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arXiv 1710.08613nucl-th
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夸克平均场模型下的单$Ξ^-$超核

Single-$Ξ^-$ hypernuclei with quark mean field model

Jinniu Hu, Hong Shen

备注：
17 pages, 3 figures, 1 tables, accepted to Phys. Rev. C
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摘要：

用夸克平均场模型研究了单$Ξ^-$超核.在夸克水平上，$Ξ^-$超子由一个$d$夸克和两个$s$夸克组成，它们被谐振子势限制。在强子的情况下，重子通过在不同重子中的夸克之间交换$σ, ~ω$和$ρ$介子而相互作用。利用几种稳定核的基态性质和核饱和密度下$Λ$和$Ξ$单原子势的经验值，采用不同的参数集，研究了从$\ce{_{Ξ^{-}}^{12}Be}$到$\ce{^{208}_{Ξ^-}Tl}$的$Ξ^-$单原子结合能.对于$\ce{Ξ^{-}{+}^{14}N}$的束缚态（即，在KEK-E373实验中，对KISO事件命名为$\ce{^{15}_{Ξ^-}C}$）系统，在QMF-NK 1 S、QMF-NK 2S和QMF-NK 3S参数组下，发现$Ξ^-$的结合能在$5.61-5.89$ MeV附近，$1p$的结合能在$0.94-1.21$ MeV附近，其单个$Ξ$势为$-12$ MeV.这些结果和用高斯展开方法得到的关于$\ce{Ξ^{-}{+}^{12}Be}$的集团模型的结果表明，在KISO事例中，$Ξ^-$超子可能占据$1p$态.此外，对于$\ce{Ξ^{-}{+}^{207}Pb}$，在$27$ MeV附近获得$Ξ^-$结合能（即，$\ce{^{208}_{Ξ^-}Tl}$）系统。能量与实验观察到的$\ce{^{208}_ΛPb}$的单- $Λ$结合能几乎相当。它表明，$Λ$和$Ξ^-$超子似乎同时出现在中子星中。

英文摘要：

The single-$Ξ^-$ hypernuclei are studied using a quark mean field model. At the quark level, the $Ξ^-$ hyperon is composed of one $d$ quark and two $s$ quarks, which are confined by the harmonic oscillator potentials. In the case of hadrons, the baryons interact with each other by exchanging $σ, ~ω$, and $ρ$ mesons between quarks in different baryons. The single-$Ξ^-$ binding energies of $Ξ$ hypernuclei are investigated from $\ce{_{Ξ^{-}}^{12}Be}$ to $\ce{^{208}_{Ξ^-}Tl}$ using different parameter sets, which are determined by the ground-state properties of several stable nuclei and the empirical values of the single-$Λ$ and $Ξ$ potentials at the nuclear saturation density. For the bound states of $\ce{Ξ^{-}{+}^{14}N}$ (i.e., $\ce{^{15}_{Ξ^-}C}$) system named as KISO event in KEK-E373 experiment, it is found that the $Ξ^-$ binding energies are around $5.61-5.89$ MeV for $1s$ state and $0.94-1.21$ MeV for $1p$ state with QMF-NK1S, QMF-NK2S, and QMF-NK3S parameter sets, whose single $Ξ$ potentials are $-12$ MeV. These results and those from cluster models with the Gaussian expansion method concerning on the $\ce{Ξ^{-}{+}^{12}Be}$ show that in the KISO event, the $Ξ^-$ hyperon may occupy the $1p$ state. Furthermore, the $Ξ^-$ binding energies are achieved around $27$ MeV for the $\ce{Ξ^{-}{+}^{207}Pb}$ (i.e., $\ce{^{208}_{Ξ^-}Tl}$) system. The energies were nearly comparable to the single-$Λ$ binding energy of $\ce{^{208}_ΛPb}$ observed by experiments. It demonstrates that the $Λ$ and $Ξ^-$ hyperons seem to appear simultaneously in a neutron star.

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