$\alpha +\alpha +t$ cluster structures and Hoyle-analogue states in ${}^{11}$B

Abstract

The structure of $3/2^{-}$ and $1/2^{+}$ states in ${}^{11}$B is investigated with an $\alpha +\alpha +t$ orthogonality condition model (OCM) based on the Gaussian expansion method. Full levels up to the $3/2_3^{-}$ and $1/2_2^{+}$ states around the $\alpha +\alpha +t$ threshold ($E_x$=11.1 MeV) are reproduced consistently with the experimental energy levels. It is shown that the $3/2_3^{-}$ state located around the ${}^7$Li+$\alpha$ threshold has an $\alpha +\alpha +t$ cluster structure, whereas the $3/2_1^{-}$ and $3/2_2^{-}$ states have a shell-model-like compact structure. We found that the $3/2_3^{-}$ state does not possess an $\alpha$-condensate-like nature similar to the $0_2^{+}$ state of ${}^{12}$C (Hoyle state) which has a dilute $3\alpha$-condensate structure described by a $(0S_{\alpha }{)}^3$ configuration with about $70$\% probability, although the monopole transition strength of the former is as large as that of the latter. We discuss the reasons why the $3/2_3^{-}$ state does not have the condensate character. On the other hand, the $1/2_1^{+}$ state just below the ${}^7$Li+$\alpha$ threshold has a cluster structure which can be interpreted as a parity-doublet partner of the $3/2_3^{-}$ state. We indicate that the $12.56$-MeV state ($J^{\pi }=1/2_2^{+}$) just above the $\alpha +\alpha +t$ threshold observed in the ${}^7$Li(${}^7$Li,${}^{11}$B${}^{\ast }$)$t$ reaction etc. is of the dilute-cluster-gas-like, and is a strong candidate for the Hoyle-analogue state which has a configuration of $(0S_{\alpha }{)}^2(0S_t)$ with about $65$\% probability from the analyses of the single-cluster motions in ${}^{11}$B. The structure property of the $1/2^{+}$ resonant state is analyzed with the complex scaling method.

22 pages, 9 figures

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Cited by in corpus (16)

• Alpha particle clusters and their condensation in nuclear systems
• Isoscalar dipole transition as a probe for asymmetric clustering
• Alpha cluster structures and monopole excitations in ${}^{13}$C
• Cluster structures in ${}^{11}$B
• Cluster states and monopole transitions in ${}^{16}$O
• Nuclear Alpha-Particle Condensates
• Hoyle-analogue state in 13C studied with Antisymmetrized Molecular Dynamics
• Real-time evolution method and its application to 3$\alpha$ cluster system
• Multi-cluster dynamics in ${}_{\Lambda }^{13}\mathrm{C}$ and analogy to clustering in ${}^{12}\mathrm{C}$
• Nuclear electric dipole moment in the cluster model with a triton: ${}^7$Li and ${}^{11}$B
• 2$\alpha$+$t$ cluster structure in ${}^{11}$B
• Systematic investigation of the Hoyle-analog states in light nuclei
• 2alpha+t cluster feature of $3/2_3^{-}$ state in ${}^{11}$B
• Search for $\alpha$ condensed states in ${}^{13}$C using $\alpha$ inelastic scattering
• Electric dipole moment of light nuclei - 6Li, 7Li, 9Be, 11B, and 13C -
• Persistence of cluster structure in the ground state of ${}^{11}$B