Spin assignments for $^{23}\hbox {Mg}$ levels and the astrophysical $^{22}\hbox {Na}(p,\gamma )^{23}\hbox {Mg}$ reaction

Abstract

The $^{22}\hbox {Na}(p,\gamma )^{23}\hbox {Mg}$ reaction is responsible for destruction of the long-lived radionuclide $^{22}\hbox {Na}$ produced during nova explosions. Since the reaction proceeds through resonances from levels in $^{23}\hbox {Mg}$ above the proton threshold at 7.581 MeV, the properties of these levels such as excitation energies, spins, and parities are crucial ingredients to determine the $^{22}\hbox {Na}(p,\gamma )^{23}\hbox {Mg}$ reaction rate. Despite recent studies of these levels, their spins are not well constrained in many cases. We have measured the $^{24}\mathrm{Mg}(p,d)^{23}\hbox {Mg}$ transfer reaction to determine spectroscopic properties of these levels at the Holifield Radioactive Ion Beam Facility at Oak Ridge National Laboratory. The spin of the $E_{x}$ = 7.788 MeV level in $^{23}\hbox {Mg}$ is constrained to be $J^{\pi }$ = (3/2$^+$, 5/2$^+$) through the present work. The astrophysical $^{22}\hbox {Na}(p,\gamma )^{23}\hbox {Mg}$ reaction rate at nova temperatures is updated accordingly. Nova nucleosynthesis model calculations using the newly updated $^{22}\hbox {Na}(p,\gamma )^{23}\hbox {Mg}$ reaction rate shows that the final weighted abundance of the radionuclide $^{22}\hbox {Na}$ is increased by 42% compared to that obtained by using the previous $^{22}\hbox {Na}(p,\gamma )^{23}\hbox {Mg}$ reaction rate of Sallaska et al. for a 1.35 $M_{\odot }$ ONeMg white dwarf.