Half-lives of double β~+-decay with two neutrinos

Nuclear doubleβ--decays with two neutrinos were observed for many years and a systematic law describing the relation between their half-lives and decay energies was also proposed recently[Phys Rev C,2014,89:064603].However,doubleβ+-decay(β+β+)with emission of both two positrons and two neutrinos has not been observed up to date.In this article,we perform a systematic analysis on the candidates of doubleβ+-decay,based on the 2012 nuclear mass table.Eight nuclei are found to be the good candidates for doubleβ+-decay and their half-lives are predicted according to the generalization of the systematic law to doubleβ+-decay.As far as we know,there is no theoretical result on doubleβ+-decay of nucleus154Dy and our result is the first prediction on this nucleus.This is also the first complete research on eight doubleβ+-decay candidates based on the available data of nuclear masses.It is expected that the calculated half-lives of doubleβ+-decay in this article will be useful for future experimental search of doubleβ+-decay.     

Competition between α-decay and β-decay for heavy and superheavy nuclei

In this work, the β-stable region for Z 90 is proposed based on a successful binding energy formula.The calculated β-stable nuclei in the β-stable region are in good agreement with the ones obtained by Mo¨ller et al. The half-lives of the nuclei close to the β-stable region are calculated and the competition between α-decay andβ-decay is systematically investigated. The calculated half-lives and the suggested decay modes are well in line with the experimental results. The decay modes are mostly β--decay above the β-stable region. Especially for Z 111,all the decay modes are β--decay. Regarding the nuclei above the β-stable region, α-decay and β--decay(α+β-)can occur simultaneously when Z 112. This is a very interesting phenomenon. The competition between α-decay and β-decay is very complex and drastic below the β-stable region. The predictions for half-lives and decay modes of the nuclei with Z =107–110 are presented in detail.     

Generalization of α-Decay Cluster-Model to Nuclei Near Spherical and Deformed Shell Closures

The cluster model of α-decay is extended to the regions around doubly magic spherical nucleus 208pb and around deformed shell closure 270Hs, respectively. The effects of spherical shell closures (N = 126 and Z = 82) on α-decay are investigated by introducing an N-dependent α-preformation factor and a Z-dependent one inspired by a microscopic model. Good agreement between the theoretical α-decay half-lives and the measured ones is obtained for the spherical nuclei near the doubly magic nucleus 208 Pb, where the nuclear shell effect is included in the expression of α-preformation factor. The cluster model is also generalized for the decay of deformed nuclei. The branching ratios of a-decays from the ground state of a parent nucleus to the ground state (0 ) of its deformed daughter nucleus and to the first excited state (2 ) are .calculated in the framework of the cluster model. The results indicate that a measurement of c spectroscopy is a feasible method to extract the information of nuclear deformation of superheavy nuclei around the deformed nucleus 270 Hs.     

Competition between α-decay and β-decay for heavy andsuperheavy nuclei

In this work, the β-stable region for Z≥90 is proposed based on a successful binding energy formula. The calculated β-stable nuclei in the β-stable region are in good agreement with the ones obtained by Möller et al. The half-lives of the nuclei close to the β-stable region are calculated and the competition between α-decay and β-decay is systematically investigated. The calculated half-lives and the suggested decay modes are well in line with the experimental results. The decay modes are mostly β^--decay above the β-stable region. Especially for Z≤111, all the decay modes are β^--decay. Regarding the nuclei above the β-stable region, α-decay and β^--decay (α+β^-) can occur simultaneously when Z≥112. This is a very interesting phenomenon. The competition between α-decay and β-decay is very complex and drastic below the β-stable region. The predictions for half-lives and decay modes of the nuclei with Z=107-110 are presented in detail.     

α结团模型在形变核区域的推广

将α结团模型推广至形变核,计算偶偶形变母核α衰变基态到子核基态和子核第一激发态的分支比,显示出α衰变精细结构的测量是提取核形变信息的有效手段.The cluster model of α-decay is extended to deformed nuclei. The branching ratios of α-decays from the ground state of a parent nucleus to the ground state 0~(+) of its deformed daughter nucleus and to the first excited state 2~(+) are calculated in the framework of the cluster model. The results indicate that a measurement of α spectroscopy is a feasible method to extract the information of nuclear deformation.     

Nuclear mass parabola and its applications

We propose a method for extracting the properties of the isobaric mass parabola based on the total doubleβ-decay energies of isobaric nuclei.Two important parameters of the mass parabola,the location of the most β-stable nuclei Z_A and the curvature parameter b_A,are obtained for 251 A values,based on the total double β-decay energies of nuclei compiled in the AME2016 database.The advantage of this approach is that the pairing energy term P_A caused by the odd-even variation can be removed in the process,as well as the mass excess M(A,Z_A) of the most stable nuclide for the mass number A,which are employed in the mass parabolic fitting method.The Coulomb energy coefficient a_c=0.6910 MeV is determined by the mass difference relation for mirror nuclei,and the symmetry energy coefficient is also studied by the relation a_(sym)(A)=025 b_AZ_A.     

The contribution of the first forbidden transitions to the nuclear β~--decay half-life

β-decay half-life is a key quantity for nuclear structure and nucleosynthesis studies.There exist large uncertainties in the contributions of allowed and forbidden transitions to the total β-decay life,which limits the resolution of the predicted β-decay half-life.We systematically study the contribution of the first forbidden(FF) transitions to the β~--decay half-life,and quantify it with a formula based on simple physics considerations.We also propose a new formula for calculation of the β~--decay half-life that includes the FF contribution.It is shown that the inclusion of the contribution of FF transitions significantly improves the precision of calculations of the β~--decay half-life.By fitting of the RQRPA results for neutron-rich Z=47,57 isotopes and N=80,94 isotones,the formula for the contribution of the FF transitions gives similar results as the RQRPA calculations.However,because of limited experimental data for the branching ratios of unstable nuclei,the fit parameters are not fully constrained.Therefore,the proposed formula for the β~--decay half-life is more suitable for calculations of half-lives than of the FF contributions.The formula could be used to predict the β~--decay half-life in nuclear structure studies as well as nucleosynthesis calculations in stars.     

Generalization of α-Decay Cluster-Model to Nuclei Near Spherical and Deformed Shell Closures

The cluster model of a-decay is extended to the regions around doubly magic spherical nucleus ^208Pb and around deformed shell closure ^270Hs, respectively. The effects of spherical shell closures (N=126 and Z=82) on α-decay are investigated by introducing an N-dependent α-preformation factor and a Z-dependent one inspired by a microscopic model. Good agreement between the theoretical a-decay half-lives and the measured ones is obtained for the spherical nuclei near the doubly magic nucleus ^208Pb, where the nuclear shell effect is included in the expression of α-preformation factor. The cluster model is also generalized for the decay of deformed nuclei. The branching ratios of α-decays from the ground state of a parent nucleus to the ground state (0^ ) of its deformed daughter nucleus and to the first excited state (2^ ) are calculated in the framework of the cluster model. The results indicate that a measurement of α spectroscopy is a feasible method to extract the information of nuclear deformation of superheavy nuclei around the deformed nucleus ^270Hs.     

Systematical law of β+-decay half-lives of nuclei far from β-stable line

Experimental data of nuclear β⁺-decay half-lives are systematically analyzed and investigated. We present an exponential law between the half-life of β⁺-decay with the same forbiddenness and the nucleon number (Z,N) of parent nucleus far from the β-stable line. A formula with four parameters is proposed to describe the β⁺-decay half-lives of nuclei far from stability. Experimental β⁺-decay half-lives of the first and second forbidden transitions are well reproduced by this simple formula. The physics of the exponential law is related to the statistical properties of β⁺-decay far from β-stable line.     

Fully self-consistent calculation ofβ-decay half-lives within Skyrme energy density functional

β-decay half-lives of some magic and semi-magic nuclei have been studied in a fully self-consistent Skyrme Hartree-Fock(HF) plus charge-exchange random phase approximation(RPA).The self-consistency is addressed,in that the same Skyrme energy density functional is adopted in the calculation of ground states and Gamow-Teller excited states.First,the impact of J2 terms on the β-decay half-lives is investigated by using the SGII interaction,revealing a large influence.Subsequently,numerical calculations are performed for the selected nuclei with Skyrme energy density functionals SGII,LNS,SKX,and SAMi.Finally,comparisons to available experimental data and predictions of different theoretical models are discussed.     

Semi-gross theory of nuclear β-decay

The gross theory of β-decay is refined to take into account shell effects of the parent nuclei, and the resulting theory is named semi-gross theory. In this theory, the one-particle energy distribution in the parent nucleus is taken to have structures, and the one-particle strength function is assumed to depend on the quantum numbers of the initial state of the decaying nucleon. β-decay (partial) half-lives are calculated for 1659 nuclides, and the results are compared with experimental data as well as with those calculated by the gross theory. The β-decay strength functions are shown for two selected nuclides, and briefly discussed. These numerical studies confirm that the semi-gross theory includes some part of the shell effects correctly, although there still remain deviations of the theoretical results from experimental data, which should, at least partly, be due to shell effects of the daughter nuclei. Comparison of the present results with microscopic theories shows that the overall accuracy of the semi-gross theory is comparable with those of the microscopic theories.     

sd壳层极丰质子核的β延迟衰变谱学

远离β稳定线原子核的结构是当前核物理领域的一个前沿热点。β衰变谱学是研究核结构的重要方法,尤其适用于低产额的滴线核。本文回顾了近年来在RIBLL1装置上开展的sd壳区极丰质子核β延迟衰变谱学的实验研究。该工作获得了15个原子核精确的半衰期、衰变子核的质量、β延迟的质子和双质子发射以及$\gamma $跃迁的能谱、分支比和比较半衰期等数据,并重建了衰变纲图,大大丰富了此区域内质子滴线附近原子核的衰变谱学信息。还介绍了探测器阵列和实验方法,概括了所研究核的衰变性质和半衰期等。特别地,对几个典型核,20Mg和22Si以及26P和27S的衰变性质进行了阐述。此外,对相关话题,如三体力、镜像核衰变不对称性、与银河系中26Al超丰问题相关的热核反应率等问题进行了探讨。     

Structure of β-decay Strength Function <Emphasis Type="Italic">S</Emphasis><Subscript>β</Subscript>(<Emphasis Type="Italic">E</Emphasis>) in Halo Nuclei

It is shown that when the parent nucleus has nn Borromean halo structure, then after Gamow–Teller (GT) β^–-decay of parent state or after M1 γ-decay of Isobar Analogue Resonance (IAR) the states with np tango halo structure or mixed np tango + nn Borromean halo structure can be populated. Resonances in the GT β-decay strength function S_β(E) of halo nuclei, may have np tango halo structure or mixed np tango + nn Borromean halo structure. Correct interpretation of halo structure is important in experiments on β-decay study, interpretation of M1 γ-decay of IAR, and charge-exchange nuclear reactions analysis.     

Isobaric spin mixing from self-consistent treatment of coulomb interaction

From a self-consistent independent-particle model of the nucleus, isobaric spin mixing in the ground state of nuclei is calculated for the mass region 4 < A < 208. From this model, allowed Fermi β-decay matrix elements are calculated. The Coulomb energy differences calculated from our model turn out to be about the same as those obtained from the (p, n) reaction data. A relation of the direct Coulomb energy of a nucleus to its elastic form factor is pointed out.     

Suppression of the β+-decays of 148Dy, 150Er and 152Yb

We use the quasi-particle random-phase approximation (QRPA) with a realistic effective nucleon-nucleon interaction to describe the positron β⁺-decay of the neutron-deficient single-closed-shell nuclei ¹⁴⁸₆₆Dy₈₂, ¹⁵⁰₆₈Er₈₂ and ¹⁵²₇₀Yb₈₂ . In this framework we study the effect of the particle-particle interaction strength on the β⁺-transition strengths in these nuclei. We are able to reproduce the experimental strengths by reasonable values of the interation parameters, not very different from nucleus to nucleus.     

Beta-decay properties of exotic nuclei and the astrophysical r-process

The r-process abundances are evaluated with the use of three different β-decay models, i.e., the second version of the Gross Theory, the semi-Gross Theory and a QRPA approach. The necessary Q_β-values, as well as the neutron separation energies, are obtained from the TUYY, ETFSI and FRDM mass predictions. A comparison is made among the β-decay half-lives predicted by these β-decay models for the nuclei on a typical r-process path, as well as among the resulting r-process abundances.     

α-Decay calculations of medium mass nuclei within generalized density-dependent cluster model

The α-decay half-lives of even–even medium mass nuclei have been systematically investigated using a radial wave function within the generalized density-dependent cluster model. The α-decay width is calculated using the overlap integral of the quasi-bound initial state wave function, the scattering final state wave function, and the difference of potentials. The effective α–nucleus potential is constructed using the double-folded integral of realistic nucleon–nucleon interactions with the mass density distributions of α particles and daughter nuclei. For comparison calculations are also carried out for the Woods–Saxon shape potential. The present study is restricted to even–even nuclei with 82<N126, where the shell effect on the α-preformation factor has been taken into account for even–even N=126 isotones. The obtained α-decay half-lives are found to agree with the experimental data with a mean factor of less than 2 for both the double-folded potential and the Woods–Saxon shape potential.     

原子核Gamow-Teller共振和β衰变寿命的超越平均场描述

原子核的β衰变是决定宇宙中从铁到铀重元素合成的关键核过程之一。原子核β衰变的主导核跃迁是Gamow-Teller(GT)跃迁,因此,研究原子核β衰变寿命的关键是准确描述原子核的GT跃迁。描述原子核GT跃迁和β衰变寿命最常用的理论模型之一为无规相位近似(RPA)模型。然而,由于该模型仅考虑了一粒子一空穴激发组态,因此无法给出GT共振宽度,并容易高估β衰变寿命。为了克服上述困难,基于Skyrme密度泛函,发展了包含粒子振动耦合效应的无规相位近似(RPA+PVC)模型。相比于RPA模型,该模型在组态空间进一步考虑了一粒子一空穴和声子的耦合组态,从而包含了超越平均场的多体关联效应。为了推广至开壳原子核的研究,进一步考虑了对关联效应,发展了包含准粒子振动耦合效应的准粒子无规相位近似(QRPA+QPVC)模型。基于上述模型,研究了幻数原子核和超流原子核的GT跃迁、β衰变和β+/电子俘获。研究发现,采用同一组Skyrme相互作用参数SkM*,上述模型能够重现实验测量的GT共振宽度和跃迁强度分布,部分解释实验观测的GT跃迁强度压低问题,并同时改进对β衰变寿命的描述。该文针对上述最新研究进展进行了综述,并对将来的发展方向给出展望。     

利用改进的pn-QRPA模型研究等待点原子核的β衰变性质

r-过程等待点原子核的β衰变半衰期对研究宇宙中重元素起源有重要意义。质子-中子准粒子无规相位近似(pn-QRPA)是研究原子核β衰变的重要理论模型。本工作提出了一个改进的 pn-QRPA 模型,系统研究了满壳附近原子核的 β 衰变性质。与之前的工作相比,改进的模型采用了中子数和质子数依赖的新粒子-粒子和粒子-空穴相互作用形式。本工作首先计算了满壳附近一些已知原子核的 β衰变半衰期和 Gamow-Teller 强度分布,发现理论结果与实验数据符合较好,检验了新模型的可靠性。随后,理论预测了 $N=50$, $N=82$ 和 $N=126$附近未知的等待点原子核的 β衰变半衰期,如124Mo, 126Ru, 128Pd, 186Nd, 188Sm, 192Dy, 194Er, 196Yb, 198Hf等,预测结果与之前的模型相近。这些结果对未来满壳层附近的r-过程物理研究有参考价值。