  The $^{24}$Mg($p$, $\alpha$)$^{21}$Na reaction was measured at the Holifield
Radioactive Ion Beam Facility at Oak Ridge National Laboratory in order to
better constrain spins and parities of energy levels in $^{21}$Na for the
astrophysically important $^{17}$F($\alpha, p$)$^{20}$Ne reaction rate
calculation. 31 MeV proton beams from the 25-MV tandem accelerator and enriched
$^{24}$Mg solid targets were used. Recoiling $^{4}$He particles from the
$^{24}$Mg($p$, $\alpha$)$^{21}$Na reaction were detected by a highly segmented
silicon detector array which measured the yields of $^{4}$He particles over a
range of angles simultaneously. A new level at 6661 $\pm$ 5 keV was observed in
the present work. The extracted angular distributions for the first four levels
of $^{21}$Na and Distorted Wave Born Approximation (DWBA) calculations were
compared to verify and extract angular momentum transfer.
