SC condensation energy, was estimated at $\sim 0.00028$/site from the difference between the minimum and the intercept of the $E_g$-versus-$\Delta$ curve with the vertical axis.

Main results written in this report were obtained for the $10 \times 10$ lattice with the same boundary conditions. Calculated energies per site for several types of wave functions with $N_e = 84$ on the $10 \times 10$ lattice are shown in Fig. \[fig:DEg-D\] for the case of $U = 8$ and $t' = 0$. Here $E_g/N_s$ is plotted as a function of $\Delta$ for the three types of gap functions given in eq. (\[eq:dw\]). With the lattice, the b.c.’s and $N_e = 84$, the electronic shell structure in the limit of $U = 0$ is open, i.e., some ${\mib k}$-points are partially filled, as is illustrated in Fig. \[fig:kpoints\], which displays the electron occupancy at the ${\mib k}$-points. At each value of $\Delta$ in Fig. \[fig:DEg-D\], $g = 0.30$ was chosen as the initial value of $g$ and then the optimal value of $\mu$ was found by the least squares fit of $E_g$ as a function of $\mu$ to a parabola. Using this value of $\mu$, $g$ was optimized again. Since $E_g$ was a 