Systematic study of theαdecay preformation factors of the nuclei around the Z=82,N=126 shell closures within the generalized liquid drop model

In this study,we systematically investigate theαdecay preformation factors,Pα,and theαdecay half-lives of 152 nuclei around Z=82,N=126 closed shells based on the generalized liquid drop model(GLDM)with Pαbeing extracted from the ratio of the calculatedαdecay half-life to the experimental one.The results show that there is a remarkable linear relationship between Pαand the product of valance protons(holes)Np and valance neutrons(holes)Nn.At the same time,we extract theαdecay preformation factor values of the even–even nuclei around the Z=82,N=126 closed shells from the study of Sun et al.[J.Phys.G:Nucl.Part.Phys.,45:075106(2018)],in which theαdecay was calculated by two different microscopic formulas.We find that theαdecay preformation factors are also related to NpNn.Combining with our previous studies[Sun et al.,Phys.Rev.C,94:024338(2016);Deng et al.,ibid.96:024318(2017);Deng et al.,ibid.97:044322(2018)]and that of Seif et al.,[Phys.Rev.C,84:064608(2011)],we suspect that this phenomenon of linear relationship for the nuclei around the above closed shells is model-independent.This may be caused by the effect of the valence protons(holes)and valence neutrons(holes)around the shell closures.Finally,using the formula obtained by fitting theαdecay preformation factor data calculated by the GLDM,we calculate theαdecay half-lives of these nuclei.The calculated results agree with the experimental data well.

New behaviors ofα-particle preformation factors near doubly magic ^(100)Sn

Theα-particle preformation factors of nuclei above doubly magic nuclei ^(100)Sn and ^(208)Pb are investigated within the generalized liquid drop model.The results show that theα-particle preformation factors of nuclei near self-conjugate doubly magic ^(100)Sn are significantly larger than those of analogous nuclei just above ^(208)Pb,and they will be enhanced as the nuclei move towards the N=Z line.The proton-neutron correlation energy E_(p-n) and two protons-two neutrons correlation energy E_(2p-2n) of nuclei near ^(100)Sn also exhibit a similar situation,indicating that the interactions between protons and neutrons occupying similar single-particle orbitals could enhance theα-particle preformation factors and result in superallowed a decay.This also provides evidence of the significant role of the proton-neutron interaction onα-particle preformation.Also,the linear relationship betweenα-particle preformation factors and the product of valence protons and valence neutrons for nuclei around ^(208)Pb is broken in the100 Sn region because theα-particle preformation factor is enhanced when a nucleus near 100 Sn moves towards the N=Z line.Furthermore,the calculatedαdecay half-lives fit well with the experimental data,including the recent observed self-conjugate nuclei ^(104)Te and ^(108)Xe[Phys.Rev.Lett.121,182501(2018)].

Improved empirical formula for α particle preformation factor

In this contribution,the α preformation factors of 606 nuclei are extracted within the framework of the generalized liquid drop model(GLDM).Through the systematic analysis of the α preformation factors of even-even Po-U isotopes,we found that there is a significant weakening of influence of N=126 shell closure in uranium,which is consistent with the results of a recent experiment [J.Khuyagbaatar et al.,Phys.Rev.Lett.115,242502(2015)],implying that N=126 may not be the magic number for U isotopes.Furthermore,we propose an improved formula with only 7 parameters to calculate α preformation factors suitable for all types of α-decay;it has fewer parameters than the original formula proposed by Zhang et al.[H.F.Zhang et al.,Phys.Rev.C 80,057301(2009)]with higher precision.The standard deviation of the α preformation factors calculated by our formula with extracted values for all 606 nuclei is 0.365 with a factor of 2.3,indicating that our improved formula can accurately reproduce the α preformation factors.Encouraged by this,the α-decay half-lives of actinide elements are predicted,which could be useful in future experiments.Notably,the predicted α-decay half-lives of two new isotopes 220 Np [Z.Y.Zhang,et al.,Phys.Rev.Lett.122,192503(2019)] and 219 Np [H.B.Yang et al.,Phys.Lett.B 777,212(2018)] are in good agreement with the experimental α-decay half-lives.

Systematic study of cluster radioactivity within the generalized liquid drop model

Cluster radioactivity is studied within the generalized liquid drop model(GLDM),in which the shell correction energy,pairing energy,and cluster preformation factor are considered.The calculations show significant improvements and can reproduce the experimental data within a factor of 8.04 after considering these physical effects.In addition,the systematic trend of the cluster preformation factors is discussed in terms of the N_(p)N_(n)scheme to study the influence of the valence proton-neutron interaction and shell effect on cluster radioactivity.It is found that log10Pcis linearly related to N_(p)N_(n).This is in agreement with a recent study[L.Qi et al.,Phys.Rev.C 108,014325(2023)],in which log10Pc,obtained using different theoretical models and treatment methods than those used in this study,also had a linear relationship with N_(p)N_(n).Combined with the work by Qi et al.,this study suggests that the linear relationship between log10Pcand N_(p)N_(n)is model-independent and both the shell effect and valence proton-neutron interaction play essential roles in cluster radioactivity.An analytical formula is proposed to calculate the cluster preformation factor based on the N_(p)N_(n)scheme.In addition,the cluster preformation factors and the cluster radioactivity half-lives of some heavy nuclei are predicted,which can provide a reference for future experiments.

Model-independent trend of α-preformation probability

The α-preformation probability is directly deduced from experimental α decay energies and half-lives in an analytical way without any modified parameters. Several other model-deduced results, are used to compare with that of the present study. The key role played by the shell effects in the v-preformation process is indicated in all these cases. In detail, the α-preformation factors of different theoretical extractions are found to have similar behavior for one given isotopic chain, implying the model-independent varying trend of the preformation probability of α particle. In addition, the formation probability of heavier particle in cluster radioactivity is also obtained, and this confirms the relationship between the cluster preformation factor and the product of the cluster and daughter proton numbers.

Signatures of shell evolution in alpha decay across the N=126 shell closure

Within the alpha-cluster model, we particularly investigate the alpha decay of exotic nuclei in the vicinity of the N = 126 neutron shell plus the Z = 82 proton shell. The systematics of alpha-preformation probability（Pα）,as an indicator of the shell effect, is deduced from the ratio of the experimental decay width to the calculated one.Through the comparative analysis of the Pα trend in the N = 124-130 isotonic chain, the N = 126 and Z = 82 shell closures are believed to strongly affect the formation of the alpha particle before its penetration. Additionally, the Pα variety in Po and Rn isotopes is presented as another proof for such an influence. More importantly, it may be concluded that the expected neutron（or proton） shell effect gradually fades away along with the increasing valence proton（or neutron） number. The odd-even staggering presented in the Pα value is also discussed.

满壳层附近禁戒α衰变寿命的研究

发展了α 结团模型并用于研究满壳层 (Z =82 ,N =12 6 )附近的禁戒α衰变 ,对实验新观测到的天然α放射性核素 2 0 9Bi以及N =12 7同中子素链 (Po—U)的α衰变寿命进行了计算 ,理论结果和实验数据能够很好地符合 ,验证了α 结团模型对禁戒α衰变的适用性 .通过引入随质子数变化的α粒子预形成几率公式 ,进一步改进和完善了α 结团模型 .

基于结团形成模型系统研究Z=82,N=126闭壳附近原子核的α衰变

基于结团形成模型(cluster-formation model, CFM)系统地研究了质子数Z=82,中子数N=126闭壳附近的α衰变母核的α衰变预形成因子Pα。计算结果表明:基于结团形成模型计算得到的Pα线性地依赖于价质子(空穴)Np和价中子(空穴)Nn的乘积。这与前期工作[SUN X D, et al. Phys Rev C, 2016, 94(2):024338;DENG J G, et al. Phys Rev C, 2017, 96(2):024318]得到的结论是一致的,其中,Pα是唯象的且模型依赖的,从α衰变半衰期的理论值和实验值的比值中提取。结合前期工作可以得到这样的结论:对于Z=82,N=126闭壳附近的α衰变母核,其Pα与NpNn呈线性关系,且价质子-价中子相互作用在α结团预形成中起了很重要的作用。