For more than half a century, the structure of $^{12}$C, such as the ground band, has been understood to be well described by the three $\alpha$ cluster model based on a geometrical crystalline picture. On the contrary, recently it has been claimed that the ground state of $^{12}$C is also well described by a nonlocalized cluster model without any of the geometrical configurations originally proposed to explain the dilute gas-like Hoyle state, which is now considered to be a Bose-Einstein condensate of $\alpha$ clusters. The challenging unsolved problem is how we can reconcile the two exclusive $\alpha$ cluster pictures of $^{12}$C, crystalline vs nonlocalized structure. We show that the crystalline cluster picture and the nonlocalized cluster picture can be reconciled by noticing that they are a manifestation of supersolidity with properties of both crystallinity and superfluidity. This is achieved through a superfluid $\alpha$ cluster model based on effective field theory, which treats the Nambu-Goldstone zero mode rigorously. For several decades, scientists have been searching for a supersolid in nature.Nuclear $\alpha$ cluster structure is considered to be the first confirmed example of a stable supersolid.

中文翻译：

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原子核中$\alpha$簇结构的超固体$^{12}$C

半个多世纪以来，$^{12}$C 的结构，例如地带，已经被基于几何晶体图片的三个 $\alpha$ 簇模型很好地描述。相反，最近有人声称 $^{12}$C 的基态也可以通过非定域簇模型很好地描述，而没有最初提出的任何几何配置来解释类似稀气体的霍伊尔态，即现在被认为是 $\alpha$ 簇的玻色-爱因斯坦凝聚。具有挑战性的未解决问题是我们如何协调 $^{12}$C 的两个独家 $\alpha$ 簇图片，晶体结构与非局部结构。我们表明结晶团簇图片和非定域团簇图片可以通过注意到它们是具有结晶性和超流动性的超固体的表现来协调。这是通过基于有效场论的超流体 $\alpha$ 聚类模型实现的，该模型严格处理 Nambu-Goldstone 零模。几十年来，科学家们一直在寻找自然界中的超固体。核$\alpha$簇结构被认为是第一个被证实的稳定超固体的例子。