Physics and Engineering of Radiation Detection

2.3. Interaction of Photons with Matter 97

This means that for heavy elements the pair production cross section is significantly
higher than for lighter elements. The actual cross section can be written as

σpair=4αr^2 eZ^2

[

7

9

ln

(

183

Z^1 /^3

)

−

1

54

]

cm^2 /atom, (2.3.30)

whereαis the electron fine structure constant andreis the classical electron radius.
Fig.2.3.8 shows behavior ofσpairwith respect to atomic numberZ.

Z

0 20 40 60 80 100

pair

σ

0

10

20

30

40

50

60

70

Figure 2.3.8: Dependence of pair production

cross section of high energy photons (Eγ 

20 MeV)onatomicnumberZas calculated from

equation 2.3.30.σpairis in units ofbarn/atom.

It is also convenient to represent the pair production cross section in terms of
radiation lengthX 0 , which was described earlier in the chapter for passage of elec-
trons through matter. For high energy photons, we mentioned that the process of
pair production should be considered when defining the radiation length. Hence in
similar terms we can define the radiation length for photons in a material as the
depth at which a photon beam looses 1− 1 /e(or about 63%) of its energy through
pair production. As before,erefers to the exponential factor. The formulas for ra-
diation length for photons are the same as those for electrons since the processes of
Bremsstrahlung and pair production are connected by underlying physics. In fact,
the reader may readily recognize the similarity between the pair production cross
section 2.3.30 and the radiation length formula 2.1.15. To write the relation 2.3.30
in terms of the radiation length, we can safely ignore the 1/54 term. Henceσpair
can also be written as

σpair=

7

9

A

NA

1

X 0

, (2.3.31)

whereAis the atomic mass of the element andNAis the Avogardo’s number.

2.3.B PassageofPhotonsthroughMatter

Now that we have learned the basic processes that define the interactions a photon
may undergo while passing through matter, we are ready to discuss the gross out-
comes of such interaction. Luckily enough, although the underlying processes, as we