When the density of a nuclear system is decreased, homogeneous states undergo the so-called Mott transition towards clusterised states, e.g. alpha clustering, both in nuclei and in nuclear matter. Here we investigate such a quantum phase transition (QPT) by using microscopic energy density functional (EDF) calculations both with the relativistic and the Gogny approaches on the diluted $^{16}$O nucleus. The evolution of the corresponding single-particle spectrum under dilution is studied, and a Mott-like transition is predicted at about 1/3 of the saturation density. Complementary approaches are used in order to understand this QPT. A study of spatial localisation properties as a function of the density allows to derive a value of the Mott density in agreement with the one obtained by fully microscopic calculations in $^{16}$O and in nuclear matter. Moreover a study of the spontaneous symmetry breaking of the rotational group in $^{16}$O, down to the discrete tetrahedral one, provides further insight on the features displayed by the single-particle spectrum obtained within the EDF approach.The content of the tetrahedrally deformed A-nucleon product state in terms of spherical particle-hole configurations is investigated. Finally a study of quartet condensation and the corresponding macroscopic QPT is undertaken in infinite matter.

中文翻译：

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α粒子凝聚：核量子相变

当核系统的密度降低时，在原子核和核物质中，均质态会经历所谓的莫特过渡到聚集态，例如α 聚集态。在这里，我们通过在稀释的 $^{16}$O 核上使用相对论和 Gogny 方法使用微观能量密度泛函 (EDF) 计算来研究这种量子相变 (QPT)。研究了稀释下相应单粒子光谱的演变，并预测在饱和密度的 1/3 左右会发生莫特状跃迁。使用补充方法来理解这个 QPT。对作为密度函数的空间定位特性的研究允许推导出与通过完全微观计算在 $^{16}$O 和核物质中获得的值一致的莫特密度值。此外，对 $^{16}$O 中旋转群的自发对称性破坏，直至离散四面体的研究，提供了对 EDF 方法中获得的单粒子光谱显示的特征的进一步了解。研究了在球形粒子孔结构方面的四面体变形 A 核子产物状态。最后，在无限物质中进行了四重态凝聚和相应的宏观 QPT 的研究。研究了在球形粒子孔构型方面的四面体变形 A 核子产物状态的含量。最后，在无限物质中进行了四重态凝聚和相应的宏观 QPT 的研究。研究了在球形粒子孔构型方面的四面体变形 A 核子产物状态的含量。最后，在无限物质中进行了四重态凝聚和相应的宏观 QPT 的研究。