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Background: Odd-odd nuclei, around doubly closed shells, have been extensively used to study proton-neutron interactions. However, the evolution of these interactions as a function of the binding energy, ultimately when nuclei become unbound, is poorly known. The $^{26}$F nucleus, composed of a deeply bound $pi0d_{5/2}$ proton and an unbound $ u0d_{3/2}$ neutron on top of an $^{24}$O core, is particularly adapted for this purpose. The coupling of this proton and neutron results in a $J^{pi} = 1^{+}_1 - 4^{+}_1$ multiplet, whose energies must be determined to study the influence of the proximity of the continuum on the corresponding proton-neutron interaction. The $J^{pi} = 1^{+}_1, 2^{+}_1,4^{+}_1$ bound states have been determined, and only a clear identification of the $J^{pi} =3^{+}_1$ is missing.Purpose: We wish to complete the study of the $J^{pi} = 1^{+}_1 - 4^{+}_1$ multiplet in $^{26}$F, by studying the energy and width of the $J^{pi} =3^{+}_1$ unbound state. The method was firstly validated by the study of unbound states in $^{25}$F, for which resonances were already observed in a previous experiment.Method: Radioactive beams of $^{26}$Ne and $^{27}$Ne, produced at about $440A$,MeV by the FRagment Separator at the GSI facility, were used to populate unbound states in $^{25}$F and $^{26}$F via one-proton knockout reactions on a CH$_2$ target, located at the object focal point of the R$^3$B/LAND setup. The detection of emitted $gamma$-rays and neutrons, added to the reconstruction of the momentum vector of the $A-1$ nuclei, allowed the determination of the energy of three unbound states in $^{25}$F and two in $^{26}$F. Results: Based on its width and decay properties, the first unbound state in $^{25}$F is proposed to be a $J^{pi} = 1/2^-$ arising from a $p_{1/2}$ proton-hole state. In $^{26}$F, the first resonance at 323(33)~keV is proposed to be the $J^{pi} =3^{+}_1$ member of the $J^{pi} = 1^{+}_1 - 4^{+}_1$ multiplet. Energies of observed states in $^{25,26}$F have been compared to calculations using the independent-particle shell model, a phenomenological shell-model, and the ab initio valence-space in-medium similarity renormalization group method.Conclusions: The deduced effective proton-neutron interaction is weakened by about 30-40% in comparison to the models, pointing to the need of implementing the role of the continuum in theoretical descriptions, or to a wrong determination of the atomic mass of $^{26}$F.
The very neutron-rich oxygen isotopes 25O and 26O are investigated experimentally and theoret- ically. In this first R3B-LAND experiment, the unbound states are populated at GSI via proton- knockout reactions from 26F and 27F at relativistic energies
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
We report on the observation of excited states in the neutron-deficient phosphorus isotopes $^{26,27,28}$P via in-beam gamma-ray spectroscopy with both high-efficiency and high-resolution detector arrays. In $^{26}$P, a previously-unobserved level ha
The two-proton knockout reaction 9Be(26Ne,O2p) was used to explore excited unbound states of 23O and 24O. In 23O a state at an excitation energy of 2.79(13) MeV was observed. There was no conclusive evidence for the population of excited states in 24O.
The ground state of $^{28}$F has been observed as an unbound resonance $2underline{2}0$ keV above the ground state of $^{27}$F. Comparison of this result with USDA/USDB shell model predictions leads to the conclusion that the $^{28}$F ground state is