3 $α$模型中$(0^+)$ $^{12}$ C $(2^+)$能谱的特殊性
Peculiarity of the $^{12}$C$(0^+)$ and $^{12}$C$(2^+)$ energy spectrum in a 3$α$ model
摘要：
在3 $α$集团模型中，采用Buck，Friedrich和Wheatley的深$αα$势，在$S$和$D$波中，采用Pauli禁戒态，分析了$^{12}$ C核的最低能谱.采用直接正交化方法消除了3个$α$ -Pauli禁态.在最低的$^{12}$ C（$0_1^+)$）和$^{12}$ C（$2_1^+)$）态中显示了从弱束缚相到深相的可能的一级量子相变效应。$^{12}$ C核在深相中的基态和最低$2^+$态分别由$0^+$和$2^+$三α泛函空间的Pauli投影的临界本征态产生。
英文摘要：
Lowest energy spectrum of the $^{12}$C nucleus is analyzed in the 3$α$ cluster model with a deep $αα$-potential of Buck, Friedrich and Wheatley with Pauli forbidden states in the $S$ and $D$ waves. The direct orthogonalization method is applied for the elimination of the 3$α$-Pauli forbidden states. The effects of possible first order quantum phase transition are shown in the lowest $^{12}$C($0_1^+)$ and $^{12}$C($2_1^+)$ states from weakly bound phase to a deep phase. The ground and lowest $2^+$ states of the $^{12}$C nucleus in the deep phase are created by the critical eigen states of the Pauli projector for the $0^+$ and $2^+$ three-alpha functional spaces, respectively.
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