Photoelectric Absorption

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.

Figure 3: The bound states of electrons in a Coulomb field

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

$$E_{\gamma} = E_{e}+E_b \simeq E_{e}$$ (19)

where $E_b\sim$ eV is the bound energy which is negligible to $E_{\gamma}\sim$ keV. The momentum conservation, however, cannot be satisfied simultaneously, since an electron has a mass while a photon is a mass-zero particle. A nuclei is REQUIRED in order to absorb the photon momentum.

This processes is dominated in relatively low energy region ($\leq \sim$ keV) while a free electron or higher energy $\gamma$-rays are subject to the Compton scattering described next.