Resonant states of neutron-rich $\Lambda$ hypernucleus ${}_{\Lambda }^7$He

Abstract

The structure of neutron-rich $\Lambda$ hypernucleus, ${}_{\Lambda }^7$He is studied within the framework of an $\alpha +\Lambda +n+n$ four-body cluster model. We predict second $3/2^{+}$ and $5/2^{+}$ states, corresponding to a $0s$ $\Lambda$ coupled to the second $2^{+}$ state of ${}^6$He, as narrow resonant states with widths $\Gamma \sim 1$ MeV to be at 0.03 MeV and 0.07 MeV respect to the $\alpha +\Lambda +n+n$ threshold. From an estimation of the differential cross section for the ${}^7\mathrm{Li}(\gamma ,K^{+}{)}_{\Lambda }^7$He reaction, there is a possibility to observe these state at JLab in the future. We also calculate the second $2^{+}$ state of ${}^6$He as resonant state within the framework of an $\alpha +n+n$ three-body cluster model. Our result is $2.81$ MeV with $\Gamma =$4.63 MeV with respect to the $\alpha +n+n$ threshold. This energy position is $\sim 1$ MeV higher, and with a much broader decay width, than the recent SPIRAL data. It is suggested that an experiment at JLab to search for the second $3/2^{+}$ and $5/2^{+}$ states of ${}_{\Lambda }^7$He would provide an opportunity to confirm the second $2^{+}$ state of the core nucleus ${}^6$He.

arXiv comment6 pages, 4 figures,published in Physical Review C

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• Compact $sssc\bar{c}$ pentaquark states predicted by a quark model
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