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...     

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。     

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。     

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.     

Fusion Barrier of Super-heavy Elements in a Generalized Liquid Drop Model

The macroscopic deformed potential energies for super-heavy elements Z = 110,112,114,116,118 arc determined within a generalized liquid drop model (GLDM). A quasi-molecular mechanism is introduced to describe the deformation of a nucleus in the GLDM and the shell model simultaneously. The macroscopic energy of a twocenter nuclear system in the GLDM includes the volume-, surface-, and Coulomb-energies, the proximity effect at each mass asymmetry, and accurate nuclear radius. The shell correction is calculated by the Strutinsky method and the microscopic single particle energies are derived from a shell model in an axially deformed Woods-Saxon potential with the quasi-molecular shape. The total potential energy of a nucleus can be calculated by the macro-microscopic method as the summation of the liquid-drop energy and the Strutinsky shell correction. The theory is applied to predict the fusion barriers of the cold reactions ^64Ni ^208 spb → ^272 110*, ^70Zn ^208pb → ^278 112*, ^76Ge ^208seb → ^284 114*,^82Se ^208pb → ^29 116*, ^86Kr ^208pb → ^294 118*. It is found that the neck in the quasi-molecular shape is responsible for the deep valley of the fusion barrier. In the cold fusion path, double-hump fusion barriers could be predicted by the shell corrections and complete fusion events may occur.     

入射粒子与靶相互作用中电子能损的高阶修正

研究了在较高能入射离子（He离子、 12_C离子）与靶相互作用中电子能量损失的物理机制, 分别探讨了电子能量损失中的相对论修正、 壳修正、 密度修正以及Barkas效应和Bloch效应等修正的贡献, 发现壳修正、 Barkas效应修正和Bloch效应修正在能量小于100 MeV时是重要的, 而相对论修正和密度修正是在能量大于100 MeV时起作用。 加入各种修正项之后, 电子阻止本领的计算结果和实验值（ICRU49）符合更好。 The mechanisms of electronic energy loss in the process of incident particles interaction with Si and Al₂O₃ at proper energies are investigated. The contribution to the electronic energy loss from high order corrections, such as the relativistic correction, the shell correction, the density correction, the Barkas effect correction and the Bloch effect correction are discussed respectively. It is found that the shell correction, the Barkas effect correction and the Bloch effect correction are important at low energies, the relativistic correction and the density correction are important at high energies. The calculated results with these higher order corrections are in good agreement with the experiment data (ICRU49).     

Fusion hindrance and synthesis of superheavy elements

A mechanism for fusion hindrance is clarified, based on the observation that the sticking configuration of projectile and target is located outside of the conditional saddle point. Accordingly, the fusion process is described by two sequential steps of passing over the Coulomb barrier and shape evolution toward the spherical compound nucleus. The latter one is indispensable in massive systems. With the use of a two-step model, excitation functions of fusion reaction are calculated for various combinations of projectiles and targets which lead to superheavy elements. The hindered fusion excitation measured is reproduced precisely without any adjustable parameter. Combined with survival probabilities calculated by the statistical theory of decay, excitation functions for residues of superheavy elements are calculated to compare with the systematic data measured for the cold fusion path. The peak positions and the widths are correctly reproduced, though it is necessary to reduce the shell correction energies of the compound nuclei predicted by the structure calculations in order to reproduce their absolute values. Predictions are made for a few unknown heavier elements. Furthermore, a preliminary attempt toward the shell closure N = 184 is also presented using a neutron-rich secondary beam. The text was submitted by the authors in English.     

Effect of shell structure in the fusion reactions

The fusion reactions are studied in the central collisions ⁸²Se+ + ¹³⁴Ba and ⁸²Se+ + ¹³⁸Ba by the improved isospin-dependent quantum molecular-dynamics model, where the nucleus ¹³⁸Ba has a closed neutron shell N = 82 . Comparing the shell correction energies and fusion probabilities of these two reactions with the ones of other asymmetric or more symmetric reaction systems that form the same compound nuclei, we find the dependence of the fusion reaction on the nuclear shell structure of the colliding nuclei. The experimental data of the fusion probabilities are described well by the present model. The result suggests that the neutron shell closure N = 82 promotes fusion.     

Core–Shell Nanoparticles Driven by Surface Energy Differences in the Co–Ag,W–Fe,and Mo–Co Systems

Core–shell nanoparticles are known to form in binary systems using a one‐step gas‐condensation deposition process where a large, positive enthalpy of mixing provides the driving force for phase separation and a difference in surface energy between component atoms creates a preferential surface phase leading to a core–shell structure. Here, core–shell nanoparticles have been observed in systems with enthalpy as low as ?5 kJ mol^?1 and a surface energy difference of 0.5 J m^?2 (Mo–Co). This suggests that surface energy dominates at the nanoscale and can lead to phase separation in nanoparticles. The compositions and size dependence of the core–shell structures are also compared and no core–shell structures are observed below a critical size of 8 nm.     

Systematic study of survival probability of excited superheavy nuclei

The stability of excited superheavy nuclei (SHN) with 100 ⩽ Z ⩽ 134 against neutron emission and fission is investigated by using a statistical model. In particular, a systematic study of the survival probability against fission in the 1n-channel of these SHN is made. The present calculations consistently take the neutron separation energies and shell correction energies from the calculated results of the finite range droplet model which predicts an island of stability of SHN around Z = 115 and N = 179. It turns out that this island of stability persists for excited SHN in the sense that the calculated survival probabilities in the 1n-channel of excited SHN at the optimal excitation energy are maximized around Z = 115 and N = 179. This indicates that the survival probability in the 1n-channel is mainly determined by the nuclear shell effects.

     

Fusion probability of symmetric heavy,nuclear systems determined from evaporation-residue cross sections

Cross sections were measured for the formation of evaporation residues in ⁴⁸Ca-, ⁸⁶Kr- and ¹²⁴ Sn-induced reactions with Yb, Sb and Zr isotopes. For the nearly symmetric systems, the energy dependence of the fusion probability in central collisions was determined. The fusion probability at the expected fusion barrier as calculated from a one-dimensional heavy-ion potential was found to be reduced by several orders of magnitude. The fusion cross sections increase gradually, and only at energies appreciably above the expected fusion barrier the major part of the cross section of central collisions leads to fusion. The observed hindrance of the fusion process is compared with model predictions.     

Shell correction to atomic energy

A method for calculating a shell correction to total atomic energy within the framework of statistical theory is proposed. It is shown that the shell correction which defines the energy component which oscillates with Z is of the relative order of magntiude Z^–1. The results obtained agree well with calculations by the Hartree-Fock method.Translated from Izvestiya Vysshikh Uchebnykh Zavedenii, Fizika, No. 2, pp. 81–86, February, 1984.     

Probing Shell Correction at High Spin by Neutron Emission of Doubly Magic Nuclei 208pb and 132Sn

Shell effects in particle emission for two doubly magic nuclei 132 Sn and 208 Pb were studied in the framework of Smoluchowski equation taking into account temperature and spin-dependent shell correction. It is shown that the shell effects in the enission of pre-scission neutrons are sensitive to the spin dependence of the shell correction at a moderate excitation energy. Therefore, we propose to use neutron multiplicity as an observable to probe the shell correction at high spins.     

Probing Shell Correction at High Spin by Neutron Emission of Doubly Magic Nuclei 208Pb and 132Sn

Shell effects in particle emission for two doubly magic nuclei ^132Sn and ^208pb were studied in the framework of Smoluchowski equation taking into account temperature and spin-dependent shell correction. It is shown that the shelle ffects in the emission of pre-scission neutrons are sensitive to the spin dependence of the shell correction at a moderate excitation energy. Therefore, we propose to use neutron multiplicity as an observable to probe the shell correction at high spins.     

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.     

Single particle models in the shell correction approach

We investigate the dependence of the shell correction energy on the parameters as they occur in the Nilsson model and the single particle model with a Woods-Saxon potential. We give criteria, how these parameters should be chosen in order that the shell correction energies become fairly model-independent. The different models yield now a value of about ?20 MeV for²⁰⁸Pb, substantially larger than in previous work. Its relation to the remainder of the mass formula fit is discussed. We find that shell energies have an extremum. The minimum occurs close to the conventional parameter values (except the potential diffuseness of the protons) and close to the minimum of the total binding energy. The minimum in shell energy corresponds to a maximum bunching of single particle states. The gross properties of these extremal shells agree considerably better with the experimental spectra (for both the neutrons and the protons) than those of conventional model parameters.     

Analysis of fission excitation functions and the determination of shell effects at the saddle point

A method is proposed to deduce the shell correction energy corresponding to the fission transition state shape of nuclei in the mass region around 200, from an analysis of the first chance fission values of the ratio of fission to neutron widths, (Γ _f /Γ _n )₁. The method is applied to the typical case of the fissioning nucleus²¹²Po, formed by alpha bombardment of²⁰⁸Pb. For the calculation of the neutron width, the level densities of the daughter nucleus after neutron emission were obtained from a numerical calculation starting from shell model single particle energy level scheme. It is shown that with the use of standard Fermi gas expression for the level densities of the fission transition state nucleus in the calculation of the fission width, an apparent energy dependence of the fission barrier height is required to fit the experimental data. This energy dependence, which arises from the excitation energy dependence of shell effects on level densities, can be used to deduce the shell correction energy at the fission transition state point. It is found that in the case of²¹²Po, the energy of the actual transition state point is higher than the energy of the liquid drop model (LDM) saddle point by (3 ± 1) MeV, implying significant positive shell correction energy at the fission transition state. Further, the liquid drop model value of level density parametera is found to be a few per cent smaller for the saddle point shape as compared to its spherical shape.     

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.