Six-α cluster Bose-Einstein condensation and supersolid 12C(02+)+12C(02+) molecular structure in 24Mg
Abstract
We show for the first time that the low-spin (J 4+) six-α condensate candidate states in 24Mg, recently reported by Fujikawa et al. [Phys. Lett. B 848, 138384 (2024)], are well described by the superfluid α-cluster model (SCM). This is achieved by a rigorous treatment of the Nambu-Goldstone (NG) zero mode as the order parameter of condensation in the finite six-α system. We find that a roton rotational band with a large moment of inertia is built on the first excited NG 0+ state, analogous to the roton bands observed in three-, four-, and five-α condensates in 12C, 16O, and 20Ne, respectively. Remarkably, our calculated roton band reproduces the well-known molecular resonance with a 12C(02+)+12C(02+) structure (16+) observed at E c.m. = 32.5 MeV in inelastic 12C+12C scattering. This result provides a unified description of both the low-spin six-α condensate states and the high-spin 12C(02+)+12C(02+) molecular resonance. Analysis of the wave functions reveals a large overlap between the SCM states and a geometrical 12C(02+)+12C(02+) configuration. This dual nature -the coexistence of superfluidity and crystallinity- identifies these states as a signature of a supersolid.
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