Exploring two-neutron halo formation in the ground-state of $^{29}$F within a three-body model

Background: The F29 system is located at the lower-N boundary of the “island of inversion” and is an exotic, weakly bound system. Little is known about this system beyond its two-neutron separation energy (S2n) with large uncertainties. A similar situation is found for the low-lying spectrum of its unbound binary subsystem F28. Purpose: We investigate the configuration mixing, matter radius, and neutron-neutron correlations in the ground-state of F29 within a three-body model, exploring the possibility of F29 to be a two-neutron halo nucleus. Method: The F29 ground-state wave function is built within the hyperspherical formalism by using an analytical transformed harmonic oscillator basis. The Gogny-Pires-Tourreil (GPT) nn interaction with central, spin-orbit, and tensor terms is employed in the present calculations, together with different core+n potentials constrained by the available experimental information on F28. Results: The F29 ground-state configuration mixing and its matter radius are computed for different choices of the F28 structure and S2n value. The admixture of d waves with pf components is found to play an important role, favoring the dominance of dineutron configurations in the wave function. Our computed radii show a mild sensitivity to the F27+n potential and S2n values. The relative increase of the matter radius with respect to the F27 core lies in the range 0.1–0.4 fm depending upon these choices. Conclusions: Our three-body results for F29 indicate the presence of a moderate halo structure in its ground state, which is enhanced by larger intruder components. This finding calls for an experimental confirmation.