Systematic study of cluster radioactivity in trans-lead nuclei with various versions of proximity potential formalisms

In this study,based on the framework of the Coulomb and proximity potential model(CPPM),we systematically investigate the cluster radioactivity half-lives of 26 trans-lead nuclei by considering the cluster preformation probability,which possesses a simple mass dependence on the emitted cluster according to R.Blendowske and H.Walliser[Phys.Rev.Lett.61,1930(1988)].Moreover,we investigate 28 different versions of the proximity potential formalisms,which are the most complete known proximity potential formalisms proposed to describe proton radioactivity,two-proton radioactivity,αdecay,heavy-ion radioactivity,quasi-elastic scattering,fusion reactions,and other applications.The calculated results show that the modified forms of proximity potential 1977,denoted as Prox.77-12,and proximity potential 1981,denoted as Prox.81,are the most appropriate proximity potential formalisms for the study of cluster radioactivity,as the root-mean-square deviation between experimental data and relevant theoretical results obtained is the least;both values are 0.681.For comparison,the universal decay law(UDL)proposed by Qi et al.[Phys.Rev.C 80,044326(2009)],unified formula of half-lives forαdecay and cluster radioactivity proposed by Ni et al.[Phys.Rev.C 78,044310(2008)],and scaling law(SL)in cluster radioactivity proposed by Horoi et al.[J.Phys.G 30,945(2004)]are also used.In addition,utilizing CPPM with Prox.77-12,Prox.77-1,Prox.77-2,and Prox.81,we predict the half-lives of 51 potential cluster radioactive candidates whose cluster radioactivity is energetically allowed or observed but not yet quantified in NUBASE2020.The predicted results are in the same order of magnitude as those obtained using the compared semi-empirical and/or empirical formulae.At the same time,the competition betweenαdecay and cluster radioactivity of these predicted nuclei is discussed.By comparing the half-lives,this study reveals thatαdecay predominates.

A simple model for two-proton radioactivity

In this work,considering the preformation factor of the emitted two protons in parent nucleus S_(2p) and the effect of the parent nucleus deformation,based on the Wentzel-Kramers-Brillouin approximation and Bohr-Sommerfeld quantization condition,we improve a simple phenomenological model proposed by Bayrak[J.Phys.G:47,025102(2020)]to systematically study 2p radioactivity half-lives.This model contains two adjustable parameters V_(0) and a_(β),which are related to the depth of nuclear potential and effect of deformation.The calculated results show that this model can effectively reproduce the experimental data with a corresponding root-mean-square(RMS)standard deviation of σ=0.683.For comparison,we include the Gamow-like model(GLM)proposed by Liu et al.[Chin.Phys.C 45,044110(2021)],generalized liquid drop model(GLDM)proposed by Cui et al.[Phys.Rev.C 101,014301(2020)],effective liquid drop model(ELDM)proposed by M.Gonalves et al.[Phys.Lett.B 774,14(2017)],two-potential approach with Skyrme-Hartree-Fock(TPASHF)proposed by Pan et al.[Chin.Phys.C 45,124104(2021)],phenomenological model with a screened electrostatic barrier(SEB)propoesed by Zou et al.[Chin.Phys.C 45,104101(2021)],unified fission model(UFM)proposed by Xing et al.[Chin.Phys.C 45,124105(2021)],Coulomb and proximity potential model for deformed nuclei(CPPMDN)proposed by Santhosh[Phys.Rev.C 104,064613(2021)],two-parameter empirical formula proposed by Liu et al.[Chin.Phys.C 45,024108(2021)],and four-parameter empirical formula proposed by Sreeja et al.[Eur.Phys.J.A 55,33(2019)].In addition,we use this model to 2p predict the radioactive half-lives of some possible potential nuclei whose 2p radioactivity are energetically allowed or observed but not yet quantified in NUBASE2020.

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)].