Spectroscopy of<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mrow><mml:mmultiscripts><mml:mi mathvariant="normal">Na</mml:mi><mml:mprescripts/><mml:none/><mml:mn>28</mml:mn></mml:mmultiscripts></mml:mrow></mml:math>: Shell evolution toward the drip line

Excited states have been studied in $^{28}\mathrm{Na}$ using the $\ensuremath{\beta}$-decay of implanted $^{28}\mathrm{Ne}$ ions at the Grand Acc\'el\'erateur National d'Ions Lourds/LISE as well as the in-beam $\ensuremath{\gamma}$-ray spectroscopy at the National Superconducting Cyclotron Laboratory/S800 facility. New states of positive $({J}^{\ensuremath{\pi}}={3}^{+},{4}^{+})$ and negative $({J}^{\ensuremath{\pi}}={1}^{\ensuremath{-}}--{5}^{\ensuremath{-}})$ parity are proposed. The former arise from the coupling between $0{d}_{5/2}$ protons and $0{d}_{3/2}$ neutrons, while the latter are attributable to couplings of $0{d}_{5/2}$ protons with $1{p}_{3/2}$ or $0{f}_{7/2}$ neutrons. While the relative energies between the ${J}^{\ensuremath{\pi}}={1}^{+}--{4}^{+}$ states are well reproduced with the USDA interaction in the $N=17$ isotones, a progressive shift in the ground-state binding energy (by about 500 keV) is observed between $^{26}\mathrm{F}$ and $^{30}\mathrm{Al}$. This points to a possible change in the proton-neutron $0{d}_{5/2}\text{\ensuremath{-}}0{d}_{3/2}$ effective interaction when moving from stability to the drip line. The presence of ${J}^{\ensuremath{\pi}}={1}^{\ensuremath{-}}--{4}^{\ensuremath{-}}$ negative-parity states around 1.5 MeV as well as of a candidate for a ${J}^{\ensuremath{\pi}}={5}^{\ensuremath{-}}$ state around 2.5 MeV give further support to the collapse of the $N=20$ gap and to the inversion between the neutron $0{f}_{7/2}$ and $1{p}_{3/2}$ levels below $Z=12$. These features are discussed in the framework of shell-model and energy-density-functional calculations, leading to predicted negative-parity states in the low-energy spectra of the $^{26}\mathrm{F}$ and $^{25}\mathrm{O}$ nuclei.

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