Single-${\Xi }^{-}$ hypernuclei with quark mean field model

Abstract

The single-${\Xi }^{-}$ hypernuclei are studied using a quark mean field model. At the quark level, the ${\Xi }^{-}$ 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 $\sigma ,\omega$, and $\rho$ mesons between quarks in different baryons. The single-${\Xi }^{-}$ binding energies of $\Xi$ 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-$\Lambda$ and $\Xi$ 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 ${\Xi }^{-}$ 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 $\Xi$ 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 ${\Xi }^{-}$ hyperon may occupy the $1p$ state. Furthermore, the ${\Xi }^{-}$ 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-$\Lambda$ binding energy of $\ce{^{208}_ΛPb}$ observed by experiments. It demonstrates that the $\Lambda$ and ${\Xi }^{-}$ hyperons seem to appear simultaneously in a neutron star.

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

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Cited by in corpus (1)

• Single ${\Lambda }_c^{+}$ hypernuclei within quark mean-field model