increases by an appropriate value of $\Delta\alpha$ with each added atom. In other words an agreement between theory and experiment can be seen by using $n_c$, $\alpha$, and $\Delta\alpha$ as adjustable parameters. Note that increase in $\alpha$ is possible both by decrease in $r_1$ and increase in $r_2$ when an atom is added to the cluster. However, it appears that desired increase in $r_2$ is more probable than decrease in $r_1$. As revealed by Eqn.(14), decrease in $I$ is possible if $\Delta\alpha$/$\alpha$ increases by more than 16.6$\%$, 10$\%$ and 7.1$\%$, respectively, in case of $n_c =$ 1. 2, and 3. These aspects are depicted in Fig.4 for their better understanding.

Summing up the possible explanation for the phenomenon in the light of our preceding analysis, we may mention that :

\(1) With increasing $N$ from $N^i$ to $N^*$, $^4$He atoms in M:$^4$He$_N$ cluster (for $N \le N^*$) seem to have reasonably strong binding with M for which the cluster as whole represents a rigid rotor, to a good approximation, and its $I$ increases (or corresponding $B$ decreases) with $N$ in agreement with experiments ([*cf.*]{} Fig.1, for $N \le N^*$).

\(2) For nearly no change in $I_{N}$ from $I_{N^*}$, when $N$ 