Abstract
A systematic search for the nuclei in which the observation of discrete hyperdeformed (HD) bands may be feasible with existing detector facilities has been performed in the Cd isotopes within the framework of cranked relativistic mean-field theory. It was found that the $^{96}\mathrm{Cd}$ nucleus is a doubly magic HD nucleus owing to large proton $Z=48$ and neutron $N=48$ HD shell gaps. The best candidate for an experimental search of discrete HD bands is the $^{107}\mathrm{Cd}$ nucleus characterized by the large energy gap between the yrast and excited HD bands, the size of which is only 15% smaller than the one in the doubly magic HD $^{96}\mathrm{Cd}$ nucleus.
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