The decay of the ${}^{246}\mathrm{Bk}$ ${}^{*}$ nucleus, formed in entrance channel reactions ${}^{11}\mathrm{B}+{}^{235}\mathrm{U}$ and ${}^{14}\mathrm{N}+{}^{232}\mathrm{Th}$ at different incident energies, is studied by using the dynamical cluster-decay model (DCM) extended to include the deformations and orientations of nuclei. The main decay mode here is fission. The other (weaker) decay channels are the light particles evaporation ($A⩽4$) and intermediate mass fragments ($5⩽A⩽20$). All decay products are calculated as emissions of preformed clusters through the interaction barriers. The calculated fission cross sections ${\sigma }_{\mathrm{fiss}}$, taken as a sum of the energetically favored symmetric and near symmetric fragments ($A_{\mathrm{CN}}/2\pm 7$ and $A=106\text{−}110$ plus complementary fragments) show an excellent agreement with experimental data at all experimental incident c.m. energies for both reactions, except for the top three energies in the case of the ${}^{11}\mathrm{B}+{}^{235}\mathrm{U}$ reaction. The disagreement between the DCM calculations and data at higher incident c.m. energies for the ${}^{11}\mathrm{B}+{}^{235}\mathrm{U}$ entrance channel is associated with the presence of additional effects of noncompound, quasifission (qf) components, in contradiction with the measured anisotropy effects which indicate the other entrance channel ${}^{14}\mathrm{N}+{}^{232}\mathrm{Th}$ to contain the noncompound nucleus contribution. The prediction of two fission windows, the symmetric fission (SF) and near symmetric or heavy mass fragments (HMFs), suggests the presence of a fine structure of fission fragments, which also need an experimental verification. The only parameter of the model is the neck length parameter $▵R$ whose value is shown to depend strongly on limiting angular momentum, which in turn depends on the use of sticking or nonsticking moment of inertia for angular momentum effects.

The role of deformations and orientations of nuclei is studied for the first time in cluster decays of various radioactive nuclei, particularly those decaying to doubly closed shell, spherical ${}^{208}\mathrm{Pb}$ daughter nucleus. Also, the significance of using the correct $Q$-value of the decay process is pointed out. The model used is the preformed cluster model (PCM) of Gupta and collaborators [R. K. Gupta et al., Proc. Int. Conf. on Nuclear Reactions Mechanisms, Varenna, 1988, p. 416; Phys. Rev. C 39, 1992 (1989); 55, 218 (1997); Heavy Elements and Related New Phenomena, edited by W. Greiner and R. K. Gupta, World Sc. 1999, Vol. II, p. 731]. In this model, cluster emission is treated as a tunneling of the confining interaction barrier by a cluster considered already preformed with a relative probability $P_0$. Since both the scattering potential and potential energy surface due to the fragmentation process in the ground state of the parent nucleus change significantly with the inclusion of deformation and orientation effects, both the penetrability $P$ and preformation probability $P_0$ of clusters change accordingly. The calculated decay half-lives for all the cluster decays investigated here are generally in good agreement with measured values for the calculation performed with quadrupole deformations ${\beta }_2$ alone and “optimum” orientations of cold elongated configurations. In some cases, particularly for ${}^{14}\mathrm{C}$ decay of Ra nuclei, the inclusion of multipole deformations up to hexadecapole ${\beta }_4$ is found to be essential for a comparison with data. However, the available ${\beta }_4$-values, particularly for nuclei in the mass region $16⩽A⩽26$, need be used with caution.

We have studied the (ground-state) cluster radioactive decays within the preformed cluster model (PCM) of Gupta and collaborators [R. K. Gupta, in Proceedings of the 5th International Conference on Nuclear Reaction Mechanisms, Varenna, edited by E. Gadioli (Ricerca Scientifica ed Educazione Permanente, Milano, 1988), p. 416; S. S. Malik and R. K. Gupta, Phys. Rev. C 39, 1992 (1989)]. The relativistic mean-field (RMF) theory is used to obtain the nuclear matter densities for the double folding procedure used to construct the cluster-daughter potential with M3Y nucleon-nucleon interaction including exchange effects. Following the PCM approach, we have deduced empirically the preformation probability P0emp from the experimental data on both the $\alpha${}- and exotic cluster-decays, specifically of parents in the trans-lead region having doubly magic Pb208 or its neighboring nuclei as daughters. Interestingly, the RMF-densities-based nuclear potential supports the concept of preformation for both the $\alpha${} and heavier clusters in radioactive nuclei. P0$\alpha${}(emp) for $\alpha${} decays is almost constant (~10-2\char21{}10-3) for all the parent nuclei considered here, and P0c(emp) for cluster decays of the same parents decrease with the size of clusters emitted from different parents. The results obtained for P0c(emp) are reasonable and are within two to three orders of magnitude of the well-accepted phenomenological model of Blendowske-Walliser for light clusters.

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.