The ground states of the nuclei and are investigated using the hyperspherical formalism. Since they are located at the edge of the “big island of inversion”, we concentrate on whether we are likely to find two-neutron Borromean halos in these nuclei. A three-body model with effective - and interactions is built for based on the available data. We also give predictions for the low-lying spectrum of and two-neutron separation energy of the nucleus. Depending on parameter choice, we report an increase in the matter radii in the range 0.1-0.5 fm relative to those of the core nuclei. The results suggest a two-neutron halo structure in for a subset of parameters, reinforcing the prediction of a Borromean halo nucleus. The calculations indicate that a two-neutron halo is even more likely for . As expected, the halo is linked to the disappearance of the shell gap in these nuclei due to the inversion of the and orbitals. We study the total cross section for scattering of these nuclei from a carbon target using a Glauber model and show that these provide a clear signal to assess the halo structure.

中文翻译：

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N=28等位素40Mg和39Na中双中子晕的预测


使用超球形式主义研究原子核的基态。由于它们位于“逆温大岛”的边缘，我们关注的是是否有可能在这些原子核中发现双中子博罗米安晕。具有有效交互作用的三体模型是根据可用数据构建的。我们还预测了原子核的低位能谱和双中子分离能。根据参数选择，我们报告物质半径相对于核心核的物质半径增加了 0.1-0.5 fm 范围。结果表明参数子集存在双中子晕结构，增强了博罗米安晕核的预测。计算表明，双中子晕的可能性更大。正如预期的那样，由于 和 轨道的倒转，晕与这些原子核中壳层间隙的消失有关。我们使用 Glauber 模型研究了这些原子核从碳靶散射的总横截面，并表明这些为评估晕结构提供了清晰的信号。