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 were made 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.

中文翻译：

---

B19的三体结构：双中子晕核中的有限范围效应

在 $^{17}\text{B}+n+n$ 模型中研究了 $^{19}$B 的结构和 $B(E1)$ 转换强度，该模型由最近的实验触发，表明 $^{ 19}$B 表现出明显的双中子晕结构。实验数据的初步分析是通过使用接触$n$-$n$ 相互作用进行的，已知这些相互作用会低估其他晕核（如$^{11}$Li）中的$s$-wave 含量。在目前的工作中，具有有限范围两体相互作用的三体超球面形式主义用于描述 $^{19}$B。特别是，将使用两个不同的有限范围 $n$-$n$ 相互作用，以及范围逐渐减小的简单中心高斯势。目的是确定原子核的主要属性，并研究当使用类似接触的 $n$-$n$ 势时它们是如何变化的。还特别注意对用于解释三体效应的处方的依赖性，即三体力或密度相关的 $n$-$n$ 潜力。我们发现三体模型加上有限范围的势能提供了与实验数据一致的$^{19}$B 的描述。结果基本上独立于二体电位的短距离细节，产生约 55% 的 $(s_{1/2})^2$ 含量，明显大于初始估计。对用于三体效应的处方也几乎没有依赖性。总计算出的 $B(E1)$ 强度与实验结果一致，尽管我们略微高估了 $dB(E1)/d\varepsilon$ 分布的低能量峰值周围的数据。最后，