The Structure of Neutron-rich $^{28,29}$Mg Studied through $\beta$-decay of Spin-polarized $^{28,29}$Na Beams at TRIUMF

The structure of neutron-rich Mg isotopes in the region of Island of Inversion has been attracting much attention because of vanishing of \textit{N}=20 magic number and their large deformation in the ground states. However, most of the spins and parities of the excited states in Mg isotopes with \textit{A}$\geq$29 are left unknown. We have started systematic $\beta$-decay studies at TRIUMF, Canada, where highly spin-polarized radioactive Na beams are available. The experiment to determine the spins and parities of the states in $^{28,29}$Mg by using spin-polarized $^{28,29}$Na beams were performed at Osaka beam line in TRIUMF. The results are as follows: Many $\gamma$-transitions and energy levels were newly found in $^{28,29}$Mg. In $^{28}$Mg, spins and parities of the 4 levels reported previously were reconfirmed and those of the newly found 7.461 MeV level was assigned to be 2$^{+}$. In $^{29}$Mg, spins and parities of 3 energy levels were assigned for the first time. Shell model calculations were performed with NuShell code by using USD, USDA and USDB interactions to compare with the experimental results. In $^{29}$Mg, we also compared with MCSM calculation. The level structure in $^{28}$Mg was well explained by only sd-shell configurations.