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.

A relativistic continuum Hartree-Bogoliubov theory description of N=3 isotones

The ground-state properties of N=3 isotones and mirror nuclei have been investigated in the Rrelativistic Continuum Hartree-Bogoliubov theory with the NLSH effective interaction. Pairing correlations are taken into account by a density-dependent 5-force. The calculations show that the proton density distributions of SB and 9C have a long tail, the core has an increasing tendency of 9C and the paired off valence protons make the halo distribution shrink. The cross sections for the 8B（gC）＋12C reaction which are consistent with the experimental data are calculated using the Glauber model. On the whole, we think that SB is a one-proton halo nucleus and 9C is a two-proton halo nucleus.

Inner fission barriers of uranium isotopes in the deformed relativistic Hartree-Bogoliubov theory in continuum

The inner fission barriers of the even-even uranium isotopes from the proton to the neutron drip line are examined using the deformed relativistic Hartree-Bogoliubov theory in continuum.A periodic-like evolution for the ground state shapes is shown with respect to the neutron number,i.e.,spherical shapes at shell closures 126,184,258,and prolate dominated shapes between them.Analogous to the shape evolution,the inner fission barriers also exhibit a periodic-like behavior:peaks at the shell closures and valleys in the mid-shells.The triaxial effect on the inner fission barrier is evaluated using triaxial relativistic mean field calculations combined with a simple BCS method for pairing.When the triaxial correction is included,the inner barrier heights show good consistency with available empirical data.Additionally,the evolution from the proton to the neutron drip line aligns with results from the multi-dimensionally constrained relativistic mean field theory.A flat valley in the fission barrier height is predicted around the neutron-rich nucleus U which may play a role of fission recycling in astrophysical r-process nucleosynthesis.

相对论连续谱Hartree-Bogoliubov理论对Er偶同位素链的研究

基于相对论连续谱Hartree-Bogoliubov(RCHB)理论,在NL-SH参数下,研究了从质子滴线到中子滴线Er偶同位素链的基态特性,计算的核结合能和核均方根半径,在有实验数据进行比较的范围内,与实验数据值符合较好。计算结果显示:在中子数为N=82-126的壳层里,在84-92、94-126之间有明显的子壳层结构;62582Er184核是中子滴线核。

Mass predictions of the relativistic continuum Hartree-Bogoliubov model with radial basis function approach

The radial basis function(RBF) approach is a powerful tool to improve nuclear mass predictions. By combining the RBF approach with the latest relativistic continuum Hartree-Bogoliubov(RCHB) model, the local systematic deviations between the RCHB mass predictions and the experimental data are eliminated, and the root-meansquare(rms) mass deviation is significantly reduced from 7.923 MeV to 0.386 MeV. However, systematic deviations between the RBF improved mass predictions and the experimental data remain for nuclei with four different odd-even parities, i.e.(even Z, even N),(even Z, odd N),(odd Z, even N), and(odd Z, odd N). They can be reduced by separately training RBF for the four groups of nuclei, and the resulting rms deviation decreases to 0.229 MeV. It is found that the RBF approach can describe the deformation effects neglected in the present RCHB mass calculations, and also improves the description of the shell effect and the pairing effect.

Examination of machine learning for assessing physical effects:Learning the relativistic continuum mass table with kernel ridge regression

The kernel ridge regression(KRR)method and its extension with odd-even effects(KRRoe)are used to learn the nuclear mass table obtained by the relativistic continuum Hartree-Bogoliubov theory.With respect to the binding energies of 9035 nuclei,the KRR method achieves a root-mean-square deviation of 0.96 MeV,and the KRRoe method remarkably reduces the deviation to 0.17 MeV.By investigating the shell effects,one-nucleon and twonucleon separation energies,odd-even mass differences,and empirical proton-neutron interactions extracted from the learned binding energies,the ability of the machine learning tool to grasp the known physics is discussed.It is found that the shell effects,evolutions of nucleon separation energies,and empirical proton-neutron interactions are well reproduced by both the KRR and KRRoe methods,although the odd-even mass differences can only be reproduced by the KRRoe method.

Triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis

A triaxially deformed relativistic Hartree–Bogoliubov theory in the Woods–Saxon basis is developed with the aim of treating the triaxial deformation,pairing correlations and continuum in a unified way.In order to consider the triaxial deformation,the deformed potentials are expanded in terms of spherical harmonic functions in the coordinate space.In order to take the pairing correlations into account and treat the continuum properly,by using the Dirac Woods–Saxon basis,which has correct asymptotic behavior,the relativistic Hartree–Bogoliubov equation with triaxial deformation is solved.The formalism of triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is presented.Taking an axially deformed nucleus24Ne and a triaxially deformed nucleus76Ge as examples,the numerical checks are performed.A weakly bound nucleus112Ge is taken as an example to carry out the necessary converge checks for the numerical parameters.In addition,the ground-state properties of even–even germanium isotopes are investigated.The evolutions of two-neutron separation energy,deformation,root-mean-square radii and density distribution with mass number are analyzed.The comparison between the calculations from the relativistic Hartree–Bogoliubov theory based on harmonic-oscillator basis and the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis is performed.It is found that the neutron drip line is extended from114Ge to118Ge in the triaxially deformed relativistic Hartree–Bogoliubov theory in Woods–Saxon basis.

奇特核和超核中的晕现象

讨论奇特核和超核中的各种晕现象 .根据密度相关零程对力的相对论连续谱Hartree Bo goliubov理论给出的计算结果 ,预言了中子滴线附近的Ca原子核中可能存在着巨晕 ,并简要介绍了O ,Ni,Zr ,Sn和Pb等一些质子幻数核从质子滴线到中子滴线之间的原子核基态性质 .随后给出超核内的晕现象研究 ,如Ca超核内的中子晕和153ΛC内的单Λ超子晕 .

滴线原子核中的晕现象——中子晕、超子晕、巨晕和形变晕

描述了相对论连续谱Hartree Bogoliubov理论框架下的多种可能的晕现象。预言了中子滴线附近的Ca原子核中可能存在着巨晕 ,并简要介绍了O、Ni、Zr、Sn和Pb等一些质子幻数核从质子滴线到中子滴线之间的原子核基态性质。随后给出超核内的晕现象研究 ,如Ca超核内的中子晕和153ΛC内的单Λ超子晕。此外 ,还讨论了形变晕等奇特现象。

多Λ超核基态性质的研究

依据多Λ超核在高能重离子碰撞或天体物理中实现的可能性,以Ca为例,用相对论连续谱Hartree-Bogoliubov理论研究了系统的基态性质,包括每重子结合能、重子均方根半径和超核物质半径以及单粒子能谱等。研究表明,随着超子数目的增加,超核的每重子结合能和超子均方根半径变化趋势平缓,在5100ΛCa等一些超核内超子2s1/2和1d5/2能级排列有明显的反转,丰质子区和总核子数不变的多Λ钙超核滴线所对应的最大超子数分别为6和22。

轻核区中子晕结构的系统研究

在相对论连续谱Hartree-Bogoliubov(RCHB)理论框架下,采用非线性核子-核子有效相互作用NL-LN参数组系统计算了从锂到镁(3≤Z≤12)同位素原子核的基态性质,包括中子、质子和物质均方根半径以及密度分布.计算结果不仅再现了中子晕候选核11Li,11Be,14Be和17B中的中子晕现象,而且还预言了13Be,14,15B,31F,23,24O和31,32,34Ne也存在中子晕.

放射性核束为核物理和核天体物理提供的新机遇

简要介绍了有关放射性核束的研究现况， 特别是它为核物理和核天体物理提供的研究机遇， 以及相对论连续谱 Ｈａｒｔｒｅｅ Ｂｏｇｏｌｉｕｂｏｖ

基于形变相对论连续谱Hartree-Bogoliubov理论构建高精度原子核质量表

质量是原子核最基本的物理量之一,是理解核子间相互作用、揭示壳结构演化和确定滴线位置的关键,是研究核反应和核衰变的基本信息,同时也是探索元素起源等问题必需的核物理输入量,对粒子物理与核物理、天体物理和宇宙学等学科至关重要.尽管短寿命原子核质量的测量工作已经取得很大进展,但是在可预见的将来,大部分远离稳定谷的奇特原子核质量仍依赖理论模型预言和计算.本文介绍了原子核质量模型的重要发展历程、相对论密度泛函理论描述原子核现象的成功、基于相对论连续谱Hartree-Bogoliubov理论构建的目前唯一考虑连续谱效应的原子核质量表,以及拟基于形变相对论连续谱Hartree-Bogoliubov理论建立高精度原子核质量表的最新进展和展望.

Extending the nuclear chart by continuum:From oxygen to titanium

Nuclear masses ranging from O to Ti isotopes are systematically investigated with relativistic continuum Hartree-Bogoliubov(RCHB)theory,which can provide a proper treatment of pairing correlations in the presence of the continuum.From O to Ti isotopes,there are 402 nuclei predicted to be bound by the density functional PC-PK1.For the 234 nuclei with mass measured,the root mean square(rms)deviation is 2.23 MeV.It is found that the proton drip-lines predicted with various mass models are roughly the same and basically agree with the observation.The neutron drip-lines predicted,however,are quite diferent.Due to the continuum couplings,the neutron drip-line nuclei predicted are extended further neutron-rich than other mass models.By comparison with finite-range droplet model(FRDM),the neutron drip-line nucleus predicted by RCHB theory has respectively2(O),10(Ne),10(Na),6(Mg),8(Al),6(Si),8(P),6(S),14(K),10(Ca),10(Sc),and 12(Ti)more neutrons.

Nuclear chart in covariant density functional theory with dynamic correlations: From oxygen to tin

Nuclear masses of even-even nuclei with the proton number 8≤Z≤50(O to Sn isotopes)from the proton drip line to neutron drip line are investigated using the triaxial relativistic Hartree-Bogoliubov theory with the relativistic density functional PC-PK1.Further,the dynamical correlation energies(DCEs)associated with the rotational motion and quadrupole-shaped vibrational motion are taken into account by the five-dimensional collective Hamiltonian(5DCH)method.The root-mean-square deviation with respect to the experimental masses reduces from 2.50 to 1.59 MeV after the consideration of DCEs.The inclusion of DCEs has little influence on the position of drip lines,and the predicted numbers of bound even-even nuclei between proton and neutron drip lines from O to Sn isotopes are 569 and 564 with and without DCEs,respectively.

_Λ~ACa和_(ΛΛ)~ACa超核中的巨中子晕现象

利用密度相关零程对力的相对论连续谱Hartree Bogoliubov方法 ,对偶中子数的Ca同位素从质子滴线到中子滴线范围内的单Λ超核和双Λ超核基态性质进行了系统研究 .与通常的原子核相比 ,单Λ超核和双Λ超核中超子提供的吸引力会相应地降低中子费米面 .所预言的中子滴线超核分别为77ΛCa和78ΛΛCa ,比原来预测的通常滴线核74Ca多两个中子 .基于对双中子分离能、中子密度分布、半径、单粒子能谱、轨道占据数和连续谱贡献的分析 。

Effects of Parametrization of A Woods–Saxon Potential on Single Particle Orbits in ^(66)Ca

A Woods–Saxon potential is introduced to serve as initial conditions for an iterative solution of the exotic nuclei in relativistic mean field approach. Effects of parametrization of the Woods–Saxon potential on single particle orbits around the Fermi surface are investigated in66Ca. A semi-parabolic curve of orbital radius appears when the width of the central potential changes. The pseduospin splitting is more sensitive to the potential width than to the depth and the diffuseness. The spin-orbit splitting is more sensitive to the potential depth than to the width and the diffuseness.

Nuclear structure around ^(80)Zr

Recent years have witnessed intense activity concerning the study of nuclei with equal numbers of neutrons and protons （N = Z）. Exotic properties have been exhibited in the N = Z nuclei, especially in those with atomic masses around 80. In the present paper, the projected shell model（PSM）together with a relativistic Hartree-Bogoliubov （RHB） theory is used to study the nuclear structure near the N = Z line in the mass A ≈ 80 region. For three Zr isotopes 80,82,84Zr, the projected potential energy surfaces and ground state bands are calculated. It is shown that shape coexistence occurs in all of these nuclei. Moreover, we find that the residual neutron-proton interaction strongly affects the ground state band of 80Zr; however, it slightly modifies those of 82Zr and 84Zr.