Three-body structure of ${}^{19}\mathrm{B}$: Finite-range effects in two-neutron halo nuclei

The structure and $B\left(E1\right)$ transition strength of ${}^{19}\mathrm{B}$ are investigated in a ${}^{17}\mathrm{B}+n+n$ model, triggered by a recent experiment showing that ${}^{19}\mathrm{B}$ exhibits a well-pronounced two-neutron halo structure. Preliminary analysis of the experimental data was performed by employing contact $n\text{−}n$ interactions, which are known to underestimate the $s$-wave content in other halo nuclei, such as ${}^{11}\mathrm{Li}$. In the present Rapid Communication, the three-body hyperspherical formalism with finite-range two-body interactions is used to describe ${}^{19}\mathrm{B}$. In particular, two different finite-range $n\text{−}n$ interactions will be used as well as a simple central Gaussian potential whose range is progressively reduced. The purpose is to determine the main properties of the nucleus and investigate how they change when using contactlike $n\text{−}n$ potentials. Special attention is also paid to the dependence on the prescription used to account for three-body effects, i.e., a three-body force or a density-dependent $n\text{−}n$ potential. We have found that the three-body model plus finite-range potentials provide a description of ${}^{19}\mathrm{B}$ consistent with the experimental data. The results are essentially independent of the short-distance details of the two-body potentials, giving rise to a ${\left(s_{1/2}\right)}^2$ content of about 55%, clearly larger than the initial estimates. Very little dependence has been found as well on the prescription used for the three-body effects. The total computed $B\left(E1\right)$ strength is compatible with the experimental result, although we slightly overestimate the data around the low-energy peak of the $dB\left(E1\right)/d\varepsilon$ distribution. Finally, we show that a reduction of the $n\text{−}n$ interaction range produces a significant reduction of the $s$-wave contribution, which then should be expected in calculations using contact interactions.

Figure 1

Scaled Jacobi coordinates used in the present Rapid Communication. The three particles are labeled 1 ($n$), 2 ($n$), and 3 (core) for the purpose of defining the pairwise potentials.

Figure 2

Ground-state probability density of ${}^{19}\mathrm{B}$ as a function of $r_x\equiv r_{nn}$ and $r_y\equiv r_{c\text{−}nn}$. Left panel: calculations with the GPT $n\text{−}n$ interaction and $S_{2n}$ fixed to 0.5 MeV with the use of a three-body force. Right panel: calculations with a short-range Gaussian potential (case 1 in Table 1) and a density-dependent term to fix $S_{2n}$. Both densities are plotted with the same scale.

Figure 3

$B\left(E1\right)$ distribution for ${}^{19}\mathrm{B}$. Calculations correspond to the results with the GPT interaction and the three-body force (solid black line), and the simple Gaussian 1 (dot-dashed red line) and 2 (dashed blue line) complemented by the density-dependent term. The curves have been convoluted with the experimental resolution reported Ref. [16] as a Gaussian distribution of width $\sigma \left(\varepsilon \right)=0.25{\varepsilon }^{0.53}\mathrm{MeV}$. The thin lines are the results before the convolution.