The gap symmetry is marginal in high-Tc superconductivity: Isotropic s-wave pairing leads to either s or d-wave gap depending on the Coulomb pseudopotential

We point out that in two-dimensional systems like high-$T_c$ superconductors, an isotropic s-wave electron-phonon interaction in the momentum decoupling regime leads to either s or d-wave superconductivity depending on the conventional values of the Coulomb pseudopotential. It is therefore possible that $YBa_2Cu_3O_7$ is an anisotropic d-wave and $Bi_2Sr_2CaCu_2O_8$ an anisotropic s-wave superconductor both having the same pairing interaction and similar $T_c$'s. A transition from s-wave to d-wave superconductivity may also be possible by adjusting the doping.