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Three-\(\alpha \) configurations of the second \(J^\pi =2^+\) state in \(^{12}\)C

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Abstract

We investigate geometric configurations of \(\alpha \) (\(^4\)He nucleus) clusters in the second \(J^\pi =2^+\) state of \(^{12}\)C, which has been discussed as a rotational band member of the second \(0^+\) state, the Hoyle state. The ground and excited \(0^+\) and \(2^+\) states are described by a three-\(\alpha \) cluster model. The three-body Schrödinger equation with orthogonality conditions is accurately solved by the stochastic variational method with correlated Gaussian basis functions. To analyse the structure of these resonant states in a convenient form, we introduce a confining potential. The two-body density distributions together with the spectroscopic information clarify the structure of these states. We find that main configurations of both the second \(0^+\) and \(2^+\) states are acute-angled triangle shapes originating from the \(^8\)Be(\(0^+\))\(+\alpha \) configuration. However, the \(^{8}\textrm{Be}+\alpha \) components in the second \(2^+\) state become approximately 2/3 because the \(^8\)Be subsystem is hard to excite, indicating that the state is not an ideal rigid rotational band member of the Hoyle state.

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Data Availability

This manuscript has no associated data or the data will not be deposited. [Authors’ comment: They are available from the authors (H. Moriya or W. Horiuchi) upon reasonable request.]

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Acknowledgements

This work was in part supported by JSPS KAKENHI Grants nos. 18K03635 and 22H01214. We acknowledge the Collaborative Research Program 2022, Information Initiative Center, Hokkaido University.

Author information

Authors and Affiliations

  1. Department of Physics, Hokkaido University, Sapporo, 060-0810, Japan

    H. Moriya & W. Horiuchi

  2. Department of Physics, Osaka Metropolitan University, Osaka, 558-8585, Japan

    W. Horiuchi

  3. Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, Osaka, 558-8585, Japan

    W. Horiuchi

  4. RIKEN Nishina Center, Wako, 351-0198, Japan

    W. Horiuchi

  5. Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, Sevilla, 41080, Spain

    J. Casal

  6. Dipartimento di Fisica e Astronomia “G.Galilei”, Università degli Studi di Padova, via Marzolo 8, Padua, 35131, Italy

    L. Fortunato

  7. INFN-Sezione di Padova, via Marzolo 8, Padua, 35131, Italy

    L. Fortunato

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  1. H. Moriya
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Correspondence to H. Moriya.

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Communicated by Emiko Hiyama.

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Moriya, H., Horiuchi, W., Casal, J. et al. Three-\(\alpha \) configurations of the second \(J^\pi =2^+\) state in \(^{12}\)C. Eur. Phys. J. A 59, 37 (2023). https://doi.org/10.1140/epja/s10050-023-00947-3

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