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

The structure and $B(E1)$ transition strength of $^{19}$B are investigated in a $^{17}\text{B}+n+n$ model, triggered by a recent experiment showing that $^{19}$B exhibits a well pronounced two-neutron halo structure. Preliminary analysis of the experimental data was performed by employing contact $n$-$n$ interactions, which are known to underestimate the $s$-wave content in other halo nuclei such as $^{11}$Li. In the present work, the three-body hyperspherical formalism with finite-range two-body interactions is used to describe $^{19}$B. In particular, two different finite-range $n$-$n$ 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 contact-like $n$-$n$ 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 $n$-$n$ potential. We have found that the three-body model plus finite-range potentials provide a description of $^{19}$B consistent with the experimental data. The results are essentially independent of the short-distance details of the two-body potentials, giving rise to an $(s_{1/2})^2$ 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 $B(E1)$ strength is compatible with the experimental result, although we slightly overestimate the data around the low-energy peak of the $dB(E1)/d\varepsilon$ distribution. Finally, we show that a reduction of the $n$-$n$ interaction range produces a significant reduction of the $s$-wave contribution, which then should be expected in calculations using contact interactions.