Cluster radioactivity with effects of deformations and orientations of nuclei included

Abstract

Based on the preformed cluster model (PCM) of Gupta and collaborators, we have extended our recent study on ground-state cluster decays to parent nuclei resulting in daughters other than spherical $^{208}\mathrm{Pb}$, i.e., to deformed daughters, and the very new cases of $^{14}\mathrm{C}$ and $^{15}\mathrm{N}$ decays of $^{223}\mathrm{Ac}$, and $^{34}\mathrm{Si}$ decay of $^{238}\mathrm{U}$, taking nuclei as spherical, quadrupole deformed (${\ensuremath{\beta}}_{2}$) alone, and with higher multipole deformations up to hexadecapole (${\ensuremath{\beta}}_{2}$, ${\ensuremath{\beta}}_{3}$, ${\ensuremath{\beta}}_{4}$) together with the ``optimum'' orientations of cold decay process. Except for $^{14}\mathrm{C}$ decays of $^{221}\mathrm{Fr}$, $^{221\ensuremath{-}224,226}\mathrm{Ra}$, and $^{225}\mathrm{Ac}$ where higher multipole deformations up to ${\ensuremath{\beta}}_{4}$ are found essential, the quadrupole deformation ${\ensuremath{\beta}}_{2}$ alone is found good enough to fit the experimental data. Because the PCM treats the cluster-decay process as the tunneling of a preformed cluster, the deformations and orientations of nuclei modify both the preformation probability ${P}_{0}$ and tunneling probability $P$, and hence the decay half-life, considerably.