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

TL;DR

This paper proposes that the structure of $^{12}$C exhibits supersolidity, reconciling crystalline and nonlocalized cluster models through a superfluid $ ext{alpha}$ cluster approach, potentially marking the first confirmed natural supersolid.

Contribution

It introduces a superfluid $ ext{alpha}$ cluster model based on effective field theory that unifies two previously conflicting pictures of $^{12}$C's structure as a supersolid.

Findings

Crystalline and nonlocalized cluster pictures are manifestations of supersolidity.

Nuclear $ ext{alpha}$ cluster structure is a potential example of a stable supersolid.

The model rigorously treats the Nambu-Goldstone zero mode.

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.