Supersolidity of the α cluster structure in the nucleus ¹²C

For more than half a century, the structure of 12C, 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 12C is also well described by a nonlocalized cluster model without any of the geometrical configurations originally proposed to explain the dilute gas-likeHoyle state, which is nowconsidered 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 12C, 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.