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

TL;DR

This paper predicts and analyzes resonant states of the neutron-rich hypernucleus $^7_{\Lambda}$He using cluster models, suggesting potential experimental observation at JLab to confirm these states and improve understanding of hypernuclear structure.

Contribution

The study introduces detailed predictions of resonant states in $^7_{\Lambda}$He and its core nucleus $^6$He, providing theoretical guidance for future experimental verification.

Findings

Predicted narrow $3/2^+$ and $5/2^+$ resonant states at 0.03 and 0.07 MeV.

Calculated second $2^+$ state of $^6$He at 2.81 MeV with broad width.

Suggested experimental observation at JLab for these states.

Abstract

The structure of neutron-rich $\Lambda$ hypernucleus, $^7_{\Lambda}$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 $^7{\rm Li} (\gamma,K^+) ^7_{\Lambda}$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 $^7_{\Lambda}$He would provide an opportunity to confirm the second $2^+$ state of the core nucleus $^6$He.