for the case of $t' = 0$, contrary to the case of $t' \sim -0.1$, although a kind of average of the results in both shell states is very probable to give a finite energy gain per site in the bulk limit. Of course it is needed to treat larger lattices with $t' = 0$ but some important findings at the present stage are considered to deserve a report, with the latter problem left to be settled, since with larger sizes computation needs extremely long time.

Thirdly, we calculate the energy gain in another ordered state, i.e., spin density wave (SDW) state. We treat the SDW with a fixed wave vector $(\pi, \pi)$. Here the length unit is the lattice constant. The energy gain in the SDW state was found to quickly drop with decrease of $\rho$ from unity and to vanish at $\rho$ just below 0.84 when $t' = 0$. However, at $\rho = 0.84$ the SDW state was slightly more stable than the SC state so that the boundary between both states lies just below $\rho = 0.84$ for $t' = 0$. $t'$ is known to destabilize the SDW in the hole-doped state, while it promotes SC pairing. 