Pauli exclusion role which prevents the two $\alpha$ cluster from overlapping. But, it is well known [@Horiuchi] that this approximate prescription of the Pauli principle is not suited for the case where the presence of the third particle makes the two $\alpha$ clusters come closer to each other; in other words, the off-energy-shell behaviour of the repulsive potential is not appropriate in the three-body system. Moreover, there is no available potential reported for the $\alpha \,x$ systems ($x=n, p, d, t $ and $ ^3$He) of this type. Therefore, we do not employ this prescription in the present systematic study of the structure change of the $\alpha \,x$ systems due to the addition of $\Lambda$ particles. We take the orthogonality condition model instead which is suited even for the case of heavy overlapping between the two clusters.

$\alpha \,x$ interactions
-------------------------

As for the potentials $V_{\alpha x}$ between the clusters $\alpha$ and $x$, we employ those which have been often used in the OCM-based cluster-model study of light nuclei. Namely, they are the $V_{\alpha N}$ potential introduced in Ref. [@Kanada79], the $V_{\alpha d}$ and $V_{\alpha t}$ potentials given in Ref.[@Furutani80] and the $V_{\alpha \alpha}$ potential used in Ref. [@Hasegawa71] which 