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$^{11}$ B中的$α+α+t$团簇结构和Hoyle类似态

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

Taiichi Yamada, Yasuro Funaki

备注：
22 pages, 9 figures
发表信息：
Phys.Rev.C82:064315,2010
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摘要：

利用基于高斯展开的$α+α+t$正交条件模型（OCM）研究了$^{11}$ B中$3/2^{-}$和$1/2^{+}$态的结构.完整的水平高达$3/2^{-}_{3}$和$1/2^{+}_2$状态周围的$α+α+t$阈值（$E_x$ =11.1兆电子伏）再现与实验的能量水平一致。结果表明，位于$^{7}$ Li+ $α$阈值附近的$3/2_{3}^{-}$态具有$α+α+t$团簇结构，而$3/2_{1}^{-}$和$3/2_{2}^{-}$态具有壳模型的紧凑结构.我们发现，$3/2_{3}^{-}$态不具有$α$ -凝聚态性质，而$^{12}$ C（Hoyle态）的$0^{+}_{2}$态具有$3α$ -凝聚态结构，其概率约为$70$ \%，但前者的跃迁强度与后者一样大.讨论了$3/2_{3}^{-}$态不具有凝聚态性质的原因。另一方面，刚好低于$^{7}$ Li+ $α$阈值的$1/2^{+}_{1}$状态具有簇结构，其可以被解释为$3/2^{-}_3$状态的奇偶偶联体伙伴。通过对$^{11}$ B中单团簇运动的分析，我们指出，在$^7$ Li（$^{7}$ Li，$^{11}$ B $^*$）$t$反应等中观察到的$12.56$-MeV态（$J^π=1/2^{+}_{2}$）是类稀团簇气体态，是具有$(0S_α)^{2}(0S_{t})$组态的Hoyle类似态的强候选态，其几率约为$65$ \%.用复标度法分析了$1/2^{+}$共振态的结构性质。

英文摘要：

The structure of $3/2^{-}$ and $1/2^{+}$ states in $^{11}$B is investigated with an $α+α+t$ 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 $α+α+t$ 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+$α$ threshold has an $α+α+t$ 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 $α$-condensate-like nature similar to the $0^{+}_{2}$ state of $^{12}$C (Hoyle state) which has a dilute $3α$-condensate structure described by a $(0S_α)^3$ 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+$α$ 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 ($J^π=1/2^{+}_{2}$) just above the $α+α+t$ threshold observed in the $^7$Li($^{7}$Li,$^{11}$B$^*$)$t$ reaction etc. is of the dilute-cluster-gas-like, and is a strong candidate for the Hoyle-analogue state which has a configuration of $(0S_α)^{2}(0S_{t})$ 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.

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