Half-lives of deformed nuclei for exotic cluster decays

Abstract

In this paper, we considered the cluster radioactivity half-lives for all known cluster decay modes (i.e., from $^{14}\mathrm{C}$ up to $^{34}\mathrm{Si}$) that these nuclei were first satisfied by the observed systematics [Silisteanu and Scheid, Phys. Rev. C 51, 2023 (1995), Poenaru et al., Phys. Rev. C 83, 014601 (2011); Ni et al., Phys. Rev. C 78, 044310 (2008)]. The Coulomb and proximity potential model for deformed nuclei is considered as penetration of the emitter particle through the potential barrier formed by the nuclear, Coulomb, and centrifugal interactions between the emitter particle and nucleus. The spins and parities of the parent and daughter nuclei in addition to the quadrupole $({\ensuremath{\beta}}_{2})$ and hexadecapole $({\ensuremath{\beta}}_{4})$ deformations of the parent nuclei are taken into account for the calculation of the cluster radioactivity half-lives. Our results exhibit, which the minimum $\mathrm{lo}{\mathrm{g}}_{10}{T}_{1/2}$ value denotes doubly magic $^{208}\mathrm{Pb}$ ($Z=82$, $N=126$) as the daughter nuclei.