Gap anisotropy and critical temperature of anisotropic superconductors

We study the gap anisotropy and critical temperature of superconductors within Eliashberg theory. We consider a general anisotropy and spectral shape. In the attractive strong-coupling limit, we find a qualitatively new universal result: The gap becomes isotropic. This sets severe constraints on standard strong-coupling theories of high-${\mathit{T}}_{\mathit{c}}$ superconductors. In the weak-coupling limit, the gap is sensitive to anisotropy. We obtain exact results for the critical temperature both in the strong- and the weak-coupling limits. We propose a simple natural interpolation in the intermediate regime.