Exploring two-neutron halo formation in the ground state of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mmultiscripts><mml:mi mathvariant="normal">F</mml:mi><mml:mprescripts/><mml:none/><mml:mn>29</mml:mn></mml:mmultiscripts></mml:math> within a three-body model
Jagjit Singh, J. Casal, W. Horiuchi, L. Fortunato, A. Vitturi
Abstract
Background: The $^{29}\mathrm{F}$ 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 $^{28}\mathrm{F}$.Purpose: We investigate the configuration mixing, matter radius, and neutron-neutron correlations in the ground-state of $^{29}\mathrm{F}$ within a three-body model, exploring the possibility of $^{29}\mathrm{F}$ to be a two-neutron halo nucleus.Method: The $^{29}\mathrm{F}$ 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 $\text{core}+n$ potentials constrained by the available experimental information on $^{28}\mathrm{F}$.Results: The $^{29}\mathrm{F}$ ground-state configuration mixing and its matter radius are computed for different choices of the $^{28}\mathrm{F}$ structure and ${S}_{2n}$ 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 $^{27}\mathrm{F}+n$ potential and ${S}_{2n}$ values. The relative increase of the matter radius with respect to the $^{27}\mathrm{F}$ core lies in the range 0.1--0.4 fm depending upon these choices.Conclusions: Our three-body results for $^{29}\mathrm{F}$ 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.