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

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.

Figure 1

${}^{27}\mathrm{F}+n$ phase shifts for $d_{3/2}, p_{3/2}$, and $f_{7/2}$ states, corresponding to different sets (A–D). The dotted black line corresponds to $\pi /2$.

Figure 2

Ground-state probability density of ${}^{29}\mathrm{F}$ using the four $n-{}^{27}\mathrm{F}$ potential sets (A–D), as a function of $r_{nn}$ and $r_{c-nn}$ with the same scale (in ${\mathrm{fm}}^{-2}$). In all cases, the two-neutron separation energy has been adjusted to $S_{2n}=1.440$ MeV.

Figure 3

Matter radius ($R_m$) for the ground state of the ${}^{29}\mathrm{F}$ as a function of $S_{2n}$, for different sets (A–D).

Figure 4

Matter radius ($R_m$) for the ground state of the ${}^{29}\mathrm{F}$ as a function of the ${\left(p_{3/2}\right)}^2$ content for different $S_{2n}$ values.