Photoelectric Effect
Cross-Sections of Photoelectric Effect
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 comprehensive ranges of gamma-ray energies. The probability of photoelectric absorption per unit mass is approximately proportional to:
τ(photoelectric) = constant x ZN/E3.5
where Z is the atomic number, 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 gamma photon decreases, in general, with increasing photon energy, there are sharp discontinuities in the cross-section curve. These are called “absorption edges” and correspond to electrons’ binding energies 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 an electron from a bound shell, let 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 gamma photons below this edge, the interaction with electrons from K-shell is energetically impossible, and therefore the probability drops abruptly. These edges also occur at binding energies of electrons from other shells (L, M, N …).
Cross section of photoelectric effect.