2 The Interaction of Radiation with Matter
7
Fig. 2.1 The lower curve
shows, as a function of the
atomic number Z of the target
material, the photon energy E
below which photoelectric
absorption is the most
probable interaction
mechanism, while the upper
curve shows the energy above
which pair production is the
most important process. The
shaded region between the
two curves corresponds to the
domain where Compton
scattering dominates. The
cross sections are taken from
the NIST XCOM database
[24]
20
40
60
80
Z
10
–3
10
–2
10
–1
1
10
10
2
E [MeV]
photoabsorption
Compton scattering
pair production
Detailed descriptions of these processes can be found, for instance, in Refs. [8–
10, 12, 22, 23]. The focus of this section is on photoabsorption, the description of
which (as will be discussed in Sect. 2.3) is related to that of inelastic charged particle
collisions in the regime of low momentum transfer.
2.2.1 Photoabsorption
In a photoelectric absorption interaction, the incident photon disappears and its
energy is transferred to the target atom (or group of atoms). The intensity I of a
monochromatic beam of photons with energy E thus decreases exponentially as a
function of the penetration depth x in a material,
I (x) = I 0 e
−μx ,
where the attenuation coefficient μ is proportional to the atomic density N of the
medium and the photoabsorption cross section σ γ ,
μ (E) = Nσ γ (E) .
Let us first consider a (dipole-allowed) transition between the ground state |0
of an atom and a discrete excited state |n with excitation energy E n . The integral
photoabsorption cross section of the line is given by
σ
(n)
γ (E) dE =
2π 2 α ( ¯
hc)
2
mc 2
f n .