Alpha cluster structures and monopole excitations in ${}^{13}$C

Abstract

The structure of $1/2^{\pm }$ states in ${}^{13}$C up to around the $3\alpha +n$ threshold ($E_x=12.3$~MeV) is investigated with a full four-body $3\alpha +n$ orthogonality condition model (OCM) calculation, where the $3\alpha$ OCM, the model space of which is the subspace of the $3\alpha +n$ model, describes well the structure of the low-lying states of ${}^{12}$C including the $2_2^{+}$, $0_3^{+}$, and $0_4^{+}$ states, which have been recently observed above the Hoyle state ($0_2^{+}$). A full spectrum up to the $1/2_5^{-}$ ($1/2_3^{+}$) state is reproduced consistently with the lowest five $1/2^{-}$ (three $1/2^{+}$) states of experimental spectrum. It is shown that the $1/2_2^{-}$ and $1/2_3^{-}$ states are characterized by the dominant cluster configurations of ${}^9$Be($3/2^{-}$,$1/2^{-}$)+$\alpha$, while the ground state $1/2_1^{-}$ has a shell-model-like structure. The observed monopole transition strengths to the $1/2_{2,3}^{-}$ states are consistently reproduced for the first time. These results indicate that the excited $1/2^{-}$ states have cluster structures. They are compared to those by the previous work with the shell model. On the other hand, the $1/2_1^{+}$ state is found to have a loosely bound neutron structure in which the extra neutron moves around ${}^{12}$C(g.s) core with $1S$ orbit, reflecting the fact that this state appears by $1.9$ MeV just below the ${}^{12}$C(g.s)+$n$ threshold, while the $1/2_2^{+}$ and $1/2_3^{+}$ states are characterized by ${}^9$Be+$\alpha$ structures. We found that the $1/2_5^{+}$ state located above the $3\alpha +n$ threshold is the Hoyle analogue state in ${}^{13}$C, the wave function of which is described by product states of constituent clusters, $(0S{)}_{\alpha }^3(S{)}_n$, with the probability of $52$ %.

39 pages, 9 figures, version accepted for publication in Physical Review C

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Cited by in corpus (20)

• Evidence for Triangular D_3h Symmetry in 12C
• Alpha particle clusters and their condensation in nuclear systems
• Experimental investigation of a linear-chain structure in the nucleus 14C
• Review of the electric dipole moment of light nuclei
• Candidates for the 5$\alpha$ condensed state in ${}^{20}$Ne
• Nonlocalized Clustering and Evolution of Cluster Structure in Nuclei
• Evidence for Triangular D'(3h) Symmetry in 13C
• Standard model contribution to the electric dipole moment of the deuteron, ${}^3$H, and ${}^3$He nuclei
• Real-time evolution method and its application to 3$\alpha$ cluster system
• Hoyle-analogue state in 13C studied with Antisymmetrized Molecular Dynamics
• Electric dipole moment of ${}^{13}$C
• Multi-cluster dynamics in ${}_{\Lambda }^{13}\mathrm{C}$ and analogy to clustering in ${}^{12}\mathrm{C}$
• Effect of the Pauli exclusion principle in the electric dipole moment of ${}^9$Be with $|\Delta S|=1$ interactions
• Shape of 13C studied by the real-time evolution method
• Monopole and dipole transitions of the cluster states of 18O
• Search for $\alpha$ condensed states in ${}^{13}$C using $\alpha$ inelastic scattering
• alpha+28Si and 16O+16O molecular states, and their isoscalar monopole strengths
• Electric dipole moment of light nuclei - 6Li, 7Li, 9Be, 11B, and 13C -
• The isoscalar monopole strength of 13C
• Status of the Theoretical Calculation of Nuclear Electric Dipole Moment