Relationships between the superconducting gap, pseudogap and transition temperature in High-T_c superconductors

The crossover from superconducting gap to pseudogap is considered. We show that the superconductivity is destroyed at the temperature $T_c$, with the superconducting gap being smoothly transformed into the pseudogap. Relations, which are of general interest, between the maximum values of the gap $\Delta_1$, $T_c$ and $T^*$ are established. We presents arguments that $T^*$ as a function of the doping level $x$ is approximately a straight line that crosses the abscissa at some point $x_{FC}$. In the vicinity of this point $T^*$ coincides with $T_c$, and at $x=x_{FC}$ the fermion condensation quantum phase transition takes place.