For certain frequencies both Rayleigh and Compton scattering are important. As I could not see the connection between the derivations of the assosciated formulae, I wondered what made a photon "decide" wether it should be subject to one or the other phaenomenon. My reading is that Compton scattering assumes nothing but the electrons to be free, whilst Rayleigh requires them to be bound to the atom for a restoring oscillator force [tex]F_R=m\omega^2r[/tex] to act. So, if I send photons into matter the ones that hit (sufficiently) free targets will suffer Compton scattering, while the others obey Rayleigh's law (approximately)! Is that correct? If so, the classical result for free targets (Thompson scattering) should be somehow connected to the Compton Effect.