Physics and Engineering of Radiation Detection

74 Chapter 2. Interaction of Radiation with Matter

We can now compute the effective radiation length using equation 2.1.17.

1

X 0

= w 1

1

X 0 C

+w 2

1

XO 0

+w 3

1

X 0 O

=

0. 2730

43. 0

+

0. 3635

34. 46

+

0. 3635

34. 46

=2. 742 × 10 −^2

⇒X 0 =36. 43 gcm−^1

This is our required effective radiation length. As an exercise, let us see how

different it is from the one computed using the more accurate relation 2.1.14.

The reader is encouraged to carry out the computations to verify that the

individual radiation lengths thus calculated are

X 0 C =37. 37 gcm−^1 and

X 0 O =29. 37 gcm−^1.

The effective radiation length inCO 2 as calculated from equation 2.1.17 is

then given by

1

X 0

=

0. 2730

37. 37

+

0. 3635

29. 37

+

0. 3635

29. 37

=3. 206 × 10 −^2

⇒X 0 =31. 19 gcm−^1

The percent relative error in the radiation length as computed from equa-

tion 2.1.16 as compared to this one is

 =

36. 43 − 31. 19

36. 43

100

=16.8%.

Hence with far less computations, we have gotten a result that is accurate to

better than 73%. However, as shown in Fig.2.1.2, the relative error increases

as we go higher inZ. Equation 2.1.16 should therefore be used only for low

to moderateZelements.

2.1.E ConservationLaws........................

Although the reader should already be aware of the fundamental conservation laws of
particle physics but this section has been introduced to serve as a memory refresher.
An extensive discussion on the many conservation laws that exist in particle physics
is, of course, beyond the scope of this book. We will therefore restrict ourselves to
the following three laws that are generally employed to compute kinematic quantities
related to the field of radiation detection.

Conservation of energy


Conservation of momentum