Scaling Limit Analysis of Borromean Halos

The analysis of the core recoil momentum distribution of neutron-rich isotopes of light exotic nuclei is performed within a model of halo nuclei described by a core and two neutrons dominated by the s-wave channel. We adopt the renormalized three-body model with a zero-range force, which accounts for the Efimov physics. This model is applicable to nuclei with large two-neutron halos compared to the core size, and a neutron–core scattering length larger than the interaction range. The halo wave function in momentum space is obtained by using as inputs the two-neutron separation energy and the energies of the singlet neutron–neutron and neutron–core virtual states. Within our model, we obtain the momentum probability densities for the Borromean exotic nuclei Lithium-11 (¹¹Li), Berylium-14 (¹⁴Be) and Carbon-22 (²²C). A fair reproduction of the experimental data was obtained in the case of the core recoil momentum distribution of ¹¹Li and ¹⁴Be, without free parameters. By extending the model to ²²C, the combined analysis of the core momentum distribution and matter radius suggest (i) a ²¹C virtual state well below 1 MeV; (ii) an overestimation of the extracted matter ²²C radius; and (iii) a two-neutron separation energy between 100 and 400 keV. (author)