ANISOTROPIC S-WAVE OR D-WAVE PAIRING IN THE HUBBARD-MODEL

The pairing instability in the Hubbard model for a 2D lattice is exami ned by using the perturbation approach. The two-particle interactions in both singlet and tripler channels are considered. The kernel of two -particle interactions in the charge and spin channels and the irreduc ible charge and spin response functions are also obtained. The expansi on of the equation for the t-matrix over the Legendre polynomials is u sed to find the singularity in the harmonics of the t-matrix equation for different orbital momenta l. A pairing instability in the singlet channel can be seen either in the state with l = 0 (s-wave) or in the state with l = 2 (d-wave). T-c for both s- and d-wave states is calcul ated by using the pole condition of the t-matrix. The strongly anisotr opic s-wave state near the antiferromagnetic or SDW instability resemb les the d(x2-y2) wave symmetry.