The stability and/or instability of ${}_{60}^{133-137}\mathrm{Nd},$ ${}_{64}^{144-158}\mathrm{Gd},$ ${}_{80}^{176-194}\mathrm{Hg},$ and ${}_{82}^{192-198}\mathrm{Pb}$ parents are studied with respect to the $\alpha$ and heavy-cluster decays. The $\alpha$-decay studies also include the heavier ${}^{199-210}\mathrm{Pb}$ nuclei, for reasons of spherical magic shells at $Z=82\mathrm{}$ and $N=126.\mathrm{}$ The calculations are made by using the preformed cluster-decay model, and the obtained $\alpha$-decay half-lives are compared with the available experimental data. Having met with a very good success for the comparisons of $\alpha$-decay half-lives and in giving the associated known magic or submagic closed-shell structures of both the parent nuclei and daughter products, the interplay of closed-shell effects in the cluster-decay calculations is investigated. The cluster-decay calculations also give the closed shell effects of known spherical magicities, both for the parent and daughter nuclei, and further predict new (deformed) closed-shells at $Z=72\mathrm{}–74$ and $N=96\mathrm{}–104$ due to both the stability and instability of Hg and Pb parents against cluster decays. Specifically, a new deformed daughter radioactivity is predicted for various cluster decays of ${}^{186-190}\mathrm{Hg}$ and ${}^{194,195}\mathrm{Pb}$ parents with the best possible measurable cases identified as the ${}^8\mathrm{Be}$ and ${}^{12}\mathrm{C}$ decays of ${}^{176,177}\mathrm{Hg}$ and/or ${}^{192}\mathrm{Pb}$ parents. The predicted decay half-lives are within the measurable limits of the present experimental methods. The interesting point to note is that the parents with measurable cluster-decay rates are normal deformed nuclei at the transition between normal and superdeformation.

• Received 4 June 2003

DOI:https://doi.org/10.1103/PhysRevC.68.034321