Near the $\beta$-stability line, nuclei with magic numbers are expected to exhibit spherical ground states. However, mass measurements of neutron-rich nuclei near the $N=20$ island of inversion have indicated an excess in the binding energies. These results, together with subsequent spectroscopic studies and theoretical works, point to the structural evolution from normal configurations to intruder-deformed configurations characterized by particle-hole excitations across the shell gap. Despite evidence of intruder-dominant ground states for the ${}^{30,31}\mathrm{Na}$ isotopes in the vicinity of $N=20$, a question remains as to whether the deformation persists into the ground-state bands beyond the first excited states. Here we report on a heavy-ion inelastic scattering measurement performed with GRETINA, the TRIPLEX device, and the S800 spectrograph to study the low-lying excitations in neutron-rich ${}^{30,31}\mathrm{Na}$. The observed gamma rays for the $\left(4^{+}\right)\to \left(3^{+}\right), \left(3^{+}\right)\to 2_{\text{g.s.}}^{+}$, and $\left(4^{+}\right)\to 2_{\text{g.s.}}^{+}$ decays in ${}^{30}\mathrm{Na}$ and for the $(7/2^{+})\to (5/2^{+})$ and $(5/2^{+})\to 3/2_{\text{g.s.}}^{+}$ decays in ${}^{31}\mathrm{Na}$ were used to extract the reduced transition probabilities $B(E2\uparrow )$. We report the first measurement of the $B(E2\uparrow )$ between the $3/2_{\text{g.s.}}^{+}$ and the $(7/2^{+})$ states in ${}^{31}\mathrm{Na}$. The results from this study are compared to shell-model calculations, confirming the persistence of large collectivity in the low-lying excited states consistent with the formation of the well-deformed ground-state bands in ${}^{30,31}\mathrm{Na}$.

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• Electromagnetic transitions
• Inelastic scattering reactions
• Low & intermediate energy heavy-ion reactions
• Nuclear structure & decays
• 20 ≤ A ≤ 38
• Collective models
• Radioactive beams
• Shell model