Level inversion of N=9 isotones in the relativistic mean-field theory

We have studied the ground state properties of N=8 and N=9 isotones in the framework of the nonlinear relativistic mean-field (RMF) theory using force parameters NL-SH. Calculations show that the RMF theory can describe experimental data of binding energies and radii for these nuclei. The RMF theory can also reproduce the level inversion of N=9 isotones well if the ρ tensor coupling is included. One-neutron halos in ¹⁵C and ¹⁴B are predicted.     

Theoretical Study on N = 126 Shell Evolution

The nuclei around magic number N = 126 are investigated in the deformed relativistic mean field (RMF) model with effective interactions TMA. We focus investigations on the N = 126 isotonic chain. The N = 126 shell evolution is studied by analyzing the variations of two-neutron (proton) separation energies, quadruple deformations, single particle levels etc. The good agreement of two-neutron separation energies between experimental data and calculated values is reached. The RMF theory predicts that the sizes of N = 126 shell become smaller and smaller with the increasing of proton number Z. However, the N = 126 shell exists in our calculated region all along. According to the calculated two-proton separation energies, the RMF theory suggests ²²⁰Pu is a two-proton drip-line nucleus in the N = 126 isotonic chain.     

Relativistic Consistent Angular-Momentum Projected Shell-Model:Relativistic Mean Field

We develop a relativistic nuclear structure model, relativistic consistent angular-momentum projected shell-model (RECAPS), which combines the relativistic mean-field theory with the angular-momentum projection method. In this new model, nuclear ground-state properties are first calculated consistently using relativistic mean-field (RMF) theory. Then angular momentum projection method is used to project out states with good angular momentum from a few important configurations. By diagonalizing the hamiltonian, the energy levels and wave functions are obtained. This model is a new attempt for the understanding of nuclear structure of normal nuclei and for the prediction of nuclear properties of nuclei far from stability. In this paper, we will describe the treatment of the relativistic mean field. A computer code, RECAPS-RMF, is developed. It solves the relativistic mean field with axial-symmetric deformation in the spherical harmonic oscillator basis. Comparisons between our calculations and existing relativistic mean-field calculations are made to test the model. These include the ground-state properties of spherical nuclei ¹⁶O and ²⁰⁸Pb, the deformed nucleus ²⁰Ne. Good agreement is obtained.     

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.     

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.     

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.     

Inhibited transitions and isomeric states in the N = 50 isotones

Measured E2 transition rates in the N = 50 isotones (⁹⁰Zr–⁹⁴Ru) are satisfactorily reproduced by a shell model 0699 0 with proton configurations (p_1/2g_9/2)ⁿ. The inhibited 8⁺→6⁺ E2 transition in ⁹⁴Ru and its connection with seniority mixing is discussed. Isomeric states are predicted in ⁹¹Nb and ⁹³Tc. 0699     

Properties of A = 7-9 Drip-Line Nuclei in RMF Theory

The relativistic mean-field （RMF） theory is used to calculate the properties of A =7-9 drip-line nuclei ^7Li, ^7;9Be, ^8;9B, and ^9C. Systematic deviations between experimental and theoretical binding energies are found. Possible reasons of these systematic deviations are discussed in terms of pairing energy. The root-mean-square （rms） radii of matter distributions for these nuclei agree with the experimental data quite well. The one-proton halo structure in ^8B is reproduced well, and the two-proton halo in ^9C is predicted. The calculations show that the RMF theory is valid in studying the properties of light drip-line nuclei.     

丰中子轻核新幻数N=16的解释(英文)

基于中子分离能的分析 ,Ozawa等提出丰中子轻核存在新幻数 N=1 6.对 N=1 6同中子素进行了形变和球形的相对论平均场计算 .相对论平均场的数值结果表明N=1 6同中子素有形状相变.这是一些丰中子核新幻数出现的可能原因. Based on the analysis of neutron-separation energies, Ozawa et al proposed a new magic number N =16 in light neutron-rich nuclei. The deformed and spherical relativistic mean-field(RMF) calculations have been carried out for N =16 isotones. The numerical relativistic mean-field results show there is a shape transition in N =16 isotones. This is the possible cause of the appearance of the new magic number in someneutron-rich nuclei.     

Measurement of transition quadrupole moments of high-spin states in the N=74 isotones Pr, Ce and La

The Doppler-Shift Attenuation Method has been used to extract transition quadrupole moments of high-spin bands in the N=74 isotones ¹³³Pr, ¹³²Ce and ¹³¹La, produced in the ³⁷Cl + ¹⁰⁰Mo reaction. The results appear to be configuration dependent and, for ¹³³Pr and ¹³²Ce, the involvement of Ω=1/2 νh_9/2 and νf_7/2 intruder orbitals appears to enhance the collectivity at high spin (I>25 ).     

Prolate and oblate 10 isomers in Sm78 and Gd78

The N = 78 isotones ¹⁴⁰Sm and ¹⁴²Gd have been studied with -particle- and HI-induced reactions. In both nuclei two close-lying 10⁺ isomers at 3.2 MeV have been established, and from the feeding E2 cascades they are characterized as the prolate and the oblate excitations. A third E2 cascade feeding into the ¹⁴²Gd 8⁺ state is interpreted as the continuation of the collective ground state sequence that might assume the properties of a perfect deformed rotor for spins above 10.     

An Isoratio Method and an Isoratio Scaling Phenomenon in Heavy-Ion Collisions

An isoratio method is proposed to study the chemical potential of neutrons (protons) from the yield ratio of isotopes (isotones) differing in neutron-excess (I = N-Z). The measured fragments in the 140 A MeV^40,48 Ca and ^58,64 Ni + ⁹ Be reactions, as well as those in the simulated ^58,64 Ni + ⁹Be reactions by using the antisymmetric molecular dynamics (AMD) model plus the secondary decay model gemini, have been adopted to perform the isoratio analysis. The results of the isoratio method verify that they are similar to that of the well known isoscaling method. The isoratio scaling phenomenon suggested by the isoratio method has also been found in the measured data and the fragments simulated by the AMD + gemini models.     

Isomerism in Ag and non-yrast levels in Pd and Rh, studied in β decay

The β decay of ⁹⁶Ag (Z=47,N=49) was investigated by measuring positrons, X rays as well as β-delayed protons and γ rays. The γ radiation was studied by means of germanium detectors and a NaI total-absorption spectrometer. Two β-decaying isomers in ⁹⁶Ag were established with half-lives of 4.40(6) and 6.9(6) s and tentative spin–parity assignments of (8⁺) and (2⁺), respectively. For both isomers, the intensities of β transitions to low-lying levels of ⁹⁶Pd (Z=46,N=50) and β-delayed proton decays to levels in ⁹⁵Rh (Z=45,N=50) were measured. Several new ⁹⁶Pd levels were firmly established. The level energies, their γ decays and the Gamow–Teller decay of ⁹⁶Ag are compared to shell-model predictions. A new low-lying level in ⁹⁵Rh was found at 680 keV excitation energy. Through a comparison with low-lying states of N=50 isotones, this level is interpreted as the first excited 7/2⁺ state built on the proton 9/2⁺ ground state. The assignments of further excited states in ⁹⁵Rh are discussed.     

Er，Yb和Hf同位素的基态占有率（英文）

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.     

An Isoratio Method to Study Free Energy and Temperature Effects in Intermediate Mass Fragments Produced in Heavy-Ion Collisions

An isoratio method, i.e., the isotopic (isotonic) ratio among three isotopes (isotones), is proposed to study the free energy and temperature effects in the intermediate mass fragments produced in heavy-ion collisions. The parameterizations for the free energy of nucleus at low temperature, which have been proposed in the framework of the density functional theory using the SKM skymre interaction, are adopted to calculate the temperature-dependent free energy of fragment. By analyzing the measured yields of fragments in the 140A MeV ^58,64Ni + ⁹Be reactions, it is verified that the free energy in the isoratio is almost the same for different reactions. A temperature-dependent pairing-energy is introduced into the parameterizations for free energy, which reveals that the weakened pairing energy at the low temperature accounts for the weakened or disappearing odd-even staggering in isoratio.     

Shell evolution at N=20 in the constrained relativistic mean field approach

The shell evolution at N = 20, a disappearing neutron magic number observed experimentally in very neutron-rich nuclides, is investigated in the constrained relativistic mean field (RMF) theory. The trend of the shell closure observed experimentally towards the neutron drip-line can be reproduced. The predicted two-neutron separation energies, neutron shell gap energies and deformation parameters of ground states are shown as well. These results are compared with the recent Hartree-Fock-Bogliubov (HFB-14) model and the available experimental data. The perspective towards a better understanding of the shell evolution is discussed.     

Shell evolution at N=20 in the constrained relativistic mean field approach

The shell evolution at N=20, a disappearing neutron magic number observed experimentally in very neutron-rich nuclides, is investigated in the constrained relativistic mean field (RMF) theory. The trend of the shell closure observed experimentally towards the neutron drip-line can be reproduced. The predicted two-neutron separation energies, neutron shell gap energies and deformation parameters of ground states are shown as well. These results are compared with the recent Hartree-Fock-Bogliubov (HFB-14) model and the available experimental data. The perspective towards a better understanding of the shell evolution is discussed.     

Microscopic Studies on the Nucleus 28O

The ground-state properties of the nucleus ²⁸O are studied in relativistic and nonrelativistic mean-field approaches. It is shown by these calculations without any adjusting parameters that ²⁸O is a weakly bound nucleus and exhibits neutron halos. The differences among various mean-field approaches have been compared and discussed.     

Skyrme型N∧相互作用下超越平均场模型的∧超核研究

使用超越平均场Skyrme-Hartree-Fock（SHF）模型对_∧9Be,_∧∧10Be,_∧13C和_∧21Ne进行计算,采用SLy4参数组的Skyrme力作为NN相互作用力,采用最近提出的SLL4参数组的Skyrme力作为N∧相互作用。计算中包含了超子的自旋-轨道力以再现单粒子态的自旋-轨道能级分裂和不交叉效应,并采用BCS方法处理对力。讨论了不同组态超核的相关性质,包含12C⊗∧[000]1/2+,12C⊗∧[110]1/2-,12C⊗∧[101]3/2-和12C⊗∧[101]1/2-及8Be⊗∧[000]1/2+,8Be⊗∧[110]1/2-,8Be⊗∧[101]3/2-和8Be⊗∧[101]1/2-。计算了_∧9Be,_∧13C的低激发能谱并与实验值进行了比较。结果表明,采用的超越平均场SHF模型能很好地再现∧超子占据s_∧轨道的正宇称能级。对8Be的计算结果表明该模型可以很好地再现8Be的集团结构,可以得出_∧9Be的真实超核态能级和9Be类似态。对_∧9Be及_∧13C的计算均再现了自旋双重态（3/2+,5/2+）,但是得到的双重态能级差依然与实验值有出入。此外,对于上述超核体系均在∧超子占据∧[000]1/2+轨道时产生了收缩效应。还对_∧21Ne进行了计算并和超越平均场RMF模型计算结果进行比较,发现两者计算结果虽有细节上的出入,但是结果基本一致。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⊗∧[000]1/2+, 12C⊗∧[110]1/2-, 12C⊗∧[101]3/2-, 12C⊗∧[101]1/2-, 8Be⊗∧[000]1/2+, 8Be⊗∧[110]1/2-, 8 Be⊗∧[101]3/2- and 8Be⊗∧[101]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 ∧[000]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.