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

Jia-Lin An, Li-Yang Wang, Kaiyuan Zhang, Shi-Sheng Zhang

Abstract

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.

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

Abstract

Microscopic description of two-neutron () halo candidates F and 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 halo nucleus 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 knockout reactions. It turns out that the calculated RCSs agree well with the available experimental data and a pronounced increase occurs to F + C and Na + C, which deviate from the original trend of their neighbours. Furthermore, the narrower longitudinal momentum distributions of the fragments after knockout reactions demonstrate that F and Na have the dilute halo structure. Such a new combination is promising to suggest new halo candidates for future measurements.

Paper Structure

This paper contains 7 sections, 3 equations, 4 figures, 1 table.

Table of Contents

  1. Introduction
  2. Theoretical Framework
  3. Results and discussion
  4. Validity for $^{11}$Li bombarding a carbon target
  5. Application to $^{31}$F on a carbon target
  6. Application to $^{39}$Na on a carbon target
  7. Summary

Figures (4)

  • Figure 1: (Color Online) Inclusive longitudinal momentum distributions of $^{9}$Li residues after $2n$ removal reaction of $^{11}$Li + $^{12}$C at the incident energy 800 MeV/A. The red and blue solid/dashed lines denote our/their ogawa2001 predictions with the Glauber model for the configurations $(s_{1/2})^{2}$ and $(p_{1/2})^{2}$, respectively. The black solid line shows the results of mixed configuration $s_{1/2}p_{1/2}$. Experimental data (closed black circles) are taken from Ref. Kobayashi1988PRL for comparison.
  • Figure 2: (Color online) Two-dimensional neutron density distributions for $^{27,29,31}$F in the $xz$ plane with the $z$ axis as the symmetry axis. Here the results for $^{29}$F are obtained from a constrained calculation with a deformation parameter $\beta_2=$ 0.3.
  • Figure 3: (Color online) (a) RCSs $\sigma_{R}$ of $^{21\text{--}31}$F + $^{12}$C at 240 MeV/A. Open red points stand for our predictions with the Glauber model with inputs from the DRHBc theory. For $^{29}$F + $^{12}$C, the RCS is obtained from a constrained DRHBc calculations with a commonly proposed deformation parameter $\beta_2 =$ 0.3. Experimental data (closed black circles) are taken from Ref. Bagchi2020PRLhomma2017measurements for comparison. The dashed grey line shows the linear fit to the experimental data for $^{21\text{--}27}$F + $^{12}$C. (b) Inclusive longitudinal momentum distributions of residues after $2n$ removal reactions of $^{29,31}$F + $^{12}$C at 240 MeV/A.
  • Figure 4: (Color online) (a) RCSs $\sigma_{R}$ of $^{22\text{--}39}$Na + $^{12}$C at 240 and 1000 MeV/A. Open red points stand for our predictions with the DRHBc + Glauber approach, in comparison with a linear fit (the dashed grey line) on available experimental data (closed black circles) for $^{22\text{--}35}$Na Suzuki2014EPJ. Open green square shows the result for $^{39}$Na + $^{12}$C at 1000 MeV/A calculated by Horiuchi Horiuchi2024PLB. (b) Same as Fig. \ref{['fig:F']} (b), but for $^{37,39}$Na.