Neutron-rich Lambda Hypernuclei

The J-PARC E10 experiment aims to produce $\Lambda$ hypernuclei close to the neutron drip-line to investigate hyperon-nucleon interactions in the asymmetric nuclear medium. Although the $\Lambda$ hyperon has an isospin $I$=0, a dependence of the $\Lambda N$ interaction on the overall isospin of $\Lambda$ hypernuclei may arise due to a coupling to $\Sigma$($I$=1) channel known as the ``$\Lambda N$-$\Sigma N$ mixing'' and may be investigated in structures of the neutron-rich $\Lambda$ hypernuclei. The structure of a highly neutron-rich hypernucleus, $^6_\Lambda{\rm H}$, is discussed theoretically quite extensively in connection with the contribution of the $\Lambda N$-$\Sigma N$ mixing to the binding. One of promising methods to produce the neutron-rich $\Lambda$ hypernuclei is the application of the double charge-exchange (DCX) reactions, such as the $(K^-,\pi^+)$ and the $(\pi^-,K^+)$ reactions. Recently, we carried out the first phase of the J-PARC E10 experiment to search for $^6_\Lambda{\rm H}$ by utilizing the $^6{\rm Li}(\pi^-,K^+)$ reaction. The experiment was designed to have a high sensitivity to search for the neutron-rich $\Lambda$ hypernuclei with high-resolution magnetic spectrometers and high-intensity pion beams available at the K1.8 beam line of the J-PARC 50 GeV Proton-Synchrotron facility. The yield of the reaction was extremely smaller than that in the $^{10}{\rm B}(\pi^-,K^+)^{10}_{~\Lambda}{\rm Li}$ reaction obtained in the previous KEK-E521 experiment at KEK-PS. A comparison will be made with the result of the measurement of the $^6{\rm Li}(K^-_{\rm stopped},\pi^+)$ reaction to search for $^6_\Lambda{\rm H}$ reported by the FINUDA experiment at DA$\Phi$NE.