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

M. Vandebrouck 1 A. Lepailleur 1 O. Sorlin 1 T. Aumann C. Caesar M. Holl V. Panin F. Wamers S.R. Stroberg J.D. Holt Francois de Oliveira Santos 1 H. Alvarez-Pol L. Atar V. Avdeichikov S. Beceiro-Novo D. Bemmerer J. Benlliure C. A. Bertulani S.K. Bogner J.M. Boillos K. Boretzky M.J.G. Borge M. Caamano E. Casarejos W. Catford J. Cederkäll M. Chartier L. Chulkov D. Cortina-Gil E. Cravo R. Crespo U. Datta Pramanik P. Diaz Fernandez I. Dillmann Z. Elekes J. Enders O. Ershova A. Estrade F. Farinon L.M. Fraile M. Freer D. Galaviz H. Geissel R. Gernhauser J. Gibelin 2 P. Golubev K. Göbel J. Hagdahl T. Heftrich M. Heil M. Heine 3 A. Heinz A. Henriques H. Hergert A. Hufnagel A. Ignatov H.T. Johansson B. Jonson J. Kahlbow N. Kalantar-Nayestanaki R. Kanungo A. Kelic-Heil A. Knyazev T. Kröll N. Kurz M. Labiche C. Langer T. Le Bleis R. Lemmon S. Lindberg J. Machado J. Marganiec F.M. Marqués 2 A. Movsesyan E. Nacher M. Najafi E. Nikolskii T. Nilsson C. Nociforo S. Paschalis A. Perea M. Petri S. Pietri R. Plag R. Reifarth G. Ribeiro C. Rigollet M. Röder D. Rossi D. Savran H. Scheit A. Schwenk H. Simon I. Syndikus J. Taylor O. Tengblad R. Thies Y. Togano P. Velho V. Volkov A. Wagner H. Weick C. Wheldon G. Wilson J.S. Winfield P. Woods D. Yakorev M. Zhukov A. Zilges K. Zuber 
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 $\pi0d_{5/2}$ proton and an unbound $\nu0d_{3/2}$ 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.
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M. Vandebrouck, A. Lepailleur, O. Sorlin, T. Aumann, C. Caesar, et al.. Effective proton-neutron interaction near the drip line from unbound states in $^{25,26}$F. Physical Review C, 2017, 96, pp.054305. ⟨10.1103/PhysRevC.96.054305⟩. ⟨in2p3-01568314⟩



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