Physics and Engineering of Radiation Detection

94 Chapter 2. Interaction of Radiation with Matter

This corresponds to an energy of

Ei =

hc

λi

=

(

6. 62 × 10 −^34

)(

2. 99 × 108

)

5. 870 × 10 −^12

=3. 372 × 10 −^14 J

= 210. 5 keV.

To compute the energy of the scattered electron we assume that the binding

energy of the atom is negligibly small. Then the energy of the scattered

electron would simply be equal to the difference in the energy of the incident

photon and the scattered photon, that is

Ee ≈ Ei−Es

= 210. 5 −150 = 60. 5 keV.

A.3 ThompsonScattering

Thompson scattering is an elastic scattering process between a free electron and a
photon of low energy. Bylow energywe mean the energy at which the quantum
effects are not significant. Therefore in order to derive kinematic quantities related
to Thompson scattering, the concepts of classical electromagnetic theory suffice.
The differential and total cross sections for Thompson scattering are given by

dσth

dΩ

= r^2 esin^2 θ (2.3.21)

and σth =

8 π

3

re^2 =6. 65 × 10 −^29 m^2 , (2.3.22)

whereθis the photon scattering angle with respect to its original direction of motion
andreis the classical electron radius.

A.4 RayleighScattering

In this elastic scattering process there is very minimal coupling of photons to the
internal structure of the target atom. The theory of Rayleigh scattering, first pro-
posed by Lord Rayleigh in 1871, is applicable when the radius of the target is much
smaller than the wavelength of the incident photon. A Rayleigh scattered photon
hasalmostthe same wavelength as the incident photon, which implies that the en-
ergy transfer during the process is extremely small. For most of the x-rays and low
energyγ-rays, the Rayleigh process is the predominant mode of elastic scattering.
The cross section for this process is inversely proportional to the fourth power of
the wavelength of the incident radiation and can be written as (13)

σry=

8 πa^6

3

[

2 πnm

λ 0

] 4 [

m^2 − 1

m^2 +1

] 2

. (2.3.23)