Effects of $\alpha$-cluster breaking on 3$\alpha$ cluster structures in ${}^{12}$C

Abstract

To clarify the effects of $\alpha$-cluster breaking on 3$\alpha$ cluster structures in ${}^{12}$C, we investigate ${}^{12}$C using a hybrid model that combines the Brink-Bloch cluster model with the $p_{3/2}$ subshell closure wave function. We have found that $\alpha$-cluster breaking caused by spin-orbit force significantly changes cluster structures of excited $0^{+}$ states through orthogonality to lower states. Spatially developed cluster components of the $0_2^{+}$ state are reduced. The $0_3^{+}$ state changes from a vibration mode in the bending motion of three $\alpha$ clusters to a chain-like 3$\alpha$ structure having an open triangle configuration. As a result of these structure changes of $0^{+}$ states, the band assignment for the $2_2^{+}$ state is changed by the $\alpha$-cluster breaking effect. Namely, in model calculations without the $\alpha$-cluster breaking effect, the $0_2^{+}$ state is assigned to be the band-head of the $2_2^{+}$ state. However, when we incorporate $\alpha$-cluster breaking caused by the spin-orbit force, the $0_3^{+}$ state is regarded as the band-head of the $2_2^{+}$ state.

arXiv comment11 pages, 7 figures

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• Evidence for Z=6 `magic number' in neutron-rich carbon isotopes
• Nonlocalized Clustering and Evolution of Cluster Structure in Nuclei
• Monopole excitation of the Hoyle state and linear-chain state in 12C
• Consistent description of 12C and 16O using finite range three-body interaction
• Multi-cluster dynamics in ${}_{\Lambda }^{13}\mathrm{C}$ and analogy to clustering in ${}^{12}\mathrm{C}$
• Improved version of simplified method for including tensor effect in cluster models
• Consistency between the monopole strength of the Hoyle state determined by structural calculation and that extracted from reaction observables
• Analysis of delocalization of clusters in linear-chain $\alpha$-cluster states with entanglement entropy
• Cluster structures and monopole transitions of ${}^{14}$C
• Low-lying level structure of $\Lambda$ hypernuclei and spin dependence of $\Lambda N$ interaction with antisymmetrized molecular dynamics
• Explicit inclusion of spin-orbit contribution in THSR wave function
• Excitation energy shift and size difference of low-energy levels in $p$-shell $\Lambda$ hypernuclei
• Consistent description for cluster dynamics and single-particle correlation
• Independent measurement of the Hoyle state $\beta$ feeding from 12B using Gammasphere
• Tensor correlations in ${}^4$He and ${}^8$Be with antisymmetrized quasi cluster model
• Effective Mass of $\alpha$-Cluster in ${}^{12}$C Nucleus
• Structures of $p$-shell double-$\Lambda$ hypernuclei studied with microscopic cluster models
• Relation between transition density and proton inelastic scattering by ${}^{12}$C target at $E_p=$ 65 and 200 MeV
• Cluster structures of the $0^{+}$ states of ${}_{\Lambda }^{13}\mathrm{C}$ with the 3$\alpha +\Lambda$ four-body orthogonality condition model
• Examination of the $\alpha$-cluster breaking in the four $0^{+}$ bands of ${}^{12}$C with the variation of multiple bases of the antisymmetrized molecular dynamics