Photoelectric Absorption of X-rays

In the photoelectric effect, a photon undergoes an interaction with an electron that is bound in an atom. In this interaction, the incident photon completely disappears, and an energetic photoelectron is ejected by the atom from one of its bound shells. The kinetic energy of the ejected photoelectron (E_e) is equal to the incident photon energy (hν) minus the binding energy of the photoelectron in its original shell (E_b).

E_e=hν-E_b

Therefore photoelectrons are only emitted by the photoelectric effect if a photon reaches or exceeds threshold energy – the binding energy of the electron – the work function of the material. For very high X-rays with energies of more than hundreds of keV, the photoelectron carries off the majority of the incident photon energy – hν.

At small values of gamma-ray energy, the photoelectric effect dominates. The mechanism is also enhanced for materials of high atomic number Z. It is not simple to derive an analytic expression for the probability of photoelectric absorption of gamma-ray per atom over all ranges of gamma-ray energies. The probability of photoelectric absorption per unit mass is approximately proportional to:

τ_{(photoelectric)} = constant x Z^N/E^3.5

where Z is the atomic number, and the exponent n varies between 4 and 5. E is the energy of the incident photon. The proportionality to higher powers of the atomic number Z is the main reason for using high Z materials, such as lead or depleted uranium in gamma-ray shields.

Although the probability of the photoelectric absorption of photons decreases, in general, with increasing photon energy, there are sharp discontinuities in the cross-section curve. These are called “absorption edges,” and they correspond to the binding energies of electrons from an atom’s bound shells. For photons with the energy just above the edge, the photon energy is sufficient to undergo the photoelectric interaction with electrons from a bound shell, let’s say K-shell. The probability of such interaction is just above this edge, much greater than that of photons of energy slightly below this edge. For photons below this edge, the interaction with an electron from K-shell is energetically impossible; therefore, the probability drops abruptly. These edges also occur at binding energies of electrons from other shells (L, M, N …).

Interaction of X-rays with Matter

Although many possible interactions are known, there are three key interaction mechanisms with the matter. The strength of these interactions depends on the energy of the X-rays and the elemental composition of the material. Still, not much on chemical properties, since the X-ray photon energy is much higher than chemical binding energies. The photoelectric absorption dominates at low-energies of X-rays, while Compton scattering dominates at higher energies.

• Photoelectric absorption
• Compton scattering
• Rayleigh scattering

See above:

X-rays