterisation depends only on the charges and masses of colliding nuclei, it is very useful for predicting/ understanding the fusion process in low energy heavy-ion reactions. Received: 24 February 1999 / Accepted: 16 March 2000     

Special features of nuclear reactions induced by loosely bound <Superscript>6</Superscript>He and <Superscript>6,7</Superscript>Li nuclei in the vicinity of the Coulomb barrier height

Excitation functions are measured for complete-fusion and transfer reactions induced by the interaction of ⁶He and ⁶Li with ²⁰⁶Pb, ²⁰⁹Bi, and Pt. Data obtained for fusion reactions induced by ⁶He ions deviate from the predictions of the statistical model of compound-nucleus decay at projectile energies in the vicinity of the Coulomb barrier height. A strong enhancement of cross sections for fusion reactions induced by the interaction of ⁶He with target nuclei is observed. The cross sections for reactions of cluster transfer, neutron transfer from ⁶He, and deuteron transfer from ⁶Li at deep-subbarrier energies are also found to be enhanced. These results are discussed from the point of view of the effect of the cluster structure of nuclei on the interaction probability at energies in the vicinity of the Coulomb barrier height.     

弱束缚弹核引起的熔合反应

⁶Li, ⁹Be为弱束缚核. 通过弱束缚弹核⁶Li, ⁹Be轰击靶²⁰⁸Pb,²⁰⁸Be的实验熔合激发函数与理论预言的比较, 讨论了弱束缚弹核破裂对熔合过程 的影响. 比较结果显示, 弱束缚弹核与重靶核的完全熔合截面在垒上能区 明显压低. 由部分熔合截面与完全熔合截面之和得到总熔合截面. 研究结果 表明, 破裂对总熔合截面几乎没有影响. 由此可见, 弱束缚核的部分熔合 可能发生在强吸收区域附近. 最后还给出了全熔合截面与部分熔合截面 之间的关系.     

Analytic estimates of the product yields for nuclear reaction in the ultralow energy range

Simple analytic expressions for estimation of product yields from reactions between light nuclei in the ultralow collision energy range are given. It is shown that, even in the case of total absorption targets and large spread of incident beam energies, these expressions can be factorized and naturally define the effective target thickness and the range of particle collision energies in the entrance channel that in turn defines the yield of reaction products.     

Origin of Unexpected Isotopic Trends in Synthesis of Superheavy Nuclei

We investigate the dependence of the yield of superheavy nuclei with Z = 110, 112, 114 on the neutron excess of the projectile nucleus with a two-parameter Smoluchowski equation. It is confirmed that in some cases, the cold fusion reactions with less neutron excess are more favourable than those with more neutron excess. In order to probe the origin of these unexpected isotopic trends, we also investigate the probabilities of capture, fusion and survival in the cold fusion reactions in detail It is found that the maximal ER cross sections of the superheavy nuclei exponentially increase as a function of Bf - Sn with Bf being the fission barrier and Sn being the neutron separation energy. Although the probabilities of capture and fusion have some influences, the unexpected isotopic trends mainly due to the dependence of the ER cross sections on the Bf - Sn value. Therefore, the reactions with larger Bf - Sn values should be more favourable for synthesis of superheavy nuclei.     

Transition fission states for heated nuclei

Induced fission reactions of fissioning compound nuclei that result from the capture of various incident particles (nucleons, γ rays, multiply charged ions) by target nuclei are investigated using the generalized nucleus model and the Wigner random matrix method. The effect produced on the fission widths of the compound nucleus by the competition between the excitation energies of its collective vibrational degrees of freedom that lead to its scission into fission fragments and its rotational and multi-quasiparticle states is analyzed. Bohr’s concept of transition fission states developed for near-barrier nuclear fission is generalized to the induced fission of nuclei with the excitation energies noticeably higher than the fission barriers. The temperature of the fissioning nucleus in the vicinity of the point of its scission into fission fragments is estimated.