论文标题
$^{12} $ c核的空间结构在3 $α$模型中具有深厚电势，含有禁止状态
Spatial Structure of the $^{12}$C Nucleus in a 3$α$ Model with Deep Potentials Containing Forbidden States
论文作者
论文摘要
最低0 $ _1^+$，0 $ _2^+$，2 $ _1^+$和2 $ _1^+$和2 $ _2^+$状态的空间结构在3 $α$中的$^{12} $ c nucleus在3 $α$模型中使用Buck，Friedrich和Friedrich和Wheatley $ litys cauli $ d $ d $ d $ d $ d $ d $ d $ s of s s $ s and s $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $ d $。三体系统中的Pauli禁止状态通过精确的正交方法处理。对地面的最大贡献和激发2 $ _1^+$绑定的状态能量来自部分波$（λ，\ ell）=（2,2）$和$（λ，\ ell）=（4,4）$。如前所述，这些界面是由0 $^+$和2 $^+$功能空间的三体Pauli投影仪的关键特征态创建的。 Pauli投影仪的这些特殊特征状态负责从弱结合的“气体样”相到深“量子液体”相的量子相变。与绑定状态相反，对于Hoyle共振0 $ _2^+$及其模拟状态2 $ _2^+$，主要贡献来自$（λ，\ ell）=（0,0）$和$（λ，\ ell）=（2,2）$配置。 $^{12} $ c（0 $ _1^+$）的估计概率密度功能和2 $ _1^+$兴奋的绑定状态大多显示三角形结构，其中$α$粒子以彼此约2.5 fm的距离移动。但是，Hoyle共振及其模拟状态的空间结构具有很大的结构，例如$^8 $ be + $α$。在霍伊尔州，最后的$α$粒子在$ r = 3.0 $ fm和$ r = 5.0 $ fm之间的距离远离双打。在Hoyle Analog 2 $ _2^+$状态下，两个Alpha粒子以约15 fm的距离移动，但最后的$α$粒子可以在距离内远距离移动到$ r = 30.0 $ fm。
The spatial structure of the lowest 0$_1^+$, 0$_2^+$, 2$_1^+$ and 2$_2^+$ states of the $^{12}$C nucleus is studied within the 3$α$ model with the Buck, Friedrich, and Wheatley $αα$ potential with Pauli forbidden states in the $S$ and $D$ waves. The Pauli forbidden states in the three-body system are treated by the exact orthogonalization method. The largest contributions to the ground and excited 2$_1^+$ bound states energies come from the partial waves $(λ, \ell)=(2,2)$ and $(λ, \ell)=(4,4)$. As was found earlier, these bound states are created by the critical eigenstates of the three-body Pauli projector in the 0$^+$ and 2$^+$ functional spaces, respectively. These special eigenstates of the Pauli projector are responsible for the quantum phase transitions from a weakly bound "gas-like" phase to a deep "quantum liquid" phase. In contrast to the bound states, for the Hoyle resonance 0$_2^+$ and its analog state 2$_2^+$, dominant contributions come from the $(λ, \ell)=(0,0)$ and $(λ, \ell)=(2,2)$ configurations, respectively. The estimated probability density functions for the $^{12}$C(0$_1^+$) ground and 2$_1^+$ excited bound states show mostly a triangular structure, where the $α$ particles move at a distance of about 2.5 fm from each other. However, the spatial structure of the Hoyle resonance and its analog state have a strongly different structure, like $^8$Be + $α$. In the Hoyle state, the last $α$ particle moves far from the doublet at the distance between $R=3.0$ fm and $R=5.0$ fm. In the Hoyle analog 2$_2^+$ state the two alpha particles move at a distance of about 15 fm, but the last $α$ particle can move far from the doublet at the distance up to $R=30.0$ fm.
