泡利原理在全同团簇组成的三团簇系统中的作用
The role of the Pauli principle in three-cluster systems composed of identical clusters
摘要：
在基于代数形式的共振群方法的微观模型中，研究了泡利原理在由三个相同的$s$ -团簇组成的核系统连续波函数形成中的作用。重点放在真正的三簇范数内核中包含的交换效应的研究。详细讨论了三费米子、三玻色子、三双中子（$3d'$）和$3α$系统。提出了构造$3α$系统范数核的简单解析方法。给出了$3α$和$3d'$系统的Pauli允许基函数的显式形式，并建立了这些基函数的渐近行为.首次给出了用$^8$ Be $=α+α$特征值对$^{12}$ C范数核的特征函数和特征值的完全分类.将$^{12}$ C范数核的谱与$^{5}$ H系统的谱进行比较。
英文摘要：
Within the microscopic model based on the algebraic version of the resonating group method the role of the Pauli principle in the formation of continuum wave function of nuclear systems composed of three identical $s$-clusters has been investigated. Emphasis is placed upon the study of the exchange effects contained in the genuine three-cluster norm kernel. Three-fermion, three-boson, three-dineutron ($3d'$) and $3α$ systems are considered in detail. Simple analytical method of constructing the norm kernel for $3α$ system is suggested. The Pauli-allowed basis functions for the $3α$ and $3d'$ systems are given in an explicit form and asymptotic behavior of these functions is established. Complete classification of the eigenfunctions and the eigenvalues of the $^{12}$C norm kernel by the $^8$Be$=α+α$ eigenvalues has been given for the first time. Spectrum of the $^{12}$C norm kernel is compared to that of the $^{5}$H system.
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