Theoretical estimates for the half lives of about 1700 isotopes of heavy elements with Z from 100 to 130 are tabulated using theoretical Q-values. The quantum mechanical tunneling probabilities are calculated within a WKB framework using microscopic nuclear potentials. The microscopic nucleus-nucleus potentials are obtained by folding the densities of interacting nuclei with a density dependent M3Y (DDM3Y) effective nucleon-nucleon interaction. The alpha-decay half lives calculated in this formalism using the experimental Q-values were found to be in good agreement over a wide range of experimental data spanning about twenty orders of magnitude. The theoretical Q-values used for the present calculations are extracted from three different mass estimates viz. Myers-Swiatecki [MS], Muntian-Hofmann-Patyk-Sobiczewski [M] and Koura-Tachibana-Uno-Yamada [KUTY].
Stability of 248-254^Cf nuclei against alpha and cluster emission is studied within our Coulomb and proximity potential model (CPPM). It is found that these nuclei are stable against light clusters (except alpha particle) and instable against heavy cluster emissions. For heavy cluster emissions the daughter nuclei lead to doubly magic 208^Pb or neighbouring one. The effect of quadrapole and hexadecapole deformations of parent nuclei, daughter nuclei and emitted cluster on half lives are also studied. The computed alpha decay half life values (with including quadrupole deformation β2) are in cl…
In the present work, we systematically study the two-proton (2p) radioactivity half-lives of nuclei close to the proton drip line within a modified Gamow-like model. Using this model, the calculated 2p radioactivity half-lives can well reproduce the experimental data. Moreover, we use this model to predict the 2p radioactivity half-lives of 22 candidates whose 2p radioactivity is energetically allowed or observed but not yet quantied in evaluated nuclear properties table NUBASE2016. The predicted results are in good agreement with the ones obtained by using Gamow-like model, effective liquid d…
In this work we present a systematic study of the proton radioactivity half-lives of spherical proton emitters within the Coulomb and proximity potential model. We investigate 28 different versions of the proximity potential formalisms developed for the description of proton radioactivity, $\mathcalα$ decay and heavy particle radioactivity. It is found that 21 of them are not suitable to deal with the proton radioactivity, because the classical turning points $r_{\text{in}}$ cannot be obtained due to the fact that the depth of the total interaction potential between the emitted proton and the …
In the present work we systematically study the half--lives of proton radioactivity for $51 \leq Z \leq 83$ nuclei based on the Gamow--like model with a screened electrostatic barrier. In this model there are two parameters while considering the screened electrostatic effect of Coulomb potential with the Hulthen potential i.e. the effective nuclear radius parameter r_0 and the screening parameter a. The calculated results can well reproduce the experimental data. In addition, we extend this model to predict the proton radioactivity half--lives of 16 nuclei in the same region within a factor of…
In the present work, we systematically study the proton radioactivity half-lives of 33 spherical nuclei based on the relationship between the Skyrme parameters and the macroscopic quantities of nuclear matter. Using the two-potential approach with the spherical Skyrme-Hartree-Fock model, the correlation between proton radioactivity half-life and macroscopic quantities was analyzed. Moreover, we obtained a new Skyrme parameter set by fitting the two most weighted macroscopic quantities. Compared with Skyrme parameters MSL0 and the theoretical model of proton radioactivity UDLP, the theoretical …
The generalized liquid drop model (GLDM) is firstly extended to study the two-proton ($2p$) radioactivity half-lives of the ground-state of nuclei. According to the comparison between the calculated half-lives and the experimental data, it is shown that the GLDM describes the $2p$ radioactivity half-lives well. In addition, by comparing its accuracy with other models, it is found that the GLDM has a comparable accuracy with them. Finally, the $2p$ radioactivity half-lives of some most probable candidates are predicted with the GLDM by inputting the \textit{Q}$_{2p}$ values (the released energy…
Ground-state two-proton (2p) radioactivity is a decay mode found in isotopes of elements with even atomic numbers located beyond the two-proton drip line. So far, this exotic process has been experimentally observed in a few light and medium-mass nuclides with Z less than or equal to 30. In this study, using state-of-the-art nuclear density functional theory, we globally analyze 2p radioactivity and for the first time identify 2p decay candidates in elements heavier than strontium. We predict a few cases where the competition between 2p emission and alpha decay may be observed. In nuclei above…
In this work, we systematically study the two-proton($2p$) radioactivity half-lives using the two-potential approach while the nuclear potential is obtained by using Skyrme-Hartree-Fock approach with the Skyrme effective interaction of {SLy8}. For true $2p$ radioactivity($Q_{2p}$ $>$ 0 and $Q_p$ $< $0, where the $Q_p$ and $Q_{2p}$ are the released energy of the one-proton and two-proton radioactivity), 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 $2p$ radioactiv…
Proton radioactivity has been investigated using the effective liquid drop model with varying mass asymmetry shape and effective inertial coefficient. An effective nuclear radius constant formula replaces the old empirical one in the calculations. The theoretical half-lives are in good agreement with the available experimental data. All the deviations between the calculated logarithmic half-lives and the experimental values are less than 0.8. The root-mean-square deviation is 0.523. Predictions for the half-lives of proton radioactivity are made for elements across the periodic table. From the…
Relativistic energy density functional approaches are known to well describe nuclear states which involve alpha clusters. Here, alpha emitting nuclei are analysed through the behavior of the spatial localisation of nucleonic states, calculated with an axially deformed RHB approach over the nuclear chart. The systematic occurrence of more localised valence states, having a n = 1 radial quantum number, allows to pinpoint nuclei in agreement with experimentally known alpha-emitters. The cases of 212Po and 104Te are investigated, showing the concomitant contributions of the pseudospin symmetry and…
Effect of deformation on half-life of two-proton (2p) radioactivity is investigated across the periodic chart for nuclei with Z$<$82. 2p-decay half-lives are estimated by employing our newly proposed semi-empirical formula wherein the nuclear deformation has been incorporated in a phenomenological way. Robustness of the formula is demonstrated as it estimates the measured values quite accurately and, hence, reliably applied to predict the other possible 2p-emitters. For many proton rich nuclei for which experimental data on the decay energies are not available, we have used the theoretical val…
Proton radioactivity is an important and common process of the natural radioactivity of proton-rich nuclei. In our previous work [J. H. Cheng et al., Nucl. Rhys. A 997, 121717 (2020)], we systematically studied the proton radioactivity half-lives of 53< Z <83 nuclei within the two-potential approach with Skyrme-Hartree-Fock. The calculations can well reproduce the experimental data of spherical nuclei. The present work is an extension of the previous work. We systematically study 32 proton radioactivity half-lives of spherical nuclei with the two-potential approach with Skyrme-Hartree-Fock (TP…
In the present work we systematically study the half--lives of proton radioactivity for spherical proton emitters with ${Z\ge 69}$ based on two--potential approach. While the nuclear potential of the emitted proton--daughter nucleus is adopted by a parameterized cosh type, the parameters of the depth and diffuseness for nuclear potential are determined by fitting experimental data of 32 spherical proton emitters. In order to reduce the deviations between experimental half-lives and calculated ones, we propose a simple analytic expression for formation probability of proton radioactivity with t…
Radioactive decay of nuclei via emission of $α$ particles has been studied theoretically in the framework of a superasymmetric fission model using the double folding (DF) procedure for obtaining the $α$-nucleus interaction potential. The DF nuclear potential has been obtained by folding in the density distribution functions of the $α$ nucleus and the daughter nucleus with a realistic effective interaction. The M3Y effective interaction has been used for calculating the nuclear interaction potential which has been supplemented by a zero-range pseudo-potential for exchange along with the density…
The potential barrier impeding the spontaneous emission of protons in the proton radioactive nuclei is calculated as the sum of nuclear, Coulomb and centrifugal contributions. The nuclear part of the proton-nucleus interaction potential is obtained in the energy density formalism using Skyrme effective interaction that results into a simple algebraic expression. The half-lives of the proton emitters are calculated for the different Skyrme sets within the improved WKB framework. The results are found to be in reasonable agreement with the earlier results obtained for more complicated calculatio…
In this study, a phenomenological model is proposed based on Wentzel-Kramers-Brillouin (WKB) theory and applied to investigate the two-proton ($2p$) radioactive half-lives of nuclei near or beyond the proton drip line. The total diproton-daughter nucleus interaction potential is composed of the Hulthen-type electrostatic term and the centrifugal term. The calculated $2p$ radioactive half-lives can accurately reproduce the existing 10 experimental datasets of five true $2p$ radioactive nuclei with $σ$ = 0.736. In addition, we extend this model to predict the half-lives of possible $2p$ radioact…
In the framework of Bohmian quantum mechanics supplemented with the Chetaev theorem on stable trajectories in dynamics in the presence of dissipative forces we have shown the possibility of the classical (without tunneling) universal description of radioactive decay of heavy nuclei, in which under certain conditions so called noise-induced transition is generated or, in other words, the stochastic channel of alpha decay, cluster radioactivity and spontaneous fission conditioned by the Kramers diffusion mechanism. Based on the ENSDF database we have found the parametrized solutions of the Krame…
Proton radioactivity in deformed nuclei with microscopic optical potential: A novel angular-dependent emission mechanism in the nanosecond-lived $^{149}$Lu
University of South China（南华大学）；Chongqing University（重庆大学）；The University of Tokyo（东京大学）；RIKEN Center for Interdisciplinary Theoretical and Mathematical Sciences（理化学研究所交叉理论数学科学中心）
In the present work, combining with the Geiger-Nuttall law, a two-parameter empirical formula is proposed to study the two-proton (2p) radioactivity. Using this formula, the calculated 2p radioactivity half-lives are in good agreement with the experimental data as well as the calculated ones 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, …
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 goo…
Time-stamped data have been used to estimate the decay half-lives of radioactive 118mSb and 64,66,68Ga nuclei. These nuclei are populated through the reaction 4He (Elab = 32 MeV) + nat In and p (Elab = 10 MeV) + natZn, respectively. The g -rays emitted by the excited daughter nuclei are detected by a single high purity germanium (HPGe) detector and the data are acquired using a CAEN 5780M desktop digitizer. Half-lives of different orders of magnitudes for the above mentioned nuclei are obtained from both the decay of parent and the growth of daughter nuclei. It is observed that the half-lives …
In this paper a short review of the theoretical problems of the pionic radioactivity is presented. The essential experimental results obtained in the 18 years of existence of the nuclear pionic radioactivity are reviewed. Moreover, using the recent results on the spontaneous fission half lives of the heavy nuclei with Z >= 100 new predictions on the pionic yields in the region of superheavy elements are established.
Effects of various nuclear interaction potentials on the decay lifetimes and the turning points of the WKB action integral has been studied. The microscopic nuclear potential obtained by folding in the density distribution functions of the two clusters with a realistic effective interaction has also been used to calculate the turning points. Half lives of alpha and ^{20}O cluster emissions from ^{228}Th have been calculated within the superasymmetric fission model using various phenomenological and the microscopic double folding potentials. Calculations of half lives with the microscopic doubl…
The half-lives of proton radioactivity of proton emitters are investigated theoretically by using KDE0v1 Skyrme interaction. The total barrier potential in the proton radioactive nuclei is calculated as the sum of the nuclear, Coulomb and centrifugal contributions. The Hartree-Fock nuclear density distributions is used in calculating the nuclear as well as the Coulomb interaction potentials. The quantum mechanical tunneling probability is calculated within the WKB approximation. These calculations provide reasonable estimates for the observed proton radioactivity lifetimes.
Half-life of proton radioactivity of spherical proton emitters is studied within the scheme of covariant density functional (CDF) theory, and for the first time the potential barrier that prevents the emitted proton is extracted with the similarity renormalization group (SRG) method, in which the spin-orbit potential along with the others that turn out to be non-negligible can be derived automatically. The spectroscopic factor that is significant is also extracted from the CDF calculations. The estimated half-lives are found in good agreement with the experimental values, which not only confir…
Cluster radioactivity is the emission of a fragment heavier than $α$ particle and lighter than mass 50. The range of clusters observed in experiments goes from $^{14}$C to $^{32}$Si while the heavy mass residue is always a nucleus in the neighborhood of the doubly-magic $^{208}$Pb nucleus. Cluster radioactivity is described in this paper as a very asymmetric nuclear fission. A new fission valley leading to a decay with large fragment mass asymmetry matching the cluster radioactivity products is found. The mass octupole moment is found to be more convenient than the standard quadrupole moment a…
The feasibility for the alpha decay and the heavy particle decay from the even-even superheavy (SH) nuclei with Z = 116-124 have been studied within the Coulomb and proximity potential model (CPPM). The Universal formula for cluster decay (UNIV) of Poenaru et al., the Universal Decay Law (UDL) and the Scaling Law of Horoi et al., has also been used for the evaluation of the decay half lives. A comparison of our predicted half lives with the values evaluated using these empirical formulas are in agreement with each other and hence CPPM could be considered as a unified model for alpha and cluste…
The proton radioactivity half-lives of spherical proton emitters are investigated theoretically. The potential barriers preventing the emission of protons are determined in the quasimolecular shape path within a generalized liquid drop model (GLDM) including the proximity effects between nuclei in a neck and the mass and charge asymmetry. The penetrability is calculated with the WKB approximation. The spectroscopic factor has been taken into account in half-life calculation, which is obtained by employing the relativistic mean field (RMF) theory combined with the BCS method with the force NL3.…
The possibility of cluster emission from trans-lead (86$\leq$Z$\leq$96) region of periodic chart has been explored comprehensively by employing few empirical formulas which are modified by adding angular momentum ($l$) or isospin-dependent ($I=(N-Z)/A$) or both terms for the calculation of cluster decay half-lives. These modified versions of the formulas are found with lesser $χ^2$ per degree of freedom and root mean-square error, in addition to the smaller values of some other statistical parameters, while compared to their corresponding old versions on available 61 experimental data of clust…
The half lives of proton radioactivity of proton emitters are investigated theoretically. Proton-nucleus interaction potentials are obtained by folding the densities of the daughter nuclei with a finite range effective nucleon-nucleon interaction having Yukawa form. The Wood-Saxon density distributions for the nuclei used in calculating the nuclear as well as the Coulomb interaction potentials are predictions of the interaction. The quantum mechanical tunneling probability is calculated within the WKB framework. These calculations provide reasonable estimates for the observed proton radioactiv…
Systematic Study of Proton, Two-Proton, Alpha, and Cluster Radioactivity Half-Lives based on the Deformed Gamow-like Model and Tabular Prior-data Fitted Network ($\mathrm{TabPFN}$)
College of Physics and Technology, Kunming University（昆明大学物理与技术学院）；School of Physics and Information Engineering, Zhaotong University（昭通大学物理与信息工程学院）；Key Laboratory of Economic System Simulation of Guizhou Province, Guizhou University of Finance and Economics（贵州省经济系统模拟重点实验室，贵州财经大学）
The alpha-decay half-lives of recently synthesized superheavy nuclei (SHN) are investigated based on a unified fission model (UFM) where a new method to calculate the assault frequency of alpha-emission is used. The excellent agreement with the experimental data indicates the UFM is a useful tool to investigate these alpha-decays. It is found that the half-lives become more and more insensitive to the Q_alpha values as the atomic number increases on the whole, which is favorable for us to predict the half-lives of SHN. In addition, a formula is suggested to compute the Q_alpha values for the n…
Half life values for proton radioactivity in nuclei have been calculated in the WKB approximation. The microscopic proton-nucleus potential has been obtained by folding the densities of daughter nuclei with two microscopic NN interactions, DDM3Y and JLM. The densities have been obtained in the Relativistic Mean Field approach in the spherical approximation using the force FSU Gold. No substantial modification of results has been observed if other common forces are employed. The calculated results for the decays from the ground state or the low-lying excited states in almost all the nuclei agre…
The predictive accuracy of the generalized liquid drop model (GLDM) formula for alpha decay half-lives has been investigated in a detailed manner and a variant of the formula with improved coefficients is proposed. The method employs the experimental alpha half-lives of the well-known alpha standards (REFERENCE) to obtain the coefficients of the analytical formula using the experimental Qalpha values (the DSR-E formula), as well as the finite range droplet model (FRDM) derived Qalpha values (the FRDMFRDM formula). The predictive accuracy of these formulae were checked against the experimental …
The alpha decay half-lives of the recently produced isotopes of the 112, 114, 116 and 118 nuclei and decay products have been calculated in the quasi-molecular shape path using the experimental Qalpha value and a Generalized Liquid Drop Model including the proximity effects between nucleons in the neck or the gap between the nascent fragments. Reasonable estimates are obtained for the observed alpha decay half-lives. The results are compared with calculations using the Density-Dependent M3Y effective interaction and the Viola-Seaborg-Sobiczewski formulae. Generalized Liquid Drop Model predicti…
The proton radioactivity lifetimes of spherical proton emitters from the ground and the isomeric states are calculated using the microscopic nucleon-nucleus interaction potentials. The daughter nuclei density distributions are folded with a realistic density dependent M3Y effective interaction supplemented by a zero-range pseudo-potential. The density dependence parameters of the interaction are extracted from the nuclear matter calculations. The saturation energy per nucleon used for nuclear matter calculations is determined from the co-efficient of the volume term of Bethe-Weizsacker mass fo…
The alpha decay half-lives of recently synthesized superheavy nuclei (SHN) are calculated by applying a new approach which estimates them with the help of their neighbors based on some simple formulas. The estimated half-life values are in very good agreement with the experimental ones, indicating the reliability of the experimental observations and measurements to a large extent as well as the predictive power of our approach. The second part of this work is to test the applicability of the Wentzel-Kramers-Brillouin (WKB) approximation for the quantum mechanical tunneling probability. We calc…
A linear relation for charged-particle emissions is presented starting from the microscopic mechanism of the radioactive decay. It relates the logarithms of the decay half-lives with two variables, called $χ'$ and $ρ'$, which depend upon the $Q$-values of the outgoing clusters as well as the masses and charges of the nuclei involved in the decay. This relation explains well all known cluster decays. It is found to be a generalization of the Geiger-Nuttall law in $α$ radioactivity and therefore we call it the universal decay law. Predictions on the most likely emissions of various clusters are …
The alpha-decay half-lives and the alpha-capture cross-sections are evaluated in the framework of unified model for alpha-decay and alpha-capture. In the framework of this model the alpha-decay and alpha-capture are considered as penetration of the alpha-particle through the potential barrier formed by nuclear, Coulomb and centrifugal interactions between alpha-particle and nucleus. The spins and the parities of parent and daughter nuclei as well as the quadrupole and hexadecapole deformations of daughter nuclei are taken into account for evaluation of the alpha-decay half-lives. The alpha-dec…
Different models for the nonlocal description of the nuclear interaction are compared through a study of their effects on the half-lives of radioactive nuclei decaying by the emission of alpha particles. The half-lives are evaluated by considering a pre-formed alpha particle ($^4$He nucleus) which tunnels through the Coulomb barrier generated by its interaction with the daughter nucleus. An effective potential obtained from a density dependent double folding strong potential between the alpha and the daughter nucleus within the nonlocal framework is found to decrease the half-lives as compared…
Alpha and cluster decay half lives for W isotopes in the range between 2p drip line and beta stability line are studied. The sensitivity of different Skyrme parametrizations in predicting the alpha decay and probable cluster decay modes from W isotopes have been analysed. The half lives are calculated using UDL. Predicted half lives are compared with ELDM and also with available experimental values. The study also revealed the role of neutron shell closure in cluster decay process.
Systematic alpha-nucleus folding potentials are used to analyze alpha-decay half-lives of superheavy nuclei. Preformation factors of about several per cent are found for all nuclei under study. The systematic behavior of the preformation factors and the volume integrals of the potentials allows to predict alpha-decay energies and half-lives for unknown nuclei. Shell closures can be determined from measured alpha-decay energies using the discontinuity of the volume integral at shell closures. For the first time a double shell closure is predicted for Z_magic = 132, N_magic = 194, and A_magic = …
$α$ decay is a common and important process for natural radioactivity of heavy and superheavy nuclei. The $α$ decay half-lives for even-even nuclei from Z=62 to Z=118 are systematically researched based on the two-potential approach with a quasi-stationary state approximation. To describe the deviations between experimental half-lives and calculated results due to the nuclear shell structure, a hindrance factor related with $α$ particle preformation probability is introduced. Our results can well reproduce the experimental data equally to the density-dependent cluster model and the generalized…
Cold reaction valleys in the radioactive decay of superheavy nuclei {286}^112, {292}^114 and {296}^116 are studied taking Coulomb and Proximity Potential as the interacting barrier. It is found that in addition to alpha particle, 8^Be, 14^C, 28^Mg, 34^Si, 50^Ca, etc. are optimal cases of cluster radioactivity since they lie in the cold valleys. Two other regions of deep minima centered on 208^Pb and 132^Sn are also found. Within our Coulomb and Proximity Potential Model half-life times and other characteristics such as barrier penetrability, decay constant for clusters ranging from alpha parti…
A systematic study on the alpha decay half lives of various isotopes of superheavy element \textit{Z} = 121 within the range 290 $\leq$ A $\leq$ 339 is presented for the first time using Coulomb and proximity potential model for deformed nuclei (CPPMDN). The calculated $α$ decay half lives of the isotopes within our formalism match well with the values computed using Viola-Seaborg systematic, Universal curve of Poenaru et al., and the analytical formula of Royer. In our study by comparing the $α$ decay half lives with the spontaneous fission half lives, we have predicted $2α$ chain from $^{309…
The Oklo data constrain the depth of the nuclear potential well to a small margin of error, determined by various unknowns, such as the reactor temperature. However, we show that even these small variations could allow the U-238 half-life to vary by more than one order of magnitude.
It is shown, that the Gamow-like model with only one adjustable parameter - radius constant is able to reproduce well the alpha-decay half-lives for all even-even nuclei with the proton number larger than 50. The systematics for odd-A and odd-odd isotopes can be also well described when ones introduces an additional hindrance factor. Similar model based on the W. J. Swiatecki idea from 1955 is developed to reproduce the spontaneous fission half-lives of transactinide nuclei. The achieved accuracy of reproduction of the data is better than that obtained in more advanced theories.
The set of parameters for alpha-nucleus potential is derived by using the data for both the alpha-decay half-lives and the fusion cross-sections around the barrier for reactions alpha+40Ca, alpha+59Co, alpha+208Pb. The alpha-decay half-lives are obtained in the framework of a cluster model using the WKB approximation. The evaluated alpha-decay half-lives and the fusion cross-sections agreed well with the data. Fusion reactions between alpha-particle and heavy nuclei can be used for both the formation of very heavy nuclei and spectroscopic studies of the formed compound nuclei.
