Universal Decay Law Research Articles

Theoretical calculations of the nuclear deformation effects on α-decay half-lives for heavy and super-heavy nuclei

α-decay half-lives of heavy and super-heavy even–even nuclei, in the range of Z = 80–118, were studied using an improved generalized liquid drop model, in which the deformation effects of both the parent and daughter nuclei are considered. The calculated values reflect a better accuracy of the agreement when compared with the experimental data of known nuclei from Hg to Og. The corresponding standard deviation reduced to 0.3670, which proves that the employed method is reliable to reproduce the α-decay half-lives. Semi-empirical formulas like the Royer formula and the universal decay law were also used for systematic calculations of α-decay half-lives. Based on a detailed analysis of the deformation effects in heavy and super-heavy nuclear regions, it was found that the nuclear deformation has a stronger influence on the super-heavy region. The competition between α-decay and spontaneous fission (SF) was also studied and it was observed that for some isotopes from Pu to Fl, the competition between two decay modes is intense, which reflects that these nuclei may follow both decay modes. A neutron magic number, N = 184, and sub-magic numbers, N = 152 and 162 were observed after the analysis of the α-decay half-lives and the SF half-lives of unknown even–even nuclei.

Extended universal decay law formula for the α and cluster decays

The Universal Decay Law (UDL) formula for the alpha and cluster decays is extended to include the effects of the angular momentum and isospin. The parameters for all formulas are obtained by fitting to available experimental data. We also evaluated the uncertainty of the parameters as well as the uncertainties of predictions of the formulas. The rms values are computed and the best rms among them is obtained for the formula including both the angular momentum and isospin terms. The modified UDL formula is applied to get the half-lives of cluster and alpha decays of nuclei. Branching ratios (alpha/cluster) are calculated and compared with experimental ones. The half-lives for heavier cluster decays are obtained by using UDL and new UDL formulas.

A new potential model for alpha decay calculations

We systematically investigate the experimental α-decay half-lives of the 263 parent nuclei in the range of 52≤Z≤107 for the ground state to ground state α-transitions in terms of a molecular potential called the Morse potential by utilizing the Wentzel-Kramers-Brillouin (WKB) approximation and Bohr-Sommerfeld quantization condition. We find out the optimum parameters of the Morse potential to explain the α-decay half-lives of the parent nuclei and compare our results with the unified model for α-decay and α capture (UMADAC) and the Universal Decay Law (UDL). In calculations of the α-decay half-lives of the parent nuclei, we achieve better results than the UMADAC and UDL models in terms of few degrees of freedom.

Predictions for the α decay of proton-rich nuclei in the range of 86⩽Z⩽98

The α decay half-lives of odd-A and odd-odd nuclei ranging in 65⩽Z⩽112 are investigated by employing the modified universal decay law and the unified fission model, both of them take into account the contribution of centrifugal potential. The good agreement with the experimental data indicates that the modified universal decay law and the unified fission model are useful tools to investigate these α-decays when they contain the effect of centrifugal potential. Relatively long half-lives are predicted by using the new mass table WS2016+RBFs to determine the Qα for many unknown proton-rich nuclei between Rn and Cf, sufficient to detect them if synthesized in a laboratory.

Screening amendment to the universal decay law for alpha decay

By generalizing the electrostatic interaction by means of a screening effect, one proposed a new empirical formula for the $$\alpha $$ decay half lives. In the absence of screening, the formula recovers the universal decay law. The impact of the screening is found to be important only for even Z nuclei and highly sensitive to shell effects, when applied to nuclei with $$Z\ge 84$$ . The proposed empirical formulas are also used for the prediction of the half-lives for even Z superheavy nuclei.

Systematic study of α decay half-lives within the Generalized Liquid Drop Model with various versions of proximity energies * *Support by National Natural Science Foundation of China (10775061, 11175054, 11675066, 11665019, 11947229), the Fundamental Research Funds for the Central Universities (lzujbky-2017-ot04, lzujbky-2020-it01), and Feitian Scholar Project of Gansu province

It is universally acknowledged that the Generalized Liquid Drop Model (GLDM) has two advantages over other α decay theoretical models: introduction of the quasimolecular shape mechanism and proximity energy. In the past few decades, the original proximity energy has been improved by numerous works. In the present work, the different improvements of proximity energy are examined when they are applied to the GLDM for enhancing the calculation accuracy and prediction ability of α decay half-lives for known and unsynthesized superheavy nuclei. The calculations of α half-lives have systematic improvements in reproducing experimental data after choosing a more suitable proximity energy for application to the GLDM. Encouraged by this, the α decay half-lives of even-even superheavy nuclei with Z=112-122 are predicted by the GLDM with a more suitable proximity energy. The predictions are consistent with calculations by the improved Royer formula and the universal decay law. In addition, the features of the predicted α decay half-lives imply that the next double magic nucleus after 208Pb is 298Fl.

Theoretical cluster decay predictions for the nuclei 245−260Md with different nuclear potentials

We have studied systematically the alpha decay and cluster radioactivity half-life of heavy [Formula: see text]Mendelevium ([Formula: see text]) isotopes. The alpha decays from Md isotopes have been studied within the framework of Coulomb and proximity potential model using 14 different versions of nuclear potentials. Also, we have studied the half-lives of alpha decay of Md nuclei within the nuclear potentials generalized liquid drop model (GLDM) and also within GLDM with modified different nuclear potentials, namely proximity potential 2010, 1977, 1988, 2000 and 2002. Moreover, the half-lives of the [Formula: see text]-decay and cluster radioactivity calculated using the Universal formula for cluster decay (UNIV) of Poenaru et al., the Universal decay law (UDL) of Qi et al. and the Unified formula of half-lives for both the [Formula: see text]-decay and cluster radioactivity (UFADCR) of Ni et al. and found to be in good agreement. Our results have been compared with experimental data and demonstrate the acceptability of the approach. Among the different proximity potentials, GLDM with proximity 1977 version (GLDM[Formula: see text][Formula: see text][Formula: see text]P77) ([Formula: see text]) provides the best description for alpha decay studies with low deviation.

Calculations of the α-decay properties of Z = 120, 122, 124, 126 isotopes * * Supported by the National Natural Science Foundation of China (11635003, 11025524, 11161130520), the National Basic Research Program of China (2010CB832903), the European Commission’ s 7th Framework Programme (Fp7-PEOPLE-2010-IRSES) under Grant Agreement Project (269131), the General Financial Grant from the China Postdoctoral Science Foundation (2017M620672), BeiJing

The α-decay properties of even-Z nuclei with Z = 120, 122, 124, 126 are predicted. We employ the generalized liquid drop model (GLDM), Royer's formula, and universal decay law (UDL) to calculate the -decay half-lives. By comparing the theoretical calculations with the experimental data of known nuclei from Fl to Og, we confirm that all the employed methods can reproduce the -decay half-lives well. The preformation factor and -decay energy show that 120, 122, and 124 might be stable. The -decay half-lives show a peak at Z = 120, N = 184, and the peak vanishes when Z = 122, 124, 126. Based on detailed analysis of the competition between -decay and spontaneous fission, we predict that nuclei nearby N = 184 undergo -decay. The decay modes of 120, 122, 124, and 126 are also presented.

The alpha-decay chains and decay mode predictions of the nuclei Z = 118, 119 and 120

The alpha decay (AD) chains of the nuclei having [Formula: see text], 119 and 120 have been investigated in terms of different theoretical models. Decay mode results that are presented in this study have been probed over the possible isotopes of the aforementioned nuclei. In the decay mode predictions, the formula of Bao et al. and the formula proposed by Soylu have been used to calculate the spontaneous fission (SF) half-lives. The AD half-lives have been computed by using the Denisov and Khuedenko, Royer, Horoi, the universal decay law (UDL), the Viola–Seaborg–Sobiczewski (VSS), the universal curve (UNIV) formulas and Wentzel–Kramers–Brillouin (WKB) approximation with Bohr–Sommerfeld quantization condition for the nuclei that have the measured experimental half-lives. Therefore, the rms values of the results of the related expressions and WKB method have been determined, in this way, AD half-life calculations of the [Formula: see text], 119 and 120 nuclei have been performed. According to the obtained results, SF half-life values for Bao et al. and Soylu are quite different from one approach to another, the predictions on decay modes of the [Formula: see text], 119 and 120 nuclei show differences. The decay modes produced by using different models used in this study would be important for the predictions of the future experimental investigations.

α decay half-life estimation and uncertainty analysis

The non-parametric bootstrap method is used to evaluate the uncertainties of two $\alpha$ decay formulas, the universal decay law (UDL) and the new Geiger-Nuttall law (NGNL). Such a method can simultaneously obtain the uncertainty of each parameter, the correlation between each pair of parameters, and the total, statistical, and systematic uncertainties of each formula. Both even-even (ee) nuclei and odd-A (oA) nuclei are used in the analysis. The collected data are separated into three parts: ee nuclei, oA nuclei without spin or parity change (oA\_nc), and oA nuclei with spin and/or parity change (oA\_c). Based on the residues between observed data and corresponding calculations, the statistical and systematic uncertainties are decomposed from the total uncertainty, from which one can clarify the effects from the shell structure, pairing, and angular momentum change on describing $\alpha$ decay half-life. If $N > 126$ and $N \leqslant 126$ nuclei are considered together, the systematic uncertainty of residues between observed and predicted half-lives are larger than if those groups are considered separately. Without shell correction term, a much larger systematic uncertainty is found if parameters obtained for $N \leqslant 126$ nuclei are used to describe the half-lives of $N > 126$ nuclei. A global hindrance on the $\alpha$ decay process is found in oA\_nc (oA\_c) nuclei comparing with ee (oA\_nc) nuclei. If parameters obtained from ee (oA\_nc) nuclei are used, the half-lives of oA\_nc (oA\_c) nuclei are generally underestimated with large systematic uncertainties, which can be related to the contribution of pairing effect and angular momentum. The recently observed superallowed decay from $^{104}$Te to $^{100}$Sn is also discussed based on uncertainty analysis. (Abstract is not fully presented because of length limitation)

Improved empirical formula forα-decay half-lives

The Royer formulas are often used to calculate the $\ensuremath{\alpha}$-decay half-lives [G. Royer, J. Phys. G 26, 1149 (2000); Nucl. Phys. A 848, 279 (2010)]. In recent years, the amount of experimental data on $\ensuremath{\alpha}$ decay has increased and these formulas have been examined again. They describe precisely the favored $\ensuremath{\alpha}$ decays. For unfavored decays, they are less accurate and important deviations may occur between the calculations and experimental data. The underlying physics of this phenomenon has been revealed and an improved formula with only eight parameters is proposed. This formula takes into account both the blocking effect of unpaired nucleons and the contribution of centrifugal potential. Compared with the original formulas and other improvements, our new formula is more simple to use and more accurate. Encouraged by this, the $\ensuremath{\alpha}$-decay half-lives of even-even nuclei and odd-$A$ nuclei with $Z=117$, 118, 119, and 120 are predicted using our improved formula and the universal decay law [C. Qi et al., Phys. Rev. Lett. 103, 072501 (2009)] with the extrapolated ${Q}_{\ensuremath{\alpha}}$ of the WS3+ mass model [N. Wang and M. Liu, Phys. Rev. C 84, 051303(R) (2011)]. The predictions of these two formulas are consistent. However, for $^{293}\mathrm{Ts}$ and $^{294}\mathrm{Og}$, predicted $\ensuremath{\alpha}$-decay half-lives by our improved formula show better agreement with experimental data, indicating that predictions by our improved formula are more reliable and useful for future new superheavy elements and isotopes experimental assignments and identifications. Meanwhile, the features of predicted $\ensuremath{\alpha}$-decay energy and half-lives imply that $N=184$ is the next neutron magic number after $N=126$.

Probing Nonexponential Decay in Floquet–Bloch Bands

Abstract Exponential decay laws describe systems ranging from unstable nuclei to fluorescent molecules, in which the probability of jumping to a lower-energy state in any given time interval is static and history-independent. These decays, involving only a metastable state and fluctuations of the quantum vacuum, are the most fundamental nonequilibrium process and provide a microscopic model for the origins of irreversibility. Despite the fact that the apparently universal exponential decay law has been precisely tested in a variety of physical systems, it is a surprising truth that quantum mechanics requires that spontaneous decay processes have nonexponential time dependence at both very short and very long times. Cold-atom experiments have proven to be powerful probes of fundamental decay processes; in this article, we propose the use of Bose condensates in Floquet–Bloch bands as a probe of long-time nonexponential decay in single isolated emitters. We identify a range of parameters that should enable observation of long-time deviations and experimentally demonstrate a key element of the scheme: tunable decay between quasi-energy bands in a driven optical lattice.

Prediction of α -decay chains and cluster radioactivity of 121300–304 and 122302–306 isotopes using the double-folding potential

The $\ensuremath{\alpha}$- and cluster-decay half-lives for the two superheavy nuclei (SHN) with $Z=121$ and 122 have been calculated within the density-dependent cluster model. The $\ensuremath{\alpha}$-nucleus potential was constructed by employing the double-folding model with a realistic $NN$ interaction whose exchange part has a finite range. We considered five isotopes for each one of the two SHN, $Z=121$ and 122, and compared the calculated $\ensuremath{\alpha}$-decay half-lives with those obtained from three semiempirical formulas, namely, the Viola-Seaborg-Sobiczewski formula, the modified Brown formula, and the semiempirical formula based on fission theory. The calculated $\ensuremath{\alpha}$-decay half-lives are in good agreement with their counterparts. We studied the competition between $\ensuremath{\alpha}$-decay and spontaneous fission and predicted possible decay modes for the SHN $^{300--304}121$ and $^{302--306}122$. The cluster decays for $^{300}121$ and $^{302}122$ have been studied within the double folding model, the unified formula, the scaling law of Horoi, and the universal decay law (UDL). We found that the UDL model predicts the possibility of heavy cluster emission from $^{300}121$ and $^{302}122$. We found that the proton and neutron numbers in the emitted clusters and their residual daughter nuclei are magic or near to the magic numbers. We hope that the theoretical prediction of $\ensuremath{\alpha}$-decay chains and cluster radioactivity could be helpful for future investigation in this field.

α -decay half-lives of superheavy nuclei with Z=122–125

For $\alpha$ decay half-life calculations in this work, the Coulomb and proximity potential model with a new semiempirical formula for diffuseness parameter developed in previous work [Phys. Rev. C 100, 024601 (2019)] is used. The present model in this work is compared with the generalized liquid-drop model (GLDM), universal decay law (UDL), and experimental half-lives in the region $Z=104-118$. Next, the predicted half-lives of 51 superheavy nuclei (SHN) with $Z=122-125$ by the present model are compared with those of GLDM, and UDL. The present model is revealed to be more accurate in reproducing experimental half-lives compared to GLDM and UDL. Moreover, it is found that the predictions of the present model and UDL are highly consistent while GLDM largely deviates from the other two. A study of the competition between $\alpha$ decay and spontaneous fission (SF) shows that $\alpha$ decay is the dominant mode. Among the studied SHN with $Z=122-125$, ${}^{295-307}122$ and ${}^{314-320}125$ are identified as potential candidates whose half-lives are relatively long enough to be experimentally detected in the future through their $\alpha$-decay chains. The identified candidates are in good agreement with other recent work.

Alpha-decay chains of Z=122 superheavy nuclei using cubic plus proximity potential with improved transfer matrix method

The alpha decay chain properties of Z = 122 isotope in the mass range 298£ A £ 350, even-even nuclei, are studied using a fission-like model with an effective combination of the cubic plus proximity potential in the pre and post-scission regions, wherein the decay rates are calculated using improved transfer matrix method, and the results are in good agreement with other phenomenological formulae such as Universal decay law, Viola-Seaborg, Royer, etc. The nuclear ground-state masses are taken from WS4 mass model. The next minimum in the half-life curves of the decay chain obtained at N=186,178 & 164 suggest the shell closure at N=184, 176 & 162 which coincides well with the predictions of two-centre shell model approach. This study also unveils that the isotopes 298-300, 302, 304-306, 308-310, 312,314122 show 7a, 5a, 4a, 3a, 2a and 1a decay chain, respectively. All the other isotopes from A = 316 to 350 may undergo spontaneous fission since the obtained SF half -lives are comparatively less. The predictions in the present study may have an impact in the experimental synthesis and detection of the new isotopes in near future.

Süper-ağır çekirdeklerin kendiliğinden fisyon yarı ömürlerinin farklı modellerdeki hesaplamaları

The spontaneous fission (SF) is a key decay energetically feasible for heavy and superheavy nuclei (Z≥90) and it is an important limiting factor which describes the stability of synthesized superheavy nuclei. Since the fission decay is complex, it is difficult to explain such a multi-dimensional system in a complete microscopic manner. In this study, SF half-lives of 284Cn and 284Fl superheavy nuclei are investigated using the direct method, the Universal Decay Law (UDL). The fission decay constant for each possible case is computed by using the UDL and then the SF half-life for 284Cn and 284Fl superheavy nuclei are predicted. The calculated SF half-lives are compared with the results of other semi-empirical formulas as well as experimental data. Furthermore, the results are compared with ones of the model in which they proposed this direct method for the SF by using nuclear proximity and Coulomb potentials. Good agreement is achieved between the results of this approach and the others. This study shows that UDL would also be used in the half-lives calculations of Spontaneous Fission of superheavy nuclei in a direct way.

Semi-empirical formula for alpha and cluster decay half-lives of superheavy nuclei

We have formulated a semi-empirical formula for alpha decay half-lives and cluster decay half-lives for superheavy nuclei of atomic number range [Formula: see text]. We have compared the logarithmic half-lives produced by the present formula with that of experiments and other formulae, such as universal decay law (UDL) [H. C. Manjunatha and K. N. Sridhar, Eur. Phys. J. A 53, 156 (2017)] and Horoi et al. [Horoi et al., J. Phys. G[Formula: see text] Nucl. Part. Phys. 30, 945 (2004)], Univ [D. Ni and Z. Ren, Phys. Rev. C 74, 014304 (2006)], Royer [G. Royer, J. Phys. G: Nucl. Part. Phys. 26, 1149 (2000)] and VSS [S. A. Gurvitz and G. Kalbermann, Phys. Rev. Lett. 59, 262 (1987)]. The constructed formula produces logarithmic half-lives for alpha and cluster decay (4He,9Be, [Formula: see text]B, [Formula: see text]C, [Formula: see text]N, [Formula: see text]O, [Formula: see text]F, [Formula: see text]Ne, [Formula: see text]Na, [Formula: see text]Mg, [Formula: see text]Al, [Formula: see text]Si, [Formula: see text]P, [Formula: see text]S, [Formula: see text]Cl, [Formula: see text]Ar, [Formula: see text]K and [Formula: see text]Ca) in superheavy nuclei of atomic number range [Formula: see text].

α Decay Properties of Even-Even Nuclei296–308120 Within the Two-Potential Approach**Supported by National Natural Science Foundation of China under Grant Nos. 11205083 and 11505100, the construct program of the key discipline in Hunan province, the Research Foundation of Education Bureau of Hunan Province, China under Grant Nos. 15A159 and 18A237, the Natural Science Foundation of Hunan Province, China under Grant Nos.

In the present work, we predict the α decay half-lives of unknown even-even nuclei296–308120 within the two-potential approach, whose α decay energy Qα is calculated using WS3+ mass model. To reduce the deviations between the predictions and experimental data due to nuclear shell effect, the analytic formula of α decay hindrance factor is introduced to the two-potential approach, whose parameters had been extracted from even-even nuclei in the region of 82 < Z ≤ 126 and 152 < N ≤ 184 in our previous work [Deng et al., Chin. Phys. C 42 (2018) 044102]. In addition, for comparing, we use a type of α decay general formula Universal Decay Law (UDL) and a semi-empirical formula in the superheavy nucleus (SEMFLS) to calculate the half-lives of even-even nuclei296–308120. The results indicate that our predicted values and the calculated values of the above two empirical formulas are mutually confirmed. Meanwhile, we systematically study α decay chains of296–308120 and predict the decay modes for superheavy nuclei to help to identify new superheavy isotopes.

Theoretical predictions for $\alpha$-decay properties of 283-339Og using a shell-effect induced generalized liquid-drop model

The $ \alpha$-decay half-lives of synthesized superheavy nuclei (SHN) from seaborgium to oganesson are calculated by employing the generalized liquid-drop model (GLDM), the Royer formula and the universal decay law (UDL) with experimental $ \alpha$-decay energies $Q_{\alpha}$. For the GLDM, we consider the shell correction. The agreement between the experimental data and the calculations indicates that all the methods we used are successful to reproduce $\alpha$-decay half-lives of known SHN. The decay-modes of known nuclei on the 294Og decay-chain are also consistent with the experiments. For the unknown nuclei, the $ \alpha$-decay half-lives have been predicted by inputting $ Q_{\alpha}$ values extracted from the newest Weizsacker-Skyrme-4 (WS4) model. In the GLDM with shell correction, we adopt the constant $ \alpha$-preformation factor $ P_{\alpha}$ as well as $ P_{\alpha}$ extracted by Cluster Formation Model (CFM). To calculate CFM $ P_{\alpha}$ values, we use FRDM binding energies and WS4 mass excess values. The relationship of $ P_{\alpha}$ and $ Q_{\alpha}$ shows that 294, 296, 314, 316, 320Og isotopes are relatively stable. The competition between $ \alpha$-decay and spontaneous fission is discussed in detail for 283-339Og isotopes. The decay-chains of 290-300Og have also been presented. Since the $ \alpha$-decay half-lives of 283-303Og isotopes are obviously lower than their spontaneous fission half-lives by more than 6 orders, these isotopes would mainly have $ \alpha$-decay. The 306-334Og isotopes may undergo spontaneous fission. The nuclei 304, 305Og would have both $ \alpha$-decay and spontaneous fission. By the shell-effect included GLDM with CFM $ P_{\alpha}$, we predict 295Og undergoes $ \alpha$-decay and $ T_{\alpha}^{1/2} = 0.37$ ms. The 296Og is also $ \alpha$-decay and has $ T_{\alpha}^{1/2} = 0.40$ ms.

Systematic study of alpha decay half-lives using new universal decay law

We have performed a systematic calculation on the alpha decay half-lives of heavy mass nuclei with 106 [Formula: see text] 118, within the universal decay law (UDL) and modified universal decay law (MUDL). The calculated half-life values are found to be in agreement with the experimental data. The standard deviations of the logarithm of half-lives are found to be the least for MUDL in all cases of even–even, even–odd, odd–even and odd–odd, so the MUDL formula is better than UDL formula for alpha decay studies. We have predicted half-lives of some superheavy nuclei (SHN) in the region [Formula: see text]–118 that are not yet experimentally detected. The decay energies are computed using three different mass models. We hope this study will help future measurements on alpha decay half-lives of SHN.