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The stability and/or instability of the deformed and superdeformed nuclei,$^{133-137}_{60}$Nd, $^{144-158}_{64}$Gd, $^{176-194}_{80}$Hg, and$^{192-198}_{82}$Pb parents, coming from three regions of differentsuperdeformations, are studied with respect to the $\alpha$ and heavy clusterdecays. The $\alpha$-decay studies also include the heavier $^{199-210}$Pbnuclei, for reasons of spherical magic shells at Z=82 and N=126. Thecalculations are made by using the preformed cluster-decay model, and theobtained $\alpha$-decay half-lives are compared with the available experimentaldata. Having met with a very good success for the comparisons of $\alpha$-decayhalf-lives and in giving the associated known magic or sub-magic closed shellstructures of both the parent nuclei and daughter products, the interplay ofclosed shell effects in the cluster-decay calculations is investigated. Thecluster-decay calculations also give the closed shell effects of knownspherical magicities, both for the parent and daughter nuclei, and furtherpredict new (deformed) closed shells at Z=72-74 and N=96-104 due to both thestability and instability of Hg and Pb parents against cluster decays.Specifically, a new deformed daughter radioactivity is predicted for variouscluster decays of $^{186-190}$Hg and $^{194,195}$Pb parents with the bestpossible measurable cases identified as the $^8$Be and $^{12}$C decays of$^{176,177}$Hg and/or $^{192}$Pb parents. The predicted decay half-lives arewithin the measurable limits of the present experimental methods. Theinteresting point to note is that the parents with measurable cluster decayrates are normal deformed nuclei at the transition between normal andsuper-deformation.Comment: 8 pages and 11 figure

Closed-shell effects from the stability and instability of nuclei against cluster decays in the mass regions 130–158 and 180–198