while the core has $l_{in}$ . When the outer particles locate at the vertexes of a N$_{out}$-side polygon, and the inner particles locate at the vertexes of a N$_{o}$-side polygon (N$_{o}$=N$_{in}$ or N$_{in}-1$, in the latter case an electron would stay at the center) , then it is straight forward to prove that the wave function would be zero if

$l_{out}\neq $N$_{out}(j_{2}+(1+(-1)^{{N}_{out}})/4)$ $\qquad (9a)$

or

$l_{in}\neq $N$_{o}(j_{1}+(1+(-1)^{{N}_{o}}/4)$ $\qquad (9b)$

where $j_{1}$ and $j_{2}$ are integers. In other words, the above configuration would be prohibited if $l_{out}($ $l_{in})$ does not relate to N$_{out}$ (N$_{o}$) in the above way.  [*Thus, a (N*]{}$_{in})-$[*N*]{}$%
_{out}$[* structure would be pursued by a first-state only if the* ]{}$L$[* can be divided as a sum of *]{}$l_{in}$[* and* ]{}$l_{out}$[* so that  the requirements (9a) and (9b) are fulfilled.* ]{} If this happens, the (N$_{in})-$N$_{out}$ structure is called a candidate of favorable structure[* (CFS)*]{} of the state.  Incidentally, for an eigenstate, both the $%
l_{out}$ and $l_{in}$ are not good quantum numbers, they appear as the angular momenta of the main component of eigenwavefunctions.

 Usually each state may have a number of CFS, some of them are not competitive due to having a too small or too large 