Prediction of two-neutron halos in the N = 28 isotones 40Mg and 39Na

The ground states of the nuclei 40Mg and 39Na are investigated using the hyperspherical formalism. Since they are located at the edge of the "big island of inversion", we concentrate on whether we are likely to find twoneutron Borromean halos in these nuclei. A three-body model with effective 𝑛-𝑛 and 38Mg+𝑛 interactions is built for 40Mg based on the available data. We also give predictions for the low-lying spectrum of 38Na = 37Na +𝑛 and two-neutron separation energy of the 39Na nucleus. Depending on parameter choice, we report an increase in the matter radii in the range 0.1 - 0.5 fm relative to those of the core nuclei. The results suggest a two-neutron halo structure in 40Mg for a subset of parameters, reinforcing the prediction of a Borromean halo nucleus. The calculations indicate that a two-neutron halo is even more likely for 39Na. As expected, the halo is linked to the disappearance of the shell gap in these nuclei due to the inversion of the 2𝑝3∕2 and 1𝑓7∕2 orbitals. We study the total cross section for scattering of these nuclei from a carbon target using a Glauber model and show that these provide a clear signal to assess the halo structure.