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 (S2n) 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 groundstate 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 S2n value. The admixture of d-waves with pf components are found to play an important role, favouring the dominance of dineutron configurations in the wave function. Our computed radii show a mild sensitivity to the 27 F + n potential and S2n 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.

The role of different continuum components in the weakly-bound nucleus 6 He is studied by coupling unbound spd-waves of 5 He by means of simple pairing contact-delta interaction. The results of our previous investigations in a model space containing only p-waves, showed the collective nature of the ground state and allowed the calculation of the electric quadrupole transitions. We extend this simple model by including also sd-continuum neutron states and we investigate the electric monopole, dipole and octupole response of the system for transitions to the continuum, discussing the contribution of different configurations.

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The exotic, neutron-rich and weakly-bound isotope 29 F stands out as a waymarker on the southern shore of the island of inversion, a portion of the nuclear chart where the effects of nuclear forces lead to a reshuffling of the single particle levels and to a reorganization of the nuclear structure far from stability. This nucleus has become very popular, as new measurements allow to refine theoretical models. We review the latest developments and suggest how to further assess the structure by proposing predictions on electromagnetic transitions that new experiments of Relativistic Coulomb Excitation should soon become able to measure. W eakly bound nuclear systems severely test our ability to disentangle the mysteries and oddities of the nuclear interactions and how nuclear systems achieve stability. One of the latest conundrums in this respect is the structure of the exotic 29-fluorine isotope. With nine protons and 20 neutrons, it is located almost on the edge of the stability valley of the nuclide chart, very close to the neutron drip-line, i.e., the dividing line (S n = 0, null separation energy) between bound and unbound neutron-rich nuclei. Pioneering researches on this isotope have recently skyrocketed, as more and more theoretical and experimental papers are being published. The main interest lies in understanding if it belongs to the so-called island of inversion, a portion of the nuclear chart where the standard list of single-particle energy levels (that are filled by nucleons, very similarly to the atomic physics counterpart, in a sort of Aufbauprinzip, a.k.a. the building-up principle, i.e., the rule that states how electronic orbitals are filled up in the atomic shell model) shows an inversion between orbitals belonging to the sdand pf-shells, see Fig. 1. This is crucial to ascertain the presence of a neutron halo (a diffused tail of nuclear matter that spreads around the central core) and its extent. This problem relates also to the disappearance of the N = 20 neutron magic number when moving away from doubly magic nuclei. This shell evolution has profound connections with tensor nuclear interactions 1,2 and with the deformation of the nuclear surface, occurring typically at mid-shell. This system, due to its mass A = 29, is still a hard nut to crack for ab initio approaches exploiting gargantuan numerical calculations. At present, simpler schematic models