GAP ANISOTROPY AND VAN HOVE SINGULARITIES IN HIGH-T-C SUPERCONDUCTORS

We compute the superconducting gap Delta(k) using a simple band structure of the CuO2 planes in the high-T-c materials. We suppose that for maximum T-c, the van Hove singularities lie close to the Fermi level as is confirmed by many photoemission experiments. We use a electron-phonon interaction with weak screening; we find a strong gap anisotropy. For Bi 2212, Delta is maximum along the 001 and 010 directions with values of the order of 22 meV and minimum along 011 with a value of 6 meV. These values are in agreement with experiments.