The $\beta$ decay of spin-polarized ${}^{31}\mathrm{Mg}$ has been measured at TRIUMF to investigate the nuclear structure of the daughter nucleus ${}^{31}\mathrm{Al}$, which has been thought to be located outside of the $N=20$ island of inversion. By taking advantage of the spatial asymmetries of the $\beta$-ray counts for the respective daughter levels, unambiguous spin-parity assignments of seven levels in ${}^{31}\mathrm{Al}$ were successfully made for the first time. The spin-parity assignments enabled level-by-level comparisons of the experimental levels with the large-scale shell-model calculation using the SDPF-M interaction. It was shown that the ${}^{31}\mathrm{Al}$ levels are categorized into three groups from the structure viewpoint: 0p0h configuration dominant states including the $5/2^{+}$ ground state, 2p2h dominant states, and states with competitive 0p0h and 2p2h configurations. Various structures in an excitation energy region below $\sim 5\text{−}\mathrm{MeV}$ excitation energy suggest competition between the spherical mean field and the nuclear correlation, as in the case of the border nucleus ${}^{30}\mathrm{Mg}$.

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• Beta decay
• Energy levels
• Nuclear spin & parity
• Nuclear structure & decays
• 20 ≤ A ≤ 38
• Radioactive beams