The Thomson scattering is described in the classical theory or in the low energy limit of the photon-electron interaction. The processes in the followings are understood in the Quantum mechanics: The case when energy of an electron is quantized, or when the electron-magnetic radiation field can be considered as a particle of a photon, which we usually see in the high energy region.
The photoelectric absorption corresponds to the first case when
electrons are trapped in an atom and its energy is quantized.
Electrons are in the bound state in a Coulomb field of the nuclei.
The energy states are conceptually illustrated in
FIG. 3. An electron in a shell
is able to absorb a photon to transfer its energy to the different state.
The energy conservation law reads
This processes is dominated in relatively low energy region ( keV) while a free electron or higher energy -rays are subject to the Compton scattering described next.