Structure of the neutron-rich nucleus Mg30

Structure of the neutron-rich nucleus $^{30}\mathrm{Mg}$, which is located close to the region of the $N=20$ ``island of inversion,'' has been investigated by $\ensuremath{\beta}\text{\ensuremath{-}}\ensuremath{\gamma}$ spectroscopy of spin-polarized $^{30}\mathrm{Na}$. From the detailed $\ensuremath{\gamma}\text{\ensuremath{-}}\ensuremath{\gamma}$ coincidence relations, nine new states have been established in $^{30}\mathrm{Mg}$. The spin-polarization of $^{30}\mathrm{Na}$ enabled firm spin-parity assignments for seven states in $^{30}\mathrm{Mg}$ by means of the spatial asymmetry of $\ensuremath{\beta}$-ray counts in coincidence with the $^{30}\mathrm{Mg}\phantom{\rule{4pt}{0ex}}\ensuremath{\gamma}$ rays. Based on the experimental information, it is shown that various characteristic structures coexist in $^{30}\mathrm{Mg}$: (i) the ground-state vibrational-like band, (ii) the deformed band built on the ${0}_{2}^{+}$ state at 1.788 MeV, (iii) the $\ensuremath{\gamma}$-vibrational band built on the ${2}_{3}^{+}$ state at 3.543 MeV, and (iv) four states around 5 MeV associated with large $\ensuremath{\beta}$-transition probabilities: ${1}^{+}$ and ${2}^{+}$ states with spherical nature, ${1}^{+}$ and ${2}^{+}$ states with collective nature. The experimental results are compared with three theoretical calculations of the CHFB $+$ LQRPA, the AMD $+$ GCM, and the large-scale shell model with the EEdf1 interaction. All these theories reasonably reproduce the three bands.