Nilsson mean-field plus the extended pairing model description of rare earth nuclei

The Nilsson mean-field plus the extended pairing model for well-deformed nuclei is applied to some representative rare earth examples. The binding energies, some low-lying pair-excited states and even-odd mass differences of Er, Yb and Hf isotopes are calculated systematically within the proton frozen-pair excitation limit. A comparison with experimental data for these nuclei shows that the results of the extended pairing model are better than those for the standard pairing model with the BCS approximation and the nearest-orbit pairing model.     

球形平均场加四极-四极和对力模型在单j壳内的量子相交叉行为(英文)

介绍了单j壳的球形平均场加几何四极-四极和标准对力模型的量子相交叉行为。在单j=15/2的壳内,计算了随模型控制参数变化的多个物理量如低激发能级、激发态间重叠积分、低激发态间的B（E2）比值和电四极矩比值。结果显示,在类转动到对激发相的演化中,多个物理量在交叉区存在非常明显的变化,如B（E2;4₁ → 2₁）/B（E2;2₁ → 0_g）,B（E2;4₂ → 2₁）/B（E2;2₁ → 0_g）等,并且这些变化在核子数达到半满壳时尤为显著。此外,尽管当j较小时,由几何四极-四极相互作用得到的低激发能级不满足转动谱规律,但当j值足够大时,这些低激发能级满足转动谱规律。The analysis of the quantum phase crossover behavior in the spherical shell model mean-field plus the geometric quadrupole-quadrupole (Q·Q) and standard pairing model within a single-j shell is reported. Several quantities, such as low-lying excitation energies, the overlaps of excited states, ratios of some B(E2) and electric quadrupole moments of some low-lying states as functions of the control parameter of the model in a j=15/2 shell are calculated. The results show that there are noticeable changes in the crossover region of the rotational-like to the pair-excitation phase transition, such as B(E2;4₁ → 2₁)/B(E2;2₁ → 0_g) and B(E2;4₂ → 2₁)/B(E2;2₁ → 0_g), especially in the half-filling case. Though the low-lying excitation energies generated from the geometric quadrupole-quadrupole interaction not satisfy the pattern of a rotational spectrum when j is small, these energies follow the pattern of a rotational spectrum when j is sufficiently large.     

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.     

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.     

关于93Mo中21/2+晕阱的来源(英文)

本研究通过壳模型计算研究了N=51的同中子素91Zr、93Mo和95Ru中高自旋晕态21/2+的同核异能态现象。计算发现,低角动量的p_1/2轨道上的质子是仅在93Mo中存在21/2+晕阱的主要原因。同时,本工作还研究了N=52的同中子素92Zr、94Mo和96Ru中10₁+-12₁+能级结构的系统性,发现94Mo中的10₁+-12₁+能级间隙相对最小,考虑到与93Mo的17/2₁+-21/2₁+能级相似的组态,这一结果为93Mo中出现21/2+晕阱提供了补充性的论证。Isomerism of the high-spin yrast 21/2+ states of the N=51 isotones 91Zr, 93Mo and 95Ru has been investigated using the shell model calculations. It is found that the low-j πp_1/2 is responsible for the only yrast trap in 93Mo. In addition, the relatively smaller 10₁+-12₁+ level spacing in 94Mo has been found by investigating the systematics of the 10₁+-12₁+ level structures in the N=52 isotones 92Zr, 94Mo and 96Ru. This result provides a supplementary argument to the origin of the 21/2+ yrast trap in 93Mo from the viewpoint of the similarity between the configurations of 10₁+-12₁+ states in 94Mo and those of 17/2₁+-21/2₁+ states in 93Mo.     

Three-dimensional potential energy surface for fission of 236U within covariant density functional theory

We calculate the three-dimensional potential energy surface(PES) for the fission of the compound nucleus ²³⁶U using covariant density functional theory with constraints on the axial quadrupole and octupole deformations(β₂, β₃)coexistence of the elongated and compact fission modes is predicted for comes shallow across a large range of quadrupole and octupole deformations for small scission line in the(β₂, β₃)plane extends to a shallow band, l...     

Multiscalar B-L extension based on S4flavor symmetry for neutrino masses and mixing

A multiscalar and nonrenormalizable B-L extension of the standard model(SM)with S₄symmetry which successfully explains the recently observed neutrino oscillation data is proposed.The tiny neutrino masses and their hierarchies are generated via the type-I seesaw mechanism.The model reproduces the recent experiments of neutrino mixing angles and Dirac CP violating phase in which the atmospheric angle(θ₂₃)and the reactor angle(θ₁₃)get the best-fit values while the solar angle(θ₁₂)and Dirac CP violating phase(δ)are in 3σrange of the best-fit value for the normal hierarchy(NH).For the inverted hierarchy(IH),θ13 gets the best-ft value andθ₂₃together withδare in the lσrange,whileθ12 is in 3δrange of the best-fit value.The effective neutrino masses are pre-dicted to be(m_ee)=6.81 meV for the NH and(m_ee)=48.48 meV for the IH,in good agreement with the most re-cent experimental data.     

Triaxiality and shape coexistence in the A ～ 30 “island of inversion”nuclei

Understanding the properties of nuclei inside "island of inversion" is still an interesting issue. Based on a simple Nilsson model with a new set of isospin-dependent parameters, and with non-axial deformations considered, we have performed three-dimensional potential-energy-surface calculations for Ne, Na, Mg and Al isotopes that are claimed to be in or nearby the A～30 island of inversion". It is found that shape coexistence and triaxial deformation(or softness) exist in these nuclei. Large deformations are obtained by the improved Nilsson parameters, which explains the observed large electric quadrupole transition probabilities. The large deformations happening in30 Ne,31Na,32 Mg and33Al indicate the quenching of the spherical N = 20 neutron shell gap. The calculations of nuclear binding and two-neutron separation energies have been also improved with the isospin-dependent parameters and the inclusion of the non-axial deformation degree of freedom.     

稀土区奇A核晕带存在从转动到振动形状演化的直接证据(英文)

原子核的形状演化效应是核结构研究的重要基础问题之一。通常认为,A=160质量区的奇A核位于大形变核区域,它们的激发态能谱将呈现出典型的转动激发特征。然而,基于E-GOS曲线方法,发现随着角动量的增加,该质量区奇A核的晕带具有显著地从转动激发演化成为振动激发的形状演化现象。此外,为深入理解原子核形状演化的微观机制,采用Total-Routhian-Surface（TRS）方法针对稀土区的奇A核进行了理论计算,结果表明,165Yb和157Dy同位素在低激发态时具有稳定的长椭形变,当角动量大于0.50 MeV后,核芯的四极形变显著减小并开始产生三轴形变。The phase transition of nuclei with increasing angular momentum (or spin) and excitation energy is one of the most fundamental topics of nuclear structure research. The odd-N nuclei with A ≈160 are widely considered belonging to the well-deformed region, and their excitation spectra are energetically favored to exhibit the rotational characteristics. In this work, however, the evidence suggesting that the nuclei changes from rotation to vibration along the yrast lines as a function of spin was found. The simple method, named as E-Gamma Over Spin (E-GOS) curves, would be used to discern the evolution from rotational to vibrational structure in nuclei for various spin ranges. Meanwhile, in order to understand the band structure properties of nuclei, theoretical calculations have been performed for the yrast bands of the odd-A rare-earth nuclei within the framework of the total routhian surface (TRS) model. The TRS plots predict that the 165Yb and 157Dy isotopes have large quadrupole shapes at low spin states. At higher rotational frequency (hω~ >0.50 MeV), a clear reduction of the quadrupole deformation is indicated by the present results, and the isotopes become rigid in the γ deformation.     

SD配对壳模型对质量数A~130区原子核的形状渡越研究(英文)

利用SD配对壳模型研究了质量数A~130区原子核的低激发态性质。为了减少参数,模型采用了等强度对力,取质子和中子对力强度等同近似,而非同类核子间的四极-四极相互作用强度取为同类核子间四极-四极相互作用强度的两倍。计算结果显示,模型的振动-转动和振动-γ不稳定运动的形状渡越特征与相互作用玻色子模型对应的形状相变特征基本吻合,从而说明SD配对壳模型是壳模型的一种合理近似。The SD-pair shell model is applied to analyze the evolution of low-lying states of even-even nuclei in A~130 mass region. In the model, the pairing and the quadrupole-quadrupole interactions are taken into account. The results show that there are clear signatures of the crossover from vibrational to rotational or from vibrational to the γ-soft shape phase.     

超越平均场模型对Ba同位素链八极形状演化研究

本文采用超越平均场模型研究了缺中子Ba同位素链114-124Ba的八极形变及其演化规律。计算了Ba链的位能曲面、低能激发谱、电四极跃迁几率、电八极跃迁几率及集体波函数的几率密度分布,并与实验相比较。理论计算较好地再现了Ba核的低能激发结构。位能曲面、低能的负宇称带、较大的B（E3;3₁- → 0₁+）和展宽的几率密度分布表明,114Ba中存在较强的八极关联。116,118Ba具有过渡核特征,而120-124Ba则为典型的四极形变原子核。     

ScF3，NaScF4，(NH4)2NaScF6的可控合成与上转换发光性能的研究

钪基氟化物化学性质稳定、声子能量低、无辐射弛豫概率较低,是一种新型高效的基质材料,并且Sc3+半径较小,能与多种氨羧络合剂形成稳定的螯合物,因而具有更加奇特的物理和化学性质,近年来,成为许多科学家研究的热点。以聚乙烯二胺(PEI)作为表面活性剂,采用水热法在反应温度为200 ℃时成功制备了ScF₃∶Yb3+/Er3+,NaScF₄∶Yb3+/Er3+,(NH₄)₂NaScF₆∶Yb3+/Er3+纳米上转换发光材料。通过X射线衍射仪(XRD)、透射电镜(TEM)、扫描电镜(SEM)和荧光光谱仪对所制备样品的晶相、形貌和发光特性进行了研究,结果显示：通过改变反应物NH₄F和Ln3+的比例(NH₄F/Ln3+=1∶1,2∶1,2.5∶1,3∶1,4∶1,6∶1,10∶1,20∶1,30∶1,40∶1,50∶1)实现了对样品产物、晶相、形貌的控制。当NH₄F/Ln3+为2.5∶1时,生成了纯立方相的ScF₃;在NH₄F/Ln3+为4∶1时,生成了六角相的NaScF₄;在NH₄F/Ln3+为40∶1时,生成了一种纯立方相的新型基质材料(NH₄)₂NaScF₆,样品结晶度高,形貌均一,有正方形片状和足球状多面体;在980 nm红外激光的激发下,不同NH₄F/Ln3+比例生成的样品发光呈现桔黄→桔红→绿→黄绿等多种颜色的变化。实验表明仅改变NH₄F一种原料的用量,就可以生成ScF₃∶Yb3+/Er3+,NaScF₄∶Yb3+/Er3+和(NH₄)₂NaScF₆∶Yb3+/Er3+ 三种不同的产物,说明NH₄F的用量对产物的生成有决定性的作用,对晶相的转换、颜色的调控亦有重要影响。     

Er,Yb：(LaLu)2O3透明陶瓷制备及上转换发光性能

采用柠檬酸燃烧法制备Er,Yb：（LaLu）₂O₃陶瓷粉体,用X射线衍射对其进行了物相鉴定,研究表明1 000℃时已经得到纯相的（LaLu）₂O₃。采用冷等静压-真空烧结法制备了Er,Yb：（LaLu）₂O₃和Er：（LaLu）₂O₃陶瓷,对陶瓷的结构和光谱性能进行了详细的研究,研究发现掺杂5% Yb³⁺和10% La³⁺样品的上转换发光强度与未掺Yb³⁺、La³⁺样品相比明显增大,根据上转换光谱显示较强发射峰位于564 nm和661 nm处,对应Er³⁺的⁴S_3/2（²H_11/2）→⁴I_15/2能级跃迁和⁴F_9/2→⁴I_15/2能级跃迁,并讨论了Er³⁺-Yb³⁺的能量传递过程及其上转换发光机制。     

Yb3+/Er3+共掺(MLaFn)x(M=0,K;n=3,4;x=1,1.5)纳米材料的控制合成及其上转换发光性质

采用水热与溶剂热结合的方法,在乙二醇-正己醇体系中,通过调节KF与RE(RE=La,Yb,Er)的量比、反应温度和反应时间实现了由LaF_3(六角相)到KLaF_4(立方相、六角相)晶型的控制合成。借助透射电子显微镜(TEM)和X射线粉末衍射(XRD)对样品的结构和微观形貌进行表征。结果表明,当KF/RE比例为2. 25时,制备的样品为片状的六角相LaF_3纳米颗粒;当KF/RE比例为3. 00时,得到具有近似球形的立方相KLaF_4纳米颗粒;当KF/RE比例为4. 25时,得到了六角相(KLaF_4)_(1. 5)纳米颗粒。上转换发射光谱显示:所有的样品在近红外光(980 nm)激发下,均有3个明显的发射峰,在522 nm、544 nm处分别对应于Er~(3+)的~4S_(3/2),~2H_(11/2)→~4I_(15/2)能级跃迁,655 nm处属于Er~(3+)的~4F_(9/2)→~4I_(15/2)能级跃迁。     

Structure Evolution in the Even-Even 124-134Xe with IBM2

We have investigated the structure evolution of the ^124-134Xe isotopic chain in the framework of the proton-neutron interacting model IBM2. The positive parity spectra of the ground state, quasi-β and quasi-γ bands are reproduced well. The staggering in ^124-130Xe are almost completely removed and the γ band agree well with the experiment data, even for the high-spin quasi-γ states. The key quantities of the collective structure evolution, including level energies, the B(E2) transition branching ratios, and the M1 excitations to 1₁⁺ mixer-symmetry states are analyzed by comparing with the experimental data. The parameters for representation of the O_πν(6) and SU_πν^*(3) features in isotopes are examined. Both experimental data and theoretical results show that the shape phase transition of ^124-134Xe isotopic chain is from the SU_πν^*(3) (triaxial rotation) to the U_πν(5) (vibration motion) with a considerable constituent of the O_πν(6) symmetry (γ-unstable rotation), where the shape phase transition rapidly takes place between the neutron number N = 76 and N = 78.     

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.     

Quadrupole interactions in pionic and muonic tantalum and rhenium

The hyperfine splitting of pionic and muonic X-rays in natural Re has been studied using the known ratio (accurate to 1.6 parts in 10⁵) of the quadrupole moments of the two naturally occurring ¹⁸⁵Re and ¹⁸⁷Re isotopes. From the hyperfine splitting of the ⁵g → 4f and 4f → 3d pionic X-rays the effective quadrupole hyperfine constants were determined to be ¹⁸⁷A₂^eff(4f) = 1.163 ± 0.010 keV and ¹⁸⁷A₂^eff(3d) = 5.39 ± 0.63 keV, giving strong interaction quadrupole shifts ₂(4f) = 46 ± 10 eV and ₂(3d) = 1.3 ± 0.6 keV. The strong interaction monopole shifts ₀ and widths Γ₀ of the 5g, 4f and 3d levels have also been measured. For the two higher orbits, standard optical-potential calculations fit the measured shifts and widths quite well. The observed deeper-lying 3d state, however, has shifts and widths that differ by a factor of 2 or more from the predictions. From the measured quadrupole hyperfine constants of the 4f level we calculate the spectroscopic quadrupole moments to be ¹⁸⁷Q^μ(gm) = 2.09 ± 0.04 b, ¹⁸⁷Q^π = 2.07 ± 0.02 b, ¹⁸⁵Q^μ = 2.21 ± 0.04 b, and ¹⁸⁵Q^π = 2.1 addition, muonic X-rays from ¹⁸¹Ta were observed; using the same methods for determining the quadrupole moment as above, a value of ¹⁸¹Q^μ = 3.28 ± 0.06 b was obtained, in good agreement with earlier published data.     

Octupole Deformations of Even-Even Rn,Th, and U Nuclei in Relativistic Mean Field Theory

The octupole deformations and other ground state properties of even-even Rn, Th and U isotopes are investigated systematically within the framework of the reflection asymmetric relativistic mean field （RAS-RMF） model. The calculation results reproduce the binding energies and the quadrupole deformations well. The calculation results indicate these nuclei at ground states evolve from neaxly-spherical （N = 130） shape to quadrupole deformation shape with the increase of the neutron number. It is also found that among the Rn isotopes, only^222,224 Rn axe oetupole deformed and the octupole deformations for them are small. However, more nuclei （N ≌ 134 148） in Th and U isotopes are octupole deformed and the octupole deformations for some of them are significant （｜β3｜- 0.1 or even larger）.