Abstract
Recent antisymmetrized molecular dynamics (AMD) calculations for ${}^{28}$Si suggest the presence of a superdeformed (SD) band with a dominant ${}^{24}\mathrm{Mg}+\ensuremath{\alpha}$ clustering for its configuration, with firm predictions for its location and associated moment of inertia. This motivates a review of the experimental results reported in the literature with a particular focus on ${}^{24}$Mg($\ensuremath{\alpha}$,$\ensuremath{\gamma}$) studies, as well as on $\ensuremath{\alpha}$-like heavy-ion transfer reactions such as ${}^{12}$C(${}^{20}$Ne,$\ensuremath{\alpha}$)${}^{28}$Si. Combining this information for the first time leads to a set of candidate SD states whose properties point to their $\ensuremath{\alpha}$-cluster structure and strong associated deformation. Analysis of data from Gammasphere allows the electromagnetic decay of these candidate states to be probed and reveals further supporting evidence for such a structure. This paper appraises this body of information and finds the evidence for an SD band is strong.
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