The effects of the trap potential and the on-site repulsion on the pairing correlation in the confined gas of Fermi atoms placed in the optical lattice were investigated using exact diagonalization method. It was found that the local Mott insulation core develops due to the strong repulsion and the singlet pairing correlation grows remotely between the core edges. It was also found that the 'Mott insulation core' appeared in the center of the trap, where each site was occupied by one atom. The results show that the superfluidity can locally develop at the surrounding of the Mott core.
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