dc Josephson current for very strong coupling

We have calculated the dc Josephson critical current ${\mathit{J}}_{\mathit{c}}$(T) for various coupling strengths covering weak, intermediate, strong, and very strong coupling regimes. We consider the temperature T variation of ${\mathit{J}}_{\mathit{c}}$(T) and its deviation from BCS values near ${\mathit{T}}_{\mathit{c}}$ and at zero temperature. The deviations can be quite significant but are too small to explain a recent experiment.