Production mechanism of superheavy nuclei in massive fusion reactions

Within the concept of the dinuclear system (DNS), a dynamical model is proposed for describing the formation of superheavy nuclei in complete fusion reactions by incorporating the coupling of the relative motion to the nucleon transfer process. The capture of two heavy colliding nuclei, the formation of the compound nucleus and the de-excitation process are calculated by using an empirical coupled channel model, solving a set of microscopically derived master equations numerically and applying statistical theory, respectively. Fusion-fission reactions and evaporation residue excitation functions of synthesizing superheavy nuclei (SHN) are investigated systematically and compared them with available experimental data. The possible factors that affecting the production cross sections of SHN are discussed in this workshop.     

Production cross sections of the superheavy nucleus 117 based on the dinuclear system model

Within the framework of the dinuclear system model,the capture of two colliding nuclei,and the formation and de-excitation process of a compound nucleus are described by using an empirical coupled channel model,solving the master equation numerically and the statistical evaporation model,respectively.In the process of heavy-ion capture and fusion to synthesize superheavy nuclei,the barrier distribution func-tion is introduced and averaging collision orientations are considered.Based on this model,the production cross sections of the cold fusion system 76-82Se+209Bi and the hot fusion systems 55Mn+238U,51V-+244Pu,59 Co+232 Th,48 Ca+247-249 Bk and 45 Sc+246-248 Cm are calculated.The isotopic dependence of the largest production cross sections is analyzed briefly,and the optimal projectile-target combination and excitation energy of the ln-4n evaporation channels are proposed.It is shown that the hot fusion systems 48Ca+247 249Bk in the3n evaporation channels and 45Sc+248Cm in the 2n-4n channels are optimal for synthesizing the superheavy element 117.     

双核模型下超重核117的生成截面研究

Within the framework of the dinuclear system model, the capture of two colliding nuclei, and the formation and de-excitation process of a compound nucleus are described by using an empirical coupled channel model, solving the master equation numerically and the statistical evaporation model, respectively. In the process of heavy-ion capture and fusion to synthesize superheavy nuclei, the barrier distribution function is introduced and averaging collision orientations are considered. Based on this model, the production cross sections of the cold fusion system ^76-82Se＋^209Bi and the hot fusion systems ^55Mn＋^238U, ^51V＋^244pu, ^59Co＋^232Th, ^48Ca＋^247-249Bk and ^45Sc＋^246-248Cm are calculated. The isotopic dependence of the largest production cross sections is analyzed briefly, and the optimal projectile-target combination and excitation energy of the 1n-4n evaporation channels are proposed. It is shown that the hot fusion systems ^48Ca＋^247-249Bk in the 3n evaporation channels and ^45Sc＋248Cm in the 2n-4n channels are optimal for synthesizing the superheavy element 117.     

Shell effect and capture cross sections in the synthesis of superheavy nuclei

The shell effect is included in the improved isospin dependent quantum molecular dynamics model in which the shell correction energy of the system is calculated by using the deformed two-center shell model.A switch function is introduced to connect the shell correction energy of the projectile and the target with that of the compound nucleus during the dynamical fusion process.It is found that the calculated capture cross sections reproduce the experimental data quantitatively at the energy near the Coulomb...     

Synthesis of heavy and superheavy elements by reactions of massive nuclei

By comparing theoretical and experimental excitation functions of evaporation residues resulting from the same compound nucleus or heavy and superheavy nuclei, it is possible to understand the effect of the entrance channel and the shell structure of reacting nuclei on the fusion mechanism. The competition of complete fusion with the quasifission process is strongly related to the intrinsic fusion barrier B _fus ^* and the quasifission barrier B _qf as well as the size of the well in the nucleus-nucleus potential. In our calculations of the excitation functions for capture, fusion, and evaporation residues, we use the relevant variables such as mass asymmetry of nuclei in the entrance channel, potential energy surface, driving potential, spin distribution, and surviving probability of compound nucleus that are responsible for the mechanism of the fusion-fission process. As a result, we obtain a beam energy window for the capture of the nuclei before the system fuses and the Γ_n/Γ_f ratio at each step along the deexcitation cascade of the compound nucleus. Calculations performed in the framework of the model taking into account the nuclear shell effect and shape of colliding nuclei allow us to reach useful conclusions about the mechanism of the fusion-fission process and the production of the evaporation residues. We analyze the ⁴⁰Ar + ¹⁷⁶Hf, ⁸⁶Kr + ¹³⁰Xe, and ¹²⁴Sn + ⁹²Zr reactions leading to ²¹⁶Th*; the ³²S + ¹⁸²W and ⁶⁰Ni + ¹⁵⁴Sm reactions leading to ²¹⁴Th*; the ⁴⁸Ca + ²⁴⁸Cm reaction leading to the ²⁹⁶116 compound nucleus; and the ⁴⁸Ca + ²⁴⁹Cf reaction leading to the ²⁹⁷118 compound nucleus.     

Formation of heavy and superheavy elements by reactions with massive nuclei

The effects of the entrance channel and shell structure on the experimental evaporation residues have been studied by analyzing the ³²S + ¹⁸²W, ⁴⁸Ti + ¹⁶⁶Er and ⁶⁰Ni + ¹⁵⁴Sm reactions leading to ²¹⁴Th^*; the ⁴⁰Ar + ¹⁸¹Ta reaction leading to ²²¹Pa^*; the ⁴⁸Ca + ²⁴³Am, ²⁴⁸Cm, ²⁴⁹Cf reactions leading to the ²⁹¹115, ²⁹⁶116 and ²⁹⁷118 superheavy compound nuclei, respectively. The fusion mechanism and the formation of evaporation residues of heavy and superheavy nuclei have been studied. In calculations of the excitation functions for capture, fusion and evaporation residues we used such characteristics as mass asymmetry of nuclei in the entrance channel, binding energies and shape of colliding nuclei, potential energy surface, driving potential, partial-fusion cross-sections and survival probability of the compound nucleus, ratio at each step along the de-excitation cascade of the compound nucleus. The calculations have allowed us to make useful conclusions about the mechanism of the fusion-fission process, which is in competition with the quasifission process, and the production of the evaporation residues.Received: 22 April 2003, Revised: 26 June 2003, Published online: 18 December 2003PACS: 25.70.Gh Compound nucleus - 25.70.-z Low and intermediate energy heavy-ion reactions - 27.80. + w - 27.90. + b      

Production cross sections for exotic nuclei with multinucleon transfer reactions

The main progresses in the multinucleon transfer reactions at energies close to the Coulomb barrier are reviewed. After a short presentation of the experimental progress and theoretical progress, the predicted production cross sections for unknown neutron-rich heavy nuclei and the trans-uranium nuclei are presented.     

Synthesis of superheavy elements and the process of complete fusion of massive nuclei

The development of various approaches to describing the complete fusion of nuclei and their connections with experimental studies is discussed. A brief account of the dinuclear-system concept (DNSC), the approach proposed at Dubna, is given. The DNSC revealed two important features of the complete fusion of massive nuclei: the existence of the inner fusion barrier B _fus ^* and the competition between complete fusion and quasifission channels in a dinuclear system formed at the capture stage. The DNSC was applied to the analysis of reactions used to synthesize superheavy elements (SHE). The DNSC provided a basis for the models of competition between complete-fusion and quasifission channels. Using these models, one can describe the cross section for SHE production in cold-and warm-fusion reactions.     

Production of super-heavy nuclei in cold fusion reactions

A model for cold-fusion reactions related to the synthesis of super-heavy nuclei in collisions of heavy projectile-nuclei with a ²⁰⁸Pb target nucleus is discussed.In the framework of this model,the production of the com-pound nucleus by two paths,the di-nuclear system path and the fusion path,are taken into account simultaneously.The formation of the compound nucleus in the framework of the di-nuclear system is related to the transfer of nucle-ons from the light nucleus to the heavy one.The fusion path is linked to the sequential evolution of the nuclear shape from the system of contacting nuclei to the compound nucleus.It is shown that the compound nucleus is mainly formed by the fusion path in cold-fusion reactions.The landscape of the potential energy related to the fusion path is discussed in detail.This landscape for very heavy nucleus-nucleus systems has an intermediate state,which is linked to the formation of both the compound nucleus and the quasi-fission fragments.The decay of the intermediate state is taken into account in the calculation of the compound nucleus production cross sections and the quasi-fission cross sections.The values of the cold-fusion cross sections obtained in the model agree well with the experimental data.     

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     

Potential energy surface and formation of superheavy nuclei with the Skyrme energy-density functional

With the Skyrme energy-density functional theory, the nucleus–nucleus potential is calculated and the potential energy surface is obtained with different effective forces for accurately estimating the formation cross sections of superheavy nuclei in massive fusion reactions. The width and height of the potential pocket are influenced by the Skyrme effective forces SkM, SkM^*, SkP, SIII, Ska, and SLy4, which correspond to the different equations of state for the isospin symmetry nuclear matter. It is found that the nucleus–nucleus potential is associated with the collision orientation and Skyrme forces. A more repulsive nuclear potential is pronounced with increasing the incompressible modulus of nuclear matter, which hinders the formation of superheavy nuclei. The available data in the fusion-evaporation reaction of ⁴⁸Ca+²³⁸U are nicely reproduced with the SkM^* parameter by implementing the potential into the dinuclear system model.     

热熔合反应合成超重核产生截面的同位素依赖性

通过在形成超重核的重离子俘获和熔合过程中引入位垒分布函数的方法对双核模型做了进一步发展. 超重核形成过程中的俘获、熔合和蒸发3个阶段分别采用了半经验的耦合道模型、数值求解主方程和统计蒸发模型的方法来描述. 计算了近年来Dubna小组利用热熔合反应⁴⁸Ca(²⁴³Am, 3n—5n)^288—286115和⁴⁸Ca(²⁴⁸Cm, 3n—5n)^293—291116合成超重新核素的蒸发余核激发函数. 系统分析了⁴⁸Ca轰击锕系元素U,Np,Pu,Am,Cm合成超重核Z=112—116产生截面的同位素依赖性. 给出了合成超重新核素最佳的弹靶组合和入射能量, 即有最大的超重核产生截面. 计算说明, 壳修正能和中子分离能是影响超重核生成截面产生同位素依赖性的主要因素.     

Possibilities of producing superheavy nuclei in multinucleon transfer reactions based on radioactive targets

The multinucleon transfer(MNT) process has been proposed as a promising approach to produce neutronrich superheavy nuclei(SHN).MNT reactions based on the radioactive targets ~(249)Cf,~(254)Es,and ~(257)Fm are investigated within the framework of the improved version of a dinuclear system(DNS-sysu) model.The MNT reaction~(238)U+~(238)U was studied extensively as a promising candidate for producing SHN.However,based on the calculated cross-sections,it was found that there is little possibility to produce SHN in the reaction ~(238)U+~(238)U.In turn,the production of SHN in reactions with radioactive targets is likely.     

Doubly magic properties in superheavy nuclei

A systematic study of global properties of superheavy nuclei in the framework of the Liquid Drop Model and the Strutinsky shell correction method is performed. The evolution equilibrium deformations, TRS graphs and α-decay energies are calculated using the TRS model. The analysis covers a wide range of even-even superheavy nuclei from Z =102 to 122. Magic numbers and their observable influence occurring in this region have been investigated. Shell closures appear at proton number Z =114 and at neutron number N =184.     

Feature of production of new superheavy nuclei in actinide-based complete-fusion reactions

Within the dinuclear system model we analyse the production of unknown superheavy nuclei in various actinide-based complete-fusion reactions. Different predictions of the properties of the heaviest nuclei are used. The dependence of the calculated evaporation residue cross-sections on the predicted shell structure and magic numbers of the heaviest nuclei is discussed.     

A systematic study of the fission and evaporation residue excitation functions in complete fusion reactions with weakly bound stable nuclei

We carry out a systematic study on the fusion-fission and evaporation residue excitation functions for the reactions of ^6,7Li, ⁹Be, ^10,11B + ²⁰⁹Bi and ^6,9Li, ⁹Be + ²⁰⁸Pb, in which the projectiles are loosely bound and have low threshold energies against breakup. The fusion cross sections are calculated by the coupled-channel model. The compound nuclei decay are analyzed with the standard statistical model. The fission and evaporation residue excitation functions are well reproduced by our calculations, proving the validity of the standard statistical model in describing the compound nuclei decay in these characteristic reactions. For the compound nuclei with A=215-220 and Z=86-88, the liquid drop fission barriers need to be scaled by 0.80-1.02 to reproduce the experimental data. And a decreasing trend of the scaling factor with increasing fissionability parameter Z²/(50A) is found.     

Effect of nuclear deformation on direct capture reactions

Direct radiative capture processes are well described by a spherical potential model. Since most nuclei are not spherical, and in order for the model to explain direct radiative captures more accurately, the effect of nuclear deformation has been analyzed with q-deformed Woods-Saxon potential in this work. The results imply that nuclear deformation largely affects the direct radiative capture, and it should be taken into account when discussing direct capture reactions.     

Macroscopic-microscopic calculations of ground state properties of superheavy nuclei

We systematically calculate the ground state properties of superheavy even-even nuclei with proton number Z=94–118. The calculations are based on the liquid drop macroscopic model and the microscopic model with the modified single-particle oscillator potential. The calculated binding energies and α-decay energies agree well with the experimental data. The reliability of the macroscopic-microscopic(MM)model for superheavy nuclei is confirmed by the good agreement between calculated results and experimental ones. Detailed comparisons between our calculations and M?ller’s are made. It is found that the calculated results also agree with M?ller’s results and that the MM model is insensitive to the microscopic single-particle potential. Calculated results are also compared with results from relativistic mean-field (RMF) model and from Skyrme-Hatree-Fock(SHF) model. In addition, half-lives, deformations and shape coexistence are also investigated. The properties of some unknown nuclei are predicted and they will be useful for future experimental researches of superheavy nuclei.     

Resonance states of superheavy hydrogen nuclei obtained in transfer reactions with exotic beams

A resonance state situated at 1.8±0.1 and, most likely, another state positioned at 2.7±0.1 MeV above the t+n+n decay threshold were observed in the missing mass energy spectrum of the ⁵H nucleus produced in the reaction ³H(t,p)⁵H. The peak located close to $E_{^5 H} = 1.8$ MeV also was seen in the ⁵H spectrum obtained from the energy distributions of ³H nuclei emitted in the reaction ²H(⁶He,⁵H)³He. The width (Γ_obs ≤ 0.5 MeV) obtained for the two ⁵H resonance states is surprisingly small. A state of ⁴H with E _res = 3.3 MeV and γ² = 2.3 MeV was obtained in the reaction ²H(t,p)⁴H from the proton spectrum.