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We study the exotic deformed nucleus 31 Ne using an approach that combines self-consistent structure and reaction theory. We utilize the fully-relativistic, microscopic deformed Hartree-Bogoliubov theory in continuum (DRHBc) to demonstrate that deformation and pairing correlations give rise to a halo structure with large-amplitude p-wave configuration in 31 Ne. We then use the valence nucleon wave functions and angle-averaged density distributions of 30 Ne from this model as input for a Glauber reaction model to study the observables of neutron-rich Neon isotopes and search for halo signatures. Our predictions of the reaction cross sections of these exotic Neon isotopes on a Carbon target can better reproduce the experimental data than those from relativistic mean field model for a spherical shape with resonances and pairing correlations contributions, as well as those from a Skyrme-Hartree-Fock model. The one-neutron removal cross section at 240 MeV/nucleon, the inclusive longitudinal momentum distribution of the 30 Ne, and the valence neutron residues from the 31 Ne breakup reaction are largely improved over previous theoretical predictions and agree well with data. These reaction data indicate a dilute density distribution in coordinate space and are a canonical signature of a halo structure.

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Using a Glauber model with our relativistic fully microscopic structure model input, we give a full description of the halo nature of $^{31}$Ne that includes a self-consistent use of pairing and continuum contributions that makes predictions consistent with reaction cross section measurements. Our predictions of total reaction and one-neutron removal cross sections of $^{31}$Ne on a Carbon target were significantly enhanced compared with those of neighboring Neon isotopes, agreeing with measurements at 240 MeV/nucleon and consistent with a single neutron halo. Furthermore, our calculations of the inclusive longitudinal momentum distribution of the $^{30}$Ne and valence neutron residues from the $^{31}$Ne breakup reaction indicate a dilute density distribution in coordinate space, another halo signature.