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

Abstract

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.

arXiv comment15 pages, 5 figures

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• Bose-Einstein condensation of five $\alpha$ clusters in ${}^{20}$Ne and supersolidity
• Six-$\alpha$ cluster Bose-Einstein condensation and supersolid ${}^{12}$C($0_2^{+})$+${}^{12}$C($0_2^{+})$ molecular structure in ${}^{24}$Mg