Abstract
The $^{24}\mathrm{Mg}(p,\ensuremath{\alpha})^{21}\mathrm{Na}$ reaction was measured at the Holifield Radioactive Ion Beam Facility of the Oak Ridge National Laboratory to study the spectroscopy of the radionuclide $^{21}\mathrm{Na}$. A 31-MeV proton beam from the 25 MV tandem accelerator bombarded isotopically enriched $^{24}\mathrm{Mg}$ targets. Recoiling $^{4}\mathrm{He}$ particles were identified by an annular silicon strip detector array. Two energy levels at ${E}_{x}=6.594$ and 7.132 MeV were observed for the first time. By comparing the experimentally obtained angular distributions and distorted wave Born approximation calculations, the spins and parities of $^{21}\mathrm{Na}$ energy levels were constrained. The astrophysically-important $^{17}\mathrm{F}(\ensuremath{\alpha},p)^{20}\mathrm{Ne}$ reaction rate was also calculated for the first time using resonance parameters for 12 energy levels.
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