Half-lives Of Cluster Radioactivity Research Articles

Effects of deformation on the cluster and the [formula omitted]-decay half-lives for isotopes of the Trans-lead and the undetected superheavy nuclei

In the present investigation, based on the Wentzel–Kramers–Brillouin (WKB) approximation, and by considering deformation of the cluster and the daughter nuclei, the cluster radioactivity half-lives of 22 Trans-lead isotopes ranging from 221Fr to 242Cm are calculated. Also, the α-decay half-lives of even–even isotopes for the superheavy nuclei with Z in the range 104≤Z≤118 are computed. For the cluster radioactivity, a preformation factor, Pc depending on the atomic numbers of the cluster and the daughter nuclei is used according to the Santhosh and Jose (2021). The α preformation factor, Pα is evaluated based on the cluster-formation model (CFM). A universal decay law (UDL) proposed by Qi et al. (2009), was used to obtain the decay half-lives of the cluster and the α-decay for checking the credibility of our approach. The effects of the deformation of decay products on the half-lives of the cluster and the α-decay have also been investigated by comparing the obtained half-lives considering deformation with ones of the spherical nuclei and the results of the UDL as well as the available experimental data. Comparison indicates that our calculated cluster and α-decay half-lives considering deformation reproduce the experimental data more accurately than the UDL and the spherical nuclei. Furthermore, the cluster radioactivity half-lives of some isotopes that whose cluster radioactivity is energetically allowed but not observed preciously yet, are predicted. Also, the cluster and the α-decay half-lives and the branching ratios between them for some not yet discovered superheavy isotopes with Z=122 and Z=124 are obtained.

Systematic study of cluster radioactivity within the generalized liquid drop model* *Supported by the National Natural Science Foundation of China (12175170), Hubei Provincial Natural Science Foundation of China (2023AFB035), Hunan Outstanding Youth Science Foundation (2022JJ10031), and Natural Science Research Project of Yichang City (A23-2-028)

Cluster radioactivity is studied within the generalized liquid drop model (GLDM), in which the shell correction energy, pairing energy, and cluster preformation factor are considered. The calculations show significant improvements and can reproduce the experimental data within a factor of 8.04 after considering these physical effects. In addition, the systematic trend of the cluster preformation factors is discussed in terms of the scheme to study the influence of the valence proton-neutron interaction and shell effect on cluster radioactivity. It is found that is linearly related to . This is in agreement with a recent study [L. Qi et al., Phys. Rev. C 108, 014325 (2023)], in which , obtained using different theoretical models and treatment methods than those used in this study, also had a linear relationship with . Combined with the work by Qi et al., this study suggests that the linear relationship between and is model-independent and both the shell effect and valence proton-neutron interaction play essential roles in cluster radioactivity. An analytical formula is proposed to calculate the cluster preformation factor based on the scheme. In addition, the cluster preformation factors and the cluster radioactivity half-lives of some heavy nuclei are predicted, which can provide a reference for future experiments.

An improved effective liquid drop model for cluster radioactivity

The effective liquid drop model (ELDM) is improved by introducing an accurate nuclear charge radius formula and an analytic expression for assaulting frequency. Within the improved effective liquid drop model (IMELDM), the experimental cluster radioactivity half-lives of the trans-lead region are calculated. It is shown that the accuracy of the IMELDM is improved compared with that of the ELDM. At last, the cluster radioactivity half-lives that are experimentally unavailable for the trans-lead nuclei are predicted by the IMELDM. These predictions may be useful for searching for new candidates for cluster radioactivity in future experiments.

Systematic study of cluster radioactivity in trans-lead nuclei with various versions of proximity potential formalisms* *Supported in part by the National Natural Science Foundation of China (12175100, 11975132), the construct program of the key discipline in Hunan province, the Research Foundation of Education Bureau of Hunan Province, China (18A237, 22A0305), Hunan Provincial Department of Education Scientific Research Project (19A440), the

In this study, based on the framework of the Coulomb and proximity potential model (CPPM), we systematically investigate the cluster radioactivity half-lives of 26 trans-lead nuclei by considering the cluster preformation probability, which possesses a simple mass dependence on the emitted cluster according to R. Blendowske and H. Walliser [Phys. Rev. Lett. 61, 1930 (1988)]. Moreover, we investigate 28 different versions of the proximity potential formalisms, which are the most complete known proximity potential formalisms proposed to describe proton radioactivity, two-proton radioactivity, α decay, heavy-ion radioactivity, quasi-elastic scattering, fusion reactions, and other applications. The calculated results show that the modified forms of proximity potential 1977, denoted as Prox.77-12, and proximity potential 1981, denoted as Prox.81, are the most appropriate proximity potential formalisms for the study of cluster radioactivity, as the root-mean-square deviation between experimental data and relevant theoretical results obtained is the least; both values are 0.681. For comparison, the universal decay law (UDL) proposed by Qi et al. [Phys. Rev. C 80, 044326 (2009)], unified formula of half-lives for α decay and cluster radioactivity proposed by Ni et al. [Phys. Rev. C 78, 044310 (2008)], and scaling law (SL) in cluster radioactivity proposed by Horoi et al. [J. Phys. G 30, 945 (2004)] are also used. In addition, utilizing CPPM with Prox.77-12, Prox.77-1, Prox.77-2, and Prox.81, we predict the half-lives of 51 potential cluster radioactive candidates whose cluster radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020. The predicted results are in the same order of magnitude as those obtained using the compared semi-empirical and/or empirical formulae. At the same time, the competition between α decay and cluster radioactivity of these predicted nuclei is discussed. By comparing the half-lives, this study reveals that α decay predominates.

Simple model for cluster radioactivity half-lives in trans-lead nuclei* *Supported in part by the National Natural Science Foundation of China (12175100, 11975132), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of the Education Bureau of Hunan Province, China (18A237), the Natural Science Foundation of Shandong Province, China (ZR2022JQ04), the Opening Project of Cooperative Innovation Center

In this study, considering the modified preformation probability to be , where and are the α-particle preformation probability and an adjustable parameter proposed by Wang et al. [Chin. Phys. C 45, 044111 (2021)], respectively, we extend a new simple model put forward by Bayrak [J. Phys. G 47, 025102 (2020)] to systematically study the cluster radioactivity half-lives of 28 trans-lead nuclei ranging from to , which is based on the Wentzel-Kramers-Brillouin approximation and Bohr–Sommerfeld quantization condition. For comparison, a universal decay law proposed by Qi et al. [Phys. Rev. C 80, 044326 (2009)], a three-parameter model-independent formula put forward by Balasubramaniam et al. [Phys. Rev. C 70, 017301 (2004)], and the semi-empirical model proposed by Tavares et al. [Eur. Phys. J. A 49, 1 (2013)] are used. Our calculated results reproduce the experimental data well, with a standard deviation of 0.818. Furthermore, we use this model to predict the cluster radioactivity half-lives of 51 possible cluster radioactive candidates whose cluster radioactivities are energetically allowed or observed but not yet quantified in NUBASE2020.

Systematic calculations of cluster radioactivity half-lives with a screened electrostatic barrier* *Supported in part by the National Natural Science Foundation of China (12175100, 11975132), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of Education Bureau of Hunan Province, China (21B0402, 18A237), the Natural Science Foundation of Hunan Province, China (2018JJ2321), the Innovation Group of Nuclear

In this study, based on Wentzel-Kramers-Brillouin theory, we systematically investigate the cluster radioactivity half-lives of 22 nuclei ranging from to using a phenomenological model that considers the screened electrostatic effect of the Coulomb potential. In this model, there are two adjustable parameters, t and g, which are related to the screened electrostatic barrier and the strength of the spectroscopic factor, respectively. The calculated results indicate that this model can effectively reproduce the experimental data, with a corresponding root-mean-square deviation of 0.660. In addition, we extend this model to predict the half-lives of possible cluster radioactive candidates whose cluster radioactivities are energetically allowed or observed but not yet quantified in the evaluated nuclear properties table NUBASE2020. The predicted results are consistent with those obtained using other theoretical models and/or empirical formulas, including the universal decay law proposed by Qi et al. [Phys. Rev. C 80, 044326 (2009)], a semi-empirical model for both α decay and cluster radioactivity proposed by Santhosh et al. [J. Phys. G 35, 085102 (2008)], and a unified formula for the half-lives of α decay and cluster radioactivity proposed by Ni et al. [Phys. Rev. C 78, 044310 (2008)].

New Geiger-Nuttall law for cluster radioactivity half-lives* *Supported in part by the National Natural Science Foundation of China (12175100, 11975132), the construct program of the key discipline in hunan province, the Research Foundation of Education Bureau of Hunan Province, China (18A237), the Shandong Province Natural Science Foundation, China (ZR2022JQ04), the Opening Project of Cooperative Innovation Center for Nuclear Fuel Cycle

In this study, derived from Balasubramaniam's formula [Phys. Rev. C 70, 017301 (2004)] and further considering the effect of the parent nucleus mass, blocking effect, and effect of reduced mass on cluster radioactivity half-lives, we propose a new Geiger-Nuttall law that is model-independent to systematically evaluate the half-lives of this process for 16 even-even nuclei and 10 odd-A nuclei. For comparison, a single universal curve for cluster radioactivity and α decay proposed by Poenaru [Phys. Rev. C 83, 014601 (2011)], a scaling law proposed by Horoi [J. Phys. G: Nucl. Part. Phys. 30, 945 (2004)], an extension of the Viola-Seaborg formula from α decay to cluster radioactivity proposed by Ren et al. [Phys. Rev. C 70, 034304 (2004)], a new semi-empirical formula for exotic cluster decay proposed by Balasubramaniam et al. [Phys. Rev. C 70, 017301 (2004)], and a unified formula for the half-lives of α decay and cluster radioactivity proposed by Ni et al. [Phys. Rev. C 78, 044310 (2008)] are also used. The calculated results of our new Geiger-Nuttall law are in good agreement with the experimental half-lives, with the least rms being 0.606, and are better than the compared values. Moreover, we extend this formula to predict the cluster radioactivity half-lives of 51 nuclei whose decay energies are energetically allowed or observed but not yet quantified in NUBASE2020.

Half-lives of deformed nuclei for exotic cluster decays

In this paper, we considered the cluster radioactivity half-lives for all known cluster decay modes (i.e., from $^{14}\mathrm{C}$ up to $^{34}\mathrm{Si}$) that these nuclei were first satisfied by the observed systematics [Silisteanu and Scheid, Phys. Rev. C 51, 2023 (1995), Poenaru et al., Phys. Rev. C 83, 014601 (2011); Ni et al., Phys. Rev. C 78, 044310 (2008)]. The Coulomb and proximity potential model for deformed nuclei is considered as penetration of the emitter particle through the potential barrier formed by the nuclear, Coulomb, and centrifugal interactions between the emitter particle and nucleus. The spins and parities of the parent and daughter nuclei in addition to the quadrupole $({\ensuremath{\beta}}_{2})$ and hexadecapole $({\ensuremath{\beta}}_{4})$ deformations of the parent nuclei are taken into account for the calculation of the cluster radioactivity half-lives. Our results exhibit, which the minimum $\mathrm{lo}{\mathrm{g}}_{10}{T}_{1/2}$ value denotes doubly magic $^{208}\mathrm{Pb}$ ($Z=82$, $N=126$) as the daughter nuclei.

Systematic calculations of cluster radioactivity half-lives in trans-lead nuclei* *This work is supported in part by the National Natura Science Foundation of China (12175100 and 11975132), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of Education Bureau of Hunan Province (18A237), the Natural Science Foundation of Hunan Province (2018JJ3324), the Innovation Group of Nuclear and

In the present work, based on the Wentzel-Kramers-Brillouin (WKB) theory, considering the cluster preformation probability (), we systematically investigate the cluster radioactivity half-lives of 22 trans-lead nuclei ranging from 221Fr to 242Cm. When the mass number of the emitted cluster 28, is obtained by the exponential relationship of to the α decay preformation probability () proposed by R. Blendowskeis [Phys. Rev. Lett. 61, 1930 (1988)], while is calculated through the cluster-formation model (CFM). When 28, is calculated through the charge-number dependence of on the decay products proposed by Ren [Phys. Rev. C 70, 034304 (2004)]. The half-lives of cluster radioactivity have been calculated by the density-dependent cluster model [Phys. Rev. C 70, 034304 (2004)] and by the unified formula of half-lives for alpha decay and cluster radioactivity [Phys. Rev. C 78, 044310 (2008)]. For comparison, a universal decay law (UDL) proposed by Qi [Phys. Rev. C 80, 044326 (2009)], a semi-empirical model for both α decay and cluster radioactivity proposed by Santhosh [J. Phys. G: Nucl. Part. Phys. 35, 085102 (2008)], and a unified formula of half-lives for alpha decay and cluster radioactivity [Phys. Rev. C 78, 044310 (2008)] are also used. The calculated results of our work, Ni's formula , and the UDL can well reproduce the experimental data and are better than those of Santhosh's model. In addition, we extend this model to predict the half-lives for 51 nuclei, whose cluster radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020.

Systematic study of cluster radioactivity half-lives based on a modified Gamow-like model

In this study, taking into account of the contribution of the centrifugal potential on half-life and the effect of electrostatic shielding, we modify the Gamow-like model proposed by Zdeb et al [2013 Phys. Rev. C 87, 024 308] to systematically investigate the cluster radioactivity half-lives of nuclei ranging from 221Fr to 238U. The calculated results can reproduce the experimental data well. Additionally, this modified Gamow-like model is applied to predict the half-lives of cluster radioactivity nuclei whose experimental half-lives have the lower limit. It is found that the predicted results are in good agreement with the ones obtained by using the Gamow-like model and a Viola-Seaborg type formula.

Cluster approach to spontaneous fission of even-even isotopes of U, Pu, Cm, Cf, Fm, No, Rf, Sg, and Hs

For even isotopes of nuclei U, Pu, Cm, Cf, Fm, No, Rf, Sg, and Hs, spontaneous fission and $\ensuremath{\alpha}$-decay half-lives are calculated within the dinuclear system model and compared with existing experimental data. Cluster radioactivity half-lives are also described for even U, Pu, and Cm isotopes. All these processes are considered for the evolution of a nucleus in the charge (mass) asymmetry coordinate and in the relative distance between the centers of clusters formed. The important roles of the driving potential and mass parameter in the charge asymmetry coordinate are shown for spontaneous fission. The global isotopic trends of spontaneous fission and $\ensuremath{\alpha}$-decay half-lives are studied. Drastic changes in the functional dependence of spontaneous fission half-life on the neutron number and in the absolute values of half-lives in the U--No and Rf--Hs nuclear groups are explained.

An improved semi-empirical relationship for cluster radioactivity * *Supported by the National Natural Science Foundation of China (U1832120, 11675265), the Natural Science Foundation for Outstanding Young Scholars of Hebei Province of China (A2020210012, A2018210146), the Continuous Basic Scientific Research Project (WDJC-2019-13) and the Leading Innovation Project (LC 192209000701)

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 of 114Ba 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.

Alpha and heavy cluster radioactivity of superheavy nuclei 100 ⩽ Z ⩽ 120

Using Cubic plus Yukawa plus Exponential (CYE) model, half lives of alpha decay and heavy cluster radioactivity of Superheavy nuclei have been systematically investigated for even-even, even-odd, odd-even and odd-odd nuclei with 100 ⩽ Z ⩽ 120. We have done our calculations by considering the Coulomb, centrifugal and Yukawa plus exponential potentials as an interacting barrier for separated fragments and the cubic potential for the overlapping region.The predicted half life time values by including deformation effects on parent and parent cluster have been compared with theAnalytical Super Asymmetric Fission (ASAF) model of D.N.Poenaru et.al. In this work, we have compared the half life time values of alpha and heavy cluster radioactivity of Super heavy nuclei leading to 208Pb. This study suggests that heavy-cluster radioactivity may be comparable to or even dominant over a decay for some of the isotopes with Z ⩾ 118. Furthermore, branching ratio calculations have been performed to find out the probable cluster emitters. The predictions for cluster emitters are in agreement with CPPM model by Santhosh et. al.,and Wentzel-Kramers-Brillouin (WKB) method by A.Soylu et. al. We hope that this study will help in future measurements on α-decay and cluster radioactivity half-lives of SHN.

α decay and cluster radioactivity within the redefined preformed cluster method

Half-lives and potential barriers of cluster radioactivity are investigated in the framework of the generalized liquid drop model (GLDM). We focus on the calculation of the preformation factor for heavy and superheavy nuclei within a redefined preformed cluster method, in which the decay constant is the product of the preformation factor, assault frequency, and penetration probability. The preformation factor is obtained from the penetrability of the potential internal barrier. The assault frequency has been estimated using classical methods and the penetration probability is calculated by the Wentzel-Kramers-Brillouin (WKB) method from tunneling through the GLDM potential barrier. The optimal mass inertia was selected for $\ensuremath{\alpha}$ decay and cluster emission by comparison of theoretical half-lives and experimental ones. The calculated preformation factor follows the preformation law formulas $S({A}_{C})=S{(\ensuremath{\alpha})}^{({A}_{C}\ensuremath{-}1)/3}$ [Phys. Rev. Lett. 61, 1930 (1988)], and the theoretical half-lives show better agreement with experimental data, including the new isotopes $^{219}\mathrm{Np}$ [Phys. Lett. B 777, 212 (2018)] and $^{220}\mathrm{Np}$ [Phys. Rev. Lett. 122, 192503 (2019)]. The predictions of cluster radioactivity half-lives are provided for heavy and superheavy nuclei, which will be useful for the detection and identification of these nuclei in the future.

Cluster radioactivity of neutron-deficient nuclei in trans-tin region

The possibility of cluster radioactivity (CR) of the neutron-deficient nuclei in the trans-tin region is explored by using the effective liquid drop model (ELDM), generalized liquid drop model (GLDM), and several sets of analytic formulas. It is found that the minimal half-lives are at Nd = 50 (Nd is the neutron number of the daughter nucleus) for the same kind cluster emission because of the Q value (released energy) shell effect at Nd = 50. Meanwhile, it is shown that the half-lives of α-like (Ae = 4n, Ze = Ne. Ze and Ne are the charge number and neutron number of the emitted cluster, respectively.) cluster emissions leading to the isotopes with Zd = 50 (Zd is the proton number of the daughter nucleus) are easier to measure than those of non-α-like (Ae = 4n + 2) cases due to the large Q values in α-like cluster emission processes. Finally, some α-like CR half-lives of the Nd = 50 nuclei and their neighbours are predicted, which are useful for searching for the new CR in future experiments.

Half-lives of cluster radioactivity using the modified generalized liquid drop model with a new preformation factor

Half-lives of clusters emitted from radioactive nuclei is determined using modified generalized liquid drop model (MGLDM), where a new preformation factor is added to the existing generalized liquid drop theoretical model with proximity 77 potential. Half-lives for radioactive nuclei whose mass numbers vary from 221 to 242, emitting C, O, F, Ne, Mg, and Si clusters, are calculated theoretically considering deformation and orientation effects and the values are in exact agreement with experimental data. Standard deviation of logarithm of half-lives using present model is found to be 0.755, which is a much better result in comparison with those of GLDM1 and GLDM2 of Bao et al. [J. Phys. G: Nucl. Part. Phys. 39, 095103 (2012)], which are 1.84 and 1.114, respectively. Also, half-lives of various radioactive nuclei whose mass numbers vary from 220 to 250 are predicted. We hope that our present study on cluster half-lives may be helpful for future works in this field.

Alpha decay and cluster radioactivity of super heavy nuclei 303,304120

The heaviest nuclei produced until now are few isotopes of the oganesson (atomic number Z = 118). We performed calculations of α-decay half-lives using the models AKRA (Akrawy, 2017), ASAF (Analytical Super-Asymmetric Fission, 1980), UNIV (Universal Formula, 2006), and semFIS (Semi-empirical formula based on Fission Theory, 1983). Cluster radioactivity half-lives are calculated with ASAF and UNIV models. The most important result of our calculations shows that 92,94Sr cluster radioactivity of 303,304120 has a branching ratio relative to α-decay of −0.10 and 0.49, respectively. We hope that future measurements will prove that cluster decay may compete with α decay.

Study of $$^{14}\hbox {C}$$ 14 C Cluster Decay Half-Lives of Heavy Deformed Nuclei

A theoretical model based on deformed Woods–Saxon, Coulomb and centrifugal terms are constructed to evaluate the half-lives for the cluster radioactivity of various super heavy nuclei. Deformation have been applied on all parts of their potential containing nuclear barrier for cluster decay. Also, both parent and daughter nuclei are considered to be deformed. The calculated results of $$^{14}\hbox {C}$$ cluster radioactivity half-lives are compared with available experimental data. A satisfactory agreement between theoretical and measured data is achieved. Also, obtained half-lives for each decay family is agreed with Geiger–Nuttall law.

Cluster decay half-lives of trans-lead nuclei based on a finite-range nucleon–nucleon interaction

Nuclear cluster radioactivity is investigated using microscopic potentials in the framework of the Wentzel–Kramers–Brillouin approximation of quantum tunneling by considering the Bohr–Sommerfeld quantization condition. The microscopic cluster–daughter potential is numerically constructed in the well-established double-folding model. A realistic M3Y-Paris NN interaction with the finite-range exchange part as well as the ordinary zero-range exchange NN force is considered in the present work. The influence of nuclear deformations on the cluster decay half-lives is investigated. Based on the available experimental data, the cluster preformation factors are extracted from the calculated and the measured half lives of cluster radioactivity. Some useful predictions of cluster emission half-lives are made for emissions of known clusters from possible candidates, which may guide future experiments.

Systematic calculations on cluster radioactivity half-lives of trans-lead nuclei with effective liquid drop model

The cluster radioactivities of trans-lead nuclei are systematically investigated by using the effective liquid drop description with the varying mass asymmetry shape and effective inertial coefficient. An effective nuclear radius constant formula is used instead of the original empirical formula in calculation. The calculated half-lives are in good agreement with the available experimental data. The root-mean-square deviation between the calculated logarithmic half-lives and the experimental ones is only 0.895. From the plots of the calculated lgT1/2 values versus the neutron (or proton) number of daughter, the shell effect of neutron magic number N=126 (or proton magic number Z=82) can be clearly seen. The odd-even-stagger can be clearly seen in the odd clusters 25Ne, 29Mg. The calculated half-lives conform to the Geiger-Nuttall law. We obtain some important conclusions about the Geiger-Nuttall law from the calculated results.