Spectroscopy of $^{28}$Na: shell evolution toward the drip line

Excited states have been studied in Na-28 using the beta-decay of implanted Ne-28 ions at the Grand Accelerateur National d'Ions Lourds/LISE as well as the in-beam gamma-ray spectroscopy at the National Superconducting Cyclotron Laboratory/S800 facility. New states of positive (J(pi) = 3(+), 4(+)) and negative (J(pi) = 1(-)-5(-)) parity are proposed. The former arise from the coupling between 0d(5/2) protons and 0d(3/2) neutrons, while the latter are attributable to couplings of 0d(5/2) protons with 1p(3/2) or 0f(7/2) neutrons. While the relative energies between the J(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 F-26 and Al-30. This points to a possible change in the proton-neutron 0d(5/2)-0d(3/2) effective interaction when moving from stability to the drip line. The presence of J(pi) = 1(-)-4(-) negative-parity states around 1.5 MeV as well as of a candidate for a J(pi) = 5-state around 2.5 MeV give further support to the collapse of the N = 20 gap and to the inversion between the neutron 0f(7/2) and 1p(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 F-26 and O-25 nuclei.