α Decay Properties of Even-Even Nuclei~(296-308)120 Within the Two-Potential Approach

In the present work,we predict the α decay half-lives of unknown even-even nuclei ~(296-308)120 within the two-potential approach,whose α decay energy Qa is calculated using WS3+mass model.To reduce the deviations between the predictions and experimental data due to nuclear shell effect,the analytic formula of α decay hindrance factor is introduced to the two-potential approach,whose parameters had been extracted from even-even nuclei in the region of 82 Z 126 and 152 N 184 in our previous work [Deng et al.,Chin.Phys.C 42(2018) 044102].In addition,for comparing,we use a type of α decay general formula Universal Decay Law(UDL) and a semi-empirical formula in the superheavy nucleus(SEMFLS) to calculate the half-lives of even-even nuclei ~(296-308)120.The results indicate that our predicted values and the calculated values of the above two empirical formulas are mutually confirmed.Meanwhile,we systematically study α decay chains of ~(296-308)120 and predict the decay modes for superheavy nuclei to help to identify new superheavy isotopes.     

α decay properties of ~(297)Og within the two-potential approach

The α decay half-life of the unknown nucleus ~(297)Og is predicted within the two-potential approach, andα preformation probabilities of 64 odd-A nuclei in the region of proton numbers 82 Z 126 and neutron numbers 152 N 184, from ~(251)Cf to ~(295)Og, are extracted. In addition, based on the latest experimental data, a new set of parameters for α preformation probabilities considering the shell effect and proton-neutron interaction are obtained.The predicted α decay half-life of ~(297)Og is 0.16 ms within a factor of 4.97. The predicted spin and parity of the ground states for ~(269)Sg,~(285)Fl and ~(293)Lv are 3/2~+, 3/2~+ and 5/2~+, respectively.     

Effects of shell correction on α decay properties

The shell correction effects on the α decay properties of heavy and superheavy nuclei have been studied in a macroscopic-microscopic manner. The macroscopic part is constructed from the generalized liquid drop model(GLDM), whereas the microscopic part, namely, the shell correction energy, brings about certain effects on the potential barriers and half-lives under a WKB approximation, which is emphasized in this work. The results show that the shell effects play a significant role in the estimation of the α decay half-lives within the actinide region.Predictions of the α decay half-lives are then generated for superheavy nuclei, which will provide useful information for future experiments.     

Calculation of decay half-lives for superheavy elements using the double folding model

α decay half-lives of some new synthesized superheavy elements, possibly synthesized superheavy elements and decay products are calculated theoretically within the WKB approximation by using microscopic m-nucleus interaction potentials. These nuclear potentials between the α particle and daughter nuclei are obtained by using the double folding integral of the matter density distribution of the α particle and daughter nuclei with a density-dependent effective nucleon-nucleon interaction, in which the zero-range exchange term is supplemented. The calculated α decay half-lives are compared with those of the different models and experimental data. It is shown that the present calculation successfully provides the half-lives of the observed αdecays for some new superheavy elements and therefore gives reliable predictions for α decay of possibly synthesized superheavy elements in future experiments.     

Calculation of α decay half-lives for superheavy elements using the double folding model＊

α decay half-lives of some new synthesized superheavy elements, possibly synthesized superheavy elements and decay products are calculated theoretically within the WKB approximation by using microscopic α-nucleus interaction potentials. These nuclear potentials between the α particle and daughter nuclei are obtained by using the double folding integral of the matter density distribution of the α particle and daughter nuclei with a density-dependent effective nucleon-nucleon interaction, in which the zero-range exchange term is supplemented. The calculated α decay half-lives are compared with those of the different models and experimental data. It is shown that the present calculation successfully provides the half-lives of the observed decays for some new superheavy elements and therefore gives reliable predictions for α decay of possibly synthesized superheavy elements in future experiments.     

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.     

α particle preformation and shell effect for heavy and superheavy nuclei

The α particle preformation factor is extracted within a generalized liquid drop model for Z = 84-92 isotopes and N = 126,128,152,162,176,184 isotones.The calculated results show clearly that the shell effects play a key role in α particle preformation.The closer the proton and neutron numbers are to the magic numbers,the more difficult the formation of the α cluster inside the mother nucleus is.The preformation factors of the isotopes reflect that N = 126 is a magic number for Po,Rn,Ra,and Th isotopes,but for U isotopes the weakening of the influence of the N =126 shell closure is evident.The trend of the factors for N = 126 and N = 128 isotones also support this conclusion.We extend the calculations for N = 152,162,176,184 isotones to explore the magic numbers for heavy and superheavy nuclei,which are probably present near Z = 108 to N = 152,162 isotones and Z = 116 to N = 176,184 isotones.The results also show that another subshell closure may exist after Z = 124 in the superheavy nuclei.This is useful for future experiments.     

Shell Effect of Superheavy Nuclei in Self-consistent Mean-Field Models

We analyze in detail the numerical results of superheavy nuclei in deformed relativistic mean-field model and deformed Skyrme-Hartree-Fock model. The common points and differences of both models are systematically compared and discussed. Their consequences on the stability of superheavy nuclei are explored and explained. The theoreticalresults are compared with new data of superheavy nuclei from GSI and from Dubna and reasonable agreement is reached.Nuclear shell effect in superheavy region is analyzed and discussed. The spherical shell effect disappears in some cases due to the appearance of deformation or superdeformation in the ground states of nuclei, where valence nucleons occupysignificantly the intruder levels of nuclei. It is shown for the first time that the significant occupation of vaJence nucleons on the intruder states plays an important role for the ground state properties of superheavy nuclei. Nuclei are stable in the deformed or superdeformed configurations. We further point out that one cannot obtain the octupole deformation of even-even nuclei in the present relativistic mean-field model with the σ,ω and ρ mesons because there is no parityviolating interaction and the conservation of parity of even-even nuclei is a basic assumption of the present relativistic mean-field model.     

Reflection-Asymmetric Shell Model Description of the Neutron-Rich^142，145Ba Nuclei

The reflection asymmetric shell model has been applied to describe the octupole deformed bands in neutron-rich even-even ^142Ba and odd-N^145Ba nuclei. The alternating parity bands of ^142Ba and the simplex s = -i bands of^145Ba are calculated and compared with the available experimental data. The calculated results are in good agreement with the experimental data. The spin and parity assignments of ground-state of^145Ba are discussed.The results show that the present work is a useful attempt to further explore the nuclear reflection asymmetry in neutron rich region.     

Shell Effect of Superheavy Nuclei in Self-consistent Mean-Field Models

We analyze in detail the numerical results of superheavy nuclei in deformed relativistic mean-field model and deformed Skyrme-Hartree-Fock model. The common points and differences of both models are systematically compared and discussed. Their consequences on the stability of superheavy nuclei are explored and explained. The theoretical results are compared with new data of superheavy nuclei from GSI and from Dubna and reasonable agreement is reached. Nuclear shell effect in superheavy region is analyzed and discussed. The spherical shell effect disappears in some cases due to the appearance of deformation or superdeformation in the ground states of nuclei, where valence nucleons occupy significantly the intruder levels of nuclei. It is shown for the first time that the significant occupation of valence nucleons on the intruder states plays an important role for the ground state properties of superheavy nuclei. Nuclei are stable in the deformed or superdeformed configurations. We further point out that one cannot obtain the octupole deformation of even-even nuclei in the present relativistic mean-field model with the σ, ω and ρ mesons because there is no parity violating interaction and the conservation of parity of even-even nuclei is a basic assumption of the present relativistic mean-field model.     

α preformation and penetration probability for heavy nuclei

The α preformation factor and penetration probability have been analyzed for even--even nuclei of Po, Rn, Ra using experimental released energies and α decay half-lives in the frame of the double folding model. It is shown that N=126 is a neutron magic number from α preformation and shell effects play an important role in α preformation. The closer the nucleon number is to the magic number, the more difficult α formation in the parent nucleus is. The preformation factor can supply information on the nuclear structure and the penetration probability mainly determines α decay half-life.     

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.     

Systematic Study on Alpha Decay Half-Lives of Superheavy Nuclei

The α-decay half-lives of a set of superheavy nuclear isotope chain from Z = 105 to 120 have been analyzed systematically within the WKB method, and some nuclear structure features are found. The decay barriers have been determined in the quasi-molecular shape path within the Generalized Liquid Drop Model (GLDM) including the proximity effects between nucleons in a neck and the mass and charge asymmetry. The results are in reasonable agreement with the published experimental data for the alpha decay half-lives of isotopes of charge 112, 114, and 116, of the element 294118 and of some decay products. A comparison of present calculations with the results by the DDM3Y effective interaction and by the Viola-Seaborg-Sobiczewski (VSS) formulae is also made. The experimental α decay half lives all stand in between the GLDM calculations and VSS formula results. This demonstrates the possibility of these models to provide reasonable estimates for the half-lives of nuclear decays by α emissions for the domain of SHN. The half-lives of these new nuclei are thus well tested from the reasonable consistence of the macroscopic, the microscopic, the empirical formulae and the experimental data. This also shows that the present data of SHN themselves are consistent.It could suggest that the present experimental claims on the existence of new elements Z = 110 ～ 118 are reliable.It is expected that greater deviations of a few SHN between the data and the model may be eliminated by further improvements on the precision of the measurements.     

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.     

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,Shell Structure,and New Elements

We systematically analyze the experimental data of alpha decay in even-even heavy nuclei far from stability and find that the Geiger-Nuttall law brea~s for an isotopic chain when its neutron number is across a marc number or there is a deformed subshell. This break can be used to identify new magic numbers of superheavy nuclei. It is also discovered that there is a new linear relation between the logarithm of half-life and the reciprocal of the square root of decay energy for N = 126 and N = 152 isotones. It could be a new law of alpha decay for nuclei with magic neutron numbers but the physics behind it is to be explored. The significance of these researches for the search of new elements is discussed.     

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.     

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.