Fully self-consistent calculation ofβ-decay half-lives within Skyrme energy density functional

β-decay half-lives of some magic and semi-magic nuclei have been studied in a fully self-consistent Skyrme Hartree-Fock(HF) plus charge-exchange random phase approximation(RPA).The self-consistency is addressed,in that the same Skyrme energy density functional is adopted in the calculation of ground states and Gamow-Teller excited states.First,the impact of J2 terms on the β-decay half-lives is investigated by using the SGII interaction,revealing a large influence.Subsequently,numerical calculations are performed for the selected nuclei with Skyrme energy density functionals SGII,LNS,SKX,and SAMi.Finally,comparisons to available experimental data and predictions of different theoretical models are discussed.

Simple Formula of β^+-Decay Half-Lives of Nuclei Far From β-Stable Line

We generalize the formula of β^+-decay half-lives [Phys.Rev.C 78 (2006) 014305] to include all availabledata of nuclei far from the β-stable line. Good agreement with experimental data is obtained by taking into accountthe even-odd (e-o) effect.It is shown that the e-o effect on β^+-deeay half-life is apparent for the allowed β^+-transition,whereas it is not apparent for the first and second forbidden transitions.This demonstrates that the allowed β^+-transitionis more sensitive to the nuclear even-odd effect than the forbidden β^+-transition.The underlying physics is discussed.This formula can be used to predict the β^+-decay half-lives of the nuclei far from β-stability.It is useful to experimentalphysicists for analyzing the data of β^+-decay.

Systematic Calculations of α-Decay Half-Lives Using Microscopic Deformed Potentials

A new version of the generalized density-dependent cluster model （GDDCM） is developed to describe an α particle tunneling through a deformed potential barrier. The microscopic deformed potential is numerically constructed in the double-folding model using the multipole ex- pansion method. The decay width of an α-cluster state is evaluated using the integral of the quasi-bound state wave function, the scattering state wave function, and the difference of poten- tials. We perform a systematic calculation of α-decay half-lives for favored transitions in even-even nuclei ranging from Z=52 to Z=104. The calculated half-lives are in good agreement with the experimental values. The relation between nuclear deformations and α-decay half-lives is also discussed in details.

Theoretical calculations of proton emission half-lives based on a deformed Gamow-like model

In this study,proton emission half-lives were investigated for deformed proton emitters with 53≤Z≤83based on the presented deformed Gamow-like model,where the deformation effect was included in the Coulomb potential.The experimental half-lives of proton emitters can be reproduced within a factor of 3.45.For comparison,the results from the universal decay law and the new Geiger-Nuttall law are also presented.Furthermore,the relevance of the half-lives to the angular momentum l for ^(117)La,^(121)Pr,^(135)Tb,and ^(141)Ho were analyzed,and the corresponding possible values of l were proposed:l=3,3,4,4.

αDecay in extreme laser fields within a deformed Gamow-like model

In this study, the effect of extreme laser fields on the α decay process of ground-state even–even nuclei was investigated.Using the deformed Gamow-like model, we found that state-of-the-art lasers can cause a slight change in the α decay penetration probability of most nuclei. In addition, we studied the correlation between the rate of change of the α decay penetration probability and angle between the directions of the laser electric field and α particle emission for different nuclei. Based on this correlation, the average effect of extreme laser fields on the half-life of many nuclei with arbitrary α particle emission angles was calculated. The calculations show that the laser suppression and promotion effects on the α decay penetration probability of the nuclei population with completely random α particle-emission directions are not completely canceled.The remainder led to a change in the average penetration probability of the nuclei. Furthermore, the possibility of achieving a higher average rate of change by altering the spatial shape of the laser is explored. We conclude that circularly polarized lasers may be helpful in future experiments to achieve a more significant average rate of change of the α decay half-life of the nuclei population.

Conservation Laws of Physics in Dirac Vacuum and β-Decay of Nuclei

The laws of conservation of energy, linear momentum. and angular momentum of a system form a closed unit according to Noether's theorem. A generalization of these laws (including spin) for elementary par- ticles taking into account the states of negative energies of the Dirac vacuum is given. A new interpretation of the β-decay of nuclei without neutrinos. using interactions with Dirac's anti-world is discussed, which ex- plains all characteristics of the β-continuum. A quantum-electrodynamic theory of β-decay is presented in which Fermi's constant g of weak interactions is determined from first principles (without neutrinos). The lat- ter is an expression of e, h, c, m, M, and R, i.e., g is not an independent constant of physics nor is it necessa- ry to measure it.

β-Decay of Light Neutron-Rich Nuclei

The β-decays of neutron-rich carbon, nitrogen and fluorine isotopes have been systematically studied using the OXBASH shell Model. In the psd, spsd and spsdpf model space, we use the WBP interaction to calculate the half-lives and neutron emission probabilities of neutron- rich carbon and nitrogen isotopes, respectively. With the USD （W） and CW interactions, we calculate the half-lives and neutron emission probabilities of neutron-rich fluorine isotope in the sd model space, respectively. The calculated half-lives and neutron emission probabilities reproduce recent experimental data very well. It seems to show that the particles of the neutron-rich carbon and nitrogen isotopes are mainly excited in the spsd space. The β-decay of 21N to the neutron bound states in 210 is mostly the first forbidden transition which makes the neutron emission probability increase. The theoretical calculation of β-decay of 25F to 25Ne with CW interaction shows that CW interaction is better than USD interaction.

2-11 Stellar -decay Rate of 59Fe and Its Impact on the 60Fe Nucleosynthesis

60Fe is a long-lived nucleus (T1=2=2.62×106 a) which is mainly synthesized in the Carbon-shell burning ofmassive stars. It still could be observed nowadays after being ejected to the space after massive star ends its life assupernova. Along with another long-lived nucleus 26Al (T1=2=7.17×105 a) which is synthesized in the similar stars,the observation of their decay could provide the information of stellar evolution. From 2002-2005 the INTEGRALsatellite with detector obtained 60Fe/26Al flux ratio in our Galaxy to be 0.148(60)[1]. It's significantly smallerthan the theoretical prediction 0.45[2], and indicated that the theory need to be improved to increase the 60Fe yieldor decrease 26Al yield. 60Fe is produced by neutron capture reactions: 58Fe(n, )59Fe and 59Fe(n, )60Fe. Thecompetition between -decay of 59Fe and its neutron capture plays an important role in 60Fe synthesis path. In thepresent work, the impact on the 60Fe synthesis of the -decay process in stellar environment is studied.

Two-proton radioactivity from excited states of proton-rich nuclei within Coulomb and Proximity Potential Model

In the present work,we extend the Coulomb and Proximity Potential Model(CPPM)to study two-proton(2p)radioactivity from excited states while the proximity potential is chosen as AW95 proposed by Aage Withner in 1995.Demonstration reveals that the theoretical results acquired by CPPM exhibit a high level of consistency with prior theoretical models such as the unified fission model(UFM),generalized liquid-drop model(GLDM)and effective liquid-drop model(ELDM).Furthermore,within the CPPM,we predicted the half-lives of potential 2p radioactive nuclei for which experimental data are currently unavailable.The predicted results were then assessed,compared with UFM,ELDM and GLDM models,and examined in detail.

Simple model for cluster radioactivity half-lives in trans-lead nuclei

In this study,considering the modified preformation probability P_(c)to be log_(10)P_(c)=(A_(c)−1)/3log_(10)P_(α)+c′,where P_(α)and c′are theα-particle preformation probability and an adjustable parameter proposed by Wang et al.[Chin.Phys.C 45,044111(2021)],respectively,we extend a new simple model put forward by Bayrak[J.Phys.G 47,025102(2020)]to systematically study the cluster radioactivity half-lives of 28 trans-lead nuclei ranging from^(222)Fr to^(242)Cm,which is based on the Wentzel-Kramers-Brillouin approximation and Bohr–Sommerfeld quantization condition.For comparison,a universal decay law proposed by Qi et al.[Phys.Rev.C 80,044326(2009)],a three-parameter model-independent formula put forward by Balasubramaniam et al.[Phys.Rev.C 70,017301(2004)],and the semi-empirical model proposed by Tavares et al.[Eur.Phys.J.A 49,1(2013)]are used.Our calculated results reproduce the experimental data well,with a standard deviation of 0.818.Furthermore,we use this model to predict the cluster radioactivity half-lives of 51 possible cluster radioactive candidates whose cluster radioactivities are energetically allowed or observed but not yet quantified in NUBASE2020.

Systematic study of proton radioactivity half‑lives

In the present study,on the basis of the screened electrostatic effect of the Coulomb potential,we propose an improved Gamow model within the centrifugal potential in which there are only two adjustable parameters,i.e.,the screened parameters t and g,which represent the combined effect of the interaction potential and reduced mass of the emitted proton-daughter nucleus on the half-life of proton radioactivity in the overlapping region.Using this model,we systematically calculated the proton radioactivity half-lives of 31 spherical nuclei and 13 deformed nuclei and obtained corresponding root-mean-square deviations of 0.274 and 0.367,respectively.The relationship between the proton radioactivity half-life of 177Tlm and the corresponding angular momentum l removed by the emitted proton is also discussed.In addition,we used the proposed model to predict the proton radioactivity half-lives of 18 nuclei whose proton radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020.For comparison,we used the universal decay law of proton radioactivity proposed by Qi et al.(Phys Rev C 85:011303,2012.https://doi.org/10.1103/PhysR evC.85.011303),and the new Geiger–Nuttall law of proton radioactivity proposed by Chen et al.(Eur Phys J 55:214,2019.https://doi.org/10.1140/epja/i2019-12927-7).

Systematic calculations of cluster radioactivity half-lives with a screened electrostatic barrier

In this study,based on Wentzel-Kramers-Brillouin theory,we systematically investigate the cluster radioactivity half-lives of 22 nuclei ranging from^(221)Fr to^(242)Cm using a phenomenological model that considers the screened electrostatic effect of the Coulomb potential.In this model,there are two adjustable parameters,t and g,which are related to the screened electrostatic barrier and the strength of the spectroscopic factor,respectively.The calculated results indicate that this model can effectively reproduce the experimental data,with a corresponding rootmean-square deviation of 0.660.In addition,we extend this model to predict the half-lives of possible cluster radioactive candidates whose cluster radioactivities are energetically allowed or observed but not yet quantified in the evaluated nuclear properties table NUBASE2020.The predicted results are consistent with those obtained using other theoretical models and/or empirical formulas,including the universal decay law proposed by Qi et al.[Phys.Rev.C 80,044326(2009)],a semi-empirical model for bothαdecay and cluster radioactivity proposed by Santhosh et al.[J.Phys.G 35,085102(2008)],and a unified formula for the half-lives ofαdecay and cluster radioactivity proposed by Ni et al.[Phys.Rev.C 78,044310(2008)].

Systematic calculations of cluster radioactivity half-lives in trans-lead nuclei

In the present work,based on the Wentzel-Kramers-Brillouin(WKB)theory,considering the cluster preformation probability(Pc),we systematically investigate the cluster radioactivity half-lives of 22 trans-lead nuclei ranging from221Fr to242Cm.When the mass number of the emitted cluster Ac<28,Pcis obtained by the exponential relationship of Pcto theαdecay preformation probability(Pα)proposed by R.Blendowskeis et al.[Phys.Rev.Lett.61,1930(1988)],while Pαis calculated through the cluster-formation model(CFM).When Ac≥28,Pcis calculated through the charge-number dependence of Pcon the decay products proposed by Ren et al.[Phys.Rev.C70,034304(2004)].The half-lives of cluster radioactivity have been calculated by the density-dependent cluster model[Phys.Rev.C 70,034304(2004)]and by the unified formula of half-lives for alpha decay and cluster radioactivity[Phys.Rev.C 78,044310(2008)].For comparison,a universal decay law(UDL)proposed by Qi et al.[Phys.Rev.C 80,044326(2009)],a semi-empirical model for bothαdecay and cluster radioactivity proposed by Santhosh[J.Phys.G:Nucl.Part.Phys.35,085102(2008)],and a unified formula of half-lives for alpha decay and cluster radioactivity[Phys.Rev.C 78,044310(2008)]are also used.The calculated results of our work,Ni’s formula,and the UDL can well reproduce the experimental data and are better than those of Santhosh’s model.In addition,we extend this model to predict the half-lives for 51 nuclei,whose cluster radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020.

New Geiger-Nuttall law for cluster radioactivity half-lives

In this study,derived from Balasubramaniam’s formula[Phys.Rev.C 70,017301(2004)]and further considering the effect of the parent nucleus mass,blocking effect,and effect of reduced mass on cluster radioactivity half-lives,we propose a new Geiger-Nuttall law that is model-independent to systematically evaluate the halflives of this process for 16 even-even nuclei and 10 odd-A nuclei.For comparison,a single universal curve for cluster radioactivity andαdecay proposed by Poenaru[Phys.Rev.C 83,014601(2011)],a scaling law proposed by Horoi[J.Phys.G:Nucl.Part.Phys.30,945(2004)],an extension of the Viola-Seaborg formula fromαdecay to cluster radioactivity proposed by Ren et al.[Phys.Rev.C 70,034304(2004)],a new semi-empirical formula for exotic cluster decay proposed by Balasubramaniam et al.[Phys.Rev.C 70,017301(2004)],and a unified formula for the half-lives ofαdecay and cluster radioactivity proposed by Ni et al.[Phys.Rev.C 78,044310(2008)]are also used.The calculated results of our new Geiger-Nuttall law are in good agreement with the experimental half-lives,with the least rms being 0.606,and are better than the compared values.Moreover,we extend this formula to predict the cluster radioactivity half-lives of 51 nuclei whose decay energies are energetically allowed or observed but not yet quantified in NUBASE2020.

Systematic study on the proton radioactivity of spherical proton emitters

In this study, based on a two-potential approach, we systematically investigated the proton radioactivity half-lives of spherical proton emitters with 69≤Z≤81 from the ground and/or isomeric state, choosing the nuclear potential to be a modified Woods–Saxon potential that contains the isospin effect of the daughter nucleus. It was found that the calculated half-lives could reproduce the experimental data well. Furthermore, we extended this model to predict the half-lives of 17 protonemitting candidates whose radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020. For comparison, the unified fission model, Coulomb potential and proximity potential model, universal decay law for proton emission, and new Geiger–Nuttall law were also used. All the predicted results are consistent with each other.

α-decay half-lives of superheavy nuclei and general predictions

The generalized liquid drop model （GLDM） and the cluster model have been employed to calculate the α-decay half-lives of superheavy nuclei （SHN） using the experimental α-decay Q values. The results of the cluster model are slightly poorer than those from the GLDM if experimental Q values are used. The prediction powers of these two models with theoretical Q values from Audi et al. （QAudi） and Muntian et al. （QM） have been tested to find that the cluster model with QAudi and QM could provide reliable results for Z 〉 112 but the GLDM with QAudi for Z 112. The half-lives of some still unknown nuclei are predicted by these two models and these results may be useful for future experimental assignment and identification.

β^--Decay Half-Lives for Waiting Point Nuclei Around N=126

We have systematically analyzed the experimental β--decay half-lives of waiting point heavy nuclei around neutron number N = 126. A new set of parameters for the exponential formula of β^--decay half-lives is proposed. The forbidden transition effects are included in the new set of parameters self-consistently. Theoretical β^--decay half-lives of nuclei around N = 126 are compared with recent theoretical results and experimental data. It is found that the new theoretical results are in better agreement with experimental data. The unknown β^--decay half-lives of some nuclei in this region are predicted for studies on nuclear structure far from stability and the nucleosynthesis in stars.

Half-lives and fine structure for the α decay of deformed even-even nuclei

The α-decay properties of well-deformed even-even nuclei are systematically calculated within the multichannel cluster model (MCCM). Instead of working in the WKB framework, the quasibound solution to the coupled Schro¨dinger equation is presented with outgoing wave boundary conditions, and the coupling potential is taken into full account in terms of the general quantum theories. The calculated α-decay half-lives are found to agree well with the experimental data with a mean factor of less than 2. The fine structure observed in α decay is also well reproduced by the four-channel microscopic calculation. Very strikingly, the MCCM can give relatively precise descriptions of the branching ratio to excited 4+ states, which is often overestimated in the usual WKB calculations. We expect it to be a significant development of theoretical models toward quantitative descriptions of α transitions to high-spin daughter states.

Photochemistry of chrysene adsorbedon several types of particle

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The role of deformations and orientations in an alpha ternary fission of Thorium

The alpha ternary fission half-lives of thorium isotopes have been studied using the Coulomb and proximity potential models.The role of the deformation effects and the angle of orientation were included during the evaluation of the total potential.Fragment combinations were identified using cold valley plots of the driving potential.The half-lives and yields were evaluated using the penetration probability.The dependence of the logarithmic half-lives on different angles of orientation was studied.The evaluated alpha ternary fission yield was compared with that of the available experiments with and without deformations.The half-lives obtained in the present work were compared with those of the available data.Possible alpha ternary fission fragments were identified in the isotopes of thorium.The alpha ternary fission half-lives were compared to the binary fission half-lives.The binary fission half-lives are dominant in the ^(209-225)Th nuclei,and the ternary fission half-lives are dominant in the isotopes of the ^(226-238)Th nuclei.