of the $\alpha+x$ core nuclei due to the participation of the $\Lambda$ particles is found to be substantially large and it plays an important role in estimating the $\Lambda \Lambda$ bond energies of those hypernuclei.
address:
- 'Institute of Particle and Nuclear Studies, High Energy Accelerator Research Organization (KEK), Tsukuba 305-0801, Japan'
- 'Department of Physics, Kyushu University, Fukuoka 812-8581,Japan'
- |
    Physics Department, Brookhaven National Laboratory, Upton, New York 11973\
    and Laboratory of Physics, Osaka Electro-Comm. University, Neyagawa 572-8530, Japan[^1]
- 'Laboratory of Physics, Kanto Gakuin University, Yokohama 236-8501, Japan'
- 'Physics Section, Tsuru University, Tsuru, Yamanashi 402-8555, Japan'
author:
- 'E. Hiyama'
- 'M. Kamimura'
- 'T. Motoba'
- 'T. Yamada'
- 'Y. Yamamoto'
title: ' Four-body cluster structure of $A=7-10$ double-$\Lambda$ hypernuclei'
---

Introduction
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A recent finding of the double-$\Lambda$ hypernucleus $_\Lambda^{ }$$_\Lambda^6$He, which is called as NAGARA event in the KEK-E373 experiment [@Nagara], has a great impact not only on the study of baryon-baryon interactions in the strangeness $S=-2$ sector but also on the study of dynamics of many-body systems with multi-strangeness. The importance of this event is attributed to the well-defined explanation of the process and the high quality experimental value of the $\Lambda 