Observed well-developed $\alpha$ cluster states in $^{16}$O, located above the four $\alpha$ threshold, are investigated from the viewpoint of Bose-Einstein condensation of $\alpha$ clusters by using a field-theoretical superfluid cluster model in which the order parameter is defined. The experimental energy levels are reproduced well for the first time by calculation. In particular, the observed 16.7 MeV $0_7^+$ and 18.8 MeV $0_8^+$ states with low-excitation energies from the threshold are found to be understood as a manifestation of the states of the Nambu-Goldstone zero-mode operators, associated with the spontaneous symmetry breaking of the global phase, which is caused by the Bose-Einstein condensation of the vacuum 15.1 MeV $0^+_6$ state with a dilute well-developed $\alpha$ cluster structure just above the threshold. This gives evidence of the existence of the Bose-Einstein condensate of $\alpha$ clusters in $^{16}$O. It is found that the emergence of the energy level structure with a well-developed $\alpha$ cluster structure above the threshold is robust, almost independently of the condensation rate of $\alpha$ clusters under significant condensation rate. The finding of the mechanism why the level structure that is similar to $^{12}$C emerges above the four $\alpha$ threshold in $^{16}$O reinforces the concept of Bose-Einstein condensation of $\alpha$ clusters in addition to $^{12}$C.

中文翻译：

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场理论超流体簇模型中 16O 中超过 4 个 α 阈值的稀 α 簇的 Bose-Einstein 凝聚

观察到的在 $^{16}$O 中发育良好的 $\alpha$ 簇状态，位于四个 $\alpha$ 阈值之上，从 $\alpha$ 簇的 Bose-Einstein 凝聚的角度通过使用场-理论超流体簇模型，其中定义了顺序参数。通过计算首次很好地再现了实验能级。特别是，发现观察到的具有来自阈值的低激发能量的 16.7 MeV $0_7^+$ 和 18.8 MeV $0_8^+$ 状态被理解为 Nambu-Goldstone 零模式算子状态的一种表现形式，与全局相的自发对称性破缺相关，这是由真空 15.1 MeV $0^+_6$ 状态的玻色-爱因斯坦凝聚引起的，具有刚好在阈值之上的稀释的发育良好的 $\alpha$ 簇结构。这提供了$^{16}$O 中$\alpha$ 簇的玻色-爱因斯坦凝聚存在的证据。结果发现，在阈值之上出现具有发达的$\alpha$团簇结构的能级结构是稳健的，几乎与显着冷凝率下$\alpha$团簇的冷凝率无关。与$^{12}$C 类似的能级结构出现在$^{16}$O 中的四个$\alpha$ 阈值之上的机制的发现加强了$\alpha$ 的玻色-爱因斯坦凝聚的概念除了 $^{12}$C 之外的集群。在显着冷凝率下几乎独立于 $\alpha$ 簇的冷凝率。与$^{12}$C 类似的能级结构出现在$^{16}$O 中的四个$\alpha$ 阈值之上的机制的发现加强了$\alpha$ 的玻色-爱因斯坦凝聚的概念除了 $^{12}$C 之外的集群。在显着冷凝率下几乎独立于 $\alpha$ 簇的冷凝率。与$^{12}$C 类似的能级结构出现在$^{16}$O 中的四个$\alpha$ 阈值之上的机制的发现加强了$\alpha$ 的玻色-爱因斯坦凝聚的概念除了 $^{12}$C 之外的集群。