Effective Liquid Drop Model Research Articles

A simple model for two-proton radioactivity* *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 and Particle Physics in USC,

In this work, considering the preformation factor of the emitted two protons in parent nucleus and the effect of the parent nucleus deformation, based on the Wentzel-Kramers-Brillouin approximation and Bohr-Sommerfeld quantization condition, we improve a simple phenomenological model proposed by Bayrak [J. Phys. G: 47, 025102 (2020)] to systematically study radioactivity half-lives. This model contains two adjustable parameters and , which are related to the depth of nuclear potential and effect of deformation. The calculated results show that this model can effectively reproduce the experimental data with a corresponding root-mean-square (RMS) standard deviation of σ = 0.683. For comparison, we include the Gamow-like model (GLM) proposed by Liu et al. [Chin. Phys. C 45, 044110 (2021)], generalized liquid drop model (GLDM) proposed by Cui et al. [Phys. Rev. C 101, 014301 (2020)], effective liquid drop model (ELDM) proposed by M. Gonalves et al. [Phys. Lett. B 774, 14 (2017)], two-potential approach with Skyrme-Hartree-Fock (TPASHF) proposed by Pan et al. [Chin. Phys. C 45, 124104 (2021)], phenomenological model with a screened electrostatic barrier (SEB) propoesed by Zou et al. [Chin. Phys. C 45, 104101 (2021)], unified fission model (UFM) proposed by Xing et al. [Chin. Phys. C 45, 124105 (2021)], Coulomb and proximity potential model for deformed nuclei (CPPMDN) proposed by Santhosh [Phys. Rev. C 104, 064613 (2021)], two-parameter empirical formula proposed by Liu et al. [Chin. Phys. C 45, 024108 (2021)], and four-parameter empirical formula proposed by Sreeja et al. [Eur. Phys. J. A 55, 33 (2019)]. In addition, we use this model to predict the radioactive half-lives of some possible potential nuclei whose radioactivity are energetically allowed or observed but not yet quantified in NUBASE2020.

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 two proton radioactivity within the effective liquid drop model

In this study, we investigated two-proton radioactivity using the effective liquid drop model with varying mass asymmetry shapes and effective inertia coefficients (VMAS-EFF). Gaudin’s expression term for Coulomb potential energy is replaced in the current study’s calculation of potential energy. The VMAS-EFF combination predicts the half-life with the lowest standard deviation ( σ =1.03) compared to other models and previous constant mass asymmetry with Werner-inertial Wheeler’s coefficient combinations. The lowest standard deviation value indicates that the VMAS-EFF combination is suitable for reproducing the experimental data. We extended the half-life predictions to another 54 nuclei and compared them with six theoretical model predictions and two empirical formula predictions. The present work also investigated the decay possibilities using quantum tunnelling by computing the driving potential (V-Q) for various states of angular momentum l = 0, 2, 3, and 4. Found that 6Be, 6B, 8C, 12O,15,16Ne, 19Mg, 22Si, 26S, 30Ar 38,39Ti, 40V, 42Cr, 45Fe, 48,49Ni, 54Zn, 58,59,60Ge and 64Se nuclei have a high chance of emission for two protons, while 7B, 10N, 14F, 17Na, 24P, 28Cl,32K, 34Ca, 36,37Sc, 44Mn, 47Co, 52Cu, 56,57,58Ga, 61,62As nuclei have a lower chance for two proton than one proton decay. The computation of separation energy findings agree well with the driving potential findings.

A study of decay chains of radioactive actinium isotopes

In this paper, we systematically studied half-lives of the different decay modes using various theoretical models such as the unified fission model (UFM) and the effective liquid drop model. Beta-decay half-lives were evaluated using semi-empirical formulae available in the literature. We compared half-lives of all the studied decay modes and identified shorter half-lives among the same in [Formula: see text]Ac nuclei. We investigated the actinium series which is similar to the thorium series. Among these decay series, alpha-emitting isotopes show great promise for cancer treatment because of their short path length and high-energy transfer of radiation. Furthermore, we predicted the decay chains of the actinium isotopes. All the decay series of actinium ends with the formation of stable nuclei or with longer half-lives. The predicted decay series and new isotopes during the decay process are helpful in the field of medicine and radiotherapy.

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.

Roles of tensor force and pairing correlation in two-proton radioactivity of halo nuclei* *Supported by the National Natural Science Foundation of China (U1832120, 11675265), the Natural Science Foundation for Outstanding Young Scholars of Hebei Province, China (A2020210012), the Natural Science Foundation of Hebei Province, China (A2021210010), the Key Laboratory of High Precision Nuclear Spectroscopy, Institute of Modern Physics, Chinese Academy

The tensor force and pairing correlation effects on the two-proton radioactivity of Mg and Si with a pronounced two-proton halo are explored in the framework of spherical Skyrme-Hartree-Fock-Bogoliubov theory. It is shown that the halo sizes are enhanced with the increase in the strength of the tensor force and pairing correlation. Furthermore, the increasing halo sizes lead to the enhancement of diproton emission. Then, the tensor force is found to have a small influence on the two-proton decay energies, and the two-proton decay energies calculated with strong surface pairing are smaller than those with weak mixed pairing. Because the two-proton decay energies are relatively large, the predicted order of magnitude of half-lives within the effective liquid drop model is not sensitive to the decay energy variation caused by the tensor force and pairing correlation, which has a value of approximately 10 s.

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.

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).

Radioactivity of Dysprosium

The effective liquid drop model (ELDM) is used to explore the one proton radioactivity of all possible Dysprosium isotopes, and the molecular phase of the di-nuclear system is used to investigate the possible barriers limiting one proton emission. The mass excess values are obtained from [Chin. Phys. C 45 (2021) 030003]. The WKB integral is used to evaluate the penetration probability. The half-lives of proton decay are compared to those of other decay modes. The decay chains of [Formula: see text]Dy are predicted. The detailed investigations of [Formula: see text]Dy show proton radioactivity when [Formula: see text]Tb is converted to [Formula: see text]Gd with the half-life of order of nanoseconds. Further, these identified proton emitters may find to be useful in the field of diagnosis and radiotherapy.

Structure and decay modes study of Th, U, and Pu isotopes using relativistic mean field model

In the present work, we have studied the structural properties, alpha and clusters (8Be, 12C, 16O, 20Ne, and 24Mg) decay half-lives for the Th, U, and Pu isotopes using the well-known Relativistic Mean-Field (RMF) theory with NL3* parameter set. We calculate the binding energy per nucleon, root-mean-square (rms) radii, two-neutron separation energies (S2n), and other observables. The results are in good agreement with the finite-range droplet model (FRDM) and experimental data. Using the calculated mass defect results from these calculations, the Effective liquid drop model (ELDM) has been used to determine alpha and cluster decay half-lives. The half-lives calculations are also carried out by using the latest empirical relations, namely Universal Decay Law (UDL), TM, VS, and the Scaling Law was given by Horoi et al., and their comparisons with ELDM results are found to be in good agreement. In the plots for log10T1/2 versus the neutron number of the daughter nucleus Nd in the corresponding decay, the half-life is found to have a minimum for the decay leading to nearly doubly magic or doubly magic daughter 208Pb nucleus (Nd=126). The Geiger-Nuttal plots for different clusters from various cluster radioactive (CR) emitters have been studied and they clearly show a linear behavior.

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

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.

Two-proton emission from excited states of proton-rich nuclei

The effective liquid drop model (ELDM) and the generalized liquid drop model (GLDM) are extended to the case of studying the two-proton (2p) radioactivity from the excited states of proton-rich nuclei. It is shown that the experimental 2p decay half-lives are reproduced well by the ELDM and the GLDM. Then, the 2p decay half-lives of excited states of some nuclei that are not yet available experimentally are predicted by the two models, which are useful for searching for the new 2p decay candidates in future. Meanwhile, the above predicted half-lives are analyzed and compared with those given by the unified fission model (UFM). Next, the influence of the uncertainties of the decay energy and the angular momentum on the half-lives are analyzed in the frame of the two models by taking the 2p radioactivity of the 21<sup>+</sup> isomeric state of <sup>94</sup>Ag for example. It is found that the half-lives go up with the increase of the angular momentum, following the law of the quadratic function. Furthermore, the strong dependence of the half-lives on the decay energy suggests that it is important and necessary to measure accurately the mass value of the parent nucleus and the daughter nucleus and the excitation energy. Finally, it is necessary to point out that the existence of the 2p radioactivity in the 21<sup>+</sup> isomeric state of<sup> 94</sup>Ag remains to be a mystery. Moreover, although the 2p radioactivity is observed from the higher excited states of <sup>17</sup>Ne and <sup>18</sup>Ne, the relevant hypotheses have not yet been further tested experimentally. The construction of a new generation of radioactive ion beam facilities, such as the high intensity heavy-ion accelerator facility (HIAF), is expected to be used to uncover the nature of the 2p radioactivity in the 21<sup>+</sup> isomeric state of <sup>94</sup>Ag and further test the hypotheses of the 2p decay from the higher excited states of <sup>17</sup>Ne and <sup>18</sup>Ne. On the other hand, some microscopic models, such as the shell model, need to be further developed by including some necessary physical factors, such as the tensor force, three-body force and accurate pairing force, to describe the mechanism of the 2p emission of the excited states more reasonably. In summary, more nuclear structure information can be extracted by studying the 2p radioactivity of the excited states. It is worth studying further although it is rather difficult to observe.

A study of alpha-decay using effective liquid drop model

In this paper, we have made an attempt to analyze the alpha-decay half-lives of in the atomic number range [Formula: see text] by considering an effective liquid drop model. The role of pre-formation probability by including iso-spin effect is included during an evaluation of half-lives. We have also compared the studied alpha-decay half-lives with that of semi-empirical formulae such as Viola Seaborg semi-empirical formulae (VSS) [J. Inorg. Nucl. Chem. 28 (1966) 741; Nucl. Phys. A 848 (2010) 279], Royer formulae [J. Phys. G: Nucl. Part. Phys. 26 (2000) 1149; Phys. Rev. C 101 (2020) 034307] and also with that of the available experiments. From this comparison, it can be concluded that the effective liquid drop model produces an alpha-decay half-lives close to the experiments.

Improved effective liquid drop model for α-decay half-lives

The effective liquid drop model (ELDM) is improved by introducing an accurate nuclear charge radius formula and an analytic expression of the effective assaulting frequency. Within the improved effective liquid drop model (IMELDM), the α-decay half-lives of 421 nuclei which have been measured in experiment are calculated. It is shown that the accuracy of the IMELDM is improved evidently compared to its predecessor. Meanwhile, by focusing on the superheavy nuclei (SHN), the α-decay half-lives of SHN are investigated within the IMELDM. It is found that the experimental α-decay half-lives of 80 SHN are reproduced well. Then, within the IMELDM the α-decay half-lives of the Z=118–121 isotopes are predicted by inputting the α-decay energies (Qα) extracted from the Weizsäcker-Skyrme-4 (WS4) mass table. At last, the competition between the α-decay and spontaneous fission (SF) of the SHN of the N=178 α-decay chains is studied in detail, which may be useful for searching for the new SHN in future.

Systematic study of two-proton radioactivity half-lives using the two-potential and Skyrme-Hartree-Fock approaches * *Supported in part by the National Natural Science Foundation of China (11205083, 11505100, 11705055), 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 (2018JJ2321), the Innovation Group

In this work, we systematically study the two-proton ( ) radioactivity half-lives using the two-potential approach, and the nuclear potential is obtained using the Skyrme-Hartree-Fock approach and the Skyrme effective interaction of SLy8. For true radioactivity ( 0 and 0, where and are the released energies of the one-proton and two-proton radioactivity, respectively), the standard deviation between the experimental half-lives and our theoretical calculations is 0.701. In addition, we extend this model to predict the half-lives of 15 possible radioactivity candidates with 0 obtained from the evaluated atomic mass table AME2016. The calculated results indicate a clear linear relationship between the logarithmic radioactivity half-lives ( ) and coulomb parameters [( + ) ] considering the effect of orbital angular momentum proposed by Liu [Chin. Phys. C 45, 024108 (2021)]. For comparison, the generalized liquid drop model (GLDM), effective liquid drop model (ELDM), and Gamow-like model are also used. Our predicted results are consistent with those obtained using other relevant models.

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

In this work, we systematically study the two-proton ([Formula: see text]) radioactivity half-lives of nuclei close to the proton drip line within a modified Gamow-like model. Using this model, the calculated [Formula: see text] radioactivity half-lives can well reproduce the experimental data. Moreover, we blackuse this model to predict the [Formula: see text] radioactivity half-lives of 22 candidates blackwhose [Formula: see text] radioactivity is energetically allowed or observed but not yet quantized in evaluated nuclear properties table NUBASE2016. blackThe predicted results are in good agreement with the ones obtained by using Gamow-like model, effective liquid drop model (ELDM), generalized liquid drop model (GLDM) as well as a four-parameter formula.

Systematic study of two-proton radioactivity within a Gamow-like model * *Supported in part by the National Natural Science Foundation of China (11205083, 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 (2018JJ2321), the Innovation Group of Nuclear and Particle

In this study, based on the Gamow-like model, we systematically analyze two-proton ( ) radioactivity half-lives of nuclei near or beyond the proton drip line. It is found that the calculated results can reproduce experimental data well. Furthermore, using this model, we predict the half-lives of possible radioactivity candidates whose radioactivity is energetically allowed or observed but not yet quantified in the latest table of evaluated nuclear properties, i.e., 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), Sreeja formula, and Liu formula.

New Geiger-Nuttall law for two-proton radioactivity * *Supported in part by the National Natural Science Foundation of China (11205083, 11505100, 11705055), the Construct Program of the Key Discipline in Hunan Province, the Research Foundation of Education Bureau of Hunan Province, China (15A159, 18A237), the Natural Science Foundation of Hunan Province, China (2015JJ3103, 2015JJ2121, 2018JJ2321), the Innovation Group of Nuclear and

In the present work, a two-parameter empirical formula is proposed, based on the Geiger-Nuttall law, to study two-proton ( ) radioactivity. Using this formula, the calculated radioactivity half-lives are in good agreement with the experimental data as well as with calculated results obtained by Goncalves et al. [Phys. Lett. B 774, 14 (2017)] using the effective liquid drop model (ELDM), Sreeja et al. [Eur. Phys. J. A 55, 33 (2019)] using a four-parameter empirical formula, and Cui et al. [Phys. Rev. C 101: 014301 (2020)] using a generalized liquid drop model (GLDM). In addition, this two-parameter empirical formula is extended to predict the half-lives of 22 possible radioactivity candidates with radioactivity released energy , obtained from the latest evaluated atomic mass table AME2016. The predicted results are highly consistent with those obtained using other theoretical models such as the ELDM, GLDM and four-parameter empirical formula.

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.