in geometrical progressions: $$\begin{aligned}
      r_n
      &=&
      r_1 a^{n-1} \qquad \enspace 
      (n=1 - n_{\rm max}) \; ,
\nonumber\\
      R_N
      &=&
      R_1 A^{N-1} \quad 
     (N \! =1 - N_{\rm max}) \; ,  %(2.5)
\nonumber\\
      \rho_\nu
      &=&
      \rho_1 \alpha^{\nu-1} \qquad 
     (\nu \! =1 - \nu_{\rm max}) \; .  %(2.5)
%(2.5)\end{aligned}$$ These basis functions have been verified to be suited for describing both short-range correlations and long-range tail behaviour of few-body systems [@Kami88; @Kame89; @Hiyama95; @Hiya96; @Hiyama00; @Hiyama02; @Kamada01]. The eigenenergy $E$ in Eq.(2.2) and the coefficients $C$ in Eq.(2.3) are to be determined by the Rayleigh-Litz variational method.

For the angular-momentum space of the wave function, the approximation with $l, L, \lambda \leq 2$ was found to be enough in getting satisfactory convergence of the binding energies of the states concerned presently. Note that no truncation is taken of the [*interactions*]{} in the angular-momentum space. As for the numbers of the Gaussian basis, $n_{\rm max}, N_{\rm max}$ and $ \nu_{\rm max}$, $4 -10$ are enough.

As far as the single $\Lambda$ hypernuclei $^6_{\Lambda}$He, $^6_{\Lambda}$Li, $^7_{\Lambda}$Li, $^8_{\Lambda}$Li, $^8_{\Lambda}$Be and $^9_{\Lambda}$Be are concerned, the wave functions are described by Eq.(2.3) but with one of $\Lambda$ particles omitted. As for the core nucleus itself, $\alpha+x$, the 