New calculations of α-decay half-lives by the Viola-Seaborg formula

The Viola-Seaborg formula is a well-known formula for α-decay half-lives of heavy nuclei. In this work we obtain new parameters of this formula through a least-square fit to even-even nuclei between Z = 84 and Z = 110 with N greater than 126. On average, the formula can reproduce the half-lives of heavy even-even nuclei within a factor of 1.3. The formula with new parameters works well for the superheavy region which is a hot topic of nuclear physics. The numerical results from the formula are compared with those from the cluster model.     

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.     

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.     

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.     

Cluster emission in superdeformed Sr isotopes in the ground state and formed in heavy-ion reaction

Cluster decay of superdeformed^{76, 78, 80}Sr isotopes in their ground state are studied taking the Coulomb and proximity potential as the interacting barrier for the post-scission region. The predictedT _1/2 values are found to be in close agreement with those values reported by the preformed cluster model (PCM). Our calculation shows that these nuclei are stable against both light and heavy cluster emissions. We studied the decay of these nuclei produced as an excited compound system in heavy-ion reaction. It is found that inclusion of excitation energy increases the decay rate (decreasesT _1/2 value) considerably and these nuclei become unstable against decay. These findings support earlier observation of Guptaet al based on PCM.     

Possible α decay chains from isotopes of superheavy element 120

We investigate the α decay half-lives of even-Z superheavy nuclei up to Z = 120 by the modified two-potential approach. Based on the density-dependent cluster model, the α daughter potential is obtained from the double folding integral, taking into account the effect of nuclear deformation. A reasonable formula related with the fissility parameter and the fission barrier height, is applied to evaluate the spontaneous fission half-lives of the studied nuclei. After the performance of the competition between α decay and spontaneous fission, possible α decay chains are proposed in pursuit of being useful for the future experiment.     

Stability of <Superscript>244–260</Superscript>Fm isotopes against alpha and cluster radioactivity

Taking Coulomb and proximity potentials as the interacting barrier we have studied the cold valley in the radioactive decay of ^244–260Fm isotopes. It is found that in addition to alpha particle minima, other minima occur at S, Ar and Ca clusters. We have computed the half-lives and other characteristics of different clusters emitted from these parents treating parent, daughter and emitted cluster as spheres. Our study reveals that most of these parents are unstable against alpha and heavy cluster (⁴⁶Ar, ^48,50Ca) emissions and stable against light cluster emission, except ⁸Be from ^244–248Fm isotopes. The most probable clusters from these parents are predicted to be ⁴⁶Ar, ^48,50Ca which indicate the role of doubly or near doubly magic clusters (Z = 20, N = 28) and also stress the role of doubly magic ²⁰⁸Pb daughter. The computed half-lives for alpha decay are in good agreement with the experimental data. It is found that the presence of neutron excess in the parent nuclei slows down the cluster decay process. The effect of quadrupole (β ₂) and hexadecapole (β ₄) deformations of parent and fragments on half-lives are also studied. It is found that inclusion of β ₂ and β ₄ reduces the height and shape of the barrier (increases barrier penetrability) and hence the half-life decreases.     

Neutron and proton shell closure in the superheavy region via cluster radioactivity in <Superscript>280–314</Superscript>116 isotopes

Based on the concept of cold valley in fission and fusion, the radioactive decay of superheavy^280–314116 nuclei was studied taking Coulomb and proximity potentials as the interacting barrier. It is found that the inclusion of proximity potential does not change the position of minima but minima become deeper which agrees with the earlier findings of Gupta and co-workers. In addition to alpha particle minima, the other deepest minima occur for ⁸Be, ^12,14C clusters. In the fission region two deep regions are found each consisting of several comparable minima, the first region centred on ²⁰⁸Pb and the second is around ¹³²Sn. The cluster decay half-lives and other characteristics are computed for various clusters ranging from alpha particle to ⁷⁰Ni. The computed half-lives for alpha decay match with the experimental values and with the values calculated using Viola-Seaborg-Sobiczewski (VSS) systematic. The plots connecting computed Q values and half-lives against neutron number of daughter nuclei were studied for different clusters and it is found that the next neutron shell closures occur at N = 162, 172 and 184. Isotopic and isobaric mass parabolas are studied for various cluster emissions and minima of parabola indicate neutron shell closure at N = 162, 184 and proton shell closure at Z = 114. Our study shows that ₁₆₂²⁷⁶114 is the deformed doubly magic and ₁₈₄²⁹⁸114 is the spherical doubly magic nuclei.      

Fusion-fission dynamics and perspectives of future experiments

The paper is focused on reaction dynamics of superheavy-nucleus formation and decay at beam energies near the Coulomb barrier. The aim is to review the things we have learned from recent experiments on fusion-fission reactions leading to the formation of compound nuclei with Z≥102 and from their extensive theoretical analysis. Major attention is paid to the dynamics of formation of very heavy compound nuclei taking place in strong competition with the process of fast fission (quasifission). The choice of collective degrees of freedom playing a fundamental role and finding the multidimensional driving potential and the corresponding dynamic equation regulating the whole process are discussed. A possibility of deriving the fission barriers of superheavy nuclei directly from performed experiments is of particular interest here. In conclusion, the results of a detailed theoretical analysis of available experimental data on the “cold” and “hot” fusion-fission reactions are presented. Perspectives of future experiments are discussed along with additional theoretical studies in this field needed for deeper understanding of the fusion-fission processes of very heavy nuclear systems.     

Cold valleys in the radioactive decay of <Superscript>248–254</Superscript>Cf isotopes

Based on the concept of cold valley in cold fission and fusion, we have investigated the cluster decay process in ^248–254Cf isotopes. In addition to alpha particle minima, other deep minima occur for S, Ar and Ca clusters. It is found that inclusion of proximity potential does not change the position of minima but minima become deeper. Taking Coulomb and proximity potential as interacting barrier for post-scission region, we computed half-lives and other characteristics for various clusters from these parents. Our study reveals that these parents are stable against light clusters and unstable against heavy clusters. Computed half-lives for alpha decay agree with experimental values within two orders of magnitude. The most probable clusters from these parents are predicted to be ⁴⁶Ar, ^48,50Ca which indicate the role of doubly or near doubly magic clusters in cluster radioactivity. Odd A clusters are found to be favorable for emission from odd A parents. Cluster decay model is extended to symmetric region and it is found that symmetric fission is also probable which stresses the role of doubly or near doubly magic ¹³²Sn nuclei. Geiger-Nuttal plots were studied for various clusters and are found to be linear with varying slopes and intercepts.      

Role of the cluster deformations in explaining the exotic decay half-lives

We investigate the influence of nuclear deformations of the cluster and daughter nuclei on the exotic cluster decay half-lives of $\ensuremath 221\leq A \leq 242$ for the favored cluster decay of the radioactive nuclei by using the semiclassical WKB method and the Bohr-Sommerfeld quantization condition. The results have also been presented for the spherical nuclei case in order to show clearly the effects of the deformations on the exotic decay half-lives. The half-lives become close to the experimental data when both the deformation of daughter and cluster nuclei are taken into account in the calculations. Furthermore, considering cluster deformations together with the orientation angles of daughter and cluster also provides positive contributions to the results.     

Systematic study of α decay half-lives for even–even nuclei within a deformed two-potential approach

In this work, we systematically study the α decay half-lives of 196 even–even nuclei using a two-potential approach improved by considering nuclear deformation. The results show that the accuracy of this model has been improved after considering nuclear deformation. In addition, we extend this model to predict the α decay half-lives of Z = 118 and 120 isotopes by inputting the α decay energies extracted from the Weizsacker–Skyrme-type (WS-type) mass model, a simple nuclear mass formula, relativistic continuum Hartree–Bogoliubov theory and Duflo-Zuker-19 (DZ19) mass model. It is useful for identifying the new superheavy elements or isotopes for future experiments. Finally, the predicted α decay energies and half-lives of Z = 118 and 120 isotopes are analyzed, and the shell structure of superheavy nuclei is discussed. It shows that the shell effect is obvious at N = 184, while the shell effect at N = 178 depends on the nuclear mass model.     

推广的液滴模型及其应用

简单介绍了近年来在研究重核和超重核衰变性质及熔合反应方面取得的理论成果和面临的挑战,着重阐述推广的液滴模型(GLDM) 理论框架及其应用。基于原子核的质量数、质子数以及反应Q 值,GLDM考虑了质量和电荷的不对称性、形状演化、亲近势和温度等,很好地描述了重核和超重核的质子放射性、 衰变、重离子放射性、自发裂变的半衰期和重离子熔合反应截面,同时也研究了原子核的粒子(质子、 、重离子) 放射性与自发裂变的竞争。Recent theoretical achievements and challenges about the fusion and decay properties of heavy and superheavy nuclei are generally introduced. Especially, the Generalized Liquid Drop Model(GLDM) as well as its application are emphatically described. Based on the mass number, proton number and the reaction Q value, the GLDM has taken the mass and charge asymmetry, the shape evolution, the proximity potential, as well as the temperature of nucleus into account, well described the proton radioactivity, the decay, the heavy particle radioactivity, the half life of spontaneous fission of heavy nuclei and superheavy nuclei, and the cross-sections of heavy ion fusion. The competitions between the spontaneous fission and other decay modes such as proton and heavy particle radioactivity, the alpha decay, and so on are also studied.     

Synthesis of superheavy nuclei in 48Ca+244Pu interactions

This article reports the results of experiments aimed at producing hypothetical long-lived superheavy elements located near the spherical-shell closures with Z≥114 and N≥72. For the synthesis of superheavy nuclei, we used a combination of neutron-rich reaction partners, with a ²⁴⁴Pu target and a ⁴⁸Ca projectile. The sensitivity of the present experiment exceeded by more than two orders of magnitude previous attempts at synthesizing superheavy nuclides in reactions of ⁴⁸Ca projectiles with actinide targets. We observed new decay sequences of genetically linked alpha decays terminated by spontaneous fission. The high measured alpha-particle energies, together with the long decay times and spontaneous fission terminating the chains, offer evidence for the decay of nuclei with high atomic numbers. The decay properties of the synthesized nuclei are consistent with the consecutive alpha decays originating from the parent nuclides ^288,289114, produced in the 3n-and 4n-evaporation channels with cross sections of about a picobarn. The present observations can be considered experimental evidence for the existence of the “island of stability” of superheavy elements and are discussed in terms of modern theoretical approaches.     

Study of heavy nuclei at FLNR (Dubna)

Experiments are described and main results presented on the synthesis and decay properties of superheavy nuclides, produced in fusion reactions induced by a ⁴⁸Ca-beam on heavy actinide targets. In such reactions neutron-rich nuclei are formed. For them, according to theory, an abrupt enhancement of stability due to nuclear shell effects is expected. The decay properties of the new nuclides are compared with calculations of theoretical models, which predict the existence of “islands of stability” in the region of hypothetical superheavy elements.     

Alpha decay and cluster decay of some neutron-rich actinide nuclei

Nuclei in the actinide region are good in exhibiting cluster radioactivity. In the present work, the half-lives of α-decay and heavy cluster emission from certain actinide nuclei have been calculated using cubic plus Yukawa plus exponential model (CYEM). Our model has a cubic potential for the overlapping region which is smoothly connected by a Yukawa plus exponential potential for the region after separation. The computed half-lives are compared with those of other theoretical models and are found to be in good agreement with each other. In this work, we have also studied the deformation effects on half-lives of cluster decay. These deformation effects lower the half-life values and it is also found that the neutron-rich parent nuclei slow down the cluster decay process. Geiger–Nuttal plots for various clusters are found to be linear and most of the emitted clusters are α-like nuclei.     

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.     

Systematic studies on α-decay half-lives for super heavy nuclei

Radioactive decay of super heavy nuclei via the emission of α-particles has been studied theoretically in the preformed cluster model (PCM). The nucleus-nucleus (NN) potential is obtained by double folding the density distributions of the α-particle and the daughter nucleus with a realistic effective interaction. The M3Y effective interaction, supplemented by a zero-range pseudo-potential for exchange term, is used to calculate the NN potential. The α decay half-lives for 317 nuclei at Z=102–120 are performed in the PCM framework with the theoretical Q values extracted from the Mller-Nix-Kratz and Liran-Marinov-Zeldes mass tables and are compared with the experimental data. The calculated results are also compared with those obtained by using Q values from the Muntian-Hofmann-Patyk-Sobiczewski and Myers-Swiatecki mass estimates.