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.     

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.     

An improved α-decay energy formula for heavy and superheavy nuclei

Based on the liquid-drop model and using the first derivative of the normalized Gaussian function to consider the shell correction, a simple α-decay energy formula is proposed for heavy and superheavy nuclei. The values of corresponding adjustable parameters are obtained by fittingα-decay energies of 209 nuclei ranging from Z = 90 to Z = 118 with N ≥ 140. The calculated results are in good agreement with the experimental data. The average and standard deviations between the experimental data and...     

Quasiparticle structure of superheavy nuclei in α-decay chains of ~(285)Fl and ~(291,293)Lv

Two mean-field potentials, Woods-Saxon and Skyrme based potentials, are used to calculate the energies of low-lying one-quasiparticle states. The spectra of the low-lying states and the α-decay spectra of nuclei belonging to the α-decay chains of ~(285)Fl and ~(291,293)Lv are calculated and compared with the available experimental data. Dependence of the splitting of the pseudospin doublets and of the energies of the unique parity neutron one-quasiparticle states on the mean field potential are discussed. As shown, the α-decay spectra could be different in the α-decay chain and at the direct production of the nucleus in a fusion reaction.     

Ground State Properties of Superheavy Nuclei in Macroscopic-Microscopic Model

The ground state properties of superheavy nuclei are systematically calculated by the macroscopic- microscopic （MM） model with the Nilsson potential. The calculations well produced the ground state binding energies, α-decay energies, and half lives of superheavy nuclei. The calculated results are systematically compared with available experimental data. The calculated results are also compared with theoretical results from other MM models and from relativistic mean-field model. The calculations and comparisons show that the MM model is reliable in superheavy region and that the MM model results are not very sensitive to the choice of microscopic single-particle potential.     

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.     

Gound State Properties of Nuclei in ^295118 α-Decay Chain

The properties of nuclei belonging to the α-decay chain of superheavy element ^295118 have been studied in the framework of axially deformed relativistic mean field （RMF） theory with the parameter set of NL-Z2 in the blocked BCS approximation. Some ground state properties such as binding energies, deformations, and α-decay energies Qα have been obtained and agree well with those from finite-range droplet model （FRDM）. The single-particle spectra of nuclei in ^295118 α-decay chain show that the shell gaps present obviously nucleon number dependence. The root-mean-square （rms） radii of proton, neutron and matter distributions change slowly from ^283112 to ^295118 but dramatically from ^279110 to ^283112, which may be due to the subshell closure at Z = 110 in ^279110. The α-decay half-lives in 295118 decay chain are evaluated by employing the cluster model and the generalized liquid drop model （GLDM）, and the overall agreement is found when they are compared with the known experimental data. The α-decay lifetimes obtained from the cluster model are slightly larger than those of GLDM ones. Finally, we predict the α-decay half-lives of Z=118, 116, 114, 112 isotopes using the cluster model and GLDM, which also indicate these two models can corroborate each other in studies on superheavy nuclei. The results from GLDM are always lower than those obtained from the cluster model.     

Global α-decay study based on the mass table of the relativistic continuum Hartree-Bogoliubov theory

The α-decay energies(Qα) are systematically investigated with the nuclear masses for 10 Z 120 isotopes obtained by the relativistic continuum Hartree-Bogoliubov(RCHB) theory with the covariant density functional PC-PK1, and compared with available experimental values. It is found that the α-decay energies deduced from the RCHB results present a similar pattern to those from available experiments. Owing to the large predicted Qαvalues( 4 Me V), many undiscovered heavy nuclei in the proton-rich side and super-heavy nuclei may have large possibilities for α-decay. The influence of nuclear shell structure on α-decay energies is also analysed.     

Half-Lives of Superheavy Nuclei in Z=113 Alpha Decay Chain

The generalized liquid drop model （GLDM）, including the proximity effects and centrifugal potential, and the cluster model with Cosh potential are used to study the half-lives of some Z = 113 isotopes and their α-decay products. The experimental half-lives of 284^113, 283^113, 282^113 and their α-decay products are well reproduced by the two models when zero angular momenta transfer is assumed. For 278^113 and its α-decay products, both the GLDM and the duster model could provide satisfactory results if we assume the α particle carry five units of angular momenta, which indicates that possible nonzero angular momenta transfer and need further experimental measurements with high precision. Finally, we show that half-lives of α-decay are quite sensitive to the angular momentum transfers, and a formula could be used to describe the correlation between α-decay half-life and angular momentum transfer successfully.     

Alpha-decay branching ratios to high-lying excited-states of the ^242Cm → ^238Pu → ^234U → ^230Th → ^226Rn decay chain

We present a systematic calculation on the α-decay branching ratios to excited-states of an even-even α-decay chain ^242Cm → ^238Pu → ^234U → ^230Th → ^226Rn by the improved barrier penetration approach. The changes of the parities between the parent nuclei and the daughter nuclei are properly taken into account. The theoretical values are compared with the available experimental data and the deviation between them is within a factor of 5 in most cases.     

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.     

Alpha decay half-lives of heavy nuclei within a generalized liquid drop model

Theoretical α-decay half-lives of the heaviest nuclei are calculated using the experimental Qα value. The barriers in the quasi-molecular shape path is determined within a Generalized Liquid Drop Model (GLDM) and the WKB approximation is used. The results are compared with calculations using the DensityDependent M3Y (DDM3Y) effective interaction and the Viola-Seaborg-Sobiczewski (VSS) formulae. The calculations provide consistent estimates for the half-lives of the α decay chains of these superheavy elements. The experimental data stand between the GLDM calculations and VSS ones in the most time.     

Alpha decay half-lives of heavy nuclei within a generalized liquid drop model

Theoretical α-decay half-lives of the heaviest nuclei are calculated using the experimental Q_α value. The barriers in the quasi-molecular shape path is determined within a Generalized Liquid Drop Model (GLDM) and the WKB approximation is used. The results are compared with calculations using the Density-Dependent M3Y (DDM3Y) effective interaction and the Viola-Seaborg-Sobiczewski (VSS) formulae. The calculations provide consistent estimates for the half-lives of the α decay chains of these superheavy elements. The experimental data stand between the GLDM calculations and VSS ones in the most time.     

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.     

Benford＇s Law and β-Decay Half-Lives

The experimental values of 2059 β-decay half-lives are systematically analyzed and investigated. We have found that they are in satisfactory agreement with Benford＇s law, which states that the frequency of occurrence of each figure, 1-9, as the first significant digit in a surprisingly large number of different data sets follows a logarithmic distribution favoring the smaller ones. Benford＇s logarithmic distribution of β-deeay half-lives can be explained in terms of Neweomb＇s justification of Benford＇s law and empirical exponential law of β-decay half-lives. Moreover, we test the calculated values of 6721 β-decay half-lives with the aid of Benford＇s law. This indicates that Benford＇s law is useful for theoretical physicists to test their methods for calculating β-decay half-lives.     

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.     

Doubly magic properties in superheavy nuclei

A systematic study of global properties of superheavy nuclei in the framework of the Liquid Drop Model and the Strutinsky shell correction method is performed. The evolution equilibrium deformations, TRS graphs and α-decay energies are calculated using the TRS model. The analysis covers a wide range of even-even superheavy nuclei from Z=102 to 122. Magic numbers and their observable influence occurring in this region have been investigated. Shell closures appear at proton number Z=114 and at neutron number N=184.     

Doubly magic properties in superheavy nuclei

A systematic study of global properties of superheavy nuclei in the framework of the Liquid Drop Model and the Strutinsky shell correction method is performed. The evolution equilibrium deformations, TRS graphs and α-decay energies are calculated using the TRS model. The analysis covers a wide range of even-even superheavy nuclei from Z =102 to 122. Magic numbers and their observable influence occurring in this region have been investigated. Shell closures appear at proton number Z =114 and at neutron number N =184.     

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.     

Molecular dynamics study for the melting curve of MgO at high pressure

Shell-model molecular dynamics method is used to study the melting temperatures of MgO at elevated temperatures and high pressures using interaction potentials. Equations of state for MgO simulated by molecular dynamics are in good agreement with available experimental data. The pressure dependence of the melting curve of MgO has been calculated. The surface melting and superheating are considered in the correction of experimental data and the calculated values, respectively. The results of corrections are compared with those of previous work. The corrected melting temperature of MgO is consistent with corrected experimental measurements. The melting temperature of MgO up to 140GPa is calculated.