shall evaluate the core-ring separation by using the approximation of uniform rotation.

 For a given CFS with the given N$_{out}$ and $l_{out}$ , let us define a quantity

$\stackrel{\_}{g}=\sqrt{\frac{l_{out}/l_{in}}{N_{out}/N_{in}}}\qquad
\qquad (12)$

On the other hand, we have

$I_{out}=m^{\ast }N_{out}<r^{2}>_{ring}\qquad \qquad (13)$

(this equation is the same as eq.(8)), and a similar equation for $I_{in}$. Thus we have

$\stackrel{\_}{g}=\sqrt{\frac{l_{out}/l_{in}}{I_{out}/I_{in}}\cdot
(<r^{2}>_{ring}/<r^{2}>_{core})}=\sqrt{\frac{\omega _{out}}{\omega _{in}}%
\cdot (<r^{2}>_{ring}/<r^{2}>_{core})}\qquad \qquad (14)$

It is believed that the uniform rotation is a good approximation for the first-states, because they should do their best to lower the energy (this is a point remain to be checked). Under this approximation

$\stackrel{\_}{g}\approx (<r^{2}>_{ring}/<r^{2}>_{core})^{1/2}\qquad
\qquad (15)$

The optimal value of the right hand side of eq.(15) has been denoted as G$%
_{opt}$ given in Table 1. Thus, if a FS has its $\stackrel{\_}{g}$ (evaluated from the definition eq.(12)) close to G$_{opt}$ , then the core-ring separation is appropriate and the FS is advantageous to binding and therefore competitive. Otherwise, it is not.

 The $\stackrel{\_}{g}/$G$_{opt}$ of the FS are also listed in Table 2, many of them are found to be very close to one. E.g., the FS of the (86)$%
_{1} $ is a (5)$_{c}-$8 structure with $\stackrel{\_}{g}$ =2.18,  the associated G$_{opt}$ 