for $r_2 = 2r_1 = 2r_o$ ([*i.e.*]{}, $\alpha = 2$) and by a maximum of $\Delta I = -n_cmr_o^2$ for $r_2 > > r_1 (= r_o)$. Such changes in $I$ for $n_c = 1, 2, 3, ...$ for different $\alpha = r_2/r_1$ are depicted in Fig.3 for their better perception.

For a possible situation where no atom jumps from orbit-1 to orbit-2 when $(n_c+1)$-th atom is added to orbit-2, it is evident that the added atom increases $I$ by $mr_o^2/\alpha^2$. We have $$\Delta I =  mr_o^2\left[\frac{2n_c}{\alpha^2} -n_c\right] 
+ mr_o^2\frac{1}{\alpha^2}.  \eqno(12)$$

which again means $I_{N+1} > I_N$ provided the added atom makes no change in $\alpha$. However, if it does and changes in $r_2$ and $r_1$ are such that $\alpha$ increases to $\alpha^* = \alpha + 
\Delta\alpha$, then by using Eqn.(12), we find $$\delta{(\Delta{I})} = \Delta I(\alpha^*) - \Delta I(\alpha) 
= -mr_o^2\frac{2(2n_c+1)\Delta\alpha}{\alpha^3}. \eqno(13)$$

We note that this $-ve$ change in $I$ can overcompensate the increase in $I$ by $mr_o^2/\alpha^2$ if

$$\Delta\alpha \ge \frac{\alpha}{2(2n_c+1)} \quad \left(= 
\frac{1}{2(2n_c+1)}\frac{r_2}{r_1}\right)\eqno(14)$$

which is obtained by equating RHS of Eqn.(13) to $ mr_o^2/{\alpha^2}$. This indicates that $I$ of the cluster can have continuous decrease with increase in $N$ (possibly from $N^*$ to $N_1$) if $\alpha = r_2/r_1$ 