Physics and Engineering of Radiation Detection

104 Chapter 2. Interaction of Radiation with Matter

Here the subscripts 1, 2, and 3 represent the three materials. Using this result we
can write the equation for the intensity of a photon beam coming out ofNmaterials
in terms of total linear and total mass attenuation coefficients as

IN = I 0 exp

(

−

∑N

i=1

μitdi

)

(2.3.46)

= I 0 exp

(

−

∑N

i=1

μimρidi

)

, (2.3.47)

whereρiis the density of theith material.

d 1 d 2 d 3

I 0

I 3

I 1 I 2

I 0

I 1

I 2

I 3

Distance

Intens

ity

Figure 2.3.12: Depiction of passage

of photons through three materials

of different thicknessess and atten-

uation coefficients. The exponen-

tial variation of photon intensity in

each material according to equation

2.3.33 is also shown.

Example:

Estimate the percentage of 100 keV photons absorbed in a cylindrical

ionization detector. The photons enter the detector through a 100μmthick

aluminum window and are attenuated in the 6cmthick bed of the filling

gas (CO 2 ) kept at atmospheric temperature and pressure. The photons

surviving the interactions leave the detector through another 100μmthick

aluminum window. The mass attenuation coefficients of 100keV photons in

aluminum, carbon, and oxygen are 0.1704cm^2 /g, 0.1514cm^2 /g, and 0.1551

cm^2 /grespectively. The densities of aluminum andCO 2 are 2.699g/cm^3 and

1. 833 × 10 −^3 g/cm^3.