  We report electronic Raman scattering measurements on
Bi$_2$Sr$_2$(Y$_{1-x}$Ca$_x$)Cu$_2$O$_{8+\delta}$ single crystals at different
doping levels. The dependence of the spectra on doping and on incoming photon
energy is analyzed for different polarization geometries, in the
superconducting and in the normal state. We find the scaling behavior of the
superconductivity pair-breaking peak with the carrier concentration to be very
different in B$_{1g}$ and B$_{2g}$ geometries. Also, we do not find evidence of
any significant variation of the lineshape of the spectra in the overdoped
region in both symmetries, while we observe a reduction of the intensity in
B$_{2g}$ upon decreasing photon energies. The normal state data are analyzed in
terms of the memory-function approach. The quasiparticle relaxation rates in
the two symmetries display a dependence on energy and temperature which varies
with the doping level.

Superconductivity;Strongly Correlated Electrons