Effective field theory for weakly bound two-neutron halo nuclei: corrections from neutron-neutron effective range

Using an effective field-theoretical approach, we investigate the properties of weakly bound two-neutron halo nuclei (also known as Borromean nuclei) that do not support a low-energy $s$-wave core-neutron resonance. Extending the recently formulated effective field theory for weakly bound Borromean nuclei, we incorporate corrections arising from the effective range of neutron-neutron scattering and evaluate their impact on the mean-square radii and electromagnetic response. In particular, we compute the ratio of the matter and charge radii, the shape of the $E1$ dipole strength function, and the electric polarizability. Our results indicate that these corrections remain numerically small when the two-neutron separation energy of the Borromean nucleus is much less than 1~MeV.