α+α+tcluster structures andC12(02+)-analog states inB11

Abstract

The structure of $3/{2}^{\ensuremath{-}}$ and $1/{2}^{+}$ states in $^{11}\mathrm{B}$ is investigated with an $\ensuremath{\alpha}+\ensuremath{\alpha}+t$ orthogonality condition model (OCM) based on the Gaussian expansion method. Full levels up to the $3/{2}_{3}^{\ensuremath{-}}$ and $1/{2}_{2}^{+}$ states around the $\ensuremath{\alpha}+\ensuremath{\alpha}+t$ threshold (${E}_{x}=11.1$ MeV) are reproduced consistently with the experimental energy levels. It is shown that the $3/{2}_{3}^{\ensuremath{-}}$ state located around the ${}^{7}\mathrm{Li}+\mathrm{\ensuremath{\alpha}}$ threshold has an $\ensuremath{\alpha}+\ensuremath{\alpha}+t$ cluster structure, whereas the $3/{2}_{1}^{\ensuremath{-}}$ and $3/{2}_{2}^{\ensuremath{-}}$ states have a shell-model-like compact structure. We found that the $3/{2}_{3}^{\ensuremath{-}}$ state does not possess an $\ensuremath{\alpha}$-condensate-like nature analogous to the ${0}_{2}^{+}$ state of $^{12}\mathrm{C}$ (Hoyle state) which has a dilute $3\ensuremath{\alpha}$-condensate structure described by a $(0{S}_{\ensuremath{\alpha}}){}^{3}$ 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 $3/{2}_{3}^{\ensuremath{-}}$ state does not have the condensate character. On the other hand, the $1/{2}_{1}^{+}$ state just below the ${}^{7}\mathrm{Li}+\mathrm{\ensuremath{\alpha}}$ threshold has a cluster structure that can be interpreted as a parity-doublet partner of the $3/{2}_{3}^{\ensuremath{-}}$ state. We indicate that the $12.56$-MeV state (${J}^{\ensuremath{\pi}}=1/{2}_{2}^{+}$) just above the $\ensuremath{\alpha}+\ensuremath{\alpha}+t$ threshold observed in the $^{7}\mathrm{Li}$($^{7}\mathrm{Li}$,$^{11}\mathrm{B}$${}^{*}$)$t$ reaction, etc., is of the dilute cluster-gas-like configuration and is a strong candidate for the product states of clusters, having a configuration of $(0{S}_{\ensuremath{\alpha}}){}^{2}(0{S}_{t})$ with about $65%$ probability, from the analyses of the single-cluster motions in $^{11}\mathrm{B}$. The structure property of the $1/{2}^{+}$ resonant state is analyzed with the complex scaling method.