Structure of A=7 iso-triplet $\Lambda$ hypernuclei studied with he four-body model

TL;DR

This study models the structure of A=7 iso-triplet $ m f extit{ extLambda}}$ hypernuclei using a four-body cluster approach, predicting binding energies, energy splittings, and a layered matter distribution with a $ m f extLambda}$ skin and halo components.

Contribution

It introduces a detailed four-body cluster model for A=7 hypernuclei, including a phenomenological charge symmetry breaking interaction, and predicts their structural properties.

Findings

Predicted $ m f extLambda}$ binding energy of 5.16 MeV for $^7_{ extLambda}$He.

Calculated energy splittings of about 0.1 MeV for certain states.

Identified a three-layer matter distribution with a $ m f extLambda}$ skin and halo in the studied hypernuclei.

Abstract

The structure of the T=1 iso-triplet hypernuclei, $^7_{\Lambda}$He, $^7_{\Lambda}$Li and $^7_{\Lambda}$Be within the framework of an $\alpha +\Lambda +N+N$ four-body cluster model is studied. Interactions between the constituent subunits are determined so as to reproduce reasonably well the observed low-energy properties of the $\alpha N$, $\alpha \Lambda$, $\alpha NN$ and $\alpha \Lambda N$ subsystems. Furthermore, the two-body $\Lambda N$ interaction is adjusted so as to reproduce the $0^+$-$1^+$ splitting of $^4_{\Lambda}$H. Also a phenomenological $\Lambda N$ charge symmetry breaking(CSB) interaction is introduced. The $\Lambda$ binding energy of the ground state in $^7_{\Lambda}$He is predicted to be 5.16(5.36) MeV with(without) the CSB interaction. The calculated energy splittings of the $3/2^+$-$5/2^+$ states in $^7_{\Lambda}$He and $^7_{\Lambda}$Li are around 0.1 MeV. We point out that there is a three-layer structure of the matter distribution, $\alpha$ particle, $\Lambda$ skin, proton or neutron halo, in the $^7_{\Lambda}{\rm He}(J=5/2^+)$, $^7_{\Lambda}{\rm Li}(J=5/2^+)$ and $^7_{\Lambda}{\rm Be}(J=1/2^+)$ states.