Abstract
The location of the high spin members of the $^{20}\mathrm{Ne}$ ${K}^{\ensuremath{\pi}}$${=0}_{4}^{+}$ rotational band is discussed by examining the low energy properties of the unique optical potential describing $^{16}(\mathit{\ensuremath{\alpha}}$,\ensuremath{\alpha}) elastic scattering on a broad range of energies and angles. In particular, the last ${J}^{\ensuremath{\pi}}$${=10}^{+}$ member is predicted to lie at about 29 MeV excitation energy and to be very broad, in contrast with the current expectations. It is suggested that the measurement of the \ensuremath{\alpha}${+\mathrm{}}^{16}$O fusion excitation function in the relevant energy range could provide a clear signature of the presence of this state. We discuss the implications of our results for the lower spin attributions to this band.
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