M:$^4$He$_N$ cluster in a manner that one atom from first orbit of radius $r_1$ moves to the orbit of radius $r_2$ of the added atom (as shown in Fig.2C); in this case the net change $\Delta I = I_{N+1} - I_N$ becomes $$\Delta I = 2mr_2^2\frac{r_1^4}{r_2^4} - mr_1^2 =
mr_1^2\left[2\frac{r_1^2}{r_2^2} -1\right] \eqno(8)$$

which assumes a $-ve$ value for $r_2 > \sqrt{2}r_1$ indicating that $I_{N+1} < I_N$ when $r_2 > \sqrt{2}r_1$. Using this possibility for $N$ increasing beyond $N^*$ by 1 atom, we have

$$\Delta I = -0.5mr_o^2\eqno(9)$$

by using Eqns.(2) and (8). Presuming further that another atom moves similarly from orbit-1 to orbit-2 when an added atom to the cluster occupies orbit-2 as shown in Fig.2D, we have

$$\Delta I = 4mr_2^2\frac{r_1^4}{r_2^4} - 2mr_1^2 =
mr_1^2\left[4\frac{r_1^2}{r_2^2} -2\right] = - 1.0mr_o^2 \eqno(10)$$

for orbits satisfying Eqn.(2). Generalizing Eqns.(8) and Eqn.(10), we have

$$\Delta I = mr_1^2\left[2n_c\frac{r_1^2}{r_2^2} - n_c\right]
 =  mr_o^2\left[\frac{2n_c}{\alpha^2} -n_c\right] \eqno(11)$$

which represents the change in $I$ when $n_c$ atoms (above $N^*$) added to orbit-2 (making total $N = N^* + n_c$) induce $n_c$ atoms from orbit-1 to jump to orbit-2. Eqn.(11) reveals that $I$ has no change if $\alpha (=r_2/r_1) = \sqrt{2}$, it decreases by $\Delta I = -0.5n_cmr_o^2$ 