Coulomb And Proximity Potential Model Research Articles

Calculation of the half-life of proton radioactivity using the empirical formula depending on angular momentum

In this paper, considering the power of the daughter nuclear charge as a function of the orbital angular momentum taken away by the emitted proton, we propose a formula for the half-life of proton radioactivity. In this formula, we have three coefficients with orbital angular momentum dependence. Using experimentally measured half-lives for 8 proton emitters with [Formula: see text], 14 proton emitters with [Formula: see text] and 18 proton emitters with [Formula: see text], we have obtained the coefficients. The root mean square deviations of our formula respect to the experimental value are found 0.2514, 0.4442 and 0.1846 for emitters [Formula: see text], 2 and 5, respectively. We have compared our results with Sreeja formula, the semiempirical relation of Hatsukawa and theoretical models such as the Coulomb and proximity potential model (CPPM) and the Gamow-like model. The better agreement with experimental data was observed for our formula in comparison with other theoretical models and Sreeja and Hatsukawa formulas.

Prediction on the alpha decay half-lives of 223−243Am isotopes

Prediction on the alpha decay half-lives of 223−243Am isotopes

A Systematic study on the alpha decay of superheavy nuclei using empirical diffuseness parameter in the coulomb and proximity potential model

Recent studies of Dehghani et al [Mod. Phys. Lett. A 33 14 1850080 (2018)] and Abdul-latif et al [Phys. Rev. C 100, 024601 (2019)] revealed the importance of the diffuseness parameter in the calculation of alpha decay half-lives from superheavy elements using proximity potentials. In the present paper, predictions of the empirical formula for the diffuseness parameter proposed by Abdul-latif et al is analyzed in view of the diffuseness parameter calculated by Dehghani et al using WKB method and considering deformed Woods–Saxon nuclear potential, deformed Coulomb potential, and centrifugal potential; and related theoretical aspects. From the conclusions, we propose three new empirical formulae for the diffuseness parameter. Using the diffuseness parameter calculated from the proposed empirical formula in the Coulomb and Proximity Potential Model (CPPM), the alpha decay half-life of 68 superheavy nuclei is calculated and compared with the experimental values. The inclusion of the diffuseness parameter in proximity potential improved the predictive power of the CPPM considerably.

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 Shandong Province Natural Science Foundation, China (ZR2022JQ04), the Opening Project of Cooperative Innovation Center for Nuclear Fuel Cycle Technology and Equipment, University of South China (2019KFZ10), the Innovation Group of Nuclear and Particle Physics in USC, Hunan Provincial Innovation Foundation for Postgraduate (CX20230962). Science and technology plan project of Hengyang City (202150063428).

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.

Heavy particle radioactivity of superheavy nuclei.

We investigated different decay modes such as heavy particle radioactivity (HPR), spontaneous fission (SF), alpha decay and beta-decay in superheavy (SH) region 104≤Z≤126. In HPR, different emissions from Zmin=28 to maximum heavy particle (HP) emission up to Zmax=Z-82 were considered. In the evaluation of Q-values, mass excess Weizsäcker-Skyrme 4+radial basis function (WS4+RBF) values were taken into account. The half-lives of cluster decay determined using modified generalised liquid drop model (MGLDM) and Coulomb and proximity potential model (CPPM) were in close agreement with the experimental results. The MGLDM produce less deviation compared with CPPM. The role of asymmetry effect, relative neutron excess, pairing effect and Coulomb effect on half-lives were studied. A band of neutron numbers from 193 to 200 shows extra stability against HPR. The HPR of 86Kr, 94Zr, 91Y and 96Mo is observed in the superheavy elements Z=118, 122-124 and 126. The dominant decay mode identified is compared with SF, alpha and beta± decay, the majority of decay chains end with the lead nuclei, which is also evident in supernova and galaxy spectrum. This study could be useful in nuclear astrophysics.

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.

Decay probability of oxygen and flourine clusters from 290−320122, 292−332124 and 298−326126 even-even isotopes

Emission probability of 17−23O and 19−25F isotopes from 290−320122, 292−332124 and 298−326126 eve-even parents were studied by calculating the barrier penetrability, decay constant and decay half-lives using the Coulomb and Proximity potential Model (CPPM). The Q-values are estimated using the WS4 mass model. Clusters like 18,20O, 23,25F show the emission probability from the selected parents with a decay half-life less than the experimental upper limit of 1030 seconds. Neutron shell closure at N = 176 and 184 is identified from the plot of log10⁡T1/2 versus the neutron number of parent nuclei.

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.

Theoretical calculation of alpha decay half-lives of Neptunium nuclei using modified generalized liquid drop model

We considered the α-decay half-lives of neptunium (ZNp = 93) nuclei in the case of deformed nuclei in the range 219 ≤ A ≤ 239 using the generalized liquid-drop model (GLDM) with 1977 nuclear proximity potential suggested by Blocki et al. (1977) [29]. Also, we analyzed the α-decay half-lives of Np isotopes within the WKB method and the Deformed Proximity Potential Model (DPPM). We consider the quadrupole and hexadecapole deformations at θ=0, θ=30, θ=45, and θ=90 degrees. The calculated half-lives and the alpha decay branching ratios are compared with experimental data and are in good agreement. We compared the results obtained with the corresponding experimental data and with the models UNIV, UDL, SemFIS, the Coulomb and Proximity Potential Model (CPPM), SLB and Royer and it is found that they match well over a wide range. The calculated results are in reasonable agreement with the experimental data. Therefore, DPPM gives reliable and accurate results for favored α-decays in the neptunium mass region.

Systematic study of two-proton radioactivity within various versions of proximity formalisms

In this work, we study the two-proton (2p) radioactivity half-lives for nuclei near or beyond the proton drip line within the Coulomb and proximity potential model (CPPM). We investigate the 28 versions of proximity potential formalisms, which were proposed for heavy-ion fusion reactions, heavy-ion elastic scattering, ternary fission and other applications. The results indicate that BW91 and Bass77 are inappropriate for handling 2p radioactivity since the classical turning point r in cannot be obtained for the depth of the total interaction potential between the released two protons and daughter nucleus being greater than the 2p radioactivity released energy. Among the other 26 proximity potential formalisms, the one proposed by Royer et al in 1984 denoted as Prox.77-8 is the best version with the lowest rms deviations between experimental data and relevant theoretical results. It is worth mentioning that the calculations of Coulomb and Proximity Potential Model for Deformed Nuclei (2021 PRC 104, 064 613) has least standard deviation (σ = 0.592) compared with present model and other models/formulae. Furthermore, we use CPPM with Prox.77-8 to predict the 2p radioactivity half-lives of 35 potential candidates whose 2p radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020. The predicted results are consistent with previous theoretical models such as the unified fission model (UFM), generalized liquid drop model (GLDM) and effective liquid drop model (ELDM).

Predictive power of theoretical models in cluster radioactivity

Many microscopic and macroscopic models are available in the literature to study the cluster radioactivity. The investigation of appropriate theoretical model to study the cluster decay process is an important aspect. We studied cluster-decay in the atomic and mass number range [Formula: see text] and [Formula: see text] using modified generalized liquid drop model (MGLDM), Coulomb and proximity potential model (CPPM) and generalized liquid drop model (GLDM). The results obtained using macroscopic models are compared with that of microscopic models. There are various mass excess tables available in the literature. But indentification of suitable mass excess table for cluster radioactivity is an also important part of this study. The macroscopic models, such as MGLDM, CPPM and GLDM, were used to analyze cluster-decay half-lives. Along with this, microscopic and semi-empirical relations were also investigated. The standard deviation is evaluated in macroscopic, microscopic and semi-empirical formulae. A detailed investigation shows that among macroscopic model-MGLDM, macroscopic-RMFM and in case of semi-empirical formulae, AZF produces less deviation. Hence, these results give an insight into prediction of cluster decay half-lives in heavy and superheavy region for unknown nuclei.

Study of cluster emissions from heavy nuclei using an empirical formula and the Coulomb and Proximity potential model for deformed nuclei

The decay characteristics of various clusters and neutron halo nuclei from heavy elements [Formula: see text] are studied within the framework of the Coulomb and Proximity Potential Model for Deformed Nuclei (CPPMDN) and using a new empirical formula proposed by us. The predictive power of our formula is verified by comparing the predictions with the available experimental data and with the predictions of other models such as CPPM, Universal Decay Law of Qi et al. (UDL), Unified Description formula (UD) of Ni et al. Using the present formula and CPPMDN, decay half-lives of various light clusters from heavy elements are calculated, and the results are compared with the predictions of UDL, UD, and predictions made by Santhosh et al. based on the Modified Generalized Liquid Drop Model (MGLDM). The decay half-lives of halo nuclei from heavy elements are also calculated using the new formula and CPPMDN and compared with the predictions of UDL, UD, and the predictions made by Santhosh et al. based on the Coulomb and Proximity Potential Model (CPPM).

Macroscopic versus microscopic models in predicting α-decay half-lives of actinide nuclei

This paper investigates the predictive power of the macroscopic and microscopic models in alpha-decay of actinide nuclei. Macroscopic theoretical models such as Coulomb and Proximity potential model (CPPM), Modified generalized liquid drop model (MGLDM) and Effective liquid drop model (ELDM) are applied in predicting the alpha-decay half-lives of actinide nuclei. The half-lives produced by these macroscopic models are compared with that of microscopic models such as Cluster model with two-potential approach (CM), Microscopic cluster model (MCM), Multichannel cluster model (MCCM) and that of experiments. The deviation of these models with the experiments is quantified using statistical treatment such as root mean square deviation [Formula: see text] (RMSD), mean deviation ([Formula: see text]), index [Formula: see text] and root mean square error (RMSE). It is found that among the microscopic and macroscopic models, ELDM and MCCM are, respectively, found to be accurate than that of other models. The microscopic model MCCM produces alpha-decay half-lives close to the experiments in the actinide region. The appropriate mass excess values have been identified to predict the exact alpha-decay half-lives in the actinide region.

Two-proton radioactivity within Coulomb and proximity potential model * *Supported 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 Natural Science Foundation of Hunan Province, China (2015JJ3103, 2018JJ2321), the Innovation Group of Nuclear and Particle Physics in USC, the Shandong Province Natural Science Foundation, China (ZR2019YQ01), Hunan Provincial Innovation Foundation For Postgraduate (CX20210942), the Opening Project of Cooperative Innovation Center for Nuclear Fuel Cycle Technology and Equipment, University of South China (2019KFZ10)

Considering the preformation probability of the two emitted protons in the parent nucleus, we extend the Coulomb and proximity potential model (CPPM) to systematically study two-proton (2p) radioactivity half-lives of the nuclei close to proton drip line. The proximity potential chosen is Prox. 81 proposed by Blocki et al. in 1981. Furthermore, we apply this model to predict the half-lives of possible 2p radioactive candidates whose 2p radioactivity is energetically allowed or observed but not yet quantified in the evaluated nuclear properties table NUBASE2016. The predicted results are in good agreement with those from other theoretical models and empirical formulas, namely the effective liquid drop model (ELDM), generalized liquid drop model (GLDM), Gamow-like model, Sreeja formula and Liu formula.

Predictions of \(\alpha \)-decay Half-lives for Neutron-deficient Nuclei with the Aid of Artificial Neural Network

In recent years, artificial neural network (ANN) has been successfully applied in nuclear physics and some other areas of physics. This study begins with the calculations of {\alpha}-decay half-lives for some neutron-deficient nuclei using Coulomb and proximity potential model (CPPM), temperature dependent Coulomb and proximity potential model (CPPMT), Royer empirical formula, new Ren B (NRB) formula, and a trained artificial neural network model (TANN ). By comparison with experimental values, the ANN model is found to give very good descriptions of the half-lives of the neutron-deficient nuclei. Moreover CPPMT is found to perform better than CPPM, indicating the importance of employing temperature-dependent nuclear potential. Furthermore, to predict the {\alpha}-decay half-lives of unmeasured neutron-deficient nuclei, another ANN algorithm is trained to predict the Q {\alpha} values. The results of the Q {\alpha} predictions are compared with the Weizs\"acker-Skyrme-4+RBF (WS4+RBF) formula. The half-lives of unmeasured neutron-deficient nuclei are then predicted using CPPM, CPPMT, Royer, NRB, and TANN , with Q{\alpha} values predicted by ANN as inputs. This study concludes that half-lives of {\alpha}-decay from neutron-deficient nuclei can successfully be predicted using ANN, and this can contribute to the determination of nuclei at the driplines.

Empirical formula for heavy cluster decay in the superheavy region

In this paper, an empirical formula to describe the heavy cluster decay with [Formula: see text] ([Formula: see text] is the charge number of the emitted cluster) from superheavy elements is proposed. The predictions of our formula are compared with the predictions of Coulomb and Proximity Potential Model (CPPM), the predictions of Analytical Super Asymmetric Fission (ASAF) model and the predictions by UDL formula of Qi et al. Excellent agreement is found between the predictions of CPPM and ASAF models and those of the present formula. Using our formula, we have calculated the decay half-lives of various heavy cluster emission from superheavy elements leading to doubly magic [Formula: see text]Pb and compared with the predictions of CPPM. The predictions of UDL formula deviate considerably from the predictions of this formula, CPPM and ASAF model, giving much lower decay half-lives, as the order of decay half-life increases. Possible heavy cluster emissions from [Formula: see text] and 122 nuclei leading to [Formula: see text]Pb and [Formula: see text]Bi are also predicted.

Alpha decay half-lives of 171-189Hg isotopes using Modified Gamow-like model and temperature dependent proximity potential

The alpha decay half-lives for $^{171-189}\mathrm{Hg}$ isotopes have been computed using the Gamow-like model (GLM), modified Gamow-like model (MGLM1), temperature-independent Coulomb and proximity potential model (CPPM), and temperature-dependent Coulomb and proximity potential model (CPPMT). New variable parameter sets were numerically calculated for the $^{171-189}\mathrm{Hg}$ using the modified Gamow-like model (termed MGLM2). The results of the computed standard deviation indicates that the modified Gamow-like model (MGLM2) and the temperature-dependent Coulomb and proximity potential model give the least deviation from available experimental values, and therefore suggests that the two models (MGLM2 and CPPMT) are the most suitable for the evaluation of $\alpha$-decay half-lives for the $\mathrm{Hg}$ isotopes.

Cluster decay half-lives and preformation probabilities

An improved semi-analytic approach to the barrier penetration probability is developed in the frame work of the Wentzel-Kramers-Brillouin (WKB) approximation. It is used to calculate decay half-lives and preformation probabilities for a set of 304 cluster emitters in the range 87 ≤ Z ≤ 96 and a set of 390 α-emitters in the range 52 ≤ Z ≤ 120. For cluster decay, the validity of our approach is tested against Coulomb and proximity potential model (CPPM) by comparing decay half-lives and barrier penetration probabilities. Our results are found to be in a good agreement with CPPM calculations and with the available experimental data. In case of α-decay, our calculations are tested against the experimental data and also a very good agreement is achieved. In both cases, results are also compared with calculations of some other well known universal decay laws that are used in many recent studies. Our approach shows a better agreement with experimental data than most of the other models. Our study is extended to calculate the assault frequency and preformation probability of the cluster inside the parent nucleus. A strong correlation is obtained for all these parameters with each other. Neutron shell closures are found to be more important in the cluster decay process than proton shell closure. It is also noted that the odd–even staggering behavior dominates the decay processes involving the emission of clusters with odd neutron number.

A Study on the Emission of 1, 2 Proton Halo Nuclei from Parent with Z = 121–128 in the Superheavy Nuclei via Cluster Radioactivity

Probabilities for the emission of various one proton and two proton halo nuclei from parent superheavy (SH) isotopes with Z = 121–128 are studied with the Coulomb and proximity potential model (CPPM) as the interacting barrier. The half-lives and other characteristics for the emission of one proton halo nuclei, 8B, 11,12N, 17F, 23Al, 27,28P, and two proton halo nuclei, 9C, 17,18Ne, 20Mg, 29S from the SH parent isotopes are determined and plotted it as a function of neutron number of daughter nuclei. The shell closure effects of parent and daughter nuclei are evident from the plot of computed half-lives. The peaks in the plot of half-life show the shell closure of parent and dips in the half-life show the shell closure of daughter nuclei. In the SH region with Z = 121–128 and N = 147–194, we observed that neutron shell closure of parent occurs at N~184 and neutron shell closure of daughter nuclei at N~174–184. Moreover, the most probable proton halo nuclei emissions are also evident from the computed half-life values. We have also studied the Geiger-Nuttall plots of log10 (T1/2) vs. Q−1/2 and log10 (T1/2) vs. −ln(P) for all the selected proton halo nuclei emitting from the SH parent isotopes with Z = 121–128 and are found to be linear. From the linearity of these plots, we found that GN law is valid for the proton halo decay also.

Theoretical studies on Alpha decay half-lives of Astatine isotopes

The half-life of a parent nucleus of Astatine isotopes [Formula: see text] decaying via alpha emission is investigated by employing Coulomb and proximity potential model (CPPM) using the WKB barrier penetration probability and other different analytical and semiempirical formulae of Royer, AKRE, Akrawy, RoyerB, MRoyerB, MRenB, SemFIS, VS and SLB. In the calculation of Alpha decay (AD) half-life the available experimental and theoretical [Formula: see text]-values with the total alpha kinetic energy have been considered. The behavior of hindrance factor with the variation of mass numbers of parent nuclei for isotopes in the range [Formula: see text] and the effect of magic number at closed shells were investigated. Through the comparison of obtained results from the systematics with the experimental data, the prediction of SemFIS formula was the best among the studied ones where it shows the minimum standard deviation of 0.829881.