Effects of deformation on the cluster and the [formula omitted]-decay half-lives for isotopes of the Trans-lead and the undetected superheavy nuclei

Abstract

In the present investigation, based on the Wentzel–Kramers–Brillouin (WKB) approximation, and by considering deformation of the cluster and the daughter nuclei, the cluster radioactivity half-lives of 22 Trans-lead isotopes ranging from 221Fr to 242Cm are calculated. Also, the α-decay half-lives of even–even isotopes for the superheavy nuclei with Z in the range 104≤Z≤118 are computed. For the cluster radioactivity, a preformation factor, Pc depending on the atomic numbers of the cluster and the daughter nuclei is used according to the Santhosh and Jose (2021). The α preformation factor, Pα is evaluated based on the cluster-formation model (CFM). A universal decay law (UDL) proposed by Qi et al. (2009), was used to obtain the decay half-lives of the cluster and the α-decay for checking the credibility of our approach. The effects of the deformation of decay products on the half-lives of the cluster and the α-decay have also been investigated by comparing the obtained half-lives considering deformation with ones of the spherical nuclei and the results of the UDL as well as the available experimental data. Comparison indicates that our calculated cluster and α-decay half-lives considering deformation reproduce the experimental data more accurately than the UDL and the spherical nuclei. Furthermore, the cluster radioactivity half-lives of some isotopes that whose cluster radioactivity is energetically allowed but not observed preciously yet, are predicted. Also, the cluster and the α-decay half-lives and the branching ratios between them for some not yet discovered superheavy isotopes with Z=122 and Z=124 are obtained.