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Background$\colon$ The $^{29}$F system is located at the lower-N boundary ofthe "island of inversion" and is an exotic, weakly bound system. Little isknown about this system beyond its two-neutron separation energy ($S_{2n}$)with large uncertainties. A similar situation is found for the low-lyingspectrum of its unbound binary subsystem $^{28}$F.  Purpose$\colon$ To investigate the configuration mixing, matter radius andneutron-neutron correlations in the ground state of $^{29}$F within athree-body model, exploring the possibility of $^{29}$F to be a two-neutronhalo nucleus.  Method$\colon$ The $^{29}$F ground-state wave function is built within thehyperspherical formalism by using an analytical transformed harmonic oscillatorbasis. The Gogny-Pires-Tourreil (GPT) nn interaction with central, spin-orbitand tensor terms is employed in the present calculations, together withdifferent core$+n$ potentials constrained by the available experimentalinformation on $^{28}$F.  Results$\colon$ The $^{29}$F ground-state configuration mixing and its matterradius 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 playan important role, favoring the dominance of dineutron configurations in thewave 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 withrespect to the $^{27}$F core lies in the range 0.1-0.4 fm depending upon thesechoices.  Conclusions$\colon$ Our three-body results for $^{29}$F indicate the presenceof a moderate halo structure in its ground state, which is enhanced by largerintruder components. This finding calls for an experimental confirmation.

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