and one by a double-peak, which implies an oscillation around an equilibrium position) are very close  to the core. This fact supports the presumption that the FS, namely the (10)$%
_{c}$-3 structure (cf. Table 2), is pursued by the state . Although the $U$ of the (10)$_{c}$-3 is higher, however no other better symmetric configurations are allowed by symmetry. Consequently, the component of the (10)$_{c}$-3 is still relatively important .  Since the outward electrons are so close, the core is strongly deformed.  There are three peaks at the outer ridge of the core, it implies that three inward electrons form a regular triangle close to the border.  Fig.5b for the (82)$_{1}$ exhibits that the four outward electrons are also very close  to the core. This fact supports again that the FS is pursued.  The core is also strongly deformed with four inward electrons forming a square close to the border.  The pursuit of the FS can also be viewed by observing the composition of the wave functions. For the (81)$_{1}$ , the BF with the largest weight (35.4%) is the {0-9,11-13}, in which the electrons are divided into two compact bunchs, and therefore supports directly the (10)$%
_{c}$-3 structure . 