2018年 第35卷 第4期
在2010年，中国科学院近代物理研究所向国家发展和改革委员会建议了重大科技基础设施——强流重离子加速器装置（High Intensity Heavy-ion Accelerator Facility，简称HIAF）。经过一系列评估和论证，HIAF于2015年12月被国家发展改革委立项。HIAF建设地址位于广东省惠州市，计划于2018年年底正式开工建造。HIAF由超导直线加速器、同步增强器、高能放射性束流线、储存环谱仪以及若干实验测量装置构成，总投资约为25亿人民币。依托HIAF，我们将拓展核素存在版图，研发先进实验技术和方法，开展前沿物理研究；同时，开展重离子束应用研究，服务国家经济社会发展。简要介绍拟建的加速器系统、实验测量装置以及相关的物理研究计划。
The Institute of Modern Physics, Chinese Academy of Sciences, proposed the Major National Science and Technology Infrastructure Facility named as High Intensity Heavy-ion Accelerator Facility (HIAF) in 2010. After a series of assessments charged by the National Development and Reform Commission of China, HIAF was officially approved by China government in December, 2015. HIAF will be constructed in Huizhou, Guangdong Province, and the groundbreaking ceremony of construction is scheduled around the end in the year of 2018. HIAF is composed of a superconducting Linac, a booster ring, a high-energy radioactive beam line, a storage ring, and a number of experiment setups. The total investment of HIAF is about 2.5 billion Chinese Yuan. The major goals for HIAF are to explore the hitherto unknown territories in nuclear chart, to approach the experimental limits, to open new domains of physics researches in experiments, and to develop new ideas and heavy-ion applications beneficial to the societies. In this paper, the accelerator complex of HIAF is briefly introduced, and the experimental setups and associated physics research program are presented.
Exploiting special symmetries to unmask simplicity within complexity that remains the "holy grail" of nuclear theory is re-examined within the framework of its historical context and current ab initio nocore shell-model approaches that exploit high-performance computing resources and applied math methodologies. Examples using the symmetry-adapted no-core shell model (SA-NCSM) that clearly demonstrate the important role group theory plays in this evolving story will serve to elucidate current state-of-the-art developments in this arena, including comparisons of excitation spectra and transition rates with experimental results for light and medium-mass nuclei. An interesting extension of the SA-NCSM, an advanced method with a novel twist that enables one to incorporate deformation from the onset, will be proffered as a further way to manage the combinatorial growth of model-space dimensionalities that remains the nemesis of all theories that seek an ab initio understanding of nuclear collectivity, and in so doing extends applicability of the theory to heavier and more exotic nuclear species.
We discuss the quantum self-organization introduced recently as one of the major underlying mechanisms of the quantum many-body systems. Atomic nuclei are actually a good example, because two types of the motion of nucleons, single-particle states and collective modes, interplay in determining their structure. The collective mode appears as a consequence of the balance between the effect of the mode-driving force (e.g., quadrupole force for the ellipsoidal deformation) and the resistance power against it. The single-particle energies are one of the sources to bring about such resistance power:a coherent collective motion is more hindered by larger spacings between relevant single particle states. Thus, the single-particle state and the collective mode are "enemies" against each other in the usual understanding. However, the nuclear forces are rich and complicated enough so as to enhance relevant collective mode by reducing the resistance power by changing single-particle energies for each eigenstate through monopole interactions. This will be demonstrated with the concrete example taken from Zr isotopes. In this way, the quantum self-organization occurs:single-particle energies can be self-organized by (i) two quantum liquids, e.g., protons and neutrons, (ii) monopole interaction (to control resistance). Thus, atomic nuclei are not necessarily like simple rigid vases containing almost free nucleons, in contrast to the naïve Fermi liquid picture a la Landau. Type Ⅱ shell evolution is considered to be a simple visible case involving excitations across a (sub)magic gap. The quantum self-organization becomes more important in heavier nuclei where the number of active orbits and the number of active nucleons are larger.
Charge radius is one of the most fundamental observables of atomic nuclei, reflecting the proton distributions in nuclei. Their precision measurements have severed as a key tool to study nuclear structure. Recently, a novel method to deduce charge radii has been developed via precise measurements of charge-changing cross sections(CCCS) of exotic nuclei at relativistic energies. This method is in particular suitable for investigation of exotic nuclei with low production yield. In 2013, we proposed to make such measurements for exotic nuclei lighter than oxygen based on the RIBLL2 beam line. Since then, the TOF-△E detector system for particleidentification(PID) and the CCCS platform have been constructed, continuously optimized and tested. So far CCCS measurements on a carbon target have been performed for more than 20 isotopes. In this contribution, we will introduce the progress of detector development, the progress in PID, and our experimental progress and plan.
Up to now, the N* production from e+e- annihilations has been studied only around charmonium region. Charmonium decays to N*s are analogous to (time-like) EM form factors in that the charm quark annihilation provides a nearly pointlike (ggg) current. Complementary to other sources, such as πN, eN and γN reactions, this new source for N* spectroscopy has a few advantages, such as an isospin filter and a low spin filter. The experimental results on N* from e+e- annihilations and their phenomenological implications are reviewed. Possible new sources on N* production from e+e- annihilations are discussed.
基于一个相对论的BUU方法，研究了△共振态的硬过程（NN → N△）及软过程（Nπ → △）产生截面及△的衰变宽度在同位旋不对称核体系下的介质修正（包括能量、密度、特别是同位旋依赖的）效应。发现类似于核子-核子弹性散射过程，△硬过程产生截面的密度修正及在同位旋不对称体系下的质量劈裂效应都比较强烈，而△的软过程产生截面及衰变宽度的密度依赖和质量劈裂效应都相对较弱。对硬过程，其截面最大的劈裂效应出现在△++和△-的产生道中，而对软过程，△++和△-的产生道中的劈裂效应则最小且与硬过程的相反。
Within the framework of the relativistic BUU approach, we investigate the effect of energy-, density-, and especially isospin-dependent medium modifications on △ production cross sections of both hard (NN → N△) and soft (Nπ → △) processes as well as its decay width. It is found that, similar to the nucleon-nucleon elastic scattering, the △ production cross section from the hard process is strongly dependent on both density and the mass splitting effect in the isospin asymmetric matter. While the dependence is relative weak from the soft one, and so is the △ decay width. Further, in the hard (soft) process, the splitting effect is largest (smallest) and of opposite sign for the △++ and △- states.
High-precision laser spectroscopy technique is used to determine the ground state properties of exotic nuclei by probing its electronic hyperfine structure and isotope shift. It provides a model-independent measurement of nuclear spin, magnetic moment, electric quadrupole moment and charge radii. These nuclear parameters can be used to investigate the nuclear structure evolution and the nuclear shapes. With the development of accelerators and isotope separators, exotic isotopes far from β stability became accessible experimentally, which enhanced the capability of the laser spectroscopy technique being applied in the field of nuclear physics. A brief introduction to experimental principle is given, followed by a review of several typical examples for the experimental investigations in the different regions of nuclear chart. This aims to demonstrate the contributions of ground state properties measurement by using laser spectroscopy technique to the nuclear structure study of exotic isotopes. This discussion involves several different nuclear theory models in order to interpret the exotic phenomena observed in the neutron-rich isotopes, such as halo structure, shell evolution, shape coexistence and so on.
Tensor force is one of the most important components of the nucleon-nucleon interaction. It plays a critical role in understanding the shell evolution in exotic nuclei. However, there are still several puzzles concerning the tensor force and its effects in the nuclear medium. In this paper, we mainly focus on the studies of tensor force in the effective interactions and its effects in finite nuclear systems within the scheme of nuclear density functional theory. In particular, we highlight the recent developments, including the quantitative analysis of tensor effects in the relativistic Hartree-Fock theory by taking the evolution of proton magic shells in the isotopic chains as an example, and the "meta-data" of tensor effects provided by the ab initio relativistic Brueckner-Hartree-Fock theory by taking the evolution of spin-orbit splitting in the single-particle spectra of neutron drops as an example. Perspectives are focused on the possible strategies for the future developments of nuclear density functional theory.
Resonance is an interesting phenomenon in nature. In nuclear physics, resonance plays an important role in the formation of many exotic phenomena. This paper introduces the recently developed RMF-CSM, RMFCGF, and RMF-CMR methods and their researches on nuclear single-particle resonances. The energies and widths of the single-particle resonant states in 120Sn and 31Ne and their evolution to mass number and deformation are given. In addition, the physical mechanism of the halo formation in 19C, 31Ne and 39Mg and the cause of energy level inversion near N=20 are analyzed. In particular, the newly developed RMF-CMR approach has been successful in describing stable and exotic nuclei and supports the prediction that Zr isotopes exist in a giant halo.
The beyond-mean-field Skyrme-Hartree-Fock approach is adopted to investigate the properties of ∧9Be, ∧∧10Be, ∧13C and ∧21Ne. The nucleon-nucleon (NN) interaction SLy4 and the nucleon-hyperon(N∧) interaction Skyrme-type SLL4 are used. The spin-orbit force of hyperon is included to show the spin-orbit splitting and non-crossing effect with BCS method to deal with pairing force. Energies of different configurations, such as 12C⊗∧1/2+, 12C⊗∧1/2-, 12C⊗∧3/2-, 12C⊗∧1/2-, 8Be⊗∧1/2+, 8Be⊗∧1/2-, 8 Be⊗∧3/2- and 8Be⊗∧1/2- are given and used to study the effects of ∧ occupying different orbitals. The calculated energy spectra, including both positive-and negative-parity levels, are given and compared to the experimental data. The observed positive-parity spin-doublet (3/2+,5/2+) are successfully reproduced, but the energy difference needs further investigation. The two well known band structures corresponding to the genuine hypernuclear states and the 9Be-analog states are also obtained and compared with the observed ones. The shrinkage effect of ∧ occupying ∧1/2+ is investigated through the density distributions of nuclear core. And finally the calculation results of ∧21Ne are given and compared with the results of RMF method, which are nearly the same but with differences in some details.
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（B4/2）。B4/2一般要大于1，而且对于原子核转动和振动，我们应有B4/2=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B4/2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.) (B4/2). The B4/2 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 B4/2 ratios in quantum phase transitional nuclei around N=90 also show a similar exotic feature.
We present a comprehensive introduction in our newly developed Variation After Projection (VAP) calculations for the low-lying nuclear states. First, we discussed the VAP calculation with a fully JTA-projected wavefunction for the ground state in even-even nucleus. This leads to the conclusion that the spin projection plays a key role in obtaining a good shell model approximation. With this conclusion, we simplified the VAP with a time-odd Hartree-Fock mean field, on which only spin projection is required. Due to the time reversal symmetry breaking, this VAP now can be applied to the yrast states in all kinds of nuclei. It turns out that our VAP yrast energies as well as the corresponding VAP wavefunctions are very close the exact ones from the full shell model calculations. Such good approximation encourages us to extend the VAP calculations further to the non-yrast nuclear states. For this purpose, we proposed a new algorithm in our VAP based on the Cauchy's interlacing theorem. This theorem ensures that the sum of the calculated lowest projected energies with the same quantum numbers can be safely minimized. After minimization, all the calculated states can be determined simultaneously. Again, all the calculated VAP energies are very close to the exact shell model results. Recently, we have added the parity projection into the VAP, and the yrast states with both parity in 12C have been calculated in the psd model space. This time, we still have good shell model approximation for both parity states. Finally, we should point out that the present algorithm should be applicable to the low-lying states in different quantum many-body systems.
在兰州重离子加速器冷却储存环（HIRFL-CSR）上，用初级束流112Sn35+轰击了靶厚约10 mm的Be靶，产生了101In的基态和低位同核异能态。这些实验产生的碎片每25 s经过放射性束流线RIBLL2的筛选后注入到实验环CSRe中，利用飞行时间探测器测量离子在CSRe中的回旋周期。在此次实验中，磁场晃动会导致离子在环内的循环周期发生改变，传统的离子鉴别方法难以完成大部分离子的鉴别。通过发展和运用单次注入离子鉴别这一新的离子鉴别方法，有效地消除了磁场晃动对于离子鉴别的影响，并清楚地将101In基态和低位同核异能态鉴别出来，从而首次在实验中观测到101In的低位同核异能态。实验得到的激发能与理论外推值在112 keV的误差范围内一致，其低位同核异能态的寿命大于200 μs。
Isochronous mass spectrometry has been applied to 112Sn projectile fragments at the HIRFL-CSR facility in Lanzhou. To produce short-lived nuclei of interest, we used projectile fragmentation of 112Sn35+ primary beams in a~10 mm thick 9Be production target. The fragments were selected and analyzed by RIBLL2 and injected into the experimental storage ring(CSRe) every 25 s. To measure revolution times of stored ions,we used a Time-Of-Flight detector installed in CSRe. A new particle identification method was developed to distinguish ions on the measured revolution time spectrum for each injection. Based on this method, the shifts of the revolution time due to instable dipole magnet fields can be corrected and the ground and isomeric states of 101In have been well-resolved. The measured excitation energy is consistent with the theoretical value in the error range of 112 keV. The lifetime of the isomeric states of 101In is more than 200 μs.
北京放射性离子束装置（Beijing Radioactive Ion-beam Facility，BRIF）是基于在线同位素分离器技术的国家大科学平台。在BRIF装置上利用100 MeV的质子束轰击较厚的反应靶产生放射性核素；反应产物经离子源电离和在线分离，在线同位素分离段可引出100~300 keV的放射性核束，质量分辨率达20 000。在基金委科学仪器基础研究专项的支持下，建成了多用途的衰变实验终端，包括束流传输管道、通用靶室、带电粒子和γ探测器、集成电子学和数据获取系统等。利用100 MeV的质子束轰击MgO厚靶产生了流强高达1×105 pps的20Na放射性核束。通过高效率地同时测量β，γ和α，第一次直接观测到20Na非常稀有的β-γ-α衰变模式。
Beijing Radioactive Ion-beam Facility(BRIF) has been commissioned as the national Radioactive Ion Beam(RIB) facility based on the Isotope Separator On Line(ISOL) technique since 2016. At BRIF, the radioactive nuclides are produced by the proton beam of 100 MeV bombarding a thick-target, the reaction products diffusing out of the target are ionized by an ion source and delivered to the online mass separator. In addition to the post-accelerated radioactive ion beams, BRIF can provide low-energy ISOL beams of 100 to 300 keV with a mass resolution of 20 000. A general-purpose decay station has been built including the ISOL beam transport line, a conventional reaction chamber, charge-particle and γ detectors with integrated electronics and data acquisition system. An intense 20Na ISOL beam up to 1×105 pps was produced by using the 100 MeV proton beam bombarding a MgO thick target. With high-efficiency measurements of β, γ and α simultaneously, very rare β-γ-α decay mode in 20Na has been directly observed for the first time in the present work.
慢速中子俘获过程（s过程）是合成比铁重元素的重要途径之一。22Ne（α，n）25Mg反应是大质量AGB星中s过程主要的中子源，其中的22Ne主要通过14N（α，γ）18F（β+）18O（α，γ）22Ne反应链合成。该反应链中关键反应18O（α，γ）22Ne在天体物理感兴趣能区的截面非常低，其天体反应率主要来自于22Ne α分离阈附近低能共振态的贡献，但目前相关能级的共振参数严重缺失。在HI-13串列加速器的Q3D磁谱仪上，通过测量18O（6Li，d）22Ne反应的角分布，利用DWBA分析确定了22Ne分离阈附近共振能级Eα=470 keV的自旋宇称为0+，为后续计算18O（α，γ）22Ne的天体反应率打下了基础。
About a half of the abundances of elements heavier than iron comes from the so-called slowneutron capture process (s-process) in Asymptotic Giant Branch (AGB) stars, with the 22Ne(α, n)25Mg reaction as one of the main neutron sources. In the beginning phase of AGB thermal pulse, 22Ne is produced by the 14N(α, γ)18F(β+)18O(α, γ)22Ne reaction sequence, in which the 18O(α, γ)22Ne reaction plays a key role. While the reaction rate of the 18O(α, γ)22Ne is mainly affected by several resonant states lying closely to the α threshold in 22Ne, up to now, the relevant 22Ne parameters are fragmentary in the energy region corresponding to the typical temperatures of s-process. The direct measurement of the 18O(α, γ)22Ne reaction rate is extremely difficult due to the very low cross section. In this work, we investigated the 22Ne resonant states via the 18O(6Li, d)22Ne reaction at the Beijing HI-13 tandem accelerator of China Institute of Atomic Energy. Based on the DWBA analysis, preliminary results showed that the spin-parity of 22Ne Eα=470 keV resonant states was assigned as 0+, which would make contributions to subsequent calculation for the reaction rate of the 18O(α, γ)22Ne.
自发裂变和α衰变是影响超重核稳定性的两个主要因素。为了探索270Ds附近的长寿命的超重核，系统地计算了电荷数在104 ≤ Z ≤ 112范围内的α衰变与自发裂变之间的竞争。采用推广的液滴模型和唯象的解析公式计算了α衰变半衰期。基于包括壳效应和同位旋效应的WKB近似方法估算了相同超重核的自发裂变半衰期，进而预测了未知超重核274-276，279Cn与267-269Ds的衰变模式。
The stability of superheavy nuclei (SHN) is controlled mainly by spontaneous fission and α decay processes. To investigate whether long lived SHN could really exist around 270Ds, the competition between α decay and spontaneous fission in the region 104 ≤ Z ≤ 112 are studied systematically. The α decay half-lives are investigated by employing a generalized liquid drop model (GLDM) and phenomenological analytical formula. Calculations of spontaneous fission half-lives for the same SHN are carried out based on the Wenzel-Kramers-Brillouin(WKB) approximation with both the shell effect and the isospin effect included. Decay modes are predicted for the unknown nuclei 274-276,279Cn and 267-269Ds.
基于结团形成模型（cluster-formation model，CFM）系统地研究了质子数Z=82，中子数N=126闭壳附近的α衰变母核的α衰变预形成因子Pα。计算结果表明：基于结团形成模型计算得到的Pα线性地依赖于价质子（空穴）Np和价中子（空穴）Nn的乘积。这与前期工作[SUN X D，et al.Phys Rev C，2016， 94 （2）：024338；DENG J G，et al.Phys Rev C，2017， 96 （2）：024318]得到的结论是一致的，其中，Pα是唯象的且模型依赖的，从α衰变半衰期的理论值和实验值的比值中提取。结合前期工作可以得到这样的结论：对于Z=82，N=126闭壳附近的α衰变母核，其Pα与NpNn呈线性关系，且价质子-价中子相互作用在α结团预形成中起了很重要的作用。
In the present work, the α decay preformation factors Pα are systematically studied within the cluster-formation model (CFM) for nuclei around Z=82, N=126 closed shells. The calculations show that the Pα calculated by CFM is linearly dependent on the product of valance protons (holes) and valance neutrons (holes) Np Nn. It is consistent with our previous works[SUN X D, et al. Phys Rev C, 2016, 94 (2):024338; DENG J G, et al. Phys Rev C, 2017, 96 (2):024318], which Pα are model-dependent and extracted from the ratios of calculated α decay half-lives to experimental data. Combining with our previous works, we confirm that the Pα is linearly dependent on the NpNn for nuclei around Z=82, N=126 shell closures. In addition, the valance proton-neutron interaction plays a key role in the α preformation.
基于两势方法（two-potential-approach，TPA）系统研究了偶-偶核、奇-A核和奇-奇核α衰变半衰期。为了考虑原子核的壳结构的影响而导致的实验半衰期与计算结果之间的偏差，引入了与α结团形成概率相关的禁戒因子和预形成因子。结合前期相关工作[X.D.Sun et al.，Phys.Rev.C 93，034316（2016）；X.D.Sun et al.，Phys.Rev.C 95，014319（2017）；X.D.Sun et al.，Phys.Rev.C 95，044303（2017）]，考虑到壳效应对α粒子预形成的影响，通过分析α衰变半衰期的实验数据，拟合得到了α粒子预形成因子/禁戒因子修正公式的参数，得到了α衰变预形成因子/禁戒因子的计算结果，证实了壳效应及质子-中子相互作用在α结团形成过程中起着重要的作用，离壳越近预形成概率越小离壳越远预形成概率越大。
In the present work, the α decay half-lives are systematically studied within the two-potentialapproach for even-even nuclei, odd-A nuclei and odd-odd nuclei. To describe the deviations between experimental half-lives and calculated results due to the nuclear shell structure, α preformation factor and hindrance factor related with α cluster preformation probability are introduced. It is consistent with our previous works[X. D. Sun et al., Phys. Rev. C 93, 034316 (2016); X. D. Sun et al., Phys. Rev. C 95, 014319 (2017); X. D. Sun et al., Phys. Rev. C 95, 044303 (2017)]. Considering the shell effect on the preformation of α and by analyzing the experimental data of the α decay half-lives, the parameters of the α preformation factor/hindrance factor correction formula are obtained. we confirm that the shell effect and the proton-neutron correlation play key roles in the α preformation where the preformation probability near the shell is less than the preformation probability far from the shell.
α condensates are exotic states in nuclear many-body systems, and can be viewed as the generalization of the Bose-Einstein condensate in nuclear physics. It is widely believed that, α condensates exist not only in 12C, but also in heavier self-conjugate nuclei such as 16O, 20Ne, 24Mg, 28Si, etc. It is important to understand the physical properties of these α condensates in heavy self-conjugate nuclei from the theoretical perspective, and the theoretical results could be a useful reference for the experimental studies. This work reviews the basic frameworks to study α condensates, including the Tohsaki-Horiuchi-Schuck-Röpke wave function, the Yamada-Schuck model, and the recently proposed semi-analytic approximation. The impacts of the four-body interactions of α particles on the physical properties of α condensates are reported. The breakup of α condensates and the one-dimensional α condensates are discussed briefly as the possible future directions in this field.
An extension of the original interacting boson model to the multi-level case including negative parity f-and p-bosons is made. An affinealgebraic approach is applied to solve the multi-level pairing problem numerically via the dual algebraic structure. The duality relation is explicitly used to construct the number-conserving unitary and number-nonconserving quasi-spin algebra, related with the Hamiltonian and the corresponding bases. After fitting to the experimental level energies of even-even 106-116Cd, several order parameters to signify the shape (phase) transition, such as occupation numbers of the bosons in the ground and a few lowest excited states, the level energy staggering in the (quasi)-γ band, are calculated to demonstrate the shape (phase) transitional behavior of these medium mass transitional nuclei.
In this work, a phenomenological analysis of the excited-state quantum phase transitions (ESQPTs) in the finite-N boson system has been carried out within the interacting boson model in order to reveal the possibility of finding ESQPTs in nuclear systems. Particularly, the angular momentum and finite-N effects on the ESQPTs in the U(5)-SU(3) and SU(3)-O(6) transitional regions have been systematically investigated. The results indicate that the main features of ESQPTs can be well preserved even at a realistic boson number for small angular momentum but will gradually disappear as the angular momentum increases.
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 → 0g），B（E2；42 → 21）/B（E2；21 → 0g）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 → 0g) and B(E2;42 → 21)/B(E2;21 → 0g), 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.
A recently developed method for calculating spectroscopic properties of medium-mass and heavy atomic nuclei with an odd number of nucleons is reviewed, that is based on the framework of nuclear energy density functional theory and the particle-core coupling scheme. The deformation energy surface of the eveneven core, as well as the spherical single-particle energies and occupation probabilities of the odd particle(s), are obtained by a self-consistent mean-field calculation with the choice of the energy density functional and pairing properties. These quantities are then used as a microscopic input to build the interacting bosonfermion Hamiltonian. Only three strength parameters for the particle-core coupling are specifically adjusted to selected data for the low-lying states of a particular odd-mass nucleus. The method is illustrated in a systematic study of low-energy excitation spectra and electromagnetic transition rates of axially-deformed odd-mass Eu isotopes. Recent applications of the method, to the calculations of the signatures of shapes phase transitions in axially-deformed odd-mass nuclei, octupole correlations in neutron-rich odd-mass Ba isotopes, are discussed.
Based on the relativistic Hartree-Bogoliubov theory in nuclear matter, the dineutron correlations and the crossover from Bardeen-Cooper-Schrieffer (BCS) region of neutron Cooper pairs to Bose-Einstein condensation (BEC) are investigated with the one-boson-exchange type of pairing force generated from the relativistic mean field (RMF) model. By introducing an effective factor χ in the RMF effective pairing interaction, the density dependence of the ratios between neutron pairing gap at Fermi surface and neutron Fermi kinetic energy △Fn/eFn and the dimensionless parameter 1/(kFna) are analyzed quantitatively. Then the criteria where dineutron correlations exactly reach the threshold of BCS-BEC crossover or unitary limit are determined to be χ=0.51 or 0.67, respectively. In addition, features of neutron pairing gap, Cooper pair wave function and dineutron coherence length are illustrated, and the value of the probability for partner neutrons correlated within the average inter-neutron distance, namely P (dn) ≃0.80, is obtained as a criterion of BCS-BEC crossover.
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.
A new iterative approach for solving the standard pairing problem is established based on polynomial approach. It provides an efficient way to derive the particle-number conserved pairing wave functions for both spherical and deformed systems, especially for large-size systems. The method reduces the complexity of solving a system for k-pairs polynomial equations into a system for one-pair polynomial equation, which can be efficiently implemented by the Newton-Raphson algorithm with a Monte Carlo sampling procedure for providing the initial guesses step by step. The present algorithm can also be used to solve a large class of Gaudin type quantum many-body problems as a more than 100 orbitals and 50 pairs system such as super-heavy nuclei and nuclear fission.
Single ∧, Ξ, and ∑ hypernuclei are systematically studied within the framework of relativistic mean-field (RMF) model with YN interactions being constrained according to the experimental data and previous theoretical efforts. By adding a hyperon to 16O, the mean-field potentials and single-particle levels for hyperons (∧, Ξ0,-, and ∑+,0,-) are compared and the impurity effects on the nuclear core are examined. In general, the ∧ and ∑0 hyperons show similar behaviors in bulk properties since both of them are electroneutral and with similar coupling constants; Ξ0 hyperon owns the shallowest mean-field potential well; and Coulomb interactions play vital roles in the charged Ξ-, ∑-, and ∑+ hyperons. As an impurity, the intruded single-hyperon makes the nuclear system more bound in most cases due to the attractive NY interaction. However, very different effects on the nucleon radii are observed for different hyperons. Besides, the effects of the ωYY tensor couplings on the spin-orbit splitting are discussed, and remarkable influences are found which even change the level ordering of Ξ hyperon.
Spin and pseudospin symmetries in the single-particle spectra of atomic nuclei are of great significance for the study of nuclear structure. In this work, taking 132Sn, ∧133Sn, and 2∧134Sn as examples, the spin and pseudospin symmetries in ∧ hypernuclei are studied by using the relativistic mean-field model. For the single-∧ spectra, results show that the spin symmetry maintains well while the pseudospin symmetry is approximately conserved. Besides, as impurities, the ∧ hyperons worsen the spin symmetry of single-neutron spectra while improve the pseudospin symmetry.
The uncertainty of the nuclear shell model is important but rarely investigated. The present work provides preliminary investigations on the uncertainty of the nuclear force and the effect model space in shell-model calculations. The most important part of the nuclear force is the central force, which is also considered to include the largest contribution from the renormalization effect. If semi-magic nuclei are considered and only the strength of the central force varies, C10 (T,S=1,0) and C11 (T,S=1,1) channels of the central force contribute to the theoretical variances of the description of the levels, while the spin-orbit force and the tensor force are kept unchanged as the bare ones. One set of the strengths of a simple nuclear force gives an 0.2 MeV root mean square (RMS) between observed and theoretical levels from 188 states in Pb and Sn isotopes and N=82 and 126 isotones. However, if levels in these isotopes and isotones are separately considered, RMS are further reduced and found to have two minimums with 15% stronger pp interaction than nn interaction, which indicates a "mirror difference" in medium and heavy nuclei. The enlarge of the model space are of great significance for the description of certain nuclei, such as the inclusion of cross-shell excitations for the nuclei with magic neutron and/or proton numbers. The neutron-rich F isotopes are investigated through three Hamiltonians. Despite the different results among Hamiltonians, the two neutron separation energies and levels are sensitive to and similarly contributed by the cross-shell excitations.
In random-interaction ensembles, the electric quadrupole moments (Q) and magnetic moments (μ) of the Iπ=11/2- isomers of the Cd isotopes predominantly present linear correlation with neutron numbers, corresponding to the recently emphasized linear Q and μ systematics in realistic nuclear system. Although the seniority scheme enhances such predominance (more essentially for μ), the configuration mixing due to quadrupolelike and δ-force-like proton-neutron interactions is responsible for the linear Q and μ systematics, respectively, at least in random-interaction ensembles. Especially, the linear μ systematics further requires the proton-neutron interaction have similar relative strength and attractive-repulsive property to realistic nuclear interaction.
The density dependence of nuclear fourth-order symmetry energy S4 is studied within the covariant density functional (CDF) theory in terms of the kinetic energy, isospin-singlet, and isospin-triplet potential energy parts of the energy density functional. When the Fock diagram is introduced, it is found that both isospin-singlet and isospin-triplet components of the potential energy plays important roles in determining the fourth-order symmetry energy. Especially, an extra suppression, which comes from the Fock terms via isoscalar meson-nucleon coupling channels, is revealed in the isospin-triplet potential part of the fourth-order symmetry energy. As an useful attempt, the generalized symmetry energy is introduced to describe the various orders of nuclear symmetry energies in a visual and self-consistent way.
In order to study the effect of curvature energy on the thermodynamic driving force (TDF) of nuclear fission, the potential and entropy barrier of 200Pb and 224Th systems are calculated by using the truncated droplet model including curvature energy, respectively. Compared with the liquid drop model, the results show that curvature energy does not affect the saddle point of 224Th, but pushes the saddle point of 200Pb backwards the ground state. The stronger the deformation dependence of the level density parameter is, the closer the saddle point of entropy barrier for these systems is to the ground state. In order to further investigate how curvature energy affects TDF through nuclear potential and entropy, respectively, the prescission neutron multiplicity (PNM) is selected as the probe, some simulations based on two schemes are carried out. The results show that curvature energy reduces the potential driving force of 200Pb and 224Th, and enhances the entropy potential driving force. Combined with the calculations and analyses of PNM, the former effect is more obvious than the latter, so curvature energy weakens TDF of two systems on whole, thus delaying the nuclear fission process of two systems.
研究了含有暗物质的夸克核心混合星的观测属性。用相对论平均场理论和有效质量口袋模型分别描述夸克核心的混合星物质内强子相和夸克相，用Gibbs相平衡条件描述强子-夸克混合相，研究了由于包含强、弱相互作用的费米子暗物质对混合星质量、半径、引力红移、自转频率和转动惯量等整体观测属性的影响。结果表明，在强、弱相互作用下，暗物质粒子质量大于等于0.5 GeV时暗物质会使混合星的状态方程比无暗物质时有一定软化，相应的混合星最大质量减少。当调节暗物质粒子质量研究表明，随着暗物质粒子质量的增大，夸克核心的混合星物质的状态方程变软，混合星的质量、半径变小，并且引力红移、自转频率和转动惯量等整体观测属性也明显依赖于暗物质粒子的质量。当暗物质粒子质量0.1 GeV时，包含强、弱作用暗物质的混合星质量达到2.0 M⊙和2.8 M⊙（其中M⊙为太阳质量），说明大质量脉冲星PSR J1859-0131和J1931-01可能是包含小质量暗粒子暗物质的强子夸克的混合星。整体观测属性的计算结果均在中子星的天文观察数据范围内，也说明强子夸克的混合星内可能包含暗物质。
The observational properties of quark core hybrid star contain dark matter are studied. The influences of containing of strongly or weakly interacting dark matter to global observational features of hybrid stars, mass, radius, gravitational red-shift, rotational period and moment of inertia are studied by using relativistic mean field theory to describe hadron phase, effective mass bag model to quark phase, and Gibbs phase equilibrium conditions to hadron-quark mixed phase respectively. Our results indicate that, both in the strong and weak interacting case, the equation of state for hybrid star matter contain dark matter become softer than that of without dark matter while the mass of dark matter particles larger than 0.5 GeV, which leads to the decrease of the mass and corresponding radius of hybrid star. With the increase of the dark matter particle mass, the equation of state for hybrid star matter become softer, this cause the decrease of the mass and radius of hybrid star obviously. The gravitational red-shift and the rotational period, obviously increase of the moment of inertia of the hybrid stars are influenced by the dark matter particle mass. When the dark matter particle mass is equal to 0.1 GeV, the masses of the star with strong and weak interacting dark matter reach to 2.0 M⊙ and 2.8 M⊙(M⊙ is the solar mass), this result indicates that the giant mass PSR, J1859-0131 and J1931-01, can be a hadron-quark hybrid star and containing dark matter with small dark particle mass. The computational results of all above global observational features of hybrid stars are in the range of astronomical observation data, these also indicate that hybrid star with quark core may contains dark matter.