Cross section measurements and R-Matrix analyses of the $^{24}$Mg($\alpha,p\gamma$)$^{27}$Al and $^{27}$Al($p,\alpha\gamma$)$^{24}$Mg reactions with HAGRiD

Alpha-induced reactions have been identified as playing an important role in various astrophysical phenomena. Sensitivity studies have indicated the $^{24}$Mg($\alpha,p$)$^{27}$Al reaction is important in understanding the energy generation in Type Ia X-ray bursts; therefore precise cross section measurements are needed. The $^{24}$Mg($\alpha,p$)$^{27}$Al cross section has not been measured directly, and no data is available for the inelastic channels which may contribute to its reaction rate. Present $^{24}$Mg($\alpha,p$)$^{27}$Al reaction rates rely exclusively on the inverse $^{27}$Al$(p,\alpha)^{24}$Mg cross section. The direct $(\alpha,p)$ and inverse $(p,\alpha)$ reactions have been performed at the University of Notre Dame's Nuclear Science Laboratory using the 5U Sta. ANA accelerator to produce a high-intensity beam with high energy resolution, providing new precision cross section measurements. The LaBr$_3$ Hybrid Array of Gamma Ray Detectors (HAGRiD) was utilized to span seven unique angles to detect the secondary $\gamma$ rays in the inelastic channels. R-Matrix analyses of the cross sections using secondary $\gamma$ rays and the inelastic channels effect on reaction rates will be presented.