We extract the damping dispersion GAMMA(omega) of excitonic polaritons
in CdS on the basis of precise measurements of the transmission and r
eflectance. On the low-energy side of the A(n=1) exciton, the damping,
which corresponds to the inverse dipole dephasing time, is independen
t of temperature, due to the scattering with impurities. On the high-e
nergy side the damping increases with temperature and with the detunin
g from the resonance frequency due to the scattering with acoustic-pho
nons between different polariton modes. The probability of exciton-pho
non scattering mediated by the deformation potential and by the piezoe
lectric effect is calculated and the measured damping spectrum is desc
ribed qualitatively and quantitatively. By analyzing our results diffe
rent relaxation channels of acoustic-phonon scattering are clearly dis
criminated.