$^{12}$ C中第二个$J^π=2^+$状态的三种$α$构型
Three-$α$ configurations of the second $J^π=2^+$ state in $^{12}$C
摘要：
我们研究了$^{12}$ C的第二$J^π=2^+$态的$α$（$^4$ He核）团簇的几何构型，它被讨论为第二$0^+$态的转动带成员.基态和激发态$0^+$和$2^+$用三$α$团簇模型描述.本文用随机变分方法和相关高斯基函数精确求解了具有正交条件的三体薛定谔方程。为了以一种方便的形式分析这些共振态的结构，我们引入了一个限制势。两体密度分布与光谱信息一起阐明了这些状态的结构。我们发现，第二态$0^+$和$2^+$的主要构型均为锐角三角形，起源于$^8$ Be（$0^+$）$+α$构型.然而，在第二个$2^+$状态下，$^8$ Be $+α$分量变为约2/3，因为8Be子系统难以激发，表明该状态不是Hoyle态的理想刚性转动带成员。
英文摘要：
We investigate geometric configurations of $α$ ($^4$He nucleus) clusters in the second $J^π=2^+$ state of $^{12}$C, which has been discussed as a rotational band member of the second $0^+$ state, the Hoyle state. The ground and excited $0^+$ and $2^+$ states are described by a three-$α$ cluster model. The three-body Schrödinger equation with orthogonality conditions is accurately solved by the stochastic variational method with correlated Gaussian basis functions. To analyse the structure of these resonant states in a convenient form, we introduce a confining potential. The two-body density distributions together with the spectroscopic information clarify the structure of these states. We find that main configurations of both the second $0^+$ and $2^+$ states are acute-angled triangle shapes originating from the $^8$Be($0^+$)$+α$ configuration. However, the $^8$Be$+α$ components in the second $2^+$ state become approximately 2/3 because the 8Be subsystem is hard to excite, indicating that the state is not an ideal rigid rotational band member of the Hoyle state.
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