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

Abstract

Background$:$ The ${}^{29}$F 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 ($S_{2n}$) with large uncertainties. A similar situation is found for the low-lying spectrum of its unbound binary subsystem ${}^{28}$F. Purpose$:$ To investigate the configuration mixing, matter radius and neutron-neutron correlations in the ground state of ${}^{29}$F within a three-body model, exploring the possibility of ${}^{29}$F to be a two-neutron halo nucleus. Method$:$ The ${}^{29}$F 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 ${}^{28}$F. Results$:$ The ${}^{29}$F ground-state configuration mixing and its matter radius are computed for different choices of the ${}^{28}$F structure and $S_{2n}$ value. The admixture of d-waves with pf components are 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 ${}^{27}$F$+n$ potential and $S_{2n}$ values. The relative increase of the matter radius with respect to the ${}^{27}$F core lies in the range 0.1-0.4 fm depending upon these choices. Conclusions$:$ Our three-body results for ${}^{29}$F 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.

Comments: 8 pages, 4 figures, Final version