Physics and Engineering of Radiation Detection

2.3. Interaction of Photons with Matter 85

K

Photon

Incident

X−ray Photon

L

Photoelectron

Orbital Electron

Figure 2.3.2: Depiction of photoelectric effect in a free atom. If

the K-shell electron is knocked off by the incident photon, another

electron from a higher energy level may fill the gap. This would

result in the emission of a photon with an energy equal to the

difference of the two energy levels.

HereXis the target atom, which gets an overall positive charge when the electron
eis knocked off from one of its shells by the incident gamma ray photonγ.
The cross section for this reaction has a strongZdependence, that is, the prob-
ability of photoelectric effect increases rapidly with atomic number of the target
atom. In addition, it also has a strong inverse relationship with energy of the inci-
dent photon. Specifically, these dependences can be expressed as

σpe∝

Zn

Eγ^3.^5

, (2.3.8)

wherenlies between 4 and 5. This relation suggests that the probability of photo-
electric effect would decrease sharply with higher incident photon energies. Figure
2.3.1 shows the typical dependence of photoelectric cross section on energy of the
incident photon in carbon and lead.
Photoelectric effect takes place predominantly in the K atomic shell and therefore
generally the cross section related to K-shell interaction is used to estimate the total
photoelectric cross section. The K-shell photoelectric cross section is given by

σpe,K=

[

32

^7

] 1 / 2

α^4 Z^5 σThcm^2 /atom. (2.3.9)

Here

 =

Eγ

mec^2

and

σTh =

8

3

πr^2 e= 665mbarn.