Calculation of multidimensional potential energy surfaces for even-even transuranium nuclei: systematic investigation of the triaxiality effect on the fission barrier

Static fission barriers for 95 even-even transuranium nuclei with charge number Z = 94-118 have been systematically investigated by means of pairing self-consistent Woods-Saxon-Strutinsky calculations using the potential energy surface approach in multidimensional(β_2, γ, β_4) deformation space. Taking the heavier (252)~Cf nucleus(with the available fission barrier from experiment) as an example, the formation of the fission barrier and the influence of macroscopic, shell and pairing correction energies on it are analyzed. The results of the present calculated β_2 values and barrier heights are compared with previous calculations and available experiments. The role of triaxiality in the region of the first saddle is discussed. It is found that the second fission barrier is also considerably affected by the triaxial deformation degree of freedom in some nuclei(e.g., the Z =112-118 isotopes). Based on the potential energy curves, general trends of the evolution of the fission barrier heights and widths as a function of the nucleon numbers are investigated. In addition, the effects of Woods-Saxon potential parameter modifications(e.g.,the strength of the spin-orbit coupling and the nuclear surface diffuseness) on the fission barrier are briefly discussed.     

可能的原子核形状及硬度演化性质:基于能量面计算的系统分析(英文)

基于（β₂,γ,β₄）形变空间下对-形变自洽的原子核能量面计算方法,系统研究分析了50 < Z < 82区偶偶核的形状及硬度演化特征。计算的平衡形变与其它理论预言及存在的实验值进行了对比。从相应的形变势能曲线提取了与β₂及γ相关的硬度参数C_β,C_γ,这与实验观测到的低位β及γ振动带信息相符。还简要讨论了转动情况下的硬度演化,例如基于蜈蚣型E-GOS曲线,表明存在不可忽略的振动效应。Nuclear shape and stiffness evolutions in even-even nuclei with 50 < Z < 82 are systematically analyzed in terms of the pairing-deformation self-consistent nuclear-energy-surface calculation in (β₂,γ,β₄) deformation space. Calculated equilibrium deformations are presented and compared with other theoretical predictions and available experimental data. The stiffness parameters C_β and C_γ respectively related to quadrupole deformations β₂ and γ are determined from the deformation energy curves, which are consistent with the observed low-lying β and/or γ bands. The stiffness evolution under rotation along the yrast line is briefly discussed, e.g., on the basis of the centipidelike E-GOS curves, showing an unnegligible vibration effect.     

红色长余辉材料Zn3(PO4)2：Mn2+,Ga3+的合成及光谱性质

采用高温固相法合成α、β和γ-Zn₃(PO₃)₂:Mn²⁺,Ga³⁺(ZPMG),XRD分析表明,高温合成过程中淬火条件有利于β相的形成,退火条件有利于γ相的形成。三种磷光粉的激发光谱分别位于246nm(α)、234nm(β和γ)的宽带谱。α相的发射光谱为位于508nm的锐线谱,β和γ相的发射光谱均存在两个谱带,分别位于508nm的绿色光谱区和616nm的红色光谱区。两种发射均归属为Mn²⁺的⁴T₁(⁴G)→⁶A_1g(⁶S)跃迁,但是由于Mn²⁺在Zn₃(PO₃)₂结构中的配位数不同,故发光颜色及强度均不同。对于余辉发射,只能观察到红色余辉光谱。     

Total Routhian Surface Calculations on Hf Isotopes

The two-dimensional total routhian surface calculations have been carried out to study the triaxial superdeformed structure of a neutron-rich nucleus ¹⁷³Hf firstly. In particular the effects of the rotational frequency ω and pairing-energy gap parameter Δ are discussed in detail in the course of shaping its triaxial superdeformation; additionally the neutron-shell correction energy is analyzed with emphasis in the confirmed triaxial superdeformed nucleus ¹⁷³Hf. Finally, more systematical results have been investigated for some confirmed superdeformed nuclei experimentally and a few predicted triaxial superdeformed nuclei theoretically with quadropole deformation ε₂≈0.4 and triaxial deformation γ≈20^º or 30^º in the Z=72 region.     

锕系原子核自发裂变性质的理论研究

运用推广的液滴模型（GLDM）来确定锕系原子核的自发裂变势垒, 采用量子力学中的WKB近似方法对相应自发裂变的半衰期进行了研究。 在GLDM中, 首次考虑了微观Strutinsky壳修正对裂变势垒的影响。 理论计算的锕系区重核自发裂变半衰期与实验值符合得很好, 表明包括微观壳修正的GLDM可以成功研究重核的自发裂变性质。 The spontaneous fission half lives of the actinides are calculated by the WKB approximation and the potential barriers are constructed by a General Liquid Drop Model (GLDM) including the proximity energy, the mass and charge asymmetry, and an accurate nucleus radius. The microscopic shell correction which plays a key role for the spontaneous fission barrier is considered for the first time. The two parameter quasi molecular shape and the proximity are described in details within the GLDM. The effects of the microscopic shell correction and proximity energy for fission barrier are discussed separately. The calcula ted spontaneous fission half lives for the actinides reasonably accord with the experimental data, implying the present GLDM combined with the microscopic shell correction can be used to study the spontaneous fission properties of heavy nuclei successfully.     

γ-Fe_2O_3/NiO核-壳纳米花的合成、微结构与磁性

利用溶剂热/热分解的方法合成出微结构可控的γ-Fe_2O_3/NiO核-壳结构纳米花.分析表明NiO壳层是由单晶结构的纳米片构成,这些纳米片不规则地镶嵌在γ-Fe_2O_3核心的表面.Fe3O4/Ni(OH)_2前驱体的煅烧时间对γ-Fe_2O_3/NiO核-壳体系的晶粒生长、NiO相含量和壳层致密度均有很大的影响.振动样品磁强计和超导量子干涉仪的测试分析表明,尺寸效应、NiO相含量和铁磁-反铁磁界面耦合效应是决定γ-Fe_2O_3/NiO核-壳纳米花磁性能的重要因素.随着NiO相含量的增加,磁化强度减小,矫顽力增大.在5 K下,γ-Fe_2O_3/NiO核-壳纳米花表现出一定的交换偏置效应(H_E=46 Oe),这来自于(亚)铁磁性γ-Fe_2O_3和反铁磁性NiO之间的耦合相互作用.与此同时,这种交换耦合效应也进一步提高了样品的矫顽力(H_C=288 Oe).     

Oblate Superdeformed High-K States in Superheavy Nuclei

Configuration-constrained calculations of potential-energy surfaces for ²⁹²122 show the occurrence of multi-quasiparticle high-K isomeric state at oblate superdeformation. Such state could play a unique role in superheavy nuclei, with possible long life time from enhanced difficulty in fission due to additional barrier at oblate deformation, retardation in α decay due to unpaired nucleons, and hindrance in γ-ray transition due to K forbiddenness.     

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.     

Macroscopic-microscopic calculations of fission potential surface of uranium isotopes in the three quadratic surfaces parametrization

Five-dimensional (5D) fission potential energy surfaces (PES) for uranium nuclei are investigated based on the macroscopic-microscopic Lublin-Strasbourg drop model in the three-quadratic-surface parametrization, and the heights of static fission barriers are obtained. Asymmetric and symmetric fission paths are presented on the 5D PES of ²³⁶U for different nuclear shapes. The calculated barrier heights, E_A and E_B, are quite consistent with the experimental data for all even-even nuclei of uranium isotopes, from ²³⁰U to ²⁴⁴U.     

一个新的自由能函数对介电高弹薄膜的多组等双轴预拉伸下力电耦合实验的预测

当介电高弹聚合物薄膜被施以面内等双轴预拉伸后, 受到厚度方向的电压作用时, 薄膜在力场和电场共同作用下产生大变形. 电场采用Maxwell应力分析, 力场采用橡胶弹性模型分析. 拟合这类变形的常用橡胶弹性模型主要有Neo-Hookean, Arruda-Boyce, Gent等模型. 这些模型对实验数据的定量拟合存在不同程度的偏差. 通过对实验数据的分析, 结合数学方法, 提出了一个新的自由能函数模型. 通过该模型对VHB4905介电高弹聚合物薄膜的多组等双轴预拉伸电力耦合实验进行拟合, 并以Neo-Hookean, Gent模型作为对照, 结果与实验数据拟合很好, 比对照模型的偏差明显缩小.     

Regional Systematics for Even-Even Medium-Heavy Nuclei

The fluctuation of the δV_np, and δV_NN is taken into account to evaluate the np interaction and pairing strength of nuclei more precisely than the simple N_πN_v[or N_nN_p/(N_n+N_p)]parametrization. Regionally elegant systematics are noticed for the excited energy of the ground β and γ bands. The systematics of the β and γ bands are presented in detail for the first time. Correlation phenomenon of the general behavior of different bands in the same region is pointed out.     

A statistical approach to describe highly excited heavy and superheavy nuclei

A statistical approach based on the Weisskopf evaporation theory has been developed to describe the deexcitation process of highly excited heavy and superheavy nuclei, in particular for the proton-rich nuclei. The excited nucleus is cooled by evaporating γ-rays, light particles(neutrons, protons, α etc) in competition with binary fission,in which the structure effects(shell correction, fission barrier, particle separation energy) contribute to the processes.The formation of residual nuclei is evaluated via sequential emission of possible particles above the separation energies.The available data of fusion-evaporation excitation functions in the ~(28)Si+~(198)Pt reaction can be reproduced nicely within the approach.     

中重核中单粒子与集体运动的竞争效应(英文)

从原子核的电四极跃迁强度B（E2）中可以提取出原子核集体性和单粒子性质竞争的重要信息,其中一个重要的观测量是B（E2;4₁+ →2₁+）/B（E2;2₁+ →g.s.）的比值（B_4/2）。B_4/2一般要大于1,而且对于原子核转动和振动,我们应有B_4/2=1.4和2.0,但球形半满壳核一般会有不一样的性质。这些核的性质主要受对关联效应影响。介绍了几种超出我们一般认识的奇特衰变性质。Te同位素的基态带有鲜明的振动特性,但114Te的E2跃迁性质却更符合转动性。这些性质可以通过大规模壳模型计算来描述。对于填充j=9/2轨道的半满壳核,它们的4+和6+显示出很强的辛若数部分守恒性质。这种奇特的部分守恒可以被解析证明。而且我们的计算表明辛若数部分守恒对相关的E2跃迁影响很大。对于N=90附近具有量子相变行为的核素,其B_4/2也会也表现出相似的奇异特性。The E2 transition strength, B(E2), gives particularly precise information on the competition between the collective and single-particle degree of freedom. An important observable to study the development of collectivity is the B(E2; 4₁+ →2₁+)/B(E2; 2₁+ →g.s.) (B_4/2). The B_4/2 ratio is usually greater than unity. These values are 1.4 and 2.0 for an ideal rotor and a vibrator, respectively. Whereas the seniority scheme usually leads to different behaviours. In this contribution I will show examples that contrast with our standard understanding. The yrast spectra of Te isotopes show a vibrational-like equally-spaced pattern but the few known E2 transitions show anomalous rotational-like behaviour, which cannot be reproduced by collective models. Large-scale shell model calculations reproduce well the equally-spaced spectra of those isotopes as well as the constant behaviour of the B(E2) values in 114Te. For nuclei involving protons or neutrons in j=9/2 orbitals, the partial conservation of seniority can lead to dramatic changes to the E2 decay pattern that have never been seen before. The B_4/2 ratios in quantum phase transitional nuclei around N=90 also show a similar exotic feature.     

Microscopical Studies of the Energy Staggering in γ-Soft Nuclei

The energy staggering in γ-or quasi γ-band of γ-soft even-even nuclei is studied with the approximate angular moment um projection of the deformed Hartree-Fock (DHF) states. In the calculations of DHF states the modified surface &interaction matrix elements are used. It is found that in the K = 2 band produced by the angular momentum projection of DHF state the energy staggering appears only in certain conditions. Some points concerning with the angular momentum projection of K = 2 DHF states are discussed. The energy spectra of nuclei ⁷⁴Se and ⁷⁶Kr are calculated and compared with the experimental data, which show the staggering pattern of γ-soft rotor, the coincidence between them are fairly good.     

Tricritical and Critical Exponents in Microcanonical Ensemble of Systems with Long-Range Interactions

We explore the tricritical points and the critical lines of both Blume-Emery-Griffiths and Ising model within long-range interactions in the microcanonical ensemble. For K=K_MTP, the tricritical exponents take the values β=1/4, 1=γ^-≠γ⁺=1/2 and 0=α^-≠α⁺=-1/2, which disagree with classical (mean field) values. When K>K_MTP, the phase transition becomes second order and the critical exponents have classical values except close to the canonical tricritical parameters (K_CTP), where the values of the critical expoents become β=1/2, 1=γ^-≠γ⁺=2 and 0=α⁺≠α⁺=1.     

相对论平均场理论对Pt同位素形状演化的研究

利用形变约束的相对论平均场理论研究了Pt同位素偶-偶核的形状演化,比较了基态结合能和四极形变的理论计算值和实验值, 分析了这些核的位能曲线、单粒子能级及其随四极形变β₂ 的变化规律,发现从N=88到N=126, Pt同位素的基态变形从球形对称核经X(5)对称性核、演化为具有稳定形变的核,再演化为球形核的变化过程.其中, ^166-172Pt是近球形核, ¹⁷⁴Pt和^192-196Pt位于球形和稳定形变之间,可能具有X(5)对称性, ^176-190Pt具有稳定的变形, ^198-202Pt是近球形核, ²⁰⁴Pt是球形核,这些结果与实验一致.     

The Optical Properties of (C59N)2

Using the extended Hubbard model and sum-over-state method, we have calculated the linear polarizability α and the third-order nonlinear polarizability γ for (C₅₉N)₂. We find that (C₅₉N)₂ has very big γ value (around esu), and its α and γ values are bigger than those of C₅₉N. In particular, when 1.2 eV≤3ω, (C₅₉N)₂ as much larger γ values than C₅₉N.     

Fission Barrier for ^240Pu in the Quadrupole Constrained Relativistic Mean Field Approach

The fission barrier for ^240pu is investigated beyond the second saddle point in the potentiM energy surface by the constrained relativistic mean field method with the newly proposed parameter set PK1. The microscopic correction for the centre-of-mass motion is essentiM to provide the correct potential energy surface. The shell effects that stabilize the nuclei against the fission is also investigated by the Strutinsky method. The shapes for the ground state, fission isomer and saddle-points, etc, are studied in detail.     

过冷水溶液中的空间光孤子

建立了在过冷水溶液中传播的光束的非局域非线性模型.过冷水的热致折射率扰动在温度扰动较小的情况下随温度增大,但在温度扰动达到一定程度后随温度减小.在求出该模型的数值孤子解后,对孤子的性态进行了研究.研究表明,在光功率较小时,过冷水表现出自聚焦的特性,而在光功率较大时,在孤子的中心区域的过冷水表现出自散焦的特性,而在孤子的外围仍表现为自聚焦.在总功率较大的情况下,孤子间的相互作用也表现出这种部分自散焦,部分自聚焦的现象.     

Unified Treatment of Systematics for Even-Even Nuclei with A≥70

By the concept of effective boson numbers, systematics of E₂₁+E₄₁+E₆₁+, R=E₂₁+/E₄₁, B(E2, 0₁⁺→2₁⁺) and Q₀ for even-even nuclei with A≥70 are presented. New features of energy spectra are noticed and an intuitive understanding is given.