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.

Two-proton radioactivity within Coulomb and proximity potential model

Considering the preformation probability of the two emitted protons in the parent nucleus,we extend the Coulomb and proximity potential model(CPPM)to systematically study two-proton(2p)radioactivity half-lives of the nuclei close to proton drip line.The proximity potential chosen is Prox.81 proposed by Blocki et al.in 1981.Furthermore,we apply this model to predict the half-lives of possible 2p radioactive candidates whose 2p radioactivity is energetically allowed or observed but not yet quantified in the evaluated nuclear properties table NUBASE2016.The predicted results are in good agreement with those from other theoretical models and empirical formulas,namely the effective liquid drop model(ELDM),generalized liquid drop model(GLDM),Gamow-like model,Sreeja formula and Liu formula.