https://doi.org/10.1140/epja/s10050-023-00947-3
Regular Article –Theoretical Physics
Three-
configurations of the second 
state in 
C
1
Department of Physics, Hokkaido University, 060-0810, Sapporo, Japan
2
Department of Physics, Osaka Metropolitan University, 558-8585, Osaka, Japan
3
Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka Metropolitan University, 558-8585, Osaka, Japan
4
RIKEN Nishina Center, 351-0198, Wako, Japan
5
Departamento de Física Atómica, Molecular y Nuclear, Facultad de Física, Universidad de Sevilla, Apartado 1065, 41080, Sevilla, Spain
6
Dipartimento di Fisica e Astronomia “G.Galilei”, Università degli Studi di Padova, via Marzolo 8, 35131, Padua, Italy
7
INFN-Sezione di Padova, via Marzolo 8, 35131, Padua, Italy
a
moriya@nucl.sci.hokudai.ac.jp
Received:
12
December
2022
Accepted:
6
February
2023
Published online:
25
February
2023
We investigate geometric configurations of (
He nucleus) clusters in the second state of C, which has been discussed as a rotational band member of the second 
state, the Hoyle state. The ground and excited and 
states are described by a three- 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 and states are acute-angled triangle shapes originating from the 
Be()
configuration. However, the 
components in the second state become approximately 2/3 because the 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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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
