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.     

Effect of time-odd fields on odd-even mass differences of semi-magic nuclei

The effect of time-odd fields of Skyrme interaction on neutron odd-even mass differences is studied in the framework of axially deformed Skyrme Hartree-Fock(DSHF)+BCS model. To this end, we take into account both the time-even and time-odd fields to calculate the one-neutron and two-neutron separation energies and pairing gaps of semi-magic Ca, Ni, and Sn isotopic chains. In the calculations, a surface-type pairing interaction(IS pairing) and an isospin dependent contact pairing interaction(IS+IV pairing)are adopted on top of Skyrme interactions SLy4, SLy6 and Sk M*, respectively. We find that the time-odd fields have in general small effects on pairing gaps, but achieve better agreement with experimental data using SLy4 and Sly6 interactions, respectively.It is also shown that the calculations with IS+IV pairing reproduce the one-neutron separation energies of Sn isotopes better than those with the IS pairing interaction when the contributions of the time-odd fields are included.     

Nuclear structure investigation of neutron-rich Mn isotopes

Structural evolution of odd-even and odd-odd Mn isotopes from the valley of stability up to neutron dripline is studied in the framework of the self-consistent mean-field theory of Hartree–Fock–Bogoliubov. Three Skyrme effective interactions, namely, SLy4, SLy5 and SLy5T, are employed to investigate the tensor force effect on the ground-state properties. It is shown that the calculated quantities with the SLy4 interaction correctly reproduce the available experimental data and agree well with finite range droplet model and relativistic mean-field predictions. An inconsistency has been observed between the curves of the separation energies and that of the charge radius around N = 40. It is explained by the flatness of the potential energy curves in this region. The SLy5 and SLy5T results point to the necessity to refit all the Skyrme parameters after including the tensor terms.     

Nuclear properties of Z=114 isotopes and shell structure of ~(298)114

The two-neutron separation energies(S_(2n)) and α-decay energies(Q_α) of the Z=114 isotopes are calculated by the deformed Skyrme-Hartree-Fock-Bogoliubov(SHFB) approach with the SLy5,T22,T32 and T43 interactions.It is found that the tensor force effect on the bulk properties is weak and the shell closure at N=184 is seen evidently with these interactions by analyzing the S_(2n) and Q_α evolutions with neutron number N.Meanwhile,the single-particle energy spectra of ~(298)114 are studied using the spherical SHFB approach with these interactions to furthermore examine the shell structure of the magic nucleus ~(298)114.It is shown that the shell structure is almost not changed by the inclusion of the tensor force in the Skyrme interactions.Finally,by examining the energy splitting of the three pairs of pseudospin partners for the protons and neutrons of ~(298)114,it is concluded that the pseudospin symmetry of the neutron states is preserved better than that of the proton states and not all of the pseudospin symmetries of the proton and neutron states are influenced by the tensor force.     

Tensor force effect on single-proton energy levels of oxygen isotopes

In the framework of the Hartree-Fock approach the proton spin-orbital splittings of the 1p orbits and the shell gaps in the oxygen isotopes are investigated with the interactions SLy5+T,SLy5+Tw,SGII+Te1,SGII+Te2,SGII+Te3 and many sets of the TIJ interactions.All of the interactions are the Skyrme interactions and contain a tensor component(tensor force).It is shown that the evolution of the single-proton levels for the oxygen isotopes is sensitive to a parameterβTwhich is associated with the tensor force strength of the Skyrme interactions.To understand this phenomenon,we systematically analyze the dependence of the spin-orbit splittings and shell gaps on the parameterβTin terms of the spin-orbit potential and the corresponding wave function.We find that the Skyrme interactions can be classified into two groups:(a)T21,T32,T43,T54,SLy5+T,SLy5+Tw,SGII+Te1 and SGII+Te2,which can roughly reproduce the experimental shell gaps of the oxygen isotopes;(b)T1J and SGII+Te3,which can not reproduce the experimental shell gaps.     

Ground-State Properties of Ca Isotopes and the Density Dependence of the Symmetry Energy

A relativistic mean field model is used to study the ground-state properties of neutron-rich nuclei in Ca isotopes. An additional isoscalar and isovector nonlinear coupling has been introduced in the relativistic mean field model, which could soften the symmetry energy, while keep the agreement with the experimental data. The sensitivity of proton and neutron density distributions and single particle states in Ca isotopes to the additional isoscalarisovector nonlinear coupling term is investigated. We found that the binding energies, the density distributions of single particle levels are strongly correlated with the density dependence of the symmetric energy in nuclear matter.     

Calculation of the ground state properties of even-even Sn isotopes

We investigate the ground-state properties of even-even Sn isotopes using the Skyrme-Hartree-Fock (SHF) and Skyrme-Hartree-Fock-Bogolyubov (SHFB) methods with SKM* and SLy4 force parameters. We focus on isotopes of even-even Sn because these isotopes are vital to the structural studies of unstable nuclei taking place at the electron radioactive-ion collider at RIKEN. In the present paper, we calculate the binding energies per particle, the rms nuclear charge radii, the rms nuclear proton density radii, and the rms nuclear neutron density radii, for even-even Sn isotopes, using the SHF and SHFB methods. We compare our results with experimental data and with the results of relativistic mean-field theory. Notably, we fit our calculated binding energies per particle to experimental results, using the aforementioned SHF methods with SKM* and SLy4 parameters     

轻核区双中子滴线核的研究

运用形变相对论平均场（RMF）理论系统地研究了轻核区的元素O, Ne, Mg, Si, S, Ar和 Ca及Ni。 计算了这8个元素的偶 偶核基态的一些性质, 如结合能、 四极形变、 平均每核子结合能以及双中子分离能等。 计算中采用了NL3参数组, 并用BCS方法处理对关联。 限于篇幅, 文中只给出O和Mg元素的计算结果。 RMF理论计算的结果和实验值基本一致。 从双中子分离能的分析可知, RMF理论计算的各元素的双中子滴线核分别为 30O, 38Ne, 42Mg, 52Si, 54S, 60Ar, 80Ca和98Ni。 最后简单讨论了Ca和Ni同位素中的中子幻数情况。 The ground state properties of even even O, Ne, Mg, Si, S, Ar, Ca and Ni isotopes were studied with the self consistent deformed relativistic mean field theory with NL3 parameter set. The calculated results of O and Mg isotopes were presented in detail. The calculated binding energies and the two neutron separation energies were in good agreement with experimental values. By examining the two neutron separation energies, it was suggested that 30O, 38Ne, 42Mg, 52Si, 54S, 60Ar, 80Ca and 98Ni are the two neutron drip line nuclei. We also briefly discussed the possible changes of neutron magic numbers in Ca and Ni isotopes. Key words: relativistic mean field; drip line nucleus; two neutron separation energy     

The neutron halo structure of 17B studied with the relativistic Hartree-Bogoliubov theory

The properties of neutron-rich boron isotopes are studied in the relativistic continuum Hartree-Bogoliubov theory in coordinate space with NL-SH, PK1 and TM2 effective interactions. Pairing corrections are taken into account by a density dependent force of zero range. The binding energies calculated for these nuclei agree with the experimental data quite well. The neutron-rich nucleus ¹⁷B has been predicted to have a two-neutron halo structure in its ground state. The halo structure of ¹⁷B is reproduced in a self-consistent way, and this halo is shown to be formed by the valence neutron level 2_s1/2.     

Investigation of neutron and proton distributions of He,Li, and Be isotopes using the new Skyrme-Force parameters

The proton and neutron densities, root-mean-square (rms) radii of proton density and neutron density, and neutron skin thickness of ^4–10He, ^6–11Li, and ^7–12Be isotopes are calculated using Skyrme-Hartree-Fock method with SLy4, SLy5, SLy6, and SLy7 force parameters. The evaluated results are compared with experimental data. Also, the results of halo nuclei (^6,8He, ¹¹Li, and ¹¹Be) are compared with the results of other isotopes for selected nuclei having the same neutron configuration.     

Properties of Zr isotopes near the neutron drip line and beyond it

The properties of neutron-rich Zr isotopes up to the neutron drip line and beyond it have been investigated on the basis of the Hartree-Fock method with the Skyrme forces (Ska, Sly4), taking into account the deformation. By the example of chains of Zr isotopes, good agreement is shown for the two-neutron separation energies and mean-square radii with the known results of Hartree-Fock-Bogolyubov calculations with the Sly4 forces. For the extremely neutron-rich Zr isotopes, states with very large deformation parameters (β ≈ 0.4?0.45) of neutron and proton density distributions can be realized. Beyond the neutron drip line with respect to emission of two neutrons, the existence of ^150,152Zr isotopes, which are stable with respect to one-neutron emission, is predicted.     

Properties of Zr hypernuclei in deformed Skyrme Hartree-Fock approach

Properties of the even-N Zr isotopes and their corresponding single-Λ and double-Λ hypernuclei are studied in the deformed Skyrme-Hartree-Fock approach. Binding energy, the two-neutron separation energies, radii are studied from beta-stable zone to the neutron drip line in this paper. The neutron drip line nuclei predicted with SLy4 and SkI4 interactions are 122Zr and 138Zr, respectively. The neutron drip line of single-Λ and double-Λ hypernuclei are Λ139Zr and 2Λ142 Zr with SkI4 interaction, respectively. The predicted hyperon drip line hypernuclei with 80Zr and 138Zr cores are 20Λ100Zr and 50Λ188Zr, respectively.     

The neutron drip line in the region of <Emphasis Type="Italic">N</Emphasis>=20 and <Emphasis Type="Italic">N</Emphasis>=28 closures

Experimental studies of neutron drip line nuclei are introduced. The neutron drip line in the oxygen-magnesium region has been explored by the projectile fragmentation of a ⁴⁸Ca beam. New neutron-rich isotopes, ³⁴Ne and ³⁷Na, have been observed together with some evidence for the particle instability of ³³Ne and ³⁶Na. Recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells, and together with the measurements of instability of doubly magic nuclide ²⁸O, they provide information on changes in neutron shell closures of very neutron-rich isotopes from carbon up to calcium. The conclusion about a rearrangement in neutron shell closures is given. The spectroscopic measurements can reveal details of the underlying microscopic structures; in-beam γ-ray spectroscopy is an effective tool to check for shell closures. The results on the γ-ray energies of the first 2⁺ level in even-even nuclei for the range N=12–32 are discussed. The strength of N=20 and N=28 shells is variable in the region from carbon up to magnesium.     

New precision mass measurements of neutron-rich calcium and potassium isotopes and three-nucleon forces

We present precision Penning trap mass measurements of neutron-rich calcium and potassium isotopes in the vicinity of neutron number N=32. Using the TITAN system, the mass of ^{51}K was measured for the first time, and the precision of the ^{51,52}Ca mass values were improved significantly. The new mass values show a dramatic increase of the binding energy compared to those reported in the atomic mass evaluation. In particular, ^{52}Ca is more bound by 1.74?MeV, and the behavior with neutron number deviates substantially from the tabulated values. An increased binding was predicted recently based on calculations that include three-nucleon (3N) forces. We present a comparison to improved calculations, which agree remarkably with the evolution of masses with neutron number, making neutron-rich calcium isotopes an exciting region to probe 3N forces.     

Clustering in neutron-rich nuclei

Clustering in nuclei is discussed putting emphasis on the investigation of the role of nuclear clustering in neutron-rich nuclei. The subjects we discuss include clustering in neutron-rich Be, B and C isotopes, clustering in the island of inversion around N = 20, and clustering in the region with A ≈ 40. Be isotopes present us typical examples of clustering in neutron-rich nuclei not only in their ground band states but also in their excited band states, for which we show the analyses based on antisymmetrized molecular dynamics (AMD). Clustering in Be isotopes near neutron dripline is intimately related to the breaking of the neutron magic number N = 8. In this connection we report our study about the possible relation of the clustering with the breaking of the neutron magic number N = 20 in the island of inversion including ³²Mg and ³⁰Ne. Our discussion is not only about the positive parity states but also about negative parity states. Recently in the latter half of sd shell and in the pf shell many excited rotational bands with large deformation have been found to exist. Since the first excited K ^π = 0⁺ and K ^π = 0^- bands in ⁴⁰Ca have been regarded as constituting inversion doublet bands having the ³⁶Ar + α structure, and since the first excited K ^π = 0^- band in ⁴⁴Ti has been concluded to have ⁴⁰Ca + α structure through the α transfer reaction and by using the unique α optical potential on ⁴⁰Ca, it is important to investigate the role of α clustering in these newly-found rotational bands with large deformation. We will report the AMD study about this problem.     

A new probe of neutron skin thickness

The correlation between neutron-to-proton yield ratio (R<,n p>) and neutron skin thickness (δ<,n p>) in neutron-rich projectile induced reactions is investigated within the framework of the Isospin-Dependent Quantum Molecular Dynamics (IQMD) model. The density distribution of the Droplet model is embedded in the initialization of the neutron and proton densities in the present IQMD model. By adjusting the diffuseness parameter of neutron density in the Droplet model for the projectile, the relationship between the neutron skin thickness and the corresponding R<,n p> is obtained. The results show strong linear correlation between R<,n p> and δ<,n p> for neutron-rich Ca and Ni isotopes. It is suggested that R<,n p> may be used as an experimental observable to extract δ<,n p> for neutron-rich nuclei, which is very interesting in the study of the nuclear structure of exotic nuclei, the equation of state (EOS) of asymmetric nuclear matter and neutron-rich matter in astrophysics, etc.     

Rearrangements in neutron shell closures far from stability

A survey of experimental results obtained at GANIL (Caen, Prance) on the study of the properties of very neutron-rich nuclei (Z = 6–20, A = 20–60) near the neutron drip line and resulting in an appearance of further evidence for the new magic number N = 16 is presented. Very recent data on mass measurements of neutron-rich nuclei at GANIL and some characteristics of binding energies in this region are discussed. Nuclear binding energies are very sensitive to the existence of nuclear shells and together with the measurements of instability of doubly magic nuclei ¹⁰He and ²⁸0 they provide information on changes in neutron shell closures of very neutron-rich isotopes. The behaviour of the two-neutron separation energies S_2n derived from mass measurements gives a very clear evidence for the existence of the new shell closure N = 16 for Z = 9 and 10 appearing between 2s_1/2 and ld_3/2 orbitals. This fact, strongly supported by the instability of C, N and O isotopes with N > 16, confirms the magic character of N = 16 for the region from carbon up to neon while the shell closure at N = 20 tends to disappear for Z ≤ 13. Decay studies of these hardly accessible short-lived neutron-rich nuclei from oxygen to silicon using the in-beam γ-ray spectroscopy are also reported.     

Proton magic even-even isotopes and giant halos of Ca isotopes with relativistic continuum Hartree-Bogoliubov theory

We study the proton magic O, Ca, Ni, Zr, Sn, and Pb isotope chains from the proton drip line to the neutron drip line with the relativistic continuum Hartree-Bogoliubov (RCHB) theory. Particulary, we study in detail the properties of even-even Ca isotopes due to the appearance of giant halos in neutron rich Ca nuclei near the neutron drip line. The RCHB theory is able to reproduce the experimental binding energiesE _b and two neutron separation energiesS _2n very well. The predicted neutron drip line nuclei are²⁸O,⁷²Ca,⁹⁸Ni,¹³⁶Zr,¹⁷⁶Sn, and²⁶⁶Pb. Halo and giant halo properties predicted in Ca isotopes withA>60 are investigated in detail through analysis of two neutron separation energies, nucleon density distributions, single particle energy levels, and the occupation probabilities of energy levels including continuum states. The spin-orbit splitting and the diffuseness of nuclear potential in these Ca isotopes, as well as the neighboring lighter isotopes in the drip line Ca region and find certain possibilities of giant halo nuclei in the Ne−Na−Mg drip line nuclei are also studied.     

Target mass correction on the 3He polarized structure function

The diffusion-effusion model has been used to analyse the release and yields of Fr and Cs isotopes from uranium carbide targets of very different thicknesses (6.3 and 148 g/cm²) bombarded by a 1 GeV proton beam. Release curves of several isotopes of the same element and production efficiency versus decay half-life are well fitted with the same set of parameters. Comparison of efficiencies for neutron-rich and neutron-deficient Cs isotopes enables separation of the contributions from the primary (p + ²³⁸U) and secondary (n + ²³⁸U) reactions to the production of neutron-rich Cs isotopes. A rather simple calculation of the neutron contribution describes these data fairly well. The FLUKA code describes the primary and secondary-reaction contributions to the Cs isotopes production efficiencies for different targets quite well.     

New evidence for a subshell gap at N=32

An 879.9(2) keV γ-ray transition has been identified following the β decay of ⁵⁸V and assigned as the 2⁺₁→0⁺₁ transition in ⁵⁸Cr₃₄. A peak in the energies of the first excited 2⁺ states for the even–even chromium isotopes is now evident at ⁵⁶Cr₃₂, providing empirical evidence for a significant subshell gap at N=32. The appearance of this neutron subshell closure for neutron-rich nuclides may be attributed to the diminished π1f_7/2–ν1f_5/2 monopole proton–neutron interaction as protons are removed from the 1f_7/2 single-particle orbital.