wave functions because they are determined by the change of the relative motion function of the clusters. The $N_k$ values in parenthesis for $^4$He are the number of $J^{\pi}=0^+$ basis functions in the major multi-channel calculation. The energy of $^4$He calculated in Table 2 with the multi-channel calculation is thus not optimized but found to be very close to that of the more extensive calculation. It is noted that the calculated $R^{\rm rms}$ value for the deuteron is smaller than in other calculations. This is due to the restricted choice of the length parameters of the basis functions, which permits us to use a relatively small channel radius of $a \sim 15$ fm. We have checked that the phase shifts for a $d+d$ single channel calculation do not change even when more extended deuteron wave functions are employed.

  ---------------- -------------------- -------- ---------- --------------- -------- ---------- --------------- ---------
     potential           cluster                                                                                
                                         $N_k$      $E$      $R^{\rm rms}$   $P_D$      $E$      $R^{\rm rms}$   $P_{D}$
                                                   (MeV)         (fm)        ($\%$)    (MeV)         (fm)        ($\%$)
                         $d(1^+)$          8      $-$2.18        1.79         5.9     $-$2.24        1.96          5.8
   AV8$^{\prime}$   $t(\frac{1}{2}^+)$     30     $-$8.22        1.69         8.4     $-$8.41          -            -
     (with TNF)     $h(\frac{1}{2}^+)$     30     $-$7.55        1.71         8.3     $-$7.74          -            -
                      $^4$He$(0^+)$      (2370)   $-$27.99       1.46         13.8    $-$28.44         -          14.1
                         $d(1^+)$          