  We previously introduced [T. Cren et al., Europhys. Lett. 52, 203 (2000)] an
energy-dependant gap function, $\Delta(E)$, that fits the unusual shape of the
quasiparticle (QP) spectrum for both BiSrCaCuO and YBaCuO. A simple
anti-resonance in $\Delta(E)$ accounts for the pronounced QP peaks in the
density of states, at an energy $\Delta_p$, and the dip feature at a higher
energy, $E_{dip}$. Here we go a step further : our gap function is consistent
with the ($T, p$) phase diagram, where $p$ is the carrier density. For large QP
energies ($E >> \Delta_p$), the total spectral gap is $\Delta(E) \simeq
\Delta_p + \Delta_\phi$, where $\Delta_\phi$ is tied to the condensation
energy. From the available data, a simple $p$-dependance of $\Delta_p$ and
$\Delta_\phi$ is found, in particular $\Delta_\phi(p) \simeq 2.3 k_B T_c(p)$.
These two distinct energy scales of the superconducting state are interpreted
by comparing with the normal and pseudogap states. The various forms of the QP
density of states, as well as the spectral function $A(k,E)$, are discussed.
