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arXiv 1712.09342nucl-th
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超越二体相互作用范式:原子核中扩展的A体对相互作用

Beyond the 2-Body Interaction Paradigm: The Case for Extended A-Body Pairing Interaction in Nuclei

V. G. Gueorguiev

摘要:

我们讨论了超越2体相互作用范式的核结构建模。我们的第一个例子与手征微扰理论建议的三个核子接触相互作用项的需要有关。着重讨论了再现$^3$ H和$^3$ He结合能的相应三核子接触相互作用项$c_D$和$c_E$的两个低能有效耦合参数之间的关系,并用$^4$ He的结合能说明了物理上相关的参数区域。基于Okubo-Lee-Suzuki有效相互作用方法在有限模型空间内求解核多体问题,进一步证明了A体相互作用项。我们使用的第三个例子是应用于具有长同位素链的重核的精确可解A体扩展配对相互作用,特别是使用$^{132}$ Sn和$^{208}$ Pb作为闭合核系统,说明了这两个同位素链的成员的扩展配对强度$G(A)$与价空间$\dim(A)$的大小之间的显著关系:$G(A)=α\dim(A)^{-β}$,其中$α=259.436$用于Sn,$α=366.77$用于Pb,而参数$β$实际上为1。这三个案例提供了证据,需要更好地理解的三核子(NNN),四核子(NNNN),和A-体的相互作用,无论是来自ChPT或从现象学的考虑。

英文摘要:

We discuss modeling of nuclear structure beyond the 2-body interaction paradigm. Our first example is related to the need of three nucleon contact interaction terms suggested by chiral perturbation theory. The relationship of the two low-energy effective coupling parameters for the relevant three nucleon contact interaction terms $c_D$ and $c_E$ that reproduce the binding energy of $^3$H and $^3$He has been emphasized and the physically relevant parameter region has been illustrated using the binding energy of $^4$He. Further justification of A-body interaction terms is outlined based on the Okubo-Lee-Suzuki effective interaction method used in solving the nuclear many-body problem within a finite model space. The third example we use is an exactly solvable A-body extended pairing interaction applied to heavy nuclei with a long isotopic chains, in particular using $^{132}$Sn and $^{208}$Pb as closed core system illustrates a remarkable relationship between the extended pairing strength $G(A)$ and the size of the valence space $\dim(A)$ for the members of these two isotope chain: $G(A)=α\dim(A)^{-β}$ with $α=259.436$ for Sn and $α=366.77$ for Pb while the parameter $β$ is practically 1. These three cases present evidence for the need of better understanding of the three-nucleon (NNN), four-nucleon (NNNN), and A-body interactions in nuclei either derived from ChPT or from a phenomenological considerations.

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