Physics and Engineering of Radiation Detection

72 Chapter 2. Interaction of Radiation with Matter

Z

0 20 40 60 80 100

Radiation Length

0

10

20

30

40

50

Z

0 20 40 60 80 100

Relative Difference (%)

0

5

10

15

20

25

Figure 2.1.1: Upper plot shows the radia-

tion lengths ing/cm^2 computed from equations

2.1.14(solid line) and 2.1.15(dashed line). The

lower plots shows the relative error in the values

computed from equation 2.1.15 with respect to

the ones computed from equation 2.1.14.

which shows the radiation lengths for different materials computed from equations
2.1.14 and 2.1.15 together with relative error in the latter assuming the former gives
the correct results.
For a mixture or compound, the effective radiation length can simply be calcu-
lated by taking the weighted mean

1

X 0

=

∑

i

wi

1

X 0 i

, (2.1.17)

wherewiandX 0 iis the fraction by weight and radiation length of theithmaterial.

Example:

Estimate the radiation length of high energy electrons in carbon dioxide.

CO 2 is commonly used as a fill gas in gas-filled detectors.

Solution:

The effective radiation length can be computed from equation 2.1.17. But we

first need to compute the radiation lengths corresponding to the individual

elements inCO 2 .SinceforlowZmaterials, equation 2.1.16 gives reasonable

results, therefore we will use this to determine the individual radiation lengths