Universal Decay Law Research Articles

Cluster radioactivity of heavy elements within an improved Coulomb and Proximity potential model

The Coulomb and Proximity potential Model (CPPM) is improved by introducing an accurate empirical expression for the nuclear surface diffuseness parameter in the expression for the proximity potential. Within the improved CPPM, the decay half-lives of experimentally detected cluster emissions from heavy elements are calculated. The results of the calculations using the Universal Decay Law (UDL) [Qi et al., Phys. Rev. Lett. 103 (2009) 072501], the improved empirical formula of Sahu et al. (ImSahuB) [Wang et al., Chin. Phys. C 45 (2021) 044111], and the empirical formula of Horoi [J. Phys. G. Nucl. Part. Phys. 30 (2004) 945] are compared with the predictions of the improved CPPM. The lowest standard deviation is obtained for the predictions using the improved CPPM. The model’s predictive power increases significantly when the proximity potential is modified by including the diffuseness parameter. Furthermore, improved CPPM is employed to calculate the decay half-lives of undiscovered cluster emissions from heavy elements, a valuable information for upcoming experimental investigations. The calculated values are compared with the predictions of the UDL, Horoi formula and the improved empirical formula of Sahu et al. (ImSahuB). There is a high degree of agreement between the improved CPPM, UDL, and Horoi formula predictions. The ImSahuB formula predict decay half-life one or two order magnitudes lower than the predictions of the other models.

Systematic study of [formula omitted]-decay in neutron-deficient nuclei

The α-decay half-lives of 266 neutron-deficient nuclei in the 52 ≤Z≤ 118 range are calculated within the density-dependent cluster model. The realistic Michigan three-range Yukawa-Paris nucleon–nucleon interaction is used to calculate the α-core interaction potential within the double-folding model (DFM) context. In addition to the double-folding model, four analytical formulas are employed to compute the half-life time for the neutron-deficient nuclei. The obtained results from the five theoretical approaches are compared to the most recent experimental data. The calculated results from the DFM and the universal decay law (UDL) were in good agreement with the experimental data. A universal curve for α-decay of neutron-deficient nuclei has been analyzed, illustrating the correlation between the decimal logarithm of the experimental half-lives and the negative decimal logarithm of penetrability. We studied the variation of log10T with the neutron number of the daughter nuclei, Nd, for different neutron-deficient isotopes in the range 78 ≤Z≤ 92. We attempt to predict the neutron energy levels for each isotope from the behavior of log10T against Nd. Moreover, the impact of higher-multipolarity deformations, up to hexacontratetrapole, on the behavior of α-decay half-lives around the neutron shell closure N=126 is investigated, both with and without including octupole deformation.

Study α decay and proton emission based on data-driven symbolic regression

α decay and proton emission were combined using symbolic regression to improve the accuracy of predicting their respective half-lives using two theoretical formulations: (1) adjustable parameters for the universal decay law and universal decay law for proton emission are obtained by regressions with fully-constrained symbolic regressions. (2) New theoretical formulas for calculating the half-life of proton emission and α decay are obtained using unconstrained symbolic regressions combined with nuclear data. Our computational analysis indicates that fully-constrained symbolic regressions and unconstrained symbolic regressions are reliable for specific and general nuclei, respectively, in terms of replicating experimental results, and are sufficiently robust to produce accurate half-life predictions. Unlike other machine learning methods that generate complex and opaque results, our approach integrates physics and machine learning to create interpretable formulas that provide intuitive parametric outcomes and transparent and dependable inferences of half-lives, even in areas with limited experimental data. The test results show that the equation yields accurate results, and can be easily applied to future α decay and proton emission studies.

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.

An improved simple model for α decay half-lives*

Abstract In this paper, using the α particle preformation probabilities from Xu et al. [Xu and Ren, Nucl. Phys. A 760, 303 (2005)], which were extracted by fitting experimental half-lives of α decay, based on a phenomenological harmonic oscillator potential model (HOPM) [Bayrak, J Phys G 47, 025102 (2020)], refitting 178 α decay half-lives of even-even nuclei obtained from the latest nuclear property table NUBASE2020, we obtain the only one adjustable parameter MeV in the HOPM, i.e., the depth of nuclear potential. The corresponding root-mean-square (rms) deviation is . Furthermore, to consider the contribution of centrifugal potential to unfavored α decay half-lives, adding a new term (d and l are the adjustable parameter and orbital angular momentum carried away by emitted α particle) to the logarithmic form of favored α decay half-lives under the HOPM framework, we propose an improved simple model (ISM) for calculating favored and unfavored α decay half-lives. Fitting the experimental half-lives of 205 unfavored α decay, we obtain . The ISM is used to calculate the unfavored α decay half-lives of 128 odd-A and 77 odd-odd nuclei. The results improve by 54.2% and 53.6%, respectively, compared with HOPM. In addition, we extend the ISM to predict the α decay half-lives of 144 nuclei with , and 120. For comparison, the improved model with eight parameters (DUR) proposed by Deng et al. [Deng, Phys. Rev. C 101, 034307 (2020)] and the modified universal decay law (MUDL) proposed by Soylu et al. [Soylu, Nucl. Phys. A 1013, 122221 (2021)] are also used. The predictions of these models and/or formulas are generally consistent with each other.

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.

Theoretical calculations of proton emission half-lives based on a deformed Gamow-like model* *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

In this study, proton emission half-lives were investigated for deformed proton emitters with based on the presented deformed Gamow-like model, where the deformation effect was included in the Coulomb potential. The experimental half-lives of proton emitters can be reproduced within a factor of 3.45. For comparison, the results from the universal decay law and the new Geiger-Nuttall law are also presented. Furthermore, the relevance of the half-lives to the angular momentum l for 117La, 121Pr, 135Tb, and 141Ho were analyzed, and the corresponding possible values of l were proposed: l = 3, 3, 4, 4.

Reynolds Number Effects on Turbulent Wakes Generated by Rectangular Cylinders With Streamwise Aspect Ratios Between 1 and 4

Abstract The effects of streamwise aspect ratio and Reynolds number on the separated shear layer and near wake of rectangular cylinders in uniform flow are investigated experimentally using a particle image velocimetry system. Four length-to-height ratios (AR = 1, 2, 3, and 4) were examined at Reynolds numbers (based on freestream velocity and cylinder height) of 3000, 7200, 14,700, and 21,000. The results show that the separated shear layer is either shed directly into the wake region (AR1 and AR2) or reattaches onto the cylinder (AR4), regardless of the Reynolds number. Meanwhile, a transitional regime occurs for AR3 where mean flow reattachment on the cylinder is highly dependent on the Reynolds number. The peak magnitudes of the Reynolds stresses, turbulent kinetic energy, turbulence production, and its transport are highest for AR1 owing to stronger vortex shedding. Aspect ratio and Reynolds number also have significant effects on shear layer transitioning from laminar to turbulence but the transition lengths, when normalized by the corresponding value at Re = 3000, follow a universal power decay law. The wake characteristics, including the recirculation length and wake formation lengths, are independent of Reynolds number for AR1 but decrease with Reynolds number for the longer cylinders, while AR2 shows the largest values. The probability density functions and joint probability density functions are used to examine the effects of Reynolds number on the fluctuating velocities and momentum transport in the shear layer and near-wake region.

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.

Theoretical predictions on the decay modes of 282−310Og

Possible decay modes of 282−310Og are studied within the framework of the Coulomb and Proximity Potential Model (CPPM), Universal Decay Law (UDL) and the Hatsukawa formula. A new diffusion parameter and a new preformation factor are included in the CPPM Model calculations. We have refitted the Hatsukawa formula to calculate the alpha and cluster decay half-lives in the superheavy region. The spontaneous fission (SF) half-lives are calculated using the shell correction energy-dependent formula of Santhosh et al. The predicted alpha decay half-lives are compared with the predictions of the UDL formula; and the predictions of Soumya et al. and Koyuncu et al. Possible heavy cluster decays from 284−297Og are also studied within the UDL formula and by using the empirical formula of Hatsukawa et al. with new fitting parameters, and a comparison is made with the predictions of Santhosh et al.

Systematic investigation of the alpha and cluster decay half-lives for heavy and superheavy nuclei within the shifted Deng-Fan potential

The half-lives of alpha decays for even-even nuclei with Z=60−118 and the cluster radioactivities for even-even emitters for which the experimental data are available, also the various cluster decays of even-even radium isotopes are calculated. Our calculations are within the framework of Wentzel-Kramers-Brillouin (WKB) method by considering the Bohr-Sommerfeld quantization condition based on the shifted Deng-Fan potential. The obtained results are compared with the squared Woods-Saxon and Cosh potentials and several theoretical models, including the universal model (UNIV), the unified fission model (UFM), the universal decay law (UDL), and Ni, Royer, Tavares and Balasubramaniam semiempirical formulas, as well as the experimental data. Good agreement between the experimental and the proposed potential model results, indicates that the shifted Deng-Fan potential is a suitable phenomenological potential to describe both alpha and cluster decays of radioactive nuclei. Also we observe the significant role of neutron magicity in the half-lives of cluster decays of radium isotopes at N=126 of daughter nuclei and the parent nucleus 214Ra.

Theoretical study on neutron halo emission from heavy elements

Theoretical study on the emission characteristics of one-neutron and two-neutron halo nuclei from heavy elements was performed within the framework of the Unified Description formula (UD), Universal Decay Law (UDL), Modified Universal Decay Law (MUDL), Gupta formula, Ren formula and the formula of Horoi et al. The predictions are compared with that of the Coulomb and Proximity Potential Model (CPPM) of Santhosh et al. [6]. One neutron halo nuclei 15C, 23O, and 24F are found to be emitted from heavy elements with a half-life within the experimental upper limit. Compared to one-neutron halo, two-neutron halo emissions are less probable to emit from heavy elements. The UDL and MUDL are found to be the most successful empirical formulae in describing the halo decay characteristics of heavy elements.

Cluster radioactivity in platinum isotopes

We studied the cluster radioactivity in Platinum isotopes using different proximity potentials in the Coulomb Proximity Potential Model (CPPM). Cluster decay with cluster nuclei like 8Be and 12C from different Platinum isotopes are considered. Logarithmic values of half-life are calculated using CPPM with different proximity potentials and compared with the half-life from the Universal Decay Law (UDL).

Surface and decay properties of newly synthesized 207,208Th isotopes for various α-decay chains

Considering various initial deformations, the ground, first excited, and second excited states binding energies are calculated using the effective field theory motivated relativistic mean-field based IOPB-I force parameter. The alpha decay chains for both the 207Th and 208Th are examined. As observed for both nuclei, it takes four subsequent α-particle emissions to reach the stable Pb nucleus. The half-lives determined by two widely used Viola-Seaborg and modified universal decay law formulas are compared with the available experimental data. The surface property-like symmetry energy is also predicted for these nuclei in the framework of the coherent density fluctuation model and establishes a connection between the decay behavior and the symmetry energy.

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)].

An empirical formula for the alpha decay half-lives

Using 377 available experimental data, we have obtained an empirical formula to calculate alpha decay half-lives based on Geiger–Nuttall law for even–even, even–odd, odd–even and odd–odd nuclei. The coefficients of Geiger–Nuttall law have been modified as a function of the atomic number of the parent nucleus and the orbital angular momentum. The obtained root mean square deviations from experimental half-lives for even–even, even–odd, odd–even and odd–odd nuclei are 0.3265, 0.5412, 0.4848 and 0.4353, respectively. For most nuclei, the obtained results from this formula are in good agreement with the experimental data. We compared our results with other formulas such as universal decay law, Royer, AKRA, MYQZR and Luo. Also, using this formula, we presented predictions for superheavy nuclei with [Formula: see text]–124 using the [Formula: see text]-values based on the finite range droplet model and Weizsäcker–Skyrme. It is found that the behavior of the half-life of alpha decay is sensitive to the used [Formula: see text]-values.

Exotic decay modes of uranium isotopes

We investigate the emission of alpha particles and various clusters from uranium isotopes using the Effective Liquid Drop Model. The study has been carried out for the isotopes ranging between the p-drip-line and beta stability line. The half-lives calculated are in good agreement with the Universal Decay law, the scaling law of Horoi et al. and also with the available experimental values. We have listed the half-lives of all probable decay modes of uranium isotopes. The uncertainties in Q-value and half-lives are also presented. It is also observed that the probability of cluster emission decreases with the increase of neutron number of parent nuclei. The linear nature Geiger-Nuttal plot has been reproduced for the prominent decay modes. The study also affirms the inevitable role of neutron magicity in cluster radioactivity. We have also analyzed the branching ratios to identify the most prominent decay modes of uranium isotopes.

A systematic analysis for one proton radioactivity of ground state nuclei

We systematically studied proton radioactivity half-lives in the atomic number range 53≤Z≤83 using macroscopic models such as Coulomb and Proximity potential model, effective liquid drop model (ELDM), Generalized liquid drop model (GLDM), Universal decay law for proton emission (UDLP), Gammow-like model (GLM) and Unified fission model (UFM). The proton decay half-lives produced by the macroscopic models are compared with those of semi-microscopic approach such as DDM3Y and using effective interaction potentials such as JLM, M3Y+EX, R3Y+EX, SLy4, SRG, SKC and SKD. After detail analysis, it is found that among macroscopic models ELDM and semi-empirical formula UDLP produce proton decay half-lives close to experiments. Furthermore, among semi-microscopic approach, DDM3Y produces proton decay half-lives close to the experiments. Thus, Both ELDM and DDM3Y model can be effectively used in the prediction of half-lives of unexplored proton emitters.

α and 2α decay of nuclei in the region 94≤Z≤101 using the modified generalized liquid drop model

The \ensuremath{\alpha} decay and $2\ensuremath{\alpha}$ decay of various isotopes of Pu, Am, Cm, Bk, Cf, Es, Fm, and Md in the mass region $A=218$ to 273 are investigated using the modified generalized liquid drop model (MGLDM) and universal decay law. The comparison of experimental alpha decay half-lives with the predicted half-lives proves the consistency of our calculations. As a result we broadened our investigation to also include a study of double alpha decay of these isotopes. There is a considerable interest in performing research on double alpha decay, as seen by the proposal submitted at CERN to investigate the double alpha radioactivity of $^{224}\mathrm{Ra}$. In view of this, the decay half-lives of most probable $2\ensuremath{\alpha}$ emitters, calculated using MGLDM by employing different preformation factors, are presented which can be beneficial for upcoming experimental investigations on this topic. A peak or dip in \ensuremath{\alpha} and $2\ensuremath{\alpha}$ decay half-life is witnessed which indicates the stability of parent or daughter isotopes correspondingly. Minimum and maximum half-lives for decay are observed when the daughter and parent nuclei, respectively, contain a magic number of neutrons. From our study, 126 and 162 are found as magic/semimagic numbers. A linear plot is obtained while plotting ${\mathrm{log}}_{10}{T}_{1/2}$ of all the isotopes against $Z{Q}^{\ensuremath{-}1/2}$, which emphasizes that our estimations are reliable.

Simple deep-learning approach for α -decay half-life studies

To exploit the potential of deep learning (DL) in $\ensuremath{\alpha}$-decay studies, we refocus on the essence of DL, which is a nonlinear input-output mapping with a hierarchical learning process. Here, instead of using the residual between experimental data and the calculation, the idea of training DL directly by experimental $\ensuremath{\alpha}$-decay half-life is used. The Levenberg-Marquardt backpropagation algorithm is utilized for fixing free parameters of the mapping. A $\mathcal{K}$-fold cross-validation method is introduced to avoid overfitting and improve the generalization performance of DL, as well as to determine hyperparameters effectively. We find that DL results with both three-dimensional ${Z,A,{Q}_{\ensuremath{\alpha}}}$ and four-dimensional ${Z,A,{Q}_{\ensuremath{\alpha}},l}$ input vectors achieve an impressive accuracy that matches or even exceeds the traditional models. Especially, DL realizes an efficient extraction of the pertinent shell and odd-even staggering effects of half-life solely from the characteristics of ${Q}_{\ensuremath{\alpha}}$ values. On the other hand, the universal decay law (UDL) describes the classical relationship between ${Z,A,{Q}_{\ensuremath{\alpha}}}$ and a-decay half-life, which is homologous with DL. Heuristically, we add the contributions of the angular momentum and blocking effect of unpaired nucleons in the UDL and develop an improved UDL formula.