Supersolidity of the $α$ cluster structure in the nucleus $^{12}$C

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 $α$ 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 $α$ clusters. The challenging unsolved problem is how we can reconcile the two exclusive $α$ 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 $α$ 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 $α$ cluster structure is considered to be the first confirmed example of a stable supersolid.

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