Energy may be removed from a beam of
γ
-rays traversing matter by two distinct mechanisms. A quantum of radiation may be scattered by an electron out of its initial direction with change of wave-length, or it may be absorbed completely by an atom and produce a photoelectron. The total absorption coefficient, μ, is defined by the equation
d
I/
dx
= -μI, and is the sum of the coefficients σ and
τ
referring respectively to the scattering and to the photoelectric effect. For radiation of low frequency, such as X-rays, the photoelectric absorption is very much more important than the absorption due to scattering, and many experiments have shown that the photoelectric absorption per atom varies as the fourth power of the atomic number and approximately as the cube of the wave-length. For radiation of high frequency, such as the more penetrating
γ
-rays, the photoelectric effect is, even for the heavy elements, smaller than the scattering absorption; and, since the scattering from each electron is always assumed to be independent of the atom from which it is derived, it is most convenient to divide μ. defined above by the number of electrons per unit volume in the material and to obtain μ
e
the absorption coefficient per electron.
Photoelectric absorption cross section of silicon near the bandgap from room temperature to sub-Kelvin temperature