A two-body problem on the square lattice is analyzed. The interaction
potential consists of strong on-site repulsion and nearest-neighbor attraction.
Exact pairing conditions are derived for s-, p-, and d-symmetric bound states.
The pairing conditions are strong functions of the total pair momentum K. It is
found that the stability of pairs increases with K. At weak attraction, the
pairs do not form at the Γ-point but stabilize at lattice momenta close
to the Brillouin zone boundary. The phase boundaries in the momentum space,
which separate stable and unstable pairs are calculated. It is found that the
pairs are formed easier along the (Ï€,0) direction than along the
(Ï€,Ï€) direction. This might lead to the appearance of ``hot pairing
spots" on the Kx and Ky axes.Comment: 7 RevTEX pages, 5 figure