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.     

Exploring the uncertainties in theoretical predictions of nuclear β-decay half-lives

Nuclear β-decay half-lives are predicted based on an empirical formula and the mass predictions from various nuclear models.It is found that the empirical formula can reproduce the nuclearβ-decay half-lives well,especially for short-lived nuclei with T_1/2<1s.The theoretical half-life uncertainties fromβ-decay energies and the parameters of the empirical formula are further investigated.It is found that the uncertainties of the half-lives are relatively large for heavy nuclei and nuclei near the neutron-drip line.For nuclei on the r-process path,the uncertainties for those with N=126 are about one order of magnitude,which are much larger than the uncertainties for those with N=50 and 82.However,theoretical uncertainties from the parameters of the empirical formula are relatively small for the nuclei on the r-process path,which indicates that the empirical formula is very suitable for predicting theβ-decay half-lives in r-process simulations.     

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.     

β~--Decay Half-Lives for Waiting Point Nuclei Around N=126

We have systematically analyzed the experimental β--decay half-lives of waiting point heavy nuclei around neutron number N = 126. A new set of parameters for the exponential formula of β~--decay half-lives is proposed. The forbidden transition effects are included in the new set of parameters self-consistently. Theoretical β~--decay half-lives of nuclei around N = 126 are compared with recent theoretical results and experimental data. It is found that the new theoretical results are in better agreement with experimental data. The unknown β~--decay half-lives of some nuclei in this region are predicted for studies on nuclear structure far from stability and the nucleosynthesis in stars.     

Calculation of double-β decay half-lives using an improved Primakoff-Rosen formula

A systematic analysis on experimental data of the half-lives of nuclear double-β decays with two neutrinos(2vββ) is performed based on the analytical formula proposed by Primakoff and Rosen.We improve the formula by considering the shell effects and refining the energy dependence of the phase-space factor.This improved formula can closely describe all available experimental half-lives of 2vβ~-β~-decays,both for ground-state transitions and transitions from ground states of parent nuclei to the first 0~+ excited states of daughter nuclei.The calculated half-lives agree with the experimental data of ground-state transitions of all known eleven nuclei with an average factor of 2.3.Further predictions are provided for 2vββ-decay candidates with decay energies above 0.5 MeV.We compare different theoretical predictions and emphasize the importance of experimental measurements on the half-lives of double-β transitions between the ground state of ~(48)Ca,~(76)Ge,and ~(136)Xe and the first 0~+ excited states of their corresponding daughter nuclei,which will be very useful for understanding the underlying mechanisms of double-β decays and for further studying the shell effects on nuclear transition matrix elements.     

Isospin effect on spontaneous fission half-lives of even-even nuclei

By using a new five-parameter formula derived from the WKB approximation, we systematically calculate the spontaneous fission half-lives of even-even nuclei with Z=90—108. The isospin effect is taken into account in the new formula. The calculated half-lives agree well with the experimental data. In addition, we predict the spontaneous fission half-lives of superheavy nuclei with Z=108—114. Our predictions may provide references for future experiments.     

Investigation of proton radioactivity with the effective liquid drop model

Proton radioactivity has been investigated using the effective liquid drop model with varying mass asymmetry shapes and effective inertial coefficients. An effective nuclear radius constant formula replaces the old empirical one in the calculations. The theoretical half-lives are in good agreement with the available experimental data. All the deviations between the calculated logarithmic half-lives and the experimental values are less than 0.8.The root-mean-square(rms) deviation is 0.523. Predictions for the half-lives of proton radioactivity are made for elements across the periodic table. From the theoretical results, there are 11 candidate nuclei for proton radioactivity in the region Z <51. In the region Z >83, no nuclei are suggested as probable candidate nuclei for proton radioactivity within the selected range of half-lives studied.     

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.     

Search for decay modes of heavy and superheavy nuclei

Spontaneous fission(SF) with a new formula based on a liquid drop model is proposed and used in the calculation of the SF half-lives of heavy and superheavy nuclei(Z = 90–120). The predicted half-lives are in agreement with the experimental SF half-lives. The half-lives of decay(AD) for the same nuclei are obtained by using the Wentzel-Kramers-Brillouin(WKB) method together with Bohr-Sommerfeld(BS) quantization condition considering the isospin-dependent effects for the cosh potential. The decay modes and branching ratios of superheavy nuclei(Z =104-118) with experimental decay modes are obtained, and the modes are compared with the experimental ones and with the predictions found in the literature. Although some nuclei have predicted decay modes that are different from their experimental decay modes, decay modes same as the experimental ones are predicted for many nuclei. The SF and AD half-lives, branching ratios, and decay modes are obtained for superheavy nuclei(Z = 119–120) with unknown decay modes and compared with the predictions obtained in a previous study. The present results provide useful information for future experimental studies performed on both the AD and SF of superheavy nuclei.     

Spherical and Deformed Shell Closures in Superheavy nuclei

The structure of superheavy nuclei has been studied using the macroscopic-microscopic model. The macroscopic energy was calculated with the continuous medium model in which the energy is expressed as a function of nucleon densities. The deformations and structures of superheavy nuclei were systematically investigated. Calculations reproduce well the available data of experimental α-decay energies and half-lives. The investigation of single-particle levels shows that the shell structure is deformation and isospin dependent. Potential-energy-surface calculations display that superheavy nuclei have in general harder shapes than the nuclei of other mass regions.     

Nuclear Level Density and Thermodynamic Functions for Nuclei with Static Deformation

The level densities of even-odd and even-even isotopes^161,162Dy,^166Er and ^171,172Yb were calculated using microscopic theory of interacting fermions and compared with experiments.It is found that the data can be well reproduced with level density formalism for nuclei with static deformation.The nuclear temperature as well as the reproduced with level density formalism for nuclei with static deformation.The nuclear temperature as well as the entropy of nuclear system as a function of excitation energy has been extracted from the BCS theory.It is shown that the entropy exhibits an S-formed shape as a function of excitation energy.This is interpreted as a phase transition.Procedure of treating the even-odd and even-even nuclear systems has been presented and discussed.     

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.     

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 decay energies and half-lives from a macroscopic-microscopic model

α decay energies of 323 heavy nuclei with Z≥82 are evaluated with a macroscopic-microscopic model. In this model, the macroscopic part is treated by the continuous medium model and the microscopic part consists of shell and pairing corrections based on the Nilsson potential. α decay half-lives are calculated by Viola-Seaborg formula. The results of α decay energies and half-lives are compared with experimental values and satisfactory agreement is found. The recoiling effect of the daughter nucleus on α decay half-life is also discussed.     

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.     

Synthesis of superheavy nuclei with <Superscript>238</Superscript>U target

The production of superheavy nuclei with Z=108-116 via hot fusion reactions of the neutron-rich projectiles with 238U target is systematically studied.The results show that the production cross sections of superheavy nuclei do not decrease monotonously as the atomic number Z increasing.The cross sections of the superheavy nuclei at Z = 112 and 115 are enhanced as compared with the whole Z-trend in synthesis of the superheavy nuclei,which clearly illustrates that the reactions with large negative Q-value and...     

Systematic study of two-proton radioactivity within a Gamow-like model

In this study,based on the Gamow-like model,we systematically analyze two-proton(2p) radioactivity half-lives of nuclei near or beyond the proton drip line.It is found that the calculated results can reproduce experimental data well.Furthermore,using this model,we predict the half-lives of possible 2p radioactivity candidates whose 2p radioactivity is energetically allowed or observed but not yet quantified in the latest table of evaluated nuclear properties,i.e.,NUBASE2016.The predicted results are in good agreement with those from other theoretical models and empirical formulas,namely the effective liquid drop model(ELDM),generalized liquid drop model(GLDM),Sreej a formula,and Liu formula.     

An improved semi-empirical relationship for cluster radioactivity

An improved semi-empirical relationship for cluster radioactivity half-lives is proposed by introducing an accurate charge radius formula and an analytic expression of the preformation probability.Moreover,the cluster radioactivity half-lives for the daughter nuclei around ²⁰⁸Pb or its neighbors and the ¹²C radioactivity half-life of114Ba are calculated within the improved semi-empirical relationship.It is shown that the accuracy of the new relationship is improved significantly compared to its predecessor.In addition,the cluster radioactivity half-lives that are experimentally unavailable for the trans-lead and trans-tin nuclei are predicted by the new semi-empirical formula.These predictions might be useful for searching for the new cluster emitters of the two islands in future experiments.     

Improved empirical formula for α particle preformation factor

In this contribution,the α preformation factors of 606 nuclei are extracted within the framework of the generalized liquid drop model(GLDM).Through the systematic analysis of the α preformation factors of even-even Po-U isotopes,we found that there is a significant weakening of influence of N=126 shell closure in uranium,which is consistent with the results of a recent experiment [J.Khuyagbaatar et al.,Phys.Rev.Lett.115,242502(2015)],implying that N=126 may not be the magic number for U isotopes.Furthermore,we propose an improved formula with only 7 parameters to calculate α preformation factors suitable for all types of α-decay;it has fewer parameters than the original formula proposed by Zhang et al.[H.F.Zhang et al.,Phys.Rev.C 80,057301(2009)]with higher precision.The standard deviation of the α preformation factors calculated by our formula with extracted values for all 606 nuclei is 0.365 with a factor of 2.3,indicating that our improved formula can accurately reproduce the α preformation factors.Encouraged by this,the α-decay half-lives of actinide elements are predicted,which could be useful in future experiments.Notably,the predicted α-decay half-lives of two new isotopes 220 Np [Z.Y.Zhang,et al.,Phys.Rev.Lett.122,192503(2019)] and 219 Np [H.B.Yang et al.,Phys.Lett.B 777,212(2018)] are in good agreement with the experimental α-decay half-lives.     

Theoretical approaches to alpha decay half-lives of super-heavy nuclei

We consider the systematics of α-decay half-lives of super-heavy nuclei versus the decay energy and the total α-kinetic energy. We calculate the half-lives using the experimental Q_α values. The computed half-lives are compared with the experimental data and with existing empirical estimates and are found to be in good agreement.Also, we obtain α-preformation factors from the ratio between theoretical and experimental results for some superheavy nuclei and evaluate the standard deviation. The results indicate the acceptability of the approach.