Physics and Engineering of Radiation Detection

90 Chapter 2. Interaction of Radiation with Matter

pecosφ

pesinφ

Incident Photon

pe 0 =0 =h/

λ

pγ

pγcosθ

pγsinθ

pe

pγ 0 =h/λ 0 θ

φ

Scattered Photon

Scattered Electron

Figure 2.3.5: Initial and final momenta of the particles involved in

Compton scattering. The momenta of the scattered electron and

photon have been broken down into their horizontal and vertical

components for ease in application of the law of conservation of

momentum. The electron is assumed to be at rest before the colli-

sion.

That is, the scattered photon continues in the same direction as the incident

photon and carries with it all of its energy. Of course this implies that the

photon has not actually interacted with the electron and therefore this should

not be regarded as a scattering process at all. However it should be noted that

this case gives us the upper bound of the scattered photon energy. This may at

first seem an intuitive conclusion but as it turns out there is a special process

known asreverse Compton scatteringin which the scattered photon energy is

actually higher than the energy of the incident photon. In this process the

electron is not at rest and therefore carries significant kinetic energy. During

its interaction with the photon it transfers some of its energy to the photon,

hence the termreverseCompton effect.

Certainly, this is a special case of Compton scattering, which is not generally

encountered in laboratories. In the case of normal Compton scattering where

the target electron is essentially at rest with respect to the incident photon,

the scattered photon energy should never exceed the incident photon energy.


Case-2 (θ=90^0 ): In this situation the incident photon flies away at right

angles to its original direction of motion after interacting with the electron.

By substituting cosθ= 0 in equation 2.3.15 we can find the energy it carries

away by the scattered photon.

Eγ=Eγ 0

[

1+

Eγ 0

m 0 c^2

]− 1

The change in photon’s wavelength in this as estimated from equation 2.3.10

is

λ=

h

m 0 c

=2. 432 fm