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.     

Shell Correction and Pairing Energies in the Dinuclear System Model

We investigate the dependences of the potential energy surfaces （PES） and the fusion probabilities for some cold fusion reactions leading to super-heavy elements on the nuclear shell effect and pairing energy. It is found that the shell effect plays an important role in the fusion of the super-heavy element while pairing energy＇s contribution is insignificant. The fusion probabilities and evaporation residue cross sections as functions of the Ge-isotope projectile bombarding ^208Pb are also investigated. It is found that evaporation residue cross sections do not always increase with the increasing neutron number of Ge-isotope.     

Predictions of synthesizing element 119 and 120

The evaporation residue cross sections of synthesizing superheavy nuclei Z=119, 120 are calculated by different sets of master equations with different dynamical variables. Two methods basically predicted similar results that the Ca induced hot fusion can 48 produce element 119 easier than produce 120, and the evaporation residue cross sections for 119 are detectable by current advanced techniques, while the evaporation residue cross sections are below 0.1 pb for producing element 120.     

Predictions of synthesizing element 119 and 120

The evaporation residue cross sections of synthesizing superheavy nuclei Z=119, 120 are calculated by different sets of master equations with different dynamical variables. Two methods basically predicted similar results that the ⁴⁸Ca induced hot fusion can produce element 119 easier than produce 120, and the evaporation residue cross sections for 119 are detectable by current advanced techniques, while the evaporation residue cross sections are below 0.1 pb for producing element 120.     

Dinuclear systems in complete fusion reactions

Formation and evolution of dinuclear systems in reactions of complete fusion are considered. Based on the dinuclear system concept, the process of compound nucleus formation is studied. Arguments confirming the validity of this concept are given. The main problems of describing the complete fusion in adiabatic approximation are listed. Calculations of evaporation residue cross sections in complete fusion reactions leading to formation of superheavy nuclei are shown. Isotopic trends of the cross sections of heavy nuclei formation in complete fusion reactions are considered.     

Fusion and quasifission within the dinuclear system model

The dinuclear system model considers a configuration of two touching nuclei which exchange nucleons. The microscopical justification of the model is presented. The fusion and quasifission processes are described in the reactions of synthesis of heavy and superheavy nuclei. The dependence of evaporation residue cross sections on isotopic composition of colliding nuclei is analyzed. The results agree with the available experimental data.     

Formation of heavy compound nuclei,their survival,and correlation with longtime-scale fission

Fusion of two massive nuclei with formation of a superheavy compound nucleus is driven by the potential energy gradient, as follows from the analysis of nuclear reaction cross sections. The conservative energy of the system is deduced in a simple approximation using regularized nuclear mass and interaction barrier values. Different reactions for the synthesis of Z = 110−118 nuclei are compared and favorable conditions are found for fusion of the stable W-Pt isotopes with radioactive fission fragment projectiles, like ⁹⁴Kr or ¹⁰⁰Sr. Thus, the cold-fusion method can be extended for a synthesis of elements with Z > 113. Survival of the evaporation residue is defined by the neutron-to-fission probability ratio and by the successful emission of gammas at the final step of the reaction. Numerical estimates are presented. Fixation of evaporation residue products must correlate with longtime-scale fission, and available experimental results are discussed. The text was submitted by the authors in English.     

Inelastic interactions of fast nucleons with nuclei and fission of nuclei

The cross section for the fission of actinide nuclei that is induced by fast neutrons is considered as a fraction of the cross section for inelastic nucleon interaction with nuclei. In turn, inelastic nucleon interaction with a nucleus is treated as scattering on intranuclear nucleons. It is shown that this interaction model describes satisfactorily the cross section for the inelastic interaction of 60- to 2200-MeV nucleons for a broad set of nuclei and that the energy dependence of the cross section for the fission of actinide nuclei that is induced by 400- to 1000–MeV protons replicates the energy dependence of the cross section for inelastic interactions with respective nuclei. From the model used, it follows that the cross sections for proton-nucleus interactions exceed cross sections for respective neutron-nucleus interactions in the energy range extending up to 550 MeV; at higher energies neutron cross sections are larger than proton cross sections.     

Properties of products originating from the interaction of 35-MeV/nucleon <Superscript>7</Superscript>Li ions with Pb nuclei

The results are presented that were obtained by measuring and analyzing the yields and kinematical features of radioactive products of the reactions initiated in a lead target by lithium ions accelerated to an energy of 35M eV per nucleon. The cross sections, charge and mass distributions, and kinematical and energy features of various reaction products associated with the fission and the evaporation channels of the decay of excited nuclei are determined. Quantities that are calculated in the present study include the momenta and kinetic energies of residual nuclei, as well as the momentum transfer and the excitation energy of intermediate nuclear systems formed upon complete and incomplete fusion. On the basis of an analysis of data obtained in our experiment, the total cross section for nuclear interaction and partial widths with respect to various channels of the decay of intermediate compound nuclei are determined in the energy range being investigated.     

基于相对论平均场理论对超重核冷熔合反应截面的研究

在形变约束的相对论平均场理论框架下计算了合成Z=102—118元素的(可能)冷熔合反应中复合核及蒸发一或两个中子剩余核的位能曲面,得到了复合核和剩余核平衡点和鞍点的性质、静态裂变垒高度和冷熔合反应的最佳入射能;利用壳修正和对修正方法计算了平衡点和鞍点的壳修正能、对修正能和微观能.利用由此得到的壳结构信息,用简单的熔合蒸发唯象模型计算了相应反应的冷熔合截面.结果发现,TM1参数提供的结构性质给出了与实验接近的反应截面.     

Evaporation residue cross sections for 40Ca + 48Ti at 25.0 and 33.9 MeV per nucleon

The fusion and subsequent decay of the system ⁴⁰Ca+⁴⁸Ti has been studied at 25.0 and 33.9 MeV per nucleon bombarding energies. Heavy residues were detected in coincidence with light particles, and evaporation residue cross sections have been extracted. Light particle distributions are well described by a simple kinematical model, and from this the average excitation energies of the system were determined.     

Evaporation residue excitation functions from fusion of 63Cu with 65Cu

Mass distributions of evaporation residues from the fusion of ⁶³Cu + ⁶⁵Cu have been measured at seven excitation energies from 55 to 105 MeV in a single irradiation experiment. They are interpreted as a mixture of residues produced by single nucleon evaporation cascades and cascades including α-particle evaporation. Compound nuclei with an average excitation energy of 55 MeV ($\text{51.5 ≦ E}{}^1\text{≦ 59}\text{MeV}$) are still found to have a probability as high as 0.3 % for decaying by emission of a single nucleon. The low-energy behaviour of the excitation function can be interpreted as a fusion barrier effect. The parameters of this barrier are determined. The evaporation residue cross section at higher energies is shown to be limited by the fission of the compound nucleus.     

超重核性质与合成机制的理论研究

探索原子核的电荷与质量极限,合成长寿命超重核是当前原子核物理研究的重要前沿问题之一。本文综述了我们近几年在超重原子核结构性质与合成机制方面取得的理论研究进展。在结构性质方面,利用处理对关联的粒子数守恒方法,基于推转壳模型,系统研究了锕系核与超镄核低激发谱,发展了多维形状约束的协变密度泛函理论并用于研究锕系核势能面和裂变位垒以及N=150同中子素中的非轴对称八极关联等。在超重核合成机制方面,系统研究了利用重离子熔合反应合成超重核的三步过程,包括俘获过程——提出了一个位垒穿透概率新公式、熔合过程——提出了一个基于动力学形变势能面的双核模型、存活过程——系统研究了激发态超重复合核存活概率等。系统研究了合成超重核的热熔合反应,得到的熔合蒸发截面与实验符合,并预言了合成119和120号超重元素的生成截面。     

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.     

Reaction cross sections for collisions involving exotic light nuclei within the glauber approach

The reaction cross sections for the interaction of exotic nuclei ⁶He and ¹¹Li with ¹²C nuclei are calculated for energies of about 0.8 GeV per nucleon. The cross sections calculated by the exact Glauber formula are compared with their counterparts found by using the formulas of the optical limit, the rigidtarget approximation, and the few-body approximation. The effect of the structure of the nuclei being considered on the calculated cross sections is examined. The root-mean-square radii of the ⁶He and ¹¹Li nuclei are estimated on the basis of experimental data on the cross sections for the interaction of these exotic nuclei with ¹²C nuclei.     

Investigating the nuclear fusion and nucleon transfer channels in the 197Au + 6He reaction at 6He energies up to 20 MeV/A

New data on the cross sections of reactions that proceed during the interaction of ⁶He and ¹⁹⁷Au nuclei in the ⁶He energy range of 40 to 120 MeV are reported. The experiments were performed using the secondary beam of the ACCULINNA separator at the Flerov Laboratory of Nuclear Reactions (FLNR), JINR. Reaction products are identified by means of activation method to measure the gamma activity of a thin-foil target assembly. Excitation functions for ⁶He fusion reactions with subsequent emission of up to 10 neutrons from the compound nucleus are measured. Cross sections for reactions with emission of charged particles and nucleon transfer were also measured. The experimental cross sections for the (⁶He, xn) reactions that proceed via the formation of a compound nucleus agree in general with calculations using models that involve the statistical approach. It is shown that the complete fusion reaction cross section drops slightly up to an energy of 114 MeV. The experimental excitation functions for the reactions resulting in the formation of mercury and gold isotopes indicate that the main contribution to their formation comes from direct processes, while the evaporation reactions (⁶He, pxn) and (⁶He, αxn) are of minor importance.     

Application of the program LISE to fusion-evaporation

A new fusion-evaporation model LisFus for fast calculation of fusion residue cross sections has been developed in the framework of the code LISE. This model can calculate very small cross sections quickly compared to programs using the Monte Carlo method. Such type of the fast calculations is necessary to estimate fusion residue yields. Using this model, the program LISE now has the possibility of calculating the transmission of fusion residues through a fragment separator. It is also possible to use fusion residue cross sections calculated by the program PACE, which has been incorporated in the LISE package. The code PACE is a modified version of JULIAN—the Hillman-Eyal evaporation code using a Monte Carlo code coupling angular momentum. A comparison between PACE and the LisFus model is presented.     

Isotopic and neutron-excess effects in nucleus-nucleus interaction and fusion cross sections

The interaction potentials and fusion cross sections for various nickel and tin isotopes are calculated. The fusion cross sections are computed with allowance for coupling to the channels of low-lying 2⁺ and 3^? vibrational states in the interacting nuclei. Good agreement with the experimental data is obtained. The isotopic dependences of interaction potentials and fusion cross sections of nuclei are analyzed in detail.     

Effect of nuclear-reaction mechanisms on the population of excited nuclear states and isomeric ratios

Experimental data on the cross sections for channels of fusion and transfer reactions induced by beams of radioactive halo nuclei and clustered and stable loosely bound nuclei were analyzed, and the results of this analysis were summarized. The interplay of the excitation of single-particle states in reaction-product nuclei and direct reaction channels was established for transfer reactions. Respective experiments were performed in stable (⁶Li) and radioactive (⁶Не) beams of the DRIBs accelerator complex at the Flerov Laboratory of Nuclear Reactions, Joint Institute for Nuclear Research, and in deuteron and ³Не beams of the U-120M cyclotron at the Nuclear Physics Institute, Academy Sciences of Czech Republic (?e? and Prague, Czech Republic). Data on subbarrier and near-barrier fusion reactions involving clustered and loosely bound light nuclei (⁶Li and ³He) can be described quite reliably within simple evaporation models with allowance for different reaction Q-values and couple channels. In reactions involving halo nuclei, their structure manifests itself most strongly in the region of energies below the Coulomb barrier. Neutron transfer occurs with a high probability in the interactions of all loosely bound nuclei with light and heavy stable nuclei at positive Q-values. The cross sections for such reactions and the respective isomeric ratios differ drastically for nucleon stripping and nucleon pickup mechanisms. This is due to the difference in the population probabilities for excited single-particle states.