Abstract
A 6\ensuremath{\alpha}-chain state has recently been discovered in $^{24}\mathrm{Mg}$ which is some 16--17 MeV above the 6\ensuremath{\alpha}-breakup threshold and yet paradoxically only 4--5 MeV wide. This surprising discovery raises the question of the possible existence of N\ensuremath{\alpha}-chain states in other 4N-nuclei. The excitation energy of this 6\ensuremath{\alpha}-chain state is very close to the value predicted by the Bloch-Brink cluster model. Therefore, to aid the experimental search for similar states in other nuclei, we present here predictions of the excitation energies of the N\ensuremath{\alpha}-chain state bandheads in the 4N-nuclei from $^{20}\mathrm{Ne}$ to $^{32}\mathrm{S}$ obtained using the Bloch-Brink cranked cluster model with the Brink-Boeker effective interaction and free variation of all parameters.
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