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

Abstract

<strong>Background:</strong> 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 &pi;0d_5/2 proton and an unbound &nu;0d_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^&pi; = 1₁⁺ &minus; 4₁⁺ 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; = 1₁⁺, 2₁⁺, 4₁⁺ bound states have been determined, and only a clear identification of the J^&pi; = 3₁⁺ is missing.<br /><strong>Purpose:</strong> We wish to complete the study of the J^&pi; = 1₁⁺ &minus; 4₁⁺&nbsp;multiplet in ²⁶F, by studying the energy and width of the J^&pi; = 3₁⁺&nbsp;unbound state. The method was first validated by the study of unbound states in ²⁵F, for which resonances were already observed in a previous experiment.<br /><strong>Method:</strong> 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 CH₂ target, located at the object focal point of the R³B/LAND setup. The detection of emitted &gamma; rays and neutrons, added to the reconstruction of the momentum vector of the A &minus; 1 nuclei, allowed the determination of the energy of three unbound states in ²⁵F and two in ²⁶F.<br /><strong>Results:</strong> Based on its width and decay properties, the first unbound state in ²⁵F, at the relative energy of 49(9) keV, is proposed to be a J^&pi; = 1/2^&minus; arising from a p_1/2&nbsp;proton-hole state. In ²⁶F, the first resonance at 323(33) keV is proposed to be the&nbsp;J^&pi; = 3₁⁺ member of the&nbsp;J^&pi; = 1₁⁺ &minus; 4₁⁺ 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.<br />&nbsp;<strong>Conclusions:</strong> The deduced effective proton-neutron interaction is weakened by about 30&ndash;40% in comparison to the models, pointing to the need for implementing the role of the continuum in theoretical descriptions or to a wrong determination of the atomic mass of ²⁶F.