Effects of deformation on the cluster and the α-decay half-lives for isotopes of the Trans-lead and the undetected superheavy nuclei

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 Fr-221 to Cm-242 are calculated. Also, the a-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, P-c depending on the atomic numbers of the cluster and the daughter nuclei is used according to the Santhosh and Jose (2021). The alpha preformation factor, P-alpha 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 halflives of the cluster and the alpha-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 a-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 alpha-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 alpha-decay half-lives and the branching ratios between them for some not yet discovered superheavy isotopes with Z = 122 and Z = 124 are obtained.