Effective proton-neutron interaction near the drip line from unbound states in ^25,26F

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 ^26F nucleus, composed of a deeply bound π0d_5/2 proton and an unbound ν0d_3/2 neutron on top of an ^24O core, is particularly adapted for this purpose. The coupling of this proton and neutron results in a J^π = 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^π = 1^+_1, 2^+_1,4^+_1 bound states have been determined, and only a clear identification of the J^π =3^+_1 is missing.Purpose: We wish to complete the study of the J^π = 1^+_1 - 4^+_1 multiplet in ^26F, by studying the energy and width of the J^π =3^+_1 unbound state. The method was firstly validated by the study of unbound states in ^25F, for which resonances were already observed in a previous experiment.Method: Radioactive beams of ^26Ne and ^27Ne, produced at about 440A MeV by the FRagment Separator at the GSI facility, were used to populate unbound states in ^25F and ^26F via one-proton knockout reactions on a CH_2 target, located at the object focal point of the R^3B/LAND setup. The detection of emitted γ-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 ^25F and two in ^26F. Results: Based on its width and decay properties, the first unbound state in ^25F is proposed to be a J^π = 1/2^- arising from a p_1/2 proton-hole state. In ^26F, the first resonance at 323(33) keV is proposed to be the J^π =3^+_1 member of the J^π = 1^+_1 - 4^+_1 multiplet. Energies of observed states in ^25,26F 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 ^26F.