As the first step of systematic studies on neutron-rich Mg isotopes, the structure of ${}^{28}$Mg has been investigated by $\beta$-decay spectroscopy of spin-polarized ${}^{28}$Na at TRIUMF. Spin-parity assignments have been successfully performed for levels in ${}^{28}$Mg by taking advantage of the anisotropic $\beta$ decay. Previous assignments for three levels were reconfirmed. New assignments were performed for four levels including a newly found 2${}^{+}$ level at 7.461 MeV. The experimental results were compared, on a level-by-level basis, with the shell-model calculation in the model space restricted to the $sd$ shell. Overall good agreement between the experimental and theoretical results indicates dominance of the normal configurations in most of the ${}^{28}$Mg levels. High performance of the present method promises successful application to heavier Mg isotopes to elucidate the shell evolution in the region of the $N=20$ island of inversion.

• Received 4 January 2012

DOI:https://doi.org/10.1103/PhysRevC.85.034310