Geometric configurations of three \(\alpha \) particles in the ground- and first-excited \(J^\pi =0^+\) states of \(^{12}\)C are discussed within two types of \(\alpha \)-cluster models which treat the Pauli principle differently. Though there are some quantitative differences especially in the internal region of the wave functions, equilateral triangle configurations are dominant in the ground state, while in the first excited \(0^+\) state isosceles triangle configurations dominate, originating from \(^8\mathrm{Be}+\alpha \) configurations.

中文翻译：

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三个- $$\alpha $$ α $$0^{+}$$ 0 + $$^{12}\mathrm {C}$$ 12 C 的状态的配置

在\(^{12}\) C的地面和第一激发\(J^\pi =0^+\)状态中三个\(\alpha \)粒子的几何配置在两种类型的\( \alpha \) -以不同方式对待泡利原理的集群模型。尽管在波函数的内部区域存在一些数量上的差异，但等边三角形构型在基态中占主导地位，而在第一激发态\(0^+\)状态下等腰三角形构型占主导地位，源于\(^8 \mathrm{Be}+\alpha \)配置。