Constraint on the astrophysical ${}^{18}\mathrm{Ne}(\alpha ,p){}^{21}\mathrm{Na}$ reaction rate through a ${}^{24}\mathrm{Mg}(p,t){}^{22}\mathrm{Mg}$ measurement

The ${}^{18}\mathrm{Ne}(\alpha ,p){}^{21}\mathrm{Na}$ reaction plays a crucial role in the $(\alpha ,p)$ process, which leads to the rapid proton capture process in x-ray bursts. The reaction rate depends upon properties of ${}^{22}\mathrm{Mg}$ levels above the $\alpha$ threshold at 8.14 MeV. Despite recent studies of these levels, only the excitation energies are known for most with no constraints on the spins. We have studied the ${}^{24}\mathrm{Mg}(p,t){}^{22}\mathrm{Mg}$ reaction at the Oak Ridge National Laboratory (ORNL) Holifield Radioactive Ion Beam Facility (HRIBF), and by measuring the angular distributions of outgoing tritons, we provide some of the first experimental constraints on the spins of astrophysically important ${}^{18}\mathrm{Ne}(\alpha ,p){}^{21}\mathrm{Na}$ resonances.

Figure 1

A schematic diagram of the experimental setup is shown. The proton beam impinged on a $500\hspace{0.5em}\mu \mathrm{g}/{\mathrm{cm}}^2{}^{24}\mathrm{Mg}$ target. Recoiling tritons from the ${}^{24}\mathrm{Mg}(p,t){}^{22}\mathrm{Mg}$ reaction were detected by the SIDAR array, and the beam was continuously monitored by a graphite beam stop.

Figure 2

Particle identification of tritons from the ${}^{24}\mathrm{Mg}(p,t){}^{22}\mathrm{Mg}$ reaction at ${\theta }_{\mathrm{lab}}=37.6^{°}({\theta }_{\mathrm{c}.\mathrm{m}.}=41.6^{°})$.

Figure 3

The number of counts per channel versus triton energy plot in the 41-MeV run at ${\theta }_{\mathrm{lab}}=37.6^{°}({\theta }_{\mathrm{c}.\mathrm{m}.}=41.6^{°})$ is shown. The inset shows an expanded view of the high-energy range (marked as red dashed box). All excitation energies are shown in MeV.

Figure 4

The angular distribution of tritons from the ${}^{24}\mathrm{Mg}(p,t){}^{22}\mathrm{Mg}$ reaction for 12 levels are shown. The solid and empty circles are from the $E_{\mathrm{beam}}=41$ MeV and $E_{\mathrm{beam}}=41.5$ MeV runs, respectively. DWBA calculations for the five possible $l$ transfers are also shown. Differential cross sections are in arbitrary units.

Figure 5

The ${}^{18}\mathrm{Ne}(\alpha ,p){}^{21}\mathrm{Na}$ reaction rate as a function of temperature. The present result is plotted in comparison with one calculated in Ref. [10].