Six-$α$ cluster Bose-Einstein condensation and supersolid $^{12}$C($0_2^+)$+$^{12}$C($0_2^+)$ molecular structure in $^{24}$Mg
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arXiv
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| Natura: | Preprint |
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2026
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| author | Ohkubo, S. Takahashi, J. Yamanaka, Y. |
| author_facet | Ohkubo, S. Takahashi, J. Yamanaka, Y. |
| contents | We show for the first time that the low-spin ($J \le 4^+$) six-$α$ condensate candidate states in $^{24}$Mg, 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 $^{12}$C, $^{16}$O, and $^{20}$Ne, respectively. Remarkably, our calculated roton band reproduces the well-known molecular resonance with a $^{12}$C($0_2^+$)+$^{12}$C($0_2^+$) structure ($16^+$) observed at $E_{\rm c.m.} = 32.5$ MeV in inelastic $^{12}$C+$^{12}$C scattering. This result provides a unified description of both the low-spin six-$α$ condensate states and the high-spin $^{12}$C($0_2^+$)+$^{12}$C($0_2^+$) molecular resonance. Analysis of the wave functions reveals a large overlap between the SCM states and a geometrical $^{12}$C($0_2^+$)+$^{12}$C($0_2^+$) configuration. This dual nature -the coexistence of superfluidity and crystallinity- identifies these states as a signature of a supersolid. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_04798 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Six-$α$ cluster Bose-Einstein condensation and supersolid $^{12}$C($0_2^+)$+$^{12}$C($0_2^+)$ molecular structure in $^{24}$Mg Ohkubo, S. Takahashi, J. Yamanaka, Y. Nuclear Theory We show for the first time that the low-spin ($J \le 4^+$) six-$α$ condensate candidate states in $^{24}$Mg, 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 $^{12}$C, $^{16}$O, and $^{20}$Ne, respectively. Remarkably, our calculated roton band reproduces the well-known molecular resonance with a $^{12}$C($0_2^+$)+$^{12}$C($0_2^+$) structure ($16^+$) observed at $E_{\rm c.m.} = 32.5$ MeV in inelastic $^{12}$C+$^{12}$C scattering. This result provides a unified description of both the low-spin six-$α$ condensate states and the high-spin $^{12}$C($0_2^+$)+$^{12}$C($0_2^+$) molecular resonance. Analysis of the wave functions reveals a large overlap between the SCM states and a geometrical $^{12}$C($0_2^+$)+$^{12}$C($0_2^+$) configuration. This dual nature -the coexistence of superfluidity and crystallinity- identifies these states as a signature of a supersolid. |
| title | Six-$α$ cluster Bose-Einstein condensation and supersolid $^{12}$C($0_2^+)$+$^{12}$C($0_2^+)$ molecular structure in $^{24}$Mg |
| topic | Nuclear Theory |
| url | https://arxiv.org/abs/2603.04798 |