Predicting reaction observables for the two-neutron halo candidates $^{31}$F and $^{39}$Na

Microscopic description of two-neutron ($2n$) halo candidates $^{31}$F and $^{39}$Na has been realized from nuclear structure to reaction observables for the first time. The reliability of the Glauber reaction model has been confirmed by exactly reproducing the momentum distributions of the benchmark $2n$ halo nucleus $^{11}$Li, with the identical structural inputs from the former work. Combined with the structure from the deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), the Glauber model is applied to predict the reaction observables, including the reaction cross sections (RCSs) for the fluorine and sodium isotopes bombarding a carbon target at 240~MeV/A and the longitudinal momentum distributions of the fragments after $2n$ knockout reactions. It turns out that the calculated RCSs agree well with the available experimental data and a pronounced increase occurs to $^{29, 31}$F + $^{12}$C and $^{37, 39}$Na + $^{12}$C, which deviate from the original trend of their neighbours. Furthermore, the narrower longitudinal momentum distributions of the fragments after $2n$ knockout reactions demonstrate that $^{31}$F and $^{39}$Na have the dilute $2n$ halo structure. Such a new combination is promising to suggest new $2n$ halo candidates for future measurements.

💡 Research Summary

In this work the authors present the first comprehensive microscopic study that links nuclear structure to reaction observables for the two‑neutron (2n) halo candidates 31F and 39Na. The approach combines the deformed relativistic Hartree‑Bogoliubov theory in continuum (DRHBc) with the Glauber model in its optical‑limit approximation. First, the reliability of the Glauber model for a genuine 2n halo system is verified by reproducing both the reaction cross sections and the longitudinal momentum distributions of the benchmark halo nucleus 11Li + 12C. Using identical structural inputs (core densities fitted by two Gaussians and 2n wave functions in (s1/2)² and (p1/2)² configurations) the calculated reaction cross section matches the reference within 1 % and the momentum distribution of the 9Li residue reproduces the experimental shape, confirming that the Glauber framework can handle the three‑body nature of a 2n halo.

The DRHBc calculations employ the PC‑PK1 density functional and a Dirac Woods‑Saxon basis, which provides realistic asymptotic behavior for weakly bound neutrons. For 31F the DRHBc predicts an extremely small two‑neutron separation energy S2n≈0.41 MeV and a moderate quadrupole deformation (β2≈0.3). The neutron density distributions show a pronounced spatial extension compared with the lighter isotopes 27F and 29F. When these densities are fed into the Glauber model, the reaction cross sections (σR) on a 12C target at 240 MeV/A follow the expected linear trend up to 27F, but then increase sharply for 29F and 31F, reproducing the available experimental data. The calculated longitudinal momentum distributions of the core residues after 2n knockout are markedly narrow (full width at half maximum ≈120–140 MeV/c), a hallmark of a dilute halo.

For 39Na the DRHBc predicts S2n≈1 MeV, an oblate deformation of the halo neutrons surrounding a prolate core, and a dominant occupation of weakly bound p‑wave orbitals. The σR values for Na isotopes up to 35Na agree with measurements, while a pronounced rise appears from 37Na to 39Na, deviating from the linear extrapolation of the lighter isotopes. This jump is attributed to a transition from d‑wave to p‑wave dominance, which enlarges the spatial extension of the valence neutrons. The model’s prediction at 1000 MeV/A is consistent with an independent calculation by Horiuchi et al., further validating the approach. The longitudinal momentum distribution after 2n removal from 39Na is narrower (FWHM≈158 MeV/c) than that from 37Na (≈182 MeV/c), providing direct evidence for a 2n halo in 39Na.

Overall, the combined DRHBc + Glauber methodology successfully bridges microscopic structure and observable reaction quantities for medium‑mass nuclei near the drip line. The simultaneous reproduction of reaction cross sections and momentum‑distribution widths for both benchmark and candidate nuclei demonstrates that 31F and 39Na possess dilute two‑neutron halos. The authors note that uncertainties remain in the choice of deformation parameters and nucleon‑nucleon interaction inputs, and they advocate future measurements of longitudinal momentum distributions in 2n knockout reactions to test the predictions. The work is supported by the National Natural Science Foundation of China and the National Key Laboratory of Neutron Science and Technology.