$\alpha +\alpha +t$ 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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