Proton radioactivity within the generalized liquid drop model with various versions of proximity potentials

In the present work, we systematically investigate the proton radioactivity half-lives of spherical proton emitters adopting a generalized liquid drop model(GLDM) with 16 different proximity potentials, of which the proximity potential Prox.77-13 gives the closest results to the experimental data. Combined with the previous conclusion that the GLDM with proximity potential Prox.77-13 can also best describe α decay half-lives, which makes the model more uniform and consistent.Further, we use the proximity potential Prox.77-13 in GLDM to predict the proton radioactivity half-lives of 14 spherical proton emitters that are allowed energetically but not yet observed experimentally or specifically quantified. Finally, we research the Geiger-Nuttall law for proton radioactivity. The results reveal that the Geiger-Nuttall law can also be well used to study the proton radioactivity half-lives of isotopes with the same orbital angular momentum l.     

Low-energy neutron-deuteron reactions with N 3 LO chiral forces

Based on the preformed cluster model (PCM), we have extended our earlier study on cluster decays of heavy parent nuclei to analyze the effects of different nuclear proximity potentials in the ground-state clusterization of superheavy nuclei with Z = 113, 115 and 117. In order to look for the possible role of deformations, calculations are performed for spherical as well as β ₂-deformed choices of fragmentation. The relevance of “hot compact” over “cold elongated” configurations due to orientations is also explored, in addition to the role of Q value and angular momentum ℓ effects. As the PCM is based on collective clusterization picture, the preformation and penetration probabilities get modified considerably, and hence do so the decay constants and half-lives of the clusters, with the use of different nuclear proximity potentials. The comparative importance of nuclear proximity potentials Prox-1977 and Prox-2000 is analyzed and the calculated decay half-lives in the framework of PCM are compared with the recent predictions of the analytical super-asymmetric fission model (ASAFM). The possible role of shell corrections is also investigated for understanding the dynamics of heavy particle radioactivity. Finally, the potential energy surfaces are compared for different proton and neutron magic numbers in superheavy mass region.

     

Theoretical study on spherical proton emission

The proton radioactivity half-lives of spherical proton emitters are investigated 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 in the WKB approximation and the assault frequency is estimated by the quantum mechanism method considering the structure of the parent nucleus.The spectroscopic factor is taken into account in half-life calculation,which is obtained by employing the relativisti...     

有效液滴模型对超铅区结团放射性的研究

利用有效液滴模型计算了超铅区结团放射半衰期.在计算Gamow势垒穿透因子时采用了碎块体积不守恒以及有效惯性系数因子,并用有效的核半径常数公式代替原来的经验公式.理论计算得到的结团放射半衰期和实验值符合得很好,其半衰期对数值的均方差只有0.895.理论结果表明,有效液滴模型能充分反映N=126和Z=82的壳效应,并且在奇数结团25Ne,29Mg中出现了明显的奇偶质量摆动现象.另外,理论计算得到的结团半衰期基本符合盖革-努塔尔定律,并基于理论结果得到了一些关于盖革-努塔尔定律的有意义的结论.     

Properties of $ \alpha$ -decay to ground and excited states of heavy nuclei

Branching ratios and half-lives of a \alpha -decay to the ground-state rotational bands as well as the high-lying excited states of even-even nuclei have been calculated in the framework of the generalized liquid drop model (GLDM) and Royer’s formula that we improved very recently. The calculation covers the isotopic chains from Ra to No in the mass regions 222 ￡ \leq A ￡ \leq 252 and 88 ￡ \leq Z ￡ \leq 102 . The agreement between the calculated results and the experimental data indicates the reliability of investigating the properties of the unfavored a \alpha -decay with our method, especially the improved Royer’s formula, which is very valuable for the analysis of experimental data. In addition, the dependence of half-lives on excitation energies of daughter nuclei has been investigated. It is shown that the influence on half-lives becomes stronger and stronger with the increase of the excitation energies.     

Partial α-decay half-lives of ground to ground and ground to excited states of Thorium family

Partial half-lives and Q-values of allowed α-decay for Thorium family are evaluated by using the WKB approximation. In order to calculate the partial half-lives, transition probabilities from ground to ground and ground to excited states of daughter nuclei are obtained. The α-decay potential barrier includes deformed volume, surface, and Coulomb parts in the deformed liquid drop model (DLDM), deformed Woods-Saxon nuclear potential and centrifugal term. The quadrupole and the hexadecapole deformations are considered in the calculations. Calculated half-lives are compared to the results of other theoretical models as well as experimental data. Comparison of the present study and other theoretical methods with experimental data indicated that the predicted half-lives using current approach are well agreed with the experimental data than results of UMADAC and CPPMDN theoretical models. Moreover, the evaluated half-lives correspond well with the Geiger-Nuttall empirical formula.     

Proton Radioactivity Within a Hybrid Method

The proton radioactivity half-lives are investigated theoretically within a hybrid method.The potential barriers preventing the emission of protons are determined in the quasimolecular shape path within a generalized liquid drop model (GLDM). The penetrability is calculated with the Wentzel-Kramers-Brillouin (WKB) approximation. The spectroscopic factor has been taken into account in halflife calculation, which is obtained by employing the relativistic mean field (RMF) theory combined with the Bardeen-Cooper-Schrieffer (BCS) method. The half-lives within the present hybrid method reproduced the experimental data very well. Some predictions for proton radioactivity are made for future experiments.     

Be,Li, He and H decay half-lives at low excitation energy

The Be, Li, He and H decay half-lives of slightly excited nuclei have been determined within a tunneling process through a potential barrier calculated from a generalized liquid drop model and quasimolecular shapes. Analytic formulae allowing to obtain rapidly these different partial half-lives are proposed. For a given decay they depend only on the mass and charge numbers of the emitter, the Q value and the excitation energy.     

Cold valleys in the radioactive decay of <Superscript>248–254</Superscript>Cf isotopes

Based on the concept of cold valley in cold fission and fusion, we have investigated the cluster decay process in ^248–254Cf isotopes. In addition to alpha particle minima, other deep minima occur for S, Ar and Ca clusters. It is found that inclusion of proximity potential does not change the position of minima but minima become deeper. Taking Coulomb and proximity potential as interacting barrier for post-scission region, we computed half-lives and other characteristics for various clusters from these parents. Our study reveals that these parents are stable against light clusters and unstable against heavy clusters. Computed half-lives for alpha decay agree with experimental values within two orders of magnitude. The most probable clusters from these parents are predicted to be ⁴⁶Ar, ^48,50Ca which indicate the role of doubly or near doubly magic clusters in cluster radioactivity. Odd A clusters are found to be favorable for emission from odd A parents. Cluster decay model is extended to symmetric region and it is found that symmetric fission is also probable which stresses the role of doubly or near doubly magic ¹³²Sn nuclei. Geiger-Nuttal plots were studied for various clusters and are found to be linear with varying slopes and intercepts.      

Effects of shell correction on α decay properties

The shell correction effects on the α decay properties of heavy and superheavy nuclei have been studied in a macroscopic-microscopic manner. The macroscopic part is constructed from the generalized liquid drop model(GLDM), whereas the microscopic part, namely, the shell correction energy, brings about certain effects on the potential barriers and half-lives under a WKB approximation, which is emphasized in this work. The results show that the shell effects play a significant role in the estimation of the α decay half-lives within the actinide region.Predictions of the α decay half-lives are then generated for superheavy nuclei, which will provide useful information for future experiments.     

Search for decay modes of heavy and superheavy nuclei

Spontaneous fission(SF) with a new formula based on a liquid drop model is proposed and used in the calculation of the SF half-lives of heavy and superheavy nuclei(Z = 90–120). The predicted half-lives are in agreement with the experimental SF half-lives. The half-lives of decay(AD) for the same nuclei are obtained by using the Wentzel-Kramers-Brillouin(WKB) method together with Bohr-Sommerfeld(BS) quantization condition considering the isospin-dependent effects for the cosh potential. The decay modes and branching ratios of superheavy nuclei(Z =104-118) with experimental decay modes are obtained, and the modes are compared with the experimental ones and with the predictions found in the literature. Although some nuclei have predicted decay modes that are different from their experimental decay modes, decay modes same as the experimental ones are predicted for many nuclei. The SF and AD half-lives, branching ratios, and decay modes are obtained for superheavy nuclei(Z = 119–120) with unknown decay modes and compared with the predictions obtained in a previous study. The present results provide useful information for future experimental studies performed on both the AD and SF of superheavy nuclei.     

New calculations of α-decay half-lives by the Viola-Seaborg formula

The Viola-Seaborg formula is a well-known formula for α-decay half-lives of heavy nuclei. In this work we obtain new parameters of this formula through a least-square fit to even-even nuclei between Z = 84 and Z = 110 with N greater than 126. On average, the formula can reproduce the half-lives of heavy even-even nuclei within a factor of 1.3. The formula with new parameters works well for the superheavy region which is a hot topic of nuclear physics. The numerical results from the formula are compared with those from the cluster model.     

Systematic study on α-decay half-lives of uranium isotopes with a screened electrostatic barrier

In the present work, we systematically study the α-decay half-lives of uranium (Z=92) isotopes based on the Gamow model with a screened electrostatic barrier. There are only two adjustable parameters in our model i.e. the parameter g and the screening parameter t in the Hulthen potential for considering the screened electrostatic effect of the Coulomb potential. The calculated results are in good agreement with experimental data, and the corresponding root-mean-square (rms) deviations of uranium isotopes with α transition orbital angular momentum l=0 and l=2 are 0.141 and 0.340, respectively. Moreover, we extend this model to predict α-decay half-lives of uranium isotopes whose α decay is energetically allowed or observed but not yet quantified in NUBASE2020. For comparison, the modified Hatsukawa formula (XLZ), the unified Royer formula (DZR), the universal decay law (UDL) and the Viola–Seaborg–Sobiczewski formula (VSS) are also used. The predictions are basically consistent with each other. Meanwhile, the results also indicate that N=126 shell closure is still robust at Z=92 and the spectroscopic factor \begin{document}$ S_{\alpha} $\end{document} is almost the same for uranium isotopes with the same l.     

Macroscopic-microscopic calculations of ground state properties of superheavy nuclei

We systematically calculate the ground state properties of superheavy even-even nuclei with proton number Z=94–118. The calculations are based on the liquid drop macroscopic model and the microscopic model with the modified single-particle oscillator potential. The calculated binding energies and α-decay energies agree well with the experimental data. The reliability of the macroscopic-microscopic(MM)model for superheavy nuclei is confirmed by the good agreement between calculated results and experimental ones. Detailed comparisons between our calculations and M?ller’s are made. It is found that the calculated results also agree with M?ller’s results and that the MM model is insensitive to the microscopic single-particle potential. Calculated results are also compared with results from relativistic mean-field (RMF) model and from Skyrme-Hatree-Fock(SHF) model. In addition, half-lives, deformations and shape coexistence are also investigated. The properties of some unknown nuclei are predicted and they will be useful for future experimental researches of superheavy nuclei.     

Alpha decay and cluster decay of some neutron-rich actinide nuclei

Nuclei in the actinide region are good in exhibiting cluster radioactivity. In the present work, the half-lives of α-decay and heavy cluster emission from certain actinide nuclei have been calculated using cubic plus Yukawa plus exponential model (CYEM). Our model has a cubic potential for the overlapping region which is smoothly connected by a Yukawa plus exponential potential for the region after separation. The computed half-lives are compared with those of other theoretical models and are found to be in good agreement with each other. In this work, we have also studied the deformation effects on half-lives of cluster decay. These deformation effects lower the half-life values and it is also found that the neutron-rich parent nuclei slow down the cluster decay process. Geiger–Nuttal plots for various clusters are found to be linear and most of the emitted clusters are α-like nuclei.     

Two-proton radioactivity of ground and excited states within a unified fission model

A unified fission model is extended to study two-proton radioactivity of the ground states of nuclei, and a good agreement between the experimental and calculated half-lives is found. The two-proton radioactivity half-lives of the ground states of some probable candidates are predicted within this model by inputting the released energies taken from the AME2020 table. It is shown that the predictive accuracy of the half-lives is comparable to those of other models. Then, two-proton radioactivity of the excited states of ¹⁴O, ^17,18Ne, ²²Mg, ²⁹S, and ⁹⁴Ag is discussed within the unified fission model and two analytical formulas. It is found that the experimental half-lives of the excited states are reproduced better within the unified fission model. Furthermore, the two formulas are not suitable for the study of two-proton radioactivity of excited states because their physical appearance deviates from the mechanism of quantum tunneling, and the parameters involved are obtained without including experimental data from the excited states.     

Two-proton radioactivity of exotic nuclei beyond proton drip-line

To search for new candidates of the true and simultaneous two-proton(2 p) radioactivity, the 2 p decay energies(Q2 p) are extracted by the Weizs?cker–Skyrme-4(WS4) model, the finite-range droplet model(FRDM), the Koura–Tachibana–Uno–Yamada(KTUY) model and the Hartree–Fock–Bogoliubov mean-field model with the BSk29 Skyrme interaction(HFB29). Then, the 2 p radioactivity half-lives are calculated within the generalized liquid drop model by inputting the four types of Q2 pvalues. By the energy and half-life constraints, it is found that the probable 2 p decay candidates are the nuclei beyond the proton-drip line in the region of Z≤50 based on the WS4 and KTUY mass models. For the FRDM mass model, the probable 2 p decay candidates are found in the region of Z≤44. However, the 2p-decaying candidates are predicted in the region of Z≤58 by the HFB29 mass model. It means that the probable 2 p decay candidates of Z50 are only predicted by the HFB29 mass model. Finally, the competition between the true 2p radioactivity and α-decay for the nuclei above the N=Z=50 shell closures is discussed. It is shown that ~(101)Te,~(111)Ba and ~(114)Ce prefer to 2p radioactivity and the dominant decay mode of ~(107)Xe and ~(116)Ce is α-decay.     

Structure of liquid bismuth calculated from pseudo-potentials and molecular dynamics

Earlier calculations on liquid bismuth have been done by using five conduction electrons. However, this metal presents, in the liquid state, a gap in its electronic density of states that clearly separates the s and the p bands. Thus, the number of free electrons to be considered is affected by the existence of the gap. Previous calculations on the structure of liquid bismuth with five conduction electrons did not give satisfactory results. Molecular dynamics calculations using an effective potential derived from the empty core potential (ECP) and from the local optimised model potential (OMP) are presented and compared with the results obtained with three (p) and five (s + p) conduction electrons. The results, obtained for the first time to our knowledge for liquid bismuth at different temperatures, with three conduction electrons and OMP are in very good agreement with the Waseda structural experimental data. This approach using three conduction electrons is confirmed by resistivity calculations using the t-matrix model.     

Comprehensive decay law for emission of charged particles and exotic cluster radioactivity

A general decay formula for the emission of charged particles from metastable nuclei is developed based on the basic phenomenon of resonances occurring in quantum scattering process under Coulomb-nuclear potential. It relates the half-lives of radioactive decays with the Q values of the outgoing elements with masses and charges of the nuclei involved in the decay. The relation is found to be a generalization of the Geiger–Nuttall law in α radioactivity and explains well all the known emissions of charged particles including clusters, alpha and proton.     

质子放射性寿命的新规律

对球形核和变形核质子放射性的半衰期进行了系统的分析和研究,提出了新的计算质子放射性寿命的解析公式。 通过对公式计算寿命和实验测量值的系统比较,发现两者之间符合得非常好,说明新公式十分准确并具有良好的预言能力。 Systematic calculations on proton radioactivity half lives of both spherical and deformed nuclei are carried out. A new formula with only four parameters is proposed for proton radioactivity half lives. The half lives calculated by using the new formula are in good agreement with the experimental ones. The new formula is simple but accurate, which is very useful for further experiments.