For the (82)$_{1}$ , the BF with the largest weight (33.4%) is the {0-8,10-13}. When $L\geq 84$, the N$_{out}$ of the FS is $\geq 6$. Since the outward electrons would separate (roughly by $r_{u}$) from each other, a larger N$_{out}$ definitely leads to a  larger ring. Consequently, the outward electrons are no more close to the core, and the ring-core structure becomes explicit. This is shown in Fig.3c to 3f for the (84)$_{1}$ to (90)$%
_{1}$ states, where the outward peak becomes larger and larger.  The point $%
\ a$ separating the inner and outer regions can be well defined. Accordingly,  the quantities related to eq.(6) to (8) can be calculated as listed  in Table 2. In particular, a quantity related to the uniformity of rotation

$\gamma =\frac{l_{out}}{I_{out}}/\frac{l_{in}}{I_{in}}=\omega
_{out}/\omega _{in}\qquad \qquad (17)$

is defined and is also listed.

It is exhibited in Table 2 that, in the range  84$\leq
L\leq 90$, $a$ and $N_{in}$ are decreasing . This coincides with the reduction of the core of the FS. In particular, the N$_{in}$ of the FS are one-to-one close to the $N_{in}$ from calculation. This fact confirms that the FSs are pursued by the first-states. In general the $N_{in}$ and $l_{in}$ 