The intensity of polaron exciton absorption in a spherical quantum dot is c
alculated. The localized electrons and holes are shown to interact with lon
g-wavelength phonons with wave vectors q approximate to 1/R, R being the ra
dius of the dot. In the case of strong electron-phonon interaction, the pol
aron effect results in multiple phonon replicas of exciton optical transiti
on. The broadening of different phonon replicas is shown to be less than th
eir separation.