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 (${\beta }_2$) alone, and with higher multipole deformations up to hexadecapole (${\beta }_2$, ${\beta }_3$, ${\beta }_4$) together with the “optimum” orientations of cold decay process. Except for ${}^{14}\mathrm{C}$ decays of ${}^{221}\mathrm{Fr}$, ${}^{221-224,226}\mathrm{Ra}$, and ${}^{225}\mathrm{Ac}$ where higher multipole deformations up to ${\beta }_4$ are found essential, the quadrupole deformation ${\beta }_2$ 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.

• Received 3 August 2009

DOI:https://doi.org/10.1103/PhysRevC.80.034317