Feasibility of extracting aΣ−admixture probability in the neutron-richΛ10Lihypernucleus

Abstract

We theoretically examine production of the neutron-rich ${}_{\ensuremath{\Lambda}}^{10}\mathrm{Li}$ hypernucleus by a double-charge exchange (${\ensuremath{\pi}}^{\ensuremath{-}}$, ${K}^{+}$) reaction on a $^{10}\mathrm{B}$ target with distorted-wave impulse approximation calculations. We calculate the inclusive spectrum at the incident momentum 1.20 GeV/$c$ by a one-step mechanism ${\ensuremath{\pi}}^{\ensuremath{-}}p\ensuremath{\rightarrow}{K}^{+}{\ensuremath{\Sigma}}^{\ensuremath{-}}$ via ${\ensuremath{\Sigma}}^{\ensuremath{-}}$ doorways caused by a ${\ensuremath{\Sigma}}^{\ensuremath{-}}p\ensuremath{\leftrightarrow}\ensuremath{\Lambda}n$ coupling. The resultant spectrum can explain the magnitude of the recent experimental data, so that the ${\ensuremath{\Sigma}}^{\ensuremath{-}}$ admixture probability in ${}_{\ensuremath{\Lambda}}^{10}\mathrm{Li}$ is found to be of the order of ${10}^{\ensuremath{-}1}%$. The (${\ensuremath{\pi}}^{\ensuremath{-}}$, ${K}^{+}$) reaction provides the ability to extract properties of wave functions with $\ensuremath{\Lambda}\text{\ensuremath{-}}\ensuremath{\Sigma}$ coupling effects in neutron-rich nuclei, as well as the reaction mechanism.