Measurement of the $\chem{^{24}Mg({p},{t}){}^{22}Mg}$ reaction for the states near the $\chem{^{21}Na+p}$ threshold

Differential cross-sections of the $^{24}$Mg(p, t)$^{22}$Mg reaction were measured at 34.68 MeV for the states near the proton threshold at 5.502 MeV in $^{22}$Mg. Among them, the new states at 5.962, 6.046, 6.246 and 6.323 MeV, which were reported previously, have been confirmed. Angular distributions for these states were analyzed by distorted-wave Born-approximation calculations to deduce the spins and parities. The angular distribution for the 5.714 MeV state, which is considered to be most crucial for the stellar reaction $^{21}$Na(p, $\gamma$)$^{22}$Mg, has been found to be consistent with $J^{\pi}=2^+$ assignment. The 6.046 MeV state is newly assigned to have $J^{\pi}=0^+$, and the 5.962 MeV state is tentatively assigned to have $J^{\pi}=(1^-)$. These two states will also play an important role for $^{22}$Mg production in novae