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

Abstract

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 $\pi 0d\_5/2$ proton and an unbound $\nu 0d\_3/2$ neutron on top of an ${}^{24}$O core, is particularly adapted for this purpose. The coupling of this proton and neutron results in a $J^{\ddot{I}}€=1^{+}\_1-4^{+}\_1$ multiplet, whose energies must be determined to study the influence of the proximity of the continuum on the corresponding proton-neutron interaction. The $J^{\ddot{I}}€=1^{+}\_1,2^{+}\_1,4^{+}\_1$ bound states have been determined, and only a clear identification of the $J^{\ddot{I}}€=3^{+}\_1$ is missing.Purpose: We wish to complete the study of the $J^{\ddot{I}}€=1^{+}\_1-4^{+}\_1$ multiplet in ${}^{26}$F, by studying the energy and width of the $J^{\ddot{I}}€=3^{+}\_1$ 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 ${\hat{I}}^3$-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 $J^{\ddot{I}}€=1/2^{-}$ arising from a $p\_1/2$ proton-hole state. In ${}^{26}$F, the first resonance at 323(33)~keV is proposed to be the $J^{\ddot{I}}€=3^{+}\_1$ member of the $J^{\ddot{I}}€=1^{+}\_1-4^{+}\_1$ 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.

14 pages, 7 figures, 3 tables, submitted to PRC