The $\Lambda$-$\Sigma$ coupling effect in the neutron-rich $\Lambda$-hypernucleus $_{\Lambda}^{10}$Li by microscopic shell model

TL;DR

This study uses microscopic shell-model calculations to analyze the $ m oldsymbol{\Lambda}$-$oldsymbol{\Sigma}$ coupling effect in the neutron-rich hypernucleus $_{oldsymbol{\Lambda}}^{oldsymbol{10}}$Li, revealing significant $ m oldsymbol{\Sigma}$-mixing and energy shifts.

Contribution

It introduces a detailed shell-model analysis of $ m oldsymbol{\Lambda}$-$oldsymbol{\Sigma}$ coupling in $_{oldsymbol{\Lambda}}^{oldsymbol{10}}$Li, highlighting the enhanced $ m oldsymbol{\Sigma}$-mixing in neutron-rich environments.

Findings

$ m oldsymbol{\Sigma}$-mixing probability is about 0.34% in $_{oldsymbol{\Lambda}}^{oldsymbol{10}}$Li.

Energy shift due to $ m oldsymbol{\Sigma}$-coupling is approximately 0.28 MeV.

The $ m oldsymbol{\Sigma}$ configuration plays a significant role in the hypernucleus structure.

Abstract

We investigate the structure of the neutron-rich $\Lambda$-hypernucleus $_{\Lambda}^{10}$Li by using microscopic shell-model calculations considering a $\Lambda$-$\Sigma$ coupling effect. The calculated $\Sigma$-mixing probability in the $_{\Lambda}^{10}$Li ground state is found to be about 0.34 % which is coherently enhanced by the $\Lambda$-$\Sigma$ coupling configurations, leading to the energy shift 0.28 MeV which is about 3 times larger than that in $_{\Lambda}^{7}$Li. The importance of the $\Sigma$ configuration obtained by the $\Sigma N$ interaction and the potentiality of the neutron-rich environment are discussed.