丰中子锰同位素的壳模型计算

利用球形壳模型和投影壳模型两种方法对Z≤28,N=40附近pf壳的丰中子核素的结构进行了一系列的研究。以丰中子的锰同位素为例讨论了对奇奇核58,60Mn的两种壳模型计算结果。结果显示,两种理论方法都很好地再现了58,60Mn实验上观测到的从低激发到高自旋态的能级。在对这两个同位素由中子g_9/2轨道闯入所产生的负宇称转动带进行描述时,两种理论计算也得到了一致的结果。通过对比,阐明了两种壳模型方法及其采用的有效相互作用在该丰中子核区的适用性,特别强调了中子g_9/2轨道的激发对于pf壳Z≤28丰中子核素结构的重要性。Recently,we have carried out a series of studies on the structures of pf shell neutron-rich nuclei around N=40 using the spherical shell model and the projected shell model respectively.As an example,these two types of shell model calculations for the neutron-rich odd-odd isotopes 58,60Mn are discussed in this paper.The results show that both the calculations reproduce the observed experimental energy levels from the lowexcitation states to the high-spin ones in 58,60Mn.Consistent results are also obtained by these two theoretical calculations when describing the negative-parity rotational band derived from the intruder neutron g_9/2 orbital in both isotopes.Through comparison,we show the applicability of these two shell model methods and the adopted effective interactions in the present neutron-rich mass region.The significance of the excitations from neutron g_9/2 orbital to the structures of the neutron-rich nuclei in pf shell with Z≤28 are especially emphasized in this paper.     

α particle preformation and shell effect for heavy and superheavy nuclei

The α particle preformation factor is extracted within a generalized liquid drop model for Z = 84-92 isotopes and N = 126,128,152,162,176,184 isotones.The calculated results show clearly that the shell effects play a key role in α particle preformation.The closer the proton and neutron numbers are to the magic numbers,the more difficult the formation of the α cluster inside the mother nucleus is.The preformation factors of the isotopes reflect that N = 126 is a magic number for Po,Rn,Ra,and Th isotopes,but for U isotopes the weakening of the influence of the N =126 shell closure is evident.The trend of the factors for N = 126 and N = 128 isotones also support this conclusion.We extend the calculations for N = 152,162,176,184 isotones to explore the magic numbers for heavy and superheavy nuclei,which are probably present near Z = 108 to N = 152,162 isotones and Z = 116 to N = 176,184 isotones.The results also show that another subshell closure may exist after Z = 124 in the superheavy nuclei.This is useful for future experiments.     

形变相关的壳修正对N=126处断前中子发射的同位素效应的影响

利用动力学加统计模型就形变相关的壳修正（DDSC）对中子126壳层附近209,213,217Fr断前中子发射的影响进行了研究。模拟结果表明,DDSC抬升了复合核的裂变位垒,且213Fr的升高约为209,217Fr的2倍,但却没有改变鞍点位置。尽管位垒升高延缓了系统的裂变,但其动力学过程受热力学驱动力（TDF）和核阻尼间竞争的主导,因此准确提取壳修正的作用还需考虑核耗散的形变关系。在裂变第一阶段,当核耗散取一体耗散（OBD）参数时,壳修正没有改变断前中子发射的同位素效应,然而当核耗散取标准参数设置（SPS）时,由于213Fr的TDF存在着异常增强,故该规律未能展现。在裂变第二阶段,位垒升高引起的断前中子发射的增强受到了TDF与核阻尼间竞争的反制,故断前中子发射的同位素效应仍未能显现。综合两阶段情况,DDSC对N=126处断前中子发射的同位素效应的影响受第一阶段规律的支配。The effect of deformation-dependent shell correction (DDSC) on the emission of prescission neutron (EPN) is studied within a dynamical and statistical model for three isotopes of 209,213,217Fr near the neutron 126 closure-shell. The results show that the fission barriers are enhanced with DDSC, and the increment of 213Fr is almost 2 times those of 209,217Fr, but those saddle points are not changed. Although the enhancement of fission barrier delays nuclear fission, the fission dynamics process is controlled by the competition between thermodynamic driving force (TDF) and nuclear damping, so the deformation-dependence of nuclear dissipation must be considered in order to extract the role of shell correction. The shell correction doesn't alter isotope effect of EPN with OBD nuclear dissipation in the first phase of nuclear fission, but the rule does not been exhibited because that there is abnormal enhancement of TDF using SPS nuclear dissipation. The increment of EPN caused by the rise of fission barrier is countered by the competition between TDF and nuclear damping in the second phase of nuclear fission, hence the effect of EPN cannot exhibit. The effect of DDSC on EPN near the neutron 126 closure-shell is dominated by the rules in the first phase of nuclear fission.     

丰中子锶同位素的投影壳模型研究

利用考虑跨壳激发的投影壳模型（PSM）方法,研究了质子数Z=38、中子数N=63和64大形变丰中子101,102Sr同位素的结构性质。主要计算了转动谱、转动惯量和电磁跃迁性质等（如B（E2）和g因子）,并与相应的实验数据进行系统比较和相关的理论预言。结果表明,PSM可以利用理论计算的能带图解释101,102Sr同位素的转动惯量、电磁跃迁随自旋的变化,分析晕带的结构。PSM理论可以很好地再现实验结果,说明PSM方法及其采用的有效相互作用可以外推研究丰中子核区101,102Sr同位素的原子核结构。对于101,102Sr同位素,核子开始填布质子g_9/2和中子h_11/2轨道,通过更为仔细地分析能带图中来自质子g_9/2和中子h_11/2轨道对各转动带的组态成分的贡献,清晰地表明丰中子核结构性质对不同核子填布的依赖。Recently, we have carried out systematically studies on the structural properties of proton number Z=38, neutron number N=63 and 64 neutron-rich isotopes 101,102Sr by using the projected shell model (PSM) with consideration of cross shell excitation. The rotation spectra, the moment of inertia and the electromagnetic transition properties (such as B(E2) and g-factor) are calculated and compared with the corresponding experimental data in this paper. Furthermore, more high spin states are predicted in the calculation and expected to be confirmed experimentally. The results show that the PSM can not only well analyze the structural properties of yrast bands in 101,102Sr but also interpret the variation of the moment of inertia, electromagnetic transition with spins in terms with the theoretical band diagram. The good agreement with the experimental data suggests that the PSM with the adopted effective interactions can be generalized to study the nuclear structure of 101,102Sr isotopes in neutron-rich mass region. For 101,102Sr isotopes, the nucleons begin to fill proton g_9/2 and neutron h_11/2 orbital, the dependence of nuclear structure and properties on the different orbital occupies is described by carefully analyzing the contribution from proton g_9/2 and neutron h_11/2 orbital to the configuration of rotational bands in band diagram.     

原子核基态性质的系统研究

在Skyrme-Hartree-Fock-Bogoliubov（SHFB）理论框架下,利用SkOP1,SkOP2,SKC和SKD 4套新的Skyrme相互作用参数系统地研究了Ca,Ni,Sn和Pb同位素链上原子核的结合能、电荷半径等基态性质,并重点讨论了丰中子Ca核的新中子幻数以及Pb的同位素位移现象。通过与实验数据和SLy5相互作用参数的结果对比,发现这4套相互作用参数都能很好地再现结合能的实验数据,其预言精度比SLy5要高。对于丰中子Ca核,只有SKC和SKD相互作用参数能够再现N=28处的壳效应,而对于实验上发现的新幻数N=32和34,所有的相互作用参数均不能再现这一结果。对于电荷半径,发现所有的相互作用参数均不能很好地预言Ca同位素链电荷半径的演化规律以及Pb的同位素位移现象。另外,还将这些相互作用参数推广至远离β稳定线原子核的单粒子能级结构研究,发现其不适用于描述其随同位旋的演化行为。因此,为了更好地描述远离β稳定线原子核的宏观性质及单粒子能级,建议在拟合Skyrme相互作用参数时,除自旋-轨道耦合项包括合理的同位旋依赖外,还要考虑张量力成分。The nuclear ground state properties of Ca, Ni, Sn and Pb isotopes, such as the binding energies, the charge radii, are studied systematically by 4 sets of new Skyrme parametrizations SKC, SKD, SkOP1 and SkOP2 in the framework of the Skyrme-Hartree-Fock-Bogoliubov (SHFB) method. The new magic numbers of neutronrich Ca isotopes and the isotopic shift of Pb isotopes are discussed emphatically. By the comparisons between the calculations and the experimental data and results from the SLy5 interaction parametrization, it is found that the experimental binding energies can be reproduced accurately by all parametrizations. The calculated accuracies of SKC, SKD SkOP1 and SkOP2 parametrizations are higher than the ones of SLy5 parametrization. For the neutron-rich Ca nuclei, the shell effect of N=28 can be reproduced by the SKC and SKD parametrizations, but the magic numbers at N=32 and 34 are not found by the calculations of all the parametrizations. For the charge radii, the experimental evolution tendency of Ca isotopes and isotopic shift of Pb isotopes can not be reproduced by all the parametrizations. In addition, all Skyrme parametrizations are extended to study the structure of the nuclei far from the β stability line, it is shown that the single-particle energy evolutions with the isospin are not suitable for being studied by these parametrizations. Thus the tensor force component should be considered besides the isospin dependence in spin-orbit coupling term when the Skyrme interaction parametrizations are fitted.     

SO（8）对关联和代数壳模型中的SU（3）四极基底（英文）

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.     

r-过程路径核β——衰变半衰期的估算

分析了20 < A < 190范围内丰中子核β衰变的实验数据,根据半衰期随质子数、中子数以及衰变能变化所呈现的壳效应和对效应等特点,提出了一种有效估算丰中子核β衰变寿命的公式。新的计算公式形式简单包含了较少的参数、计算量小。用该公式能较为准确地再现丰中子核的β衰变半衰期。用RIKEN最新测量丰中子核半衰期检验了该公式的外推能力,本工作可以为r-过程研究提供可靠的输入数据。Experimental data of the β--decay half-lives for the nuclei with atomic number between 20 and 190 are investigated. We have systematically studied the shell effects and pairing effects on β--decay half-lives versus the decay energy Q and nucleon numbers (Z, N). An empirical formula has been proposed to calculate the β--decay half-lives of neutron-rich nuclei. The empirical formula is simple and has relatively few parameters. Experimental β--decay half-lives of the neutron-rich nuclei are well reproduced by the new formula. In addition, the extrapolating capacity of this formula has been checked with the very recent experimental data from RIKEN. The predicted half-lives for r-process relevant nuclei with the current formula can be served as the reliable input of r-process model calculations.     

Ab initio calculations of mirror energy difference in sd-shell nuclei

Mirror energy difference is a key observable in isospin symmetry breaking, containing rich information about nuclear structure. Understanding the mechanisms underlying mirror energy difference is important in nuclear physics. In the present work, we extensively investigated mirror energy difference using ab initio valence-space inmedium similarity renormalization group approach, focusing specifically on sd-shell nuclei. The low-lying spectra of Al isotopes and N = 8 isotones, together with their...     

Probe the 2s_(1/2) and 1d_(3/2) state level inversion with electron-nucleus scattering

The neutron-rich even-even nuclei26–40Mg,28–46Si,30–48S,and32–56Ar are calculated with the RMF model and the phase-shift electron scattering method.Results show that level inversion of the 2s1/2and 1d3/2proton states may occur for the magnesium,silicon,sulphur,and argon isotopes with more neutrons away from the stability line.Calculations show that the variation of the central charge densities for30–48S,and32–56Ar are very sensitive to the 2s1/2and 1d3/2proton state level inversion,and the level inversion can lead to a large measurable central charge depletion to the charge density distributions for the neutron-rich isotopes.Calculations also show that the charge density diferences between the isotopes with and without central charge depletion can reveal not only the level inversion of the 2s1/2and 1d3/2proton states but also the behavior of the proton wave functions of both states.The results can provide references for the possible study of the nuclear level inversion and nuclear bubble phenomenon with electron scattering of short-lived nuclei at RIKEN or/and GSI in the future.In addition,direct nuclear reaction44S(n,d)43P or44S(3H,α)43P might also be a possible way to study the 2s1/2and 1d3/2proton state level inversion.     

Monopole effects,core excitations,and β decay in the A = 130 hole nuclei near ~(132)Sn

The proton and neutron cross-shell excitations across the Z = 50 shell are investigated in the southwest quadrant of ~(132) Sn by large-scale shell-model calculations with extended pairing and multipole-multipole force. The model space allows proton(neutron) core excitations, and both the low-and high-energy states for ~(130) In are well described, as found by comparison with the experimental data. The monopole effects between the proton orbit and neutron orbit are studied as the new monopole correction that perfectly reproduces the first 1~+ level in ~(130) In. The energy interval of proton(neutron) core excitations in ~(130) In lies in the range of 4.5-6.5(2.0-4.1) MeV, and the high energy yrast states are predicted as neutron core excitations. The decays are calculated among the A=130 nuclei of ~(130) In, ~(130) Sn and ~(130) Cd.     

丰中子Zn核素奇特核结构讨论和展望

不稳定核结构是当前核物理研究的前沿热点问题之一,尤其是针对丰中子幻数核附近的区域。中子数N=40, 50附近镍区域核素展现出丰富的结构特征,激励了众多理论和实验研究。原子核的基本性质与核的结构密切相关,这里我们选择分析丰中子Zn(Z=30)同位素的基本性质来进一步了解这一核区的核结构特征。本文回顾了在欧洲核子中心(CERN)的ISOLDE测量Zn 同位素的实验,基于62–80Zn 核素基态和长寿命同核异能态的自旋、磁矩、电四极矩以及电荷均方根半径等基本性质,并结合各种大规模壳模型计算结果,系统地讨论了这一核区的壳结构演化、幻数特征、奇特形变和形状共存,以及核子间关联激发等物理现象。最后,基于已有的实验数据和物理现象,以及理论预言的 N=50以上镍核区的能级演化特征,我们提出在ISOLDE的共线共振电离谱装置上测量更加丰中子的81,82Zn 核素基本性质的实验设想。     

同位旋效应对N=9同中子素能级间隙的影响

在单粒子壳模型下, 研究了N=8及N=9同中子素的基态性质. 通过在伍兹--萨克逊势深中引入同位旋依赖项, 考虑了同位旋效应对核平均势的影响. 理论计算的均方根半径和自旋宇称值与实验结果整体上符合较好, 尤其是N=9同中子素中的2s_1/2与1d_5/2中子能级间的能级反转得到了较好的解释. 计算结果还显示在¹⁴B和¹⁵C基态中存在单中子晕.     

平均场加区分质子和中子的邻近轨道对力模型及对超铀区核的统一描述

利用严格可解的平均场加区分质子和中子的邻近轨道相互作用对力模型,对超铀区部分大形变核进行了统一的描述.计算了^227—233Th,^232—239U,^236—243Pu同位素和同中异质素²²⁸Ra-²²⁹Ac-²³⁰Th-²³¹Pa-²³²U,²³²Th-²³³Pa-²³⁴U-²³⁵Np-²³⁶Pu,²³⁶U-²³⁷Np-²³⁸Puv-²³⁹Am的结合能,对激发能和奇偶能差并与相应核的实验值进行了比较     

Large-Scale Shell Model for Nuclear Structure and Nuclear Astrophysics Studies

The study of neutron-rich nuclei near 132Sn is interesting and important for both nuclear  structure and nuclear astrophysics. For a considerably large model space allowing cross-shell excitations, a new effective Hamiltonian is determined by employing the extended pairing-plus-quadrupole model with monopole corrections. Calculations for two mass regions, for the north-east quadrant of 132Sn with Z > 50 and N > 82 and for the south-west quadrant with Z < 50 and N < 82, have been performed recently. The structure of these nuclei is analyzed in detail, and the role of the monopole corrections canbe clearly seen.     

Spin-dependent nuclear weak processes and nucleosynthesis in stars

Spin dependent nuclear weak processes and nucleosynthesis in stars are investigated based on recent advances in shell model studies of stable and unstable exotic nuclei. Three topics on (1) neutrino-nucleus reactions in supernova explosions and nucleosynthesis of light elements as well as Mn, (2) electron capture reaction rates on Ni and Co isotopes at high densities and temperatures in the core-collapse process, and (3) new β-decay half-lives of N=126 isotones obtained by including both the Gamow-Teller and the first-forbidden transitions, and the effects on the element abundance in the r-process at the third peak region (A∼195), are studied with the use of new shell model Hamiltonians.     

Isospin Effect on Level Spacing of N=9 Isotones

The ground-state properties of N=8 and N=9 isotones are investigated in the framework of the single-particle shell model. The isospin effect on the average nuclear potential is taken into account by introducing an isospin-dependent term in the depth of the Woods-Saxon potential. The theoretical results of RMS radii and spin-parity values are in agreement with the experimental data. Especially, the level inversion between neutron levels 2s_1/2 and 1d_5/2 in N=9 isotones is reproduced. A detailed discussion on numerical results is given and one-neutron halos in the ground states of ¹⁴B and ¹⁵C are presented.     

Proton electric pygmy dipole resonance

The evolution of the low-lying E1 strength in proton-rich nuclei is analyzed in the framework of the self-consistent relativistic Hartree-Bogoliubov model and the relativistic quasiparticle random-phase approximation (RQRPA). Model calculations are performed for a series of N=20 isotones and Z=18 isotopes. For nuclei close to the proton drip line, the occurrence of pronounced dipole peaks is predicted in the low-energy region below 10 MeV excitation energy. From the analysis of the proton and neutron transition densities and the structure of the RQRPA amplitudes, it is shown that these states correspond to the proton pygmy dipole resonance.