Feasibility of extracting a $Σ^-$ admixture probability in the neutron-rich $^{10}_Λ$Li hypernucleus

Abstract

We examine theoretically production of the neutron-rich $^{10}_Λ$Li hypernucleus by a double-charge exchange ($π^-$, $K^+$) reaction on a $^{10}$B target with distorted-wave impulse approximation calculations. The result shows that the magnitude and shape of the calculated spectrum at 1.20 GeV/c by a one-step mechanism $π^-p \to K^+ Σ^-$ via $Σ^-$ doorways caused by a $Σ^-p \leftrightarrow Λn$ coupling can explain the recent experimental data, and the $Σ^-$ admixture probability in $^{10}_Λ$Li is found to be the order of 10$^{-1}$ %. The ($π^-$, $K^+$) reaction provides a capability of extracting properties of wave functions with $Λ$-$Σ$ coupling effects in neutron-rich nuclei, together with the reaction mechanism.

13 pages, 3 figures