Excited states in $^{28}$Na have been studied using the $beta$-decay of implanted $^{28}$Ne ions at GANIL/LISE as well as the in-beam $gamma$-ray spectroscopy at the NSCL/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 a 0d$_{3/2}$ neutron, while the latter are due to couplings 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 $^{26}$F and $^{30}$Al. 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 0f$_{7/2}$ and 1p$_{3/2}$ levels below Z=12. These features are discussed in the framework of Shell Model and EDF calculations, leading to predicted negative parity states in the low energy spectra of the $^{26}$F and $^{25}$O nuclei.
The structure of the $^{24}$F nucleus has been studied at GANIL using the $beta$ decay of $^{24}$O and the in-beam $gamma$-ray spectroscopy from the fragmentation of projectile nuclei. Combining these complementary experimental techniques, the level
scheme of $^{24}$F has been constructed up to 3.6 Mev by means of particle-$gamma$ and particle-$gammagamma$ coincidence relations. Experimental results are compared to shell-model calculations using the standard USDA and USDB interactions as well as ab-initio valence-space Hamiltonians calculated from the in-medium similarity renormalization group based on chiral two- and three-nucleon forces. Both methods reproduce the measured level spacings well, and this close agreement allows unidentified spins and parities to be consistently assigned.
A long-lived $J^{pi}=4_1^+$ isomer, $T_{1/2}=2.2(1)$ms, has been discovered at 643.4(1) keV in the weakly-bound $^{26}_{9}$F nucleus. It was populated at GANIL in the fragmentation of a $^{36}$S beam. It decays by an internal transition to the $J^{pi
}=1_1^+$ ground state (82(14)%), by $beta$-decay to $^{26}$Ne, or beta-delayed neutron emission to $^{25}$Ne. From the beta-decay studies of the $J^{pi}=1_1^+$ and $J^{pi}=4_1^+$ states, new excited states have been discovered in $^{25,26}$Ne. Gathering the measured binding energies of the $J^{pi}=1_1^+-4_1^+$ multiplet in $^{26}_{9}$F, we find that the proton-neutron $pi 0d_{5/2} u 0d_{3/2}$ effective force used in shell-model calculations should be reduced to properly account for the weak binding of $^{26}_{9}$F. Microscopic coupled cluster theory calculations using interactions derived from chiral effective field theory are in very good agreement with the energy of the low-lying $1_1^+,2_1^+,4_1^+$ states in $^{26}$F. Including three-body forces and coupling to the continuum effects improve the agreement between experiment and theory as compared to the use of two-body forces only.
