2017年 第34卷 第1期
对多夸克态特别是双重子态的半个世纪的研究进展进行了概述。利用动力学对称性，推导了能够合理地描述多夸克态质量的Gursey-Radicati 公式，然后在MIT 袋模型和可以很好描述重子-重子相互作用的夸克蜕定域色屏蔽模型中讨论了各种可能的双重子。
The progress in the study of multi-quark states for the last half century is reviewed schematically and the dibaryon sector is emphasized. By employing the dynamical symmetry, the Gursey-Radicati mass formula, which can give a reasonable description of the masses of multi-quark states, can be reproduced. The dibaryons in bag model and realistic quark model, quark delocalization color screening model, are discussed.
The mass and shape of skyrmion in an uniform magnetic field are investigated. Base on the symmetry of the system, an axially symmetric ansatz of the soliton is proposed to perform the study. The baryon number is shown to be always conserved even in a nonzero magnetic background. It is found that with the increase of the strength of magnetic field, the static mass of skyrmion first decreases then increases, as the dominant role shift from the linear term of magnetic field to the quadratic term of magnetic field, while the soliton size first increase then decrease. Finally, in the core part of magnetar, the equation of state have strong dependence of magnetic field, which also modifies the mass limit for magnetar.
Quantum electrodynamics in (2+1) dimensions (QED3) is an important nonperturbative system. This seems relatively simple Abel system, there are several issues that need to be clarified: whether or not the partition function of the system depends on chemical potential; whether or not there exists dynamical chiral symmetric breaking; whether or not the boson can acquires nonzero mass. In this paper, we give an in sight of the traits of QED3 from the dependence of density, temperature and massive boson to discuss those problems.
三维QED 具有两个和QCD类似的性质：动力学手征对称破缺和禁闭。为了研究动力学手征对称破缺，基于彩虹近似，在Dyson-Schwinger 方程框架下，通过迭代求解有限温下的费米子自能方程，讨论了不同的费米速度下费米子手征凝聚与费米子味数之间的关系。发现在有限温下，对于固定的费米子味数，费米手征凝聚随费米速度的变大而单调减小。
Analogous to Quantum QCD, QED3 has two interesting features: dynamical chiral symmetry breaking (DCSB) and confinement. By adopting the rainbow approximation, we numerically solve the fermion self-energy equation at finite temperature in the framework of Dyson-Schwinger equations and discuss the relation between chiral condensate and fermion flavor for several fermion velocities in the finite temperature QED3. It is found that the fermion chiral condensate decreases monotonically with the fermion velocity increasing for a fixed N at finite temperature.
The symmetry energy characterizes the isospin dependent part of the equation of state of isospin asymmetric strong interaction matter and it plays a critical role in many issues of nuclear physics and astrophysics. In this talk, we briefly review the current status on the determination of the symmetry energy in nucleon (nuclear) and quark matter. For nuclear matter, while the subsaturation density behaviors of the symmetry energy are relatively well-determined and significant progress has been made on the symmetry energy around saturation density, the determination of the suprasaturation density behaviors of the symmetry energy remains a big challenge. For quark matter, which is expected to appear in dense matter at high baryon densities, we briefly review the recent work about the effects of quark matter symmetry energy on the properties of quark stars and the constraint of possible existence of heavy quark stars on quark matter symmetry energy. The results indicate that the u and d quarks could feel very different interactions in isospin asymmetric quark matter, which may have important implications on the isospin effects of partonic dynamics in relativistic heavy-ion collisions.
基于兰州量子分子动力学（LQMD） 模型，系统研究了低能反质子引起的核反应中原子核碎裂机制和粒子产生。在LQMD输运模型中，考虑了反重子-重子、重子-重子和介子-重子碰撞可能产生的弹性散射、湮灭反应、电荷交换和非弹性散射。发展了并合模型，用于相空间构造初级碎片产生。处于激发态的碎片退激是基于统计模型描述。研究结果说明超子主要是由于奇异性交换产生；重碎片裂变会导致中等质量区域碎片产额增加；反质子引起的核反应有利于产生s=-2 和s=1 奇特超核，并给出了产生截面。
Within the framework of the Lanzhou quantum molecular dynamics (LQMD) transport model, the nuclear fragmentation and particle production induced by low-energy antiprotons have been investigated thoroughly. Production of strange particles in the antiproton induced nuclear reactions is modeled within the LQMD model, in which all possible reaction channels such as elastic scattering, annihilation, charge exchange and inelastic scattering in antibaryon-baryon, baryon-baryon and mesonbaryon collisions have been included. A coalescence approach is developed for constructing the primary fragments in phase space. The secondary decay process of the fragments is described by the well-known statistical code. It is found that the strangeness exchange reactions dominate the hyperon production. A bump structure in the domain of intermediate mass for heavy targets appears owing to the contribution of fission fragments. It has advantage to produce heavier hyperfragments and hypernuclides with strangeness s = -2 (double-Λ fragments) and s = 1 (Λ-fragments) in antiproton induced reactions. The production cross sections are evaluated.
在手征SU（3） 夸克模型下应用共振群方法讨论了三个非奇异的双重子态的性质。计算中的模型参数取自我们以前的工作，拟合核子-核子相互作用散射相移确定下来的。首先，研究了氘核的性质，这是非常重要的，因为氘核是多年来实验上唯一发现的双重子态。氘核属于核子-核子系统，它是自旋为S =1 和同位旋为T =0 的双重子态。我们计算了氘核的结合能、散射长度以及氘核的相对运动波函数，结果表明手征SU（3） 夸克模型可以合理描述氘核的性质并且发现张量力对形成松散束缚态的氘核是重要的。然后，给出了S = 3 和T =0 的ΔΔ双重子态的理论预言结果，这里考虑了分波耦合和隐色道耦合效应，计算了结合能和均方根半径。结果表明，隐色道耦合效应比分波耦合效应大，也就是说隐色道耦合效应在形成（ΔΔ）ST=30 双重子态中是重要的。我们的理论预言结果在几十个MeV 左右，低于ΔΔ道的阈值但是高于NΔπ的阈值. 出乎意料地，我们的预言结果很接近最近2014 年WASA的实验结果。接着，给出了对S = 0 和T =3 的ΔΔ双重子态性质的最新研究结果，这里在以前的单道计算基础上考虑了隐色道耦合效应。结果表明，隐色道耦合对（ΔΔ）ST=03的结合能也有较大的影响。但是，和（ΔΔ）ST=30 一样，它的质量低于ΔΔ道的阈值但是高于NΔπ的阈值。最后，对S = 3 以及S = 0 两个不同ΔΔ自旋态，详细比较了两者结构之间的差异。结果表明，σ'介子交换和OGE 交换对自旋S = 0 和S = 1 态提供的吸引作用分别是主要的，从而导致耦合道计算中系统的结合能变大。
In the present work we discuss three dibaryons without strangeness in the chiral SU(3) quark model by solving the resonating group method (RGM) equation. In the calculation, the model parameters are taken from our previous work in which the nucleon-nucleon (NN) scattering phase shifts are fitted quite well. Firstly, the structure of deuteron is discussed, which is very important since it is the first dibaryon confirmed by experiment in the past many years. Deuteron belongs to NN system with spin S =1 and isospin T =0, the binding energy, scattering length and the relative wave functions of deuteron are discussed. The results show that the chiral SU(3) quark model describes the properties of deuteron quite well and tensor interaction is important in forming the deuteron loosely bound. Secondly, the predicted results of ΔΔ dibaryon with S =3 and T =0 are shown, the resultant binding energy and size of root-mean-square (RMS) of six quarks are calculated by including the L coupling and hidden color channel (CC) coupling. The results show that the CC coupling effect is much larger than the L mixing effect, which means that CC coupling plays an important role in forming the spin S =3 ΔΔ dibayon state. Our predicted binding energy is several tens MeV, it is lower than the threshold of the ΔΔ channel and higher than the mass of NΔπ. Unexpectedly, our predicted mass is quite close to the recent confirmation by WASA experiments in 2014. Thirdly, we present our new results of ΔΔ dibaryon with S = 0 and T =3, obtained recently by extending the single-channel calculation to including the CC coupling. It is seen that the CC coupling also has a relatively large effect on (ΔΔ)ST=03 state. However, its mass is still lower than the threshold of the ΔΔ channel and higher than the mass of NΔπ, similar as that of (ΔΔ)ST=30 state. Finally, we further make some comparisons between S = 3 and S = 0 ΔΔ states to show the difference of the two dibaryons. The results show that the attractive interactions from σ' meson and OGE exchanges are dominantly important for S =0 and S =3 states, respectively, so their binding energies all become larger in coupled-channel calculation.
利用时间相关Hartree-Fock 理论和完整Skyrme 有效相互作用研究了16O+16O 碰撞在库仑位垒附近的熔合动力学。数值计算是在没有任何对称性约束的三维笛卡尔基下完成。将时间相关Hartree-Fock 理论和冻结密度近似下的能量密度泛函方法给出的库仑位垒与实验结果进行了比较，发现同位旋标量的张量项能降低自旋饱和体系16O+16O的库仑位垒，而库仑位垒高度随着同位旋矢量的张量项的耦合常数减小而降低。并计算了包含和不包含张量力的16O+16O熔合截面，发现张量力对16O+16O碰撞在库仑位垒附近的熔合动力学影响较小。
The fusion dynamics of 16O+16O around Coulomb barrier has been studied in the timedependent Hartree-Fock (TDHF) theory with the full Skyrme effective interaction. The calculations have been carried out in three-dimensional Cartesian basis without any symmetry restrictions. We have included the full tensor force and all the time-odd terms in Skyrme energy density functional (EDF). The Coulomb barrier obtained from the dynamical TDHF calculations and EDF with frozen density approximation has been compared with the available experimental data. The isoscalar tensor terms and the rearrangement of other terms are found to decrease the barrier height in the spin-saturated system 16O+16O, while the energy of Coulomb barrier tends to decrease as the isovector coupling constant decreases. The fusion cross section for 16O+16O collision has been calculated with and without the tensor force. We found that the tensor force has minor effect on the fusion dynamics of 16O+16O at the energies around Coulomb barrier.
核对称能的密度依赖性对于原子核物理和天体物理中的许多问题很重要。基于密度依赖的结团模型，奇特的结团放射性被用来约束核对称能及其斜率的大小。在密度依赖的结团模型中，清楚地给出了结团放射性子核208Pb的中子皮大小与对称能的斜率参数L（ρ0） 之间的关联。发现从M3Y核子-核子相互作用得到的结团-208Pb 同位旋矢量势对于对称能的斜率参数L（ρ0） 非常重要。基于结团放射性实验数据和新的208Pb 的中子皮大小实验数据，成功得到对称能的斜率参数L（ρ0） 的大小。也讨论了利用质子放射性数据提取的斜率参数L（ρ0）。
The density-dependence of symmetry energy is of particular importance to many problems in nuclear physics and astrophysics. Exotic cluster radioactivity is proposed to constrain the density slope of symmetry energy L(ρ0) by using the density-dependent cluster model (DDCM) where the cluster radioactivity serves as a link between the neutron skin thickness of 208Pb and the density slope L(ρ0). The isovector part of cluster-208Pb potential constructed from the M3Y nucleon-nucleon interaction is found to be very important in determining the density slope parameter L(ρ0). The correlation between the neutron skin thickness of 208Pb and the density slope parameter are obtained from cluster radioactivities around 208Pb with measured data. The constraint of L(ρ0) from proton radioactivity is also discussed.
基于相对论Hartree-Fock-Bogoliubov （RHFB） 近似分别探索了质量-电荷极限下的超重元素与极端中质比下的奇特原子核中的新幻数问题。研究结果表明，赝自旋对称性的守恒和破缺与超重核区球形幻数结构的形成密切相关，并分别决定了中子与质子的新幻数结构。同时，理论模型之间的差异也与之密切相关。在中重奇特核区，RHFB近似很好地再现了Ca 同位素中的新幻数N = 32，34，其中同位旋矢量道中洛伦兹张量耦合扮演了较为关键的角色。以此为例，研究证明了显式考虑交换（Fock） 项的RHFB 近似的可靠性。
Recent applications of the relativistic Hartree-Fock-Bogoliubov (RHFB) approach in exploring the new magicities under extreme conditions are presented for the superheavy elements with the limits of mass and charge and for the exotic nuclei with extreme neutron-to-proton ratios. It is found that the emergence of new magic shells in superheavy region is tightly related to the restoration and violation of pseudo-spin symmetry, respectively for the neutron and proton ones, in which the model deviations are indicated and discussed. In medium-heavy exotic nuclei, the occurrence of new magicity N = 32, 34 in Ca isotopes is well reproduced by the RHFB approach, in which the isovector Lorentz tensor couplings are found to play an essential role. The results exemplify that the RHFB approach, which considers the exchange (Fock) terms explicitly, furnishes a new theoretical instrument for advancing relativistic nuclear mean-field approaches.
将基于组合方法的角动量投影的位能曲面群用于研究铅同位素原子核190，192Pb 的超形变转动带。位能曲面群计算中采用了Gogny D1S 以及Skyrme SkP SLy4 三种相互作用。如用Gogny D1S 相互作用，190Pb 原子核没有明显的超形变转动带，而192Pb 原子核有非常显著的超形变转动带。用W. K. B. 方法计算了192Pb 原子核的超形变带穿透宽度。该穿透宽度很大与用GW模型（Nucl. Phys. A 660 （1999）197）分析实验数据给出的结果相近。在Gogny D1S 相互作用情形下，就角动量投影对位能曲面群的影响作了讨论，发现角动量投影压低了分隔超形变转动带与正常形变转动带之间的位垒。还用Skyrme SkP 和SLy4 相互作用计算了角动量投影的位能曲面群，发现位垒明显高于Gogny D1S 相互作用给出的位垒。在Skyrme 相互作用情形下，192Pb 原子核的超形变带穿透宽度明显小于Gogny 相互作用给出的宽度，但是较SB方法（Phys. Rev. C，60 （1999） 051305） 分析实验数据得到的结果高出几个数量级。于是，对SB 方法提出了质疑，因为它给出了极其微小的传播宽度。
The combined method is applied to calculate the angular momentum projected potential energy surfaces (AMPPES) of 190,192Pb. The Supper-deformed(SD) rotational bands of the two nuclei are studied with the AMPPES computed with the Gogny D1S and Skyrme SkP and SLy4 interactions. It is found that there is no pronounced SD band in 190Pb in the case of the Gogny interaction, which is consistent with the experimental observation. A well developed SD band with the Gogny interaction is found in 192Pb. The tunneling width of 192Pb is comparable to that given by the GW approach (Nucl. Phys. A 660 (1999)197) and orders of magnitude larger than that given by the SB approach (Phys. Rev. C 60 (1999) 051305). The influence of the angular momentum projection on the potential energy surfaces is examined in the case of the Gogny interaction for 190,192Pb. It is shown that the angular momentum projection suppresses the barrier separating the SD and ND rotational bands. Higher barriers of the AMPPESs for the two nuclei computed with the Skyrme SkP and SLy4 interactions are obtained compared with those given by the Gogny force. The tunneling width of 192Pb is also big for the Skyrme interactions. We put the SB approach into question which gives only an extremely small spreading width.
建立了SO（8） 同位旋标量、同位旋矢量及总的配对基与微观壳模型坐标空间部分的Elliott SU（3） 基之间的对应关系。从该代数间的互补关系导出了在壳模型的粒子数守恒代数U（4Ω） 中所包含的具有同位旋T 及自旋S 的Wigner 超多重态（不可约） 表示。其重要性在于，该结果能用于研究对相互作用和四极-四极相互作用在核谱中的竞争效应并揭示其配对基中的SU（3） 组份。虽然仅展示了该理论对ds 壳的计算，其方法也适用于研究多壳的情形。
We establish a correspondence between the SO(8) isoscalar, isovector and total pairing bases and the Elliott's SU(3) basis in the algebraic structure of the spatial part of the microscopic shell model. It is derived from the complementarity of these algebras to the same T, S, (S,T) irreducible representations (irreps) of the Wigners supermultiplets, contained in the shell-model number-conserving algebra U(4Ω). This important result allows for the evaluation of the content of SU(3) irreps into the different types of pairing bases which leads to an investigation of the complementarity and competitive effects of pairing and the quadrupole-quadrupole interactions on the energy spectra of the nuclear systems. The theory is valid for any shell and for a number of shells as well, but we illustrate it with the results for a single ds-shell.
Symmetry plays an important role in understanding the nuclear structure properties from the rotation of a nucleus to the spin, parity and isospin of nuclear states. This simplifies the complexity of the nuclear problems in one way or the other. Seniority is also a well known quantum number which arises due to the symmetry in the pairing interaction of nuclei. We present empirical as well as theoretical evidences based on decay rates which support the goodness of seniority at higher spins as well as in nrich or, n-deficient nuclei. We find that the generalized seniority governs the identical trends of high-spin isomers in different semi-magic chains, where different set of nucleon orbitals from different valence spaces are involved.
Nuclear matrix element in double beta decay under the closure approximation is outlined, in which neutrino potential for neutrinoless double beta decay is studied with focusing on its statistical property. It is shown from the analysis that Fermi and Gamow-Teller parts provide almost the same positive values with the Fermi part slightly larger than the Gamow-Teller part in general, while the tensor part includes small but non-negligible positive and negative values. Positive correlation of the values between Fermi, Gamow-Teller, and tensor parts has been clarified. The statistics provides a gross view of understanding amplitude of constitutional components of the nuclear matrix element.
The studies of thermal fission rates are relevant to novel reactors, astrophysical environments, and survival probabilities of compound superheavy nuclei. This has been conventionally studied by the Bohr-Wheeler statistical model that depends on phenomenological level densities and fission barriers. In this context, we propose to study the thermal fission rates based on microscopic temperature dependent nuclear energy density functional theory. The microscopic temperature dependent fission barrier heights and curvatures, and collective mass parameters can be self-consistently obtained. The fission lifetimes from low to high temperatures can be given by the imaginary free energy method in a consistent framework. Microscopic temperature dependent fission barriers play an essential role in fission studies.
采用Skyrme Hartree-Fock 模型和微观的核子-超子相互作用对Ar 同位素和40Ca 及相应超核的超形变态进行了研究，计算结果表明，基态的Λ 超子分离能比激发态的大。这一结果与反对称化分子动力学模型的结果一致，而与相对论平均场的结果相反。这区别主要来源于不同模型中不同的相互作用导致的核心核及相应超核密度分布的不同。
The superdeformed (SD) states in medium heavy hypernuclei with core nuclei of Ar isotopes and 40Ca are studied in the frame of Skyrme Hartree-Fock (SHF)+ BCS model together with a microscopic ΛN interaction. The calculation indicates that the Λ separation energy SΛ of ground state is larger than that of SD state. The result is consistent with the antisymmetrized molecular dynamics (AMD) calculation, but inconsistent with that of relativistic mean field (RMF). The difference comes from the different interaction and density distribution in the core nuclei and the corresponding hypernuclei.
在SD 对壳模型的理论框架下讨论了原子核形状相变模式。研究结果表明，该理论模型可以把相互作用玻色子模型中U（5）-SU（3）以及U（5）-SO（6） 形状相变模式再现出来，相互作用玻色子模型中有关临界点对称性的特征也可以很好地描述。本文同时也发现原子核从振动到转动的形状相变可以通过改变相互作用强度来实现。
The nuclear shape phase transitional patterns were studied in the SD-pair shell model. The results show that the transitional patterns similar to the U(5)-SU(3) and U(5)-SO(6) transitions in the interacting boson model can be produced. The signatures of the critical point symmetry in the interacting boson model are also produced approximately. It is also found that the shape phase transitional pattern between vibration and rotation can also be produced by changing the interactional strength.
讨论了核结构模型中两体以上相互作用的可能形式。首先以基于手征微扰论并适于描述轻核的三体接触型相互作用为例，讨论了能合理描述3H 和3He 结合能的三核子接触型相互作用相关的两个低能有效耦合参数cD 和cE间的关系并通过4He 结合能给出了相应的物理参数区。其次通过Okubo-Lee-Suzuzki 有效相互作用方法对核多体问题在有限模型空间的求解，论证了A-体相互作用项。最后利用包含了A-体推广对力的可解模型对重核的同位素长链进行了分析。以132Sn 为核芯，通过对Sn 同位素链的计算揭示了推广对力参数G（A） 与模型价核子空间维数dim（A） 间的显著关系：G（A）=259.436 dim（A）-0.9985。这些分析结果说明，有必要对核中经手征微扰论或其它唯象理论所得到的NNN-，NNNN-，及A-体相互作用作进一步的研究。
We discuss modeling of nuclear structure beyond the 2-body interaction paradigm. Our first example is related to the need of three nucleon contact interaction terms suggested by chiral perturbation theory. The relationship of the two low-energy effective coupling parameters for the relevant three nucleon contact interaction terms cD and cE that reproduce the binding energy of 3H and 3He has been emphasized and the physically relevant parameter region has been ilustrated using the binding energy of 4He. Further justification of A-body interaction terms is outlined based on the Okubo-Lee-Suzuki effective interaction method used in solving the nuclear many-body problem within a finite model space. The third example we use is an exactly solvable A-body extended paring interaction applied to heavy nuclei with a long isotopic chain; in particular using 132Sn as closed core system illustrates a remarkable relationship between the extended pairing strength G(A) and the size of the valence space dim(A) for the members of the Sn-isotope chain: G(A)=αdim(A)-β with α=259.436 and β =0.9985 which is actually a one parameter expression since β is practically 1. These three cases present evidence for the need of better understanding of the NNN-, NNNN-, and A-body interactions in nuclei either derived from ChPT or from a phenomenological considerations.
一个模型适合描述哪些物理量? 这个问题可以通过模型的物理来源来回答。比如，液滴模型适合描述重核和远离满壳核。这是因为液滴近似更适用于核子数多的核以及液滴模型不包含壳效应。这样的回答是定性的并需要清楚模型的物理来源。是否可能仅通过模型的数学形式和实验数据就能给出半定量的解答? 利用最近提出的不确定度分解方法尝试对液滴模型适合描述哪些核这一问题进行半定量的回答。并且不需已知液滴模型的物理来源，仅需其数学形式以及实验数据。通过不确定度分解方法，液滴模型与实验数据间的残差可以分解为系统不确定度和统计不确定度。两者分别代表了模型的缺陷和模型不精确的参数带来的不确定度。基于这一分解，核素图上的原子核可以按其对应的残差被半定量地划分为系统不确定度主导、统计不确定度主导、以及中间区域。液滴模型适合描述的核就是统计不确定度主导残差的核而不是像通常认为的是残差最小的核。从核素图上看，统计不确定度主导残差的核正是重核以及远离满壳核，与液滴模型物理来源一致，但得到这一结果的过程是半定量的且仅需液滴模型的数学形式以及实验数据。如果对由统计不确定度主导残差的核重新拟合液滴模型的参数，模型可以很好地描述这些核（标准差小于0.7 MeV）。
Which data are well described by a theoretical model? Such questions can be answered through the physical origin of the model. For example, the liquid drop model (LDM) well describes the heavy and far from shell nuclei. Because the liquid-drop assumption is more suitable for nuclei with more nucleons and LDM does not include the shell effect. Such answer is qualitative and needs a clear view on the physical origin of the model. Is it possible to give an semi-quantitatively answer only from the mathematical form of the model and the observed data. In the present work, the recently suggested uncertainty decomposition method (UDM) is used to answer which nuclei are well described by LDM. The residues between LDM and the observed data can be decomposed through UDM to systematic and statistical uncertainties, which represent the uncertainty of the deficiency of the model and the indeterminate parameters, respectively. Based on UDM, the chart of nuclides are semi-quantitatively divided into three parts, areas dominated by the systematic and statistical uncertainties, and the cross area. Contrary to the common sense, the well described nuclei by LDM are not the nuclei with small residues, but actually the nuclei of which the residues are dominated by the statistical uncertainty. These nuclei are indeed the heavy and far from shell nuclei, which agrees with the physical consideration of LDM. But only the mathematical form of the model and the experimental data are needed during the use of UDM. The nuclides dominated by the statistical uncertainty can be well described by LDM (standard deviation less than 0.7 MeV) with parameters fitting to these nuclei.
采用基于推转壳模型的粒子数守恒方法对105Cd 和106Cd 中的反磁转动带进行了研究，在计算当中，粒子数严格守恒，并且堵塞效应也是严格考虑的。计算结果很好地再现了实验上观测到的I-Ω 关系、转动惯量以及约化跃迁几率B（E2）。通过检验双剪角，即两个质子空穴角动量的合拢，对反磁转动中的双剪刀机制进行了分析。研究表明剪刀角的合拢非常敏感地依赖于对关联。
The antimagnetic rotation bands in 105;106Cd are investigated by the cranked shell model with pairing correlations treated by a particle-number conserving method, in which the blocking effects are taken into account exactly. The experimental moments of inertia, I-Ω relation and the reduced B(E2) transition probabilities are well reproduced. The two-shears-like mechanism for the antimagnetic rotation is investigated by examining the shears angle, i.e., the closing of the two proton hole angular momenta. The sensitive dependence of the shears angle on the nuclear pairing correlations is revealed.
应用严格求解的Nilsson 平均场加推广对力模型，在同时考虑质子-质子和中子-中子间对力相互作用的情况下，对稀土区的152-164Er，154-166Yb 和156-168Hf 核素的结合能、奇偶能差、低激发态转动惯量等基态性质进行系统的统一描述。通过计算结果与实验数值比较分析显示，对力相互作用在阐明以上核素能谱的基态性质中起到了关键的作用。应用拟合上述物理量所确定的模型参数，对156-162Yb 核素基态中价核子配成角动量J = 0，1，… ，12的价核子对占有率的计算结果显示，配成角动量为偶数价核子对的占有率远远高于配成角动量为奇数价核子对的占有率，其数值结果揭示了配成角动量为S，D和G的价核子对在所考虑的核素基态性质中占主导地位。
The Nilsson mean-field plus extended-pairing model for deformed nuclei is applied to describe the ground-state properties of selected rare-earth nuclei. Binding energies, even-odd mass differences, moments of inertia for the ground-state band of 152-164Er, 154-166Yb, and 156-168Hf are calculated systematically in the model employing both proton-proton and neutron-neutron pairing interactions. In comparison with the corresponding experimental data, it is shown that for these rare-earth nuclei, pairing interaction is crucial in elucidating the properties of the ground state. With model parameters determined by fitting the energies of these states, ground-state occupation probabilities of valence nucleon pairs with angular momentum J =0,1, …,12 for even-even 156-162Yb are calculated. It is inferred that the occupation probabilities of valence nucleon pairs with even angular momenta are much higher than those of valence nucleon pairs with odd angular momenta. The results clearly indicate that S, D, and G valence nucleon pairs dominate in the ground state of these nuclei.