Toward a unified description of the one-neutron halo nuclei \(^{15}\)C and \(^{19}\)C from structure to reaction

To achieve a unified description of the one-neutron halo nuclei \(^{15}\)C and \(^{19}\)C from structural properties to reaction dynamics, we combine the microscopic, self-consistent deformed relativistic Hartree–Bogoliubov theory in the continuum (DRHBc) with the Glauber model. For \(^{15}\)C, the valence neutron orbital with dominant \(2s_{1/2}\) components supports the experimental ground-state spin-parity and halo formation. The halo nature of \(^{19}\)C is attributed to a prolate state with the valence neutron orbital also dominated by \(2s_{1/2}\) components. The neutron densities for the halo states of \(^{15}\)C and \(^{19}\)C are significantly more dilute than those for \(^{14,16,18}\)C. With the DRHBc calculated densities of the core nucleus and the wave functions of the valence neutron as inputs, the reaction cross sections (RCSs) of \(^{14\text {--}19}\)C bombarding a carbon target and the longitudinal momentum distributions of the core residues with one-neutron removal from \(^{15,17,19}\)C are calculated by the Glauber model. The results not only demonstrate a significant increase of RCS from \(^{14}\)C to \(^{15}\)C but also accurately reproduce the measured RCS for the \(^{19}\)C + \(^{12}\)C reaction. Compared to the \(^{16}\)C residue from the one-neutron removal of \(^{17}\)C, the longitudinal momentum distributions for \(^{14}\)C and \(^{18}\)C residues from \(^{15}\)C and \(^{19}\)C, respectively, are notably narrower and exhibit clear peak shapes, supporting the halo structure of \(^{15}\)C and \(^{19}\)C. These findings further validate the DRHBc + Glauber approach, following its successful applications to the halo nuclei \(^{31}\)Ne and \(^{37}\)Mg.